Different computational-based approaches have been extensively used for simulating the morphogenesis of multicellular systems. On the one hand, continuum-based models allow the simulation of large cell populations at the macroscopic level. This is the case for reaction-diffusion systems based on partial differential equations (PDEs) or positional information (PI). On the other hand, discrete approaches with agent-based models considering cells as autonomous entities that interact among themselves and with the microenvironment. These models have been widely employed, for instance, to simulate tumor growth in vitro [1], to study the role of extracellular matrix density in cell migration within solid tumor spheroids [2] or lumen-based organoids [3], collective cell migration [4].

In this work, we present the results of different in-vitro experiments corresponding to the morphogenesis of different human-cell-based tumor organoids, from neuroblastoma, pancreas and lung. Normally, all these experiments follow a similar protocol [5], where individual tumor cells are cultured in 3D microfluidic devices upon collagen-type I hydrogels. With the time these tumor cells are able to proliferate, self-organizing according to the architecture of the hydrogel, creating different structures. The evolution of size and shape of these tumor structures are quantified by means of microscopy-based images. Thus, this kind of organ-on-a-chip experiments constitutes a novel modelling strategy of in vitro multicellular human systems that in combination with numerical simulations provide a relevant tool for research in mechanobiology.

Therefore, in this presentation I will show our engineering-based strategy in which we integrate computational models and in-vitro experiments in order to tackle of how matrix mechanics is regulating the size and organization of tumour organoids. Different computer-based modelling strategies will be presented to simulate the morphogenesis of these in-vitro tumor organoids, clearly identifying the challenges that we face in these numerical simulations, mainly associated to the variability observed in the experiments and the difficulties associated to the parameters calibration process.

References:

[1] Hervas-Raluy, S., Wirthl, B., ... & Wall, W. A. (2023). Tumour growth: An approach to calibrate parameters of a multiphase porous media model based on in vitro observations of Neuroblastoma spheroid growth in a hydrogel microenvironment. Computers in Biology and Medicine.

[2] Gonçalves, I. G., & Garcia-Aznar, J. M. (2021). Extracellular matrix density regulates the formation of tumour spheroids through cell migration. PLoS computational biology, 17(2), e1008764.

[3] Camacho-Gómez, D., García-Aznar, J. M., & Gómez-Benito, M. J. (2022). A 3D multi-agent-based model for lumen morphogenesis: the role of the biophysical properties of the extracellular matrix. Engineering with Computers, 38(5), 4135-4149.

[4] González-Valverde, I., & García-Aznar, J. M. (2018). Mechanical modeling of collective cell migration: An agent-based and continuum material approach. Computer Methods in Applied Mechanics and Engineering, 337, 246-262.

[5] Plou, J., Juste-Lanas, Y., Olivares, V., Del Amo, C., Borau, C., & García-Aznar, J. M. (2018). From individual to collective 3D cancer dissemination: roles of collagen concentration and TGF-β. Scientific reports, 8(1), 12723.

Acknowledgments: This work was supported by the European Research Council (ICoMICS Adv grant: 101018587 and the Spanish Ministry of Science and Innovation (PID2021-122409OB-C21).

Physical forces are critical for the development, maintenance, and adaptation of various tissues in the body including bone. Bone adapts to mechanical loads through actions of bone cells: osteoclasts that specialize in bone resorption; osteoblasts that produce bone; and osteocytes embedded in bone matrix that sense mechanical forces and coordinate bone adaptation. ATP is a ubiquitous intracellular molecule critical for cellular bioenergetics, which is also one of the first signals released from bone cells that experience mechanical stimulation. Extracellular ATP is degraded by ecto-ATPases to form ADP and eventually adenosine. We developed a theoretical model describing mechanically induced ATP and ADP release, followed by their extracellular diffusion and degradation. The model was validated using experimental data for calcium signaling, ATP and vesicular release upon mechanical stimulation of a single osteoblast, and then scaled to a tissue-level injury. The route and amount of ATP release depended on mechanical forces, ranging from vesicular release of small ATP boluses upon membrane deformation, to leakage of ATP through resealable plasma membrane tears, to spillage of cellular content due to destructive forces. The total amount of ATP released indicated the degree of injury and determined the maximal distance from the injury at which responses were stimulated. The peak ATP concentration discriminated between injuries that released similar amounts of ATP due to differences in cell repair, and determined signal propagation velocity. ADP-mediated signaling was relevant for larger tissue-level injuries, conveying information about the proximity to the injury site and its geometry. After their release from an injury site, ATP, ADP, and adenosine signal through purinergic receptors, including seven P2X ATP-gated cation channels, seven G-protein coupled P2Y receptors responsive to ATP and ADP, and four P1 receptors stimulated by adenosine. All bone cells express multiple P2 receptors. We used published studies of overexpressed individual P2 receptors to fit their dependencies on ATP concentration using the Hill equation, and experimentally examined the concentration dependences of P2-mediated calcium responses to ATP and ADP in osteoblasts/osteocytes and osteoclasts. Dependence of the calcium response on ATP concentration exhibited a complex pattern that was not explained by the simple addition of individual receptor responses. To deconvolute the contribution of individual receptors to the ATP dose-response curve, we constructed a mathematical model that combined the actions of the P2Y2 receptor that has the highest affinity to ATP and induces inositol trisphosphate (IP3) mediated calcium release, and the P2X7 receptor that has the lowest ATP affinity and allows calcium influx through the pores. The model predicted interactions between these P2 receptors at the levels of receptor interactions and cellular signaling, which were validated using CRISPR/Cas9-generated P2Y2 and P2Y7 knockout cells. Our studies demonstrate how spatiotemporal signals provided by extracellular ATP and ADP encode the information regarding severity, scale and proximity of the mechanical stimulus, allowing for a well-choreographed tissue responses to physical forces.

1. Introduction

Mechanobiology is an area of intense research focus nowadays. In cellular length, it tries to describe how mechanical forces can modulate the structure and function of cells. These forces are transmitted to the nucleus, through direct physical connections to the cytoskeleton via LINC [1], and deform the nucleus, which in turn triggers different biochemical pathways. Therefore, nuclear deformations are critical structural and biophysical parameters in mechanobiology [1].

Recent studies have highlighted the variations of cellular responses with the surrounding stiffness [2]. Inspired by this, we decided to use the finite element method to investigate variations of nuclear deformations with different mechanical environments. For this aim, we modeled the realistic geometry of a single cell in Abaqus^® to measure to deformation applied to the nucleus after the contraction of the acto-myosin units.

2. Materials and Methods

We created a 3-D model of a cell with a volume of 537 nm³ including the membrane, nucleus, nuclear cap, dorsal and ventral f-actins, LINCs, and cytoplasm. We assumed that the dorsal and ventral f-actins are tied to the cell membrane in both extremities. Therefore, fibers contraction would deform the cell membrane and the nucleus as well due to, first, the contact forces between fibers and the nuclear cap, and second, the forces coming from the LINCs. Moreover, to take into account the interaction of the call with its surrounding environment, we attached it to the top surface of a substrate to simulate a traction force microscopy test. As shown in figure 1, the modeled cell has been tied to the substrate in 3 focal adhesion sites [1].

3. Results

We measured the deformation applied to the nucleus for a substrate with 3 different Young’s moduli: 2, 4, and 8 kPa. The average values of the maximum principal strain in the nucleus are 5.3%, 5.6%, and 6.0%, respectively. Figure 2 also shows the distributions of the maximum principal strain for these 3 cases. These results suggest that there is a direct relationship between strain values in the nucleus and the stiffness of the surrounding environment.

4. Discussion and Conclusions

We developed the first finite-element model of a realistic and complex single cell to quantify deformations of the nucleus after the contraction of the acto-myosin units. We showed that finite element modeling can also be regarded as a strong tool to measure the interactions between different cellular components. The simplicity of the proposed model is a promising asset for further quantifications of intracellular mechanics in 2-D and 3-D environments.

5. References

1. Ghosh S et al., Cell reports, 27(5): 1607-1620 (2019).

2. Petit C et al., Biomechanics and Modeling in Mechanobiology, 20(2):717-731 (2021).

The cortex is a thin layer located beneath the membrane of animal cells. It governs important cell mechanical properties, including cell shape. It is composed of a dense network of actin filaments and actin-binding proteins, in particular myosin motors. Myosins generate active stresses in the actin network and make it behave as an active material. The spatiotemporal organization of the cortex is tightly coupled to that of signaling molecules, in particular Rho GTPases. Indeed, the interaction between actin, myosin and Rho GTPases can give rise to self-organized patterns. Thus far, studies have focused on spatially extended patterns, like actin polymerization waves. However, spatially localized patterns are also observed in the cortex, whereby isolated spots enriched in actin, myosin and signaling molecules play a role in crucial processes, including cancer invasion. What is the origin of such spatially localized patterns? We use a simple physical theory to show that they can emerge from the coupling between active cortical mechanics and signaling reactions, through an instability called "slanted snaking". Beyond single cells, our theory could also explain the origin of spatially localized, mechanochemical cues in tissue morphogenesis.

Cytoskeletal networks play a key role in multiple mechanical and dynamical processes in cells. Recently, a continuum theory has been developed [1], allowing for the prediction of the material properties of highly crosslinked cytoskeletal networks from a phenomenological modelling of the microscopic interactions between the cytoskeleton filaments. We extend this theoretical framework to account for external forces, allowing us to explore how the properties of cytoskeletal networks are affected by the presence of various interfaces. This extended theory allows to study the interplay between cytoskeletal networks and the organelles that it interacts with,such as the centrosomes in spindles, vesicles embedded in intracellular actin networks, or even cortex-membrane interactions at the cell periphery.
[1] S. Fürthauer, D. J. Needleman, M. J. Shelley, NJP 23, 013012 (2021).

Eukaryotic cells exhibit a complicated rheology in response to mechanical stimuli, including an elastic response due to the cell cytoskeleton (a network of crosslinked filamentous proteins) and energy dissipation resulting from transport of cytosol through this network as well as transient crosslink dynamics [1]. Existing models of cytoskeletal mechanics fall into two categories: discrete (microscale) models enable inclusion of detailed biophysics but are typically computationally challenging due to the large number of discrete elements and their interactions, while continuum (macroscale) models are easier to solve but the manner in which microscale parameters and processes manifest themselves at the macroscale is usually unclear. Mathematical modelling efforts involving more rational and rigorous mathematical methods (such as discrete-to-continuum upscaling or homogenization) to systematically bridge between these two approaches are still largely missing. Our aim is to develop a multiscale framework providing such a bridge.

We introduce a discrete mathematical model for the mechanical behaviour of the eukaryotic cell cytoskeleton during intracellular transport. The model involves an initially regular array of pre-stretched protein filaments (e.g. actin, vimentin) which exhibit resistance to enthalpic stretching, joined at crosslinks to form a planar network. To mimic inertialess motion of a small object placed in the domain, we impose a quasi-static displacement of a set of crosslinks in the centre of the domain, solve for the remaining nodes through a local force balance, and calculate the net force on the object. Assuming that the inter-crosslink distance is much shorter than the lengthscale of the cell, we rationally upscale the force balance equations using the discrete-to-continuum method based on Taylor expansions to form a continuum system of governing equations, inferring the corresponding macroscopic stress tensor and strain energy.

We solve these discrete and continuum models numerically and infer force-displacement curves, which show good quantitative agreement across the parameter space. The force-displacement curves have weak dependence on the pulling angle (with respect to the initial filament orientation). The net force acting on the object increases with increasing pre-stress and larger objects. Furthermore, we linearize the continuum model to construct analytical approximations for the stress and strain fields in the neighbourhood of the moving object, and explicitly compute the net force required to generate a given deformation as a function of key parameters, such as the object and mesh sizes, the pulling angle and the network pre-stress.

Our mathematical formulation allows us to make explicit predictions of the force-displacement curve in optical-tweezers experiments [1], analytically characterizing the (linearized) rheology of the cytoskeleton. Future work will also incorporate nonlinear effects in polymer elasticity and dynamic aspects of cell rheology (poro-visco-elasticity). We also plan to apply similar ideas to other biopolymer networks, namely collagen fiber networks forming extra-cellular matrices.

Acknowledgements:

This research was funded by EPSRC grant EP/S030875/1. We thank Profs. Ming Guo and
Roger Kamm (MIT) for valuable discussions.

References:

[1] Hu, J. et al. “Size-and speed-dependent mechanical behavior in living mammalian
cytoplasm.” Proceedings of the National Academy of Sciences (2017): 9529-9534.

Abstract:

Cardiovascular diseases are the major cause of death around the world. It is estimated that 20% of the population is affected by elevated arterial wall stiffness which increases the risk of aneurysms rupture. Also, in the case of narrowed vessels due to arterial wall remodelling the blood flow is disturbed which may lead to an increased hemodynamic pressure gradient and increased cardiac load. Therefore, the parameters describing the wall stiffness and pressure gradient are used as indicators helping with diagnosis of disease severity [1]. Computational models of hemodynamics such as lumped parameter models (referred to as 0D), 1D models and 3D Fluid-Structure Interaction models (FSI) are tools for studying the cardiovascular system and may be further applied to non-invasive diagnostics and disease research [2, 3].

The parameter estimation problem may be solved by variational or sequential approach. The sequential approach is iterative in nature and requires many simulations of the forward problem which may be prohibitive in the case of FSI simulations. With a sequential approach based on the Kalman Filter, the model prediction is improved at every time step by measuring the discrepancy between model output and measurements. It was shown that the total computational time for the sequential approach is of the same order of magnitude as the CPU time needed for one forward simulation [4].

For FSI models input parameters like wall stiffness and boundary conditions strongly affect the solution. Therefore, the challenge in constructing a model is the determination of parameters which make the simulation results agree with clinical data. The Kalman filter and its various modifications are used as methods to estimate unknown parameters that may not be directly observable [2].

The goal of this work is to explore the applications of Kalman filters to estimate the unknown parameters and boundary conditions for hemodynamic models and apply it to 1-way and 2-way FSI model of the carotid artery to estimate the Young’s modulus.

Acknowledgments:

The research leading to these results is funded by the Norwegian Financial Mechanism 2014-2021 operated by the National Science Center, PL (NCN) within GRIEG programme under grant UMO 2019/34/H/ST8/00624, project non-invasivE iN-vivo assessmenT Human aRtery wALls (ENTHRAL, www.enthral.pl)

[1] D. Nolte, C. Bertoglio, Inverse problems in blood flow modeling: A review, International Journal for Numerical Methods in Biomedical Engineering 38 (8) (2022) e3613.

[2] C. J. Arthurs, N. Xiao, P. Moireau, T. Schaeffter, C. A. Figueroa, A flexible framework for sequential estimation of model parameters in computational hemodynamics, Advanced modeling and simulation in engineering sciences 7 (1) (2020) 1–37.

[3] A. Quarteroni, A. Veneziani, C. Vergara, Geometric multiscale modeling of the cardiovascular system, between theory and practice, Computer Methods in Applied Mechanics and Engineering 302 (2016) 193–252.

[4] Bertoglio, Cristóbal, Philippe Moireau, and Jean‐Frederic Gerbeau. "Sequential parameter estimation for fluid–structure problems: application to hemodynamics." International Journal for Numerical Methods in Biomedical Engineering 28.4 (2012): 434-455.

Aortic root connects the left ventricle to the ascending aorta and houses the aortic valve (AV) ensuring one-direction flow of blood during systole. The AV is normally composed of three leaflets, known as tricuspid aortic valve (TAV), but 1-2% of the population is born with only two leaflets, known as bicuspid aortic valve (BAV). The patients with BAV are considered at high risk of developing aneurysms and eventually dissection. The biomechanics of aortic root tissues are hypothesized to play an important role in the disease development. In this study, we use in-vivo echocardiographic images from TAV and BAV patients to analyze the differences in the biomechanics of aortic root tissues.

3D transesophageal echocardiographic (TEE) images of the aortic root were retrospectively acquired from 16 patients with the approval of the Institutional Review Board at the University of Pennsylvania. The images were segmented, registered, and converted into a medial model as presented in a previous study. The medial models were remeshed with an quadrilateral elements. Two methods were used for the biomechanical analysis: 1) patient-specific 3D inverse finite element (FE) modeling, and 2) population-level Bayesian inference based on radius variations.

The two approaches provided distinct advantages. The first, patient-specific approach preserves geometric details, but the effect of diastolic pressure and opening angle could not be accounted form. The second, Bayesian approach allowed us to calculate the population-level differences between TAVs and BAVs, but it discarded part of the information available from the images. The biomechanical differences we found in this work indicate that the aortic root tissue in BAV patients experience different intramural stresses that might be linked to the higher risk of aneurysm development. Future work will include implementation of growth and remodeling framework to further establish this link.

The primary function of arteries is as conduits to allow the heart to efficiently deliver blood throughout the entire body. The stiffness of arteries is a key functional parameter that can alter this efficiency, and increased arterial stiffness is a reliable predictor of cardiovascular risk [1]. However, directly determining the stiffness of the arterial wall is essentially impossible in vivo, and proxy measurements such as pulse wave velocity and total arterial compliance are the most feasible clinical measures of arterial stiffness. These, however, only reflect the average stiffness of a region of the arterial network and do not provide information about the local stiffness of arteries. As arterial stiffness is determined by changes in the tissue composition at local levels and diseases like atherosclerosis, aneurysms and dissections occur in relatively localized regions of the arteries, methods to provide accurate information about the local material properties are desirable to enable further research and novel clinical approaches.

We present our implementation of an inverse solver for estimation of local arterial stiffness with a 1D fluid-structure-interaction model of the artery. The model consists of a axisymmetric domain representing a human common carotid artery. The fluid is modeled as a Newtonian fluid with an assumed parabolic flow profile throughout the domain. We investigate two arterial wall models based on the theory of linear elasticity. The first derives from the application of Laplace’s law and the simplifying assumptions of a thin wall and is one of the most widely applied models for pulse wave propagation models of the arteries [2]. The second model is a novel implementation based on thick-walled cylinder theory. We implemented a least-squares procedure to estimate the Young’s modulus parameter in both models, and then evaluated this on experimental data collected from a laboratory phantom. Two sets of boundary conditions were compared. First, direct experimental data of measuremed inlet flow rate and outlet pressure were used. Second, a more general approach of applying a parameterized common carotid inflow and Windkessel outlet was applied. The Young’s modulus estimated with the thin walled approach is in general smaller than that from the thick walled approach. The different boundary conditions produce some what different time courses of pressure and flow as well as a difference in estimate Young’s modulus. Further work will compare the estimated Young’s modulus with stiffness determined through direct tension testing. Additionally, the method will be applied to estimate local arterial stiffness of the common carotid artery based pressure measured by applanation tonometry and flow and geometry by ultrasound imaging.

Acknowledgments

The research leading to these results is funded by the Norwegian Financial Mechanism 2014-2021 operated by the National Science Center, PL (NCN) within GRIEG programme under grant UMO-2019/34/H/ST8/00624, project non-invasivE iN-vivo assessmenT Human aRtery wALls (ENTHRAL, www.enthral.pl)

References

[1] Laurent et al., Eur Heart J; 27(21), 2588-2605 (2006).

[2] Boileau et al., Intl J Num Meth Biomed Eng; 31(10), (2015)

Arterial stiffness is an established biomarker of cardiovascular health [1]. By combining non-invasive measurements and computational models, arterial stiffness can be inferred through solving an optimization problem. However, the non-invasive measurements are hampered by measurement errors, and some parameter values in the optimization problem must be assumed which introduces additional uncertainties. To apply a novel computational model in clinical diagnostics, uncertainty quantification needs to be performed [2]. Model parameters which lead to a large variation in the model prediction can be identified through a subsequent sensitivity analysis. A large number of model evaluations are needed to estimate these sensitivity indices, thus, limiting the application of such analysis to computationally expensive models and allowing relatively few uncertain inputs. Using the Multifidelity Monte Carlo Method (MFMC) [3, 4], we estimate Sobol main and total effect sensitivity indices of a common carotid artery (CCA) 3D-fluid-structure interaction (FSI) model by offsetting the computational burden to computationally affordable 1D- and 0D- models. Computational resources are thus distributed over the three levels of fidelity such that a few 3D-FSI model evaluations ensure accuracy of the sensitivity indices while the lower fidelity models are leveraged to reduce the computational costs of the sensitivity analysis.

We will fist consider the situation where the CCA is modeled as an idealized, straight tube. The same geometric and material parameters as well as boundary conditions are applied to all models. At the inlet, a parabolic physiological flow rate and wave form is prescribed and at the outlet, a three-element Windkessel model mimics the downstream vasculature. In the 1D-model, the artery consists of nodes along a straight line, and in the 0D-model, the artery is represented with a resistor and a capacitor as an electrical analog. The arterial wall is modeled as a linear elastic material and blood is assumed to be a Newtonian fluid. Uncertain model parameters are the vessel diameter, arterial wall thickness, and material parameters for the arterial wall. The uncertainty and sensitivities of the pulse pressure, average pressure, and the diameter change are assessed. We will present the method and implementation we have developed for the CCA model and preliminary results comparing the sensitivity indices estimated through the MFMC approach with the ones estimated with the same computational budget through Monte Carlo simulation of the 3D-FSI model.

Time permitting, results will be shown for hyperelastic material models and patient-specific anatomies.

[1] Laurent et al., Eur Heart J; 27(21), 2588-2605 (2006).
[2] FDA, Assessing the Credibility of Computational Modeling and Simulation in Medical Device Submissions (2021).
[3] Qian et al. , J Uncertainty Quantification; 6(2), 638-706 (2018).
[4] Gorodetsky et al., J Comput. Phys. 408, 109257 (2020).

Acknowledgments:
The research leading to these results is funded by the Norwegian Financial Mechanism 2014-2021 operated by the National Science Center, PL (NCN) within GRIEG programme under grant UMO-2019/34/H/ST8/00624, project non-invasivE iN-vivo assessmenT Human aRtery wALls (ENTHRAL, www.enthral.pl).

Mechanical ventilation is a life-saving therapeutic tool for treating patients with impaired pulmonary function. Despite the clear benefits of mechanical ventilation, it can cause irreversible damage to the lung tissue. The main obstacles for more protective and individualized ventilation strategies are the still insufficient knowledge and understanding of complex lung mechanics in both healthy and diseased states, which is mainly due to the limited ability for in vivo measurement. To shed light into this issue, great efforts have been made in the past in the development of computational lung models. Even most of advanced work in this context only focus on investigating the effect of ventilation on tissue strains and stresses, while coupling to the pulmonary circulation is mostly neglected so far. This is despite the fact that the main function of the lungs, namely gas exchange, takes place through a dense network of pulmonary blood vessels in the alveolar walls. Hence, the coupling between the respiratory system and pulmonary circulation is crucial for getting more insight into the main purpose of ventilation: adequate oxygen supply and carbon dioxide release, while keeping the tissue at a healthy state.
In this contribution we therefore present a physics-based, coupled porous media approach to computationally model air flow, blood flow, and gas exchange in the human lungs. Motivated by the structure of the lungs, larger airways and blood vessels are modeled as discrete zero-dimensional (0D) networks that are embedded into a three-dimensional (3D), three-phase (air, blood and tissue) porous medium, representing the smaller airways, smaller blood vessels and lung tissue in a homogenized manner. Further, the respiratory gases, oxygen and carbon dioxide, are modeled as chemical subcomponents of air and blood with a suitable exchange model in the porous domain. To connect the homogenized and the discrete representations of airways and blood vessels, respectively, a 0D-3D coupling method is used, which allows a non-matching spatial discretization of both domains. The method couples fluid flow and species transport in these phases via an outflow condition from the tips of the discrete networks into the 3D porous medium and vice versa.
Such a comprehensive coupled approach allows us to study the complex interplay of tissue deformation and perfusion, and its effects on oxygenation and carbon dioxide release. Further, the underlying multiphase porous media model can easily be extended to include additional phases, so that pathological conditions such as water accumulation in pulmonary edema can be studied in future stages of the model. We consider our model to be a promising base for investigating clinically relevant questions, which might contribute to an improved treatment in respiratory care.

Mechanosensing of cells to the surrounding material is crucial for their physiological and pathological processes. The emergent dynamics of cells arise from a variety of interactions between cells and their local environment. However, materials design to guide cellular responses is largely ad hoc due to the lack of comprehensive modelling techniques for quantitative understanding. In this paper, we propose a computational model, that couples cell dynamics and cell-materials interactions, to study the mechanosensing of fibroblast cells seeded on different hydrogels.

In recent years, micromechanism-based theoretical modelling has been proposed to capture the essential biophysical characteristics, such as the generation of contractile forces in the cytoskeleton (CSK) and cell–substrate interaction. The contractile force of a cell is primarily generated by the intracellular stress fibers (SFs). SFs are formed via phosphorylation of myosin and polymerization of actin filaments. Actin filaments in cytoplasm are connected by α-actinin proteins to form actin bundles, which are crosslinked by myosin II proteins. The actin-myosin structure generates contraction forces in CSK by the ‘walking’ of myosin II along the actin filaments. Deshpande et al. (2007) proposed a bio-chemo-mechanical model to capture these key mechanisms.

In our continuum model, we consider the following important features of SF formation: (1) an activation signal is essential to trigger the formation of actin-myosin contractile units, (2) SF association rate is dependent on the activation signal and the dissociation rate is dependent on the contractile force, and (3) the dynamic contraction of SF is similar to the well-established muscle contraction model, which can be modelled by a modified Hill model.

For the cell-substrate interactions, we have considered both specific interactions (i.e., binding of membrane molecules to substrate ligands) and nonspecific interactions (e.g., van der Waals, electrostatic forces, hydrogen bonding and steric repulsion) (Bell et al., 1984). The assembly of active/specific focal adhesion (FA) is represented by the aggregation of integrins on the membrane and binding to substrate ligands. A thermodynamic model to represent the chemical equilibrium between these two integrin states (Deshpande et al., 2008; McEvoy et al., 2017), has been adapted in this work.

This coupled model allows us to predict the coupled effects of substrate stiffness and thickness on stress fiber formation and disassociation, and affinity integrin density. We also examine the effect of substrate on the cell-cell communications of fibroblast cells.

Our modeling results have revealed that a cell can sense its neighboring cell by deforming the underlying substrate. Our simulations also provide physical insights in the enhanced mechanosensing capacity of collective cells. The present modelling framework is not only important for profound understanding of cell mechanosensing, but also has the potential to guide the rationale design of biomaterials for tissue engineering and wound healing.

The physiological behaviour of the cardiovascular system is highly affected by the mechanical response of arterial segments, that is in turn dependent from both tissue histological architecture and the contractile tone of smooth muscle cells. The former depends mainly on the different amount and arrangement of constituents (mainly, elastin and collagen fibers), while the latter on chemical drivers of vasoactivity, such as nitric oxide (NO) and reactive oxygen species (e.g., ROS and PN). It is also noteworthy that the problem is highly multiscale since global hemodynamic conditions (e.g., heart rates, resistance of downstream vasculature) highly affect local flow conditions, and hence the local pressure field and the internal stresses affecting biochemical pathways governing vascular tone. Detailed high dimensional models (2D or 3D) can generally be used to simulate local hemodynamics of specific arterial sites, while the whole arterial tree is generally described through low dimensional descriptions (i.e., lumped 1D approaches).

This work presents a comprehensive multi-scale and multi-field computational framework that accounts for: i) a lumped 1D description of the macroscale arterial tree; ii) a continuum 3D model at the microscale of the local chemo-mechano-biological response of arterial tissues (accounting for passive and active tissue behavior); iii) biochemical-dependent vasoconstriction and vasodilation (the NO-ROS-PN biochemical chain), and biochemical-dependent tissue remodeling (the GFs- MMPs biochemical chain). Simulations from 3D chemo-mechano-biological models drive how parameters of the lumped description vary as function of segment dilation, as well as tissue histology and vasoconstriction.

The applicative case study investigates the relationship between arterial vasodilation and vasoconstriction with physical exercise. The obtained numerical results are consistent with available experimental data for normal and spontaneously hypertensive phenomena.

Growing trees respond to mechanical disturbances, resulting, e.g., from environmental forces or gravity, by forming so-called reaction wood. The latter is called compression wood in gymnosperms and tension wood in angiosperms. It enables the tree to control its posture by reinforcing and reorienting the axes of stems and branches, which is a key prerequisite for reaching large heights. The movement is due to asymmetric cambial activity resulting in eccentric growth and varying growth strains. While the underlying biological mechanisms of growth strain generation are not yet fully understood, various hypotheses correlating the induced macroscopic movement with the difference in cell wall structure of reaction and non-reaction wood have been proposed. On that basis, a homogenization procedure was developed for upscaling and evaluating the macroscopic effect of growth strains implemented at the cell wall level. In particular, we aim at unraveling the effect of the characteristic composition and microstructure of tension wood containing G-layers on the elastic properties and macroscopic growth strains by employing multiscale homogenization modeling techniques, based on the concept of continuum micromechanics. A three-step homogenization scheme is employed to estimate the elastic properties of the cell wall layers based on the volume fractions of elementary components. The structural organization at the cell wall level is represented by multilayered cylindrical inclusions exhibiting transversely isotropic material behavior taking into account the previously evaluated layer properties depending on the composition of their elementary constituents, such as cellulose, hemicellulose, lignin and water. We derive the stress and strain fields corresponding to four different loading conditions, which allows for constructing the complete stiffness tensor of tension wood and upscaling the growth strains induced within the G-layer. Coupling the micromechanics model with non-linear beam mechanics, applied to a growing branch inclined with respect to the vector of gravity, allows to simulate the reorientation process induced by growth strains at the cell wall level. In combination with experimental data of the branch shape evolution found in literature of specific species, growth-related parameters can be deduced, which may lead, in further consequence, to a better understanding and predictability of the growth process.

Erythrocytes, also known as red blood cells (RBCs), are the most abundant type of cells in the human body. Their distribution in the microcirculation determines the oxygen delivery and solute transport to tissues. This process relies on the partitioning of RBCs at successive bifurcations throughout the microvascular network and it is known since the last century that RBCs partition disproportionately to the fractional blood flow rate, therefore leading to heterogeneity of the hematocrit (i.e. volume fraction of RBCs in blood) in micro-vessels. Usually, downstream of a microvascular bifurcation, the vessel branch with a higher fraction of blood flow receives an even higher fraction of RBC flux. However, both temporal and time-average deviations from this phase-separation law have been observed in recent works.

Amongst others, the specific shape and high flexibility of RBCs might cause them to linger, i.e. RBCs can temporarily reside near the bifurcation apex with diminished velocity. This is of critical importance for the cells which are travelling in the capillaries of our circulatory system, whose cross section is sometimes smaller than the erythrocytes diameter. In this presentation, we quantify how the microscopic behavior of RBC influences their partitioning, through combined in vivo experiments and in silico simulations. In vivo experiments are performed in dorsal skinfold chambers of Golden Syrian hamsters, while in silico simulations reproduced the in vivo geometries and are performed using an immersed-boundary-lattice-Boltzmann method.

We developed an approach to quantify the cell lingering at highly-confined capillary-level bifurcations and demonstrate that it correlates with deviations of the phase-separation process from established empirical predictions by Pries et al. More accurately, we demonstrate a linear correlation between the lingering amplitude and deviations from the classical model of erythrocytes partitioning from the literature, both in vivo and in silico. We also show that the lingering is more pronounced in bifurcations presenting a higher curvature at their stagnation point, i.e. the intersection of the bifurcation’s wall and the flow divider plane. This explains why some geometries present stronger lingering than others. Furthermore, we shed light on how the cell membrane rigidity can affect the lingering behavior of RBCs, e.g. rigid cells tend to linger less than softer ones. Taken together, RBC lingering is an important mechanism that should be considered when studying how abnormal RBC rigidity in diseases such as malaria and sickle-cell disease could hinder the microcirculatory blood flow or how the vascular networks are altered under pathological conditions (e.g. thrombosis, tumors, aneurysm).

Blood is a vital fluid that plays an important role in transporting necessary substances and metabolic products for the cells. It consists of about 55% plasma and 45% blood cells where red blood cell (RBC) is the most abundant. Aggregation of RBCs is reversible under normal conditions, but abnormal clusters of RBCs appear in some pathological situations, such as diabetes. The formation mechanism of these clusters is controversial nowadays, but it has been demonstrated that some high-molecular-weight molecules such as fibrinogen and dextran could promote this aggregation.

RBCs surface is covered by glycolipids and glycoproteins, which are collectively called glycocalyx. The alteration of glycocalyx can affect the function of RBCs and it has been reported that a correlation between the enhanced aggregation and the glycoprotein layer (glycocalyx) degradation of the RBCs membrane could be found in diabetes. Other research has also shown that the glycocalyx alteration due to enzyme activities enhanced RBCs aggregation under static conditions by using rat blood. Against this background, glycocalyx alternation is an important point to be studied in this research, especially how glycocalyx alteration can affect RBCs aggregation under flow.

Amylase is a digestive enzyme that plays a crucial role in breaking down polysaccharides. As RBCs are covered by glycocalyx, amylase definitely interacts with RBCs’ glycocalyx. We used pancreatic amylase at various concentrations (0 – 2000U/L) to cleave glycocalyx, mimicking the pathologies of RBCs. We first confirmed the evolution of glycocalyx brush density as a function of amylase concentration with the help of Alexa488-conjugated wheat germ agglutinin (a specific marker of glycocalyx) and confocal microscopy. The results in absence of flow showed that at high concentrations of amylase, the RBCs glycocalyx underwent degradation. Then the aggregation size and morphology were then studied with an inverted microscope equipped with a high-speed camera and a blue light source. These static situation results proved not only the number of RBCs per aggregate was affected by the degradation of glycocalyx but also their morphology was influenced at the concentration of 150kDa dextran in Phosphate Buffered Saline (PBS). The aggregation activities of RBCs under flow were later studied in an artificial polydimethylsiloxane (PDMS) microfluidic circuit with variable pressure difference. The results also showed that the amylase-treated RBCs had significantly more aggregated than non-treated RBCs in 150kDa dextran (15mg/mL in PBS). Cleavage of glycocalyx considerably affected RBCs clusters' size, morphologies, and stabilities under flow.

The mechanism by which amylase caused glycocalyx alteration induces RBCs aggregation is not yet fully understood, and further research is needed to elucidate the exact pathways involved. However, our findings provide valuable insights into the role of glycocalyx alteration in RBC aggregation in absence of flow or in presence of flow and also suggest that glycocalyx degradation by pancreatic amylase has a clear impact on aggregation.

Introduction

Red blood cells (RBCs) are the most abundant cell type in mammals. They are characterized by a high surface-to-volume ratio which gives them very high deformability. When immersed into the flow of blood plasma, this high deformability creates a fascinatingly rich and intricate dynamics due to the two-way coupling between cellular and fluid mechanics. Besides its physiological relevance, e.g. for oxygen delivery, observations of red blood cell shapes have recently been suggested as a tool for medical diagnosis [1, 2]. With some exceptions, typical experimental setups are however limited to 2D microscopic imaging which can represent a serious limitation given the complexity of 3D RBC shapes in blood flow. If properly validated, computational simulations can resolve this issue and provide a deeper understanding of RBC dynamics. Most simulation models which are currently in use, however, are based on experimental validations using static (e.g. optical tweezers) or steady-state properties. In this talk, I will present computational modeling of single RBCs in microchannels focussing specifically on dynamics and transient situations.

Methods

We use boundary-integral computer simulations for the flow computations in the Stokes regime. Membrane dynamics are computed using Skalak and Helfrich laws for shear/area elasticity and bending, respectively. Our models furthermore include the viscous dissipation inside the membrane.

Results

The two prototypical states of a red blood cell flowing in a rectangular microchannel are the croissant and the slipper state [3]. The former is a stationary shape flowing in the center of the channel. The latter is characterized by an off-center flow position and, most importantly, by a constant rotation of the membrane around the liquid interior.

In the first part of the talk, I will briefly introduce computer simulations together with experimental data from our collaboration partners demonstrating that the croissant/slipper dynamics is in fact bistable and that the final RBC shape depends on the initial position. The main focus will then be to develop computational simulations that can quantitatively reproduce the rotation frequency of the membrane in the slipper state. In the second part, I will focus on transient situations such as transitions from croissants to slippers [4] as well as RBCs passing through channels with varying geometries.

I will show that, in order to obtain a computational model which is consistent with this highly diverse range of experiments, it is essential to (i) include membrane viscosity and (ii) employ a higher-than-usual ratio of the RBC interior to that of the outer fluid. Our simulations thus allow a direct and quantitative estimation of RBC membrane viscosity.

[1] Kubánková, M. et al. Biophys J 120, 2838–2847 (2021)

[2] Recktenwald, S. M. et al. eLife 11, e81316 (2022)

[3] Guckenberger, A. et al. Soft Matter 14, 2032–2043 (2018)

[4] Recktenwald, S. M. et al. Biophys J 121, 23–36 (2021)

Sickle Cell Disease (SCD) is a highly prevalent and handicapping genetic disease characterized by hemolytic anemia and unpredictable vaso-occlusive crises (VOC). It is caused by sickle hemoglobin, which, upon deoxygenation and dehydration, polymerizes into fibers in the cytoplasm of red blood cells (RBCs), increasing their cytoplasmic viscosity and remodeling their cytoskeleton. These changes combine to decrease the RBC deformability, a factor involved in the pathophysiology of SCD, with a key role in clinical outcome and occurrence of VOC. Even with reoxygenation, sickle hemoglobin polymerization is only partially reversible. Therefore, the RBC deformability of a sickle patient is highly dispersed as circulating RBCs have undergone a variable number of desoxygenation /reoxygenation cycles. To date, the assessment of RBC deformability require sophisticated devices. A simple method, requiring only a few blood microliters, easy to implement, fast, sensitive to the different parameters governing RBC deformability, and valid for heterogeneous RBC populations is lacking.

We exploit the fact that the individual movement of an RBC under shear flow is an indicator of its deformability. By increasing the flow shear rate, the motion of an RBC suspended in a medium of 40 mPa.s viscosity gradually changes from a rigid-like flip-flopping to a wheel-like rolling motion before transiting, above a critical shear rate set by the cell deformability, to a stationary droplet-like tank-treading motion. The more deformable the cell, the lower the critical shear rate. A given shear rate defines an RBC deformability threshold above which the cell is deformable enough to tanktread. We measured the fraction, f_TT, of tanktreading RBCs in a blood sample, which is the fraction of cells having a deformability higher than this threshold. The lower the applied shear rate, the more severe the deformability test and the fewer RBCs in tanktreading motion is observed in a sample; f_TT is a marker of deformability of the whole RBC sample, which can be tuned by the applied shear rate. We show that this marker is lower in SCD than in control samples. Furthermore, we show that in vitro, this parameter is sensitive to RBC density and hydration, two common features of SCD. We performed a clinical trial on 21 SCD patients by performing weekly repeated f_TT measures over a period of 7 to 23 weeks. We show that f_TT correlates with quantitative biological markers such as level of fetal hemoglobin, reticulocytes count, and plasma LDH level in SCD patients, thus suggesting that a higher hemolysis rate is associated with a lower RBC deformability; f_TT significantly decreases when the patient undergoes a high level of pain, and, surprisingly is increased when patients have an antihypertensor treatment. Moreover, f_TT significantly decreases before VOC onset and arrival at the hospital, then gradually increases during resolution of the VOC. Overall, f_TT could be useful for clinical monitoring of SCD patient to assess treatment efficacy or predict VOC. f_TT is also a good candidate to be an effective marker for diseases associated with RBC stiffening such as malaria.

Over the past 20 years high resolution micro-CT has revolutionized the analysis of trabecular and cortical bone microstructure, facilitating efficient three-dimensional (3D) analysis. Longitudinal, in vivo, applications of this technology, which open up a fourth dimension (4D), in preclinical animal models have primarily focused on trabecular bone, with relatively few studies targeting cortical microstructural features such as porosity. This is despite the growing recognition of the role of cortical bone loss in bone fragility. Two primary factors have contributed to the dearth of in vivo studies of cortical bone: 1) radiation dose, which scales non-linearly with resolution for X-ray computed tomography, is considerably higher when targeting cortical pores as they are smaller than trabeculae; and 2) small rodents, including mice and rats, exhibit little, if any, intra-cortical remodeling comparable to larger vertebrates, including humans. This presentation details progress over the past decade to overcome these hurdles and advance in vivo imaging of cortical bone porosity. Specifically, we have pursued 4D tracking of the remodeling spaces that lie at the heart of basic multicellular units (BMUs) to shed new light on the spatio-temporal regulation of remodeling. To overcome the challenge arising from radiation dose, our group has developed synchrotron-based imaging protocols at the Biomedical Imaging and Therapy facility of the Canadian Light Source synchrotron which capitalize on in-line phase contrast micro-CT. This approach has enabled enhanced detection of cortical bone porosity, while minimizing radiation dose (1-5 Gy) and scan time (<1 minute). To address the limitation of small rodents, we have developed rabbit models of elevated cortical bone remodeling/porosity, including ovariohysterectomy, parathyroid hormone (PTH) dosing and glucocorticoid dosing. By combining synchrotron-based imaging with rabbit models, we have achieved the first 4D tracking of remodeling spaces and direct analysis of their rate of advance (linear erosion rate; LER). We have discovered that LER is reduced in animals undergoing PTH dosing compared to those withdrawn from PTH, a potential mechanism by which coupling of resorption and formation are enhanced by this hormone. We are actively developing novel 3D morphological tools for assessing remodeling spaces, to measure the extent and timing of the resorptive, reversal and formative phases of BMUs and to examine potential impacts of PTH and other interventions. We are also exploring these morphological approaches as a means to facilitate comparative analysis between rabbits and humans to establish the validity (and limitations) of this experimental platform for the study of osteoporosis etiology and treatment. Finally, a key objective of our team is the integration of 4D data into computational models of cortical bone remodeling to accelerate discovery related to the improvement of osteoporosis treatment. Direct study of the spatio-temporal regulation of BMUs is enabling a shift towards the assessment of remodeling at its fundamental level, rather than making inferences from accumulated microstructural changes.

Bone is a defining feature of all vertebrates, present in more than ~65,000 extant species today. Even cartilaginous fishes, such as sharks and rays, and thought to have possessed a bony skeleton early on in their evolutionary history before secondarily losing it. For palaeontologists studying the history of vertebrates, bone is the most commonly preserved trace of an animal and provides the literal and figurative backbone upon which to reconstruct past life.

The evolution of the earliest four-limbed terrestrial animals from water-dwelling fishes is hailed as one of the greatest ‘steps’ in evolution and is thought to have occurred during the Devonian Period, more than 360 million years ago. Significant adaptations were required in the bodies in the first tetrapods to enable them to leave the water and conquer land, including the appearance of limbs, digits and lungs, and concomitant strengthening of the limb bones, girdles and axial skeleton.

Recently, several novel imaging and computational methods such as synchrotron and computed tomography (CT) have transformed palaeontology enabling non-destructive examination of rare and irreplaceable fossils down to histological scale, the creation of digital models for complex biomechanical analyses, and revealing hitherto unseen internal anatomy. In this talk I will detail several recent research projects examining adaptations and remodelling in the bony skeletons of fish and early tetrapods as revealed by novel imaging methods.

First, high-energy computed tomography reveals the skeleton of the pectoral fin in Elpistostege, a tetrapod-like fish from the Late Devonian of Canada. The pectoral fin endoskeleton contains a humerus, radius, ulna, ulnare and four proximodistal rows of radials and two distal rows organized as digits. This tetrapod-like pattern is retained within a fin with distal lepidotrichia but represents an important stage in the early evolution of the vertebrate hand.

Secondly, the humeral microarchitecture of stem-tetrapods, batrachians, and amniotes was examined using three-dimensional synchrotron virtual histology. We show that a centralised marrow organisation (to enable haematopoiesis, the production of blood cells, as exhibited in living amniotes) did not arise during the water-land transition as originally hypothesised, but arose considerably later in Permian amniotes.

Lastly, Finite Element Analysis (FEA), a technique common in engineering and mathematical modelling to predict how structures react to various forces, is herein applied to address questions about form-function relationships in the evolution of vertebrates. FEA is applied to several of the lungfishes from the Late Devonian Gogo Formation, Australia, the most diverse lungfish assemblage in the world. The >10 described species display extreme variation in skull, dentition and mandible morphology which has been proposed as a driver for their success. Here using FEA we show that robust forms exhibit higher strain tolerances during feeding compared to more gracile forms. Our results demonstrate that biomechanical function and feeding performance are constrained by mandible morphology in Devonian lungfish.

These three case studies show significant bone adaptations observed during early fish-tetrapod evolution (across histological to gross morphological scale) as revealed by new tomographic computational methods, and highlight the universality of bone as a vertebrate tissue.

John Clement was my student at UCL. When he graduated and wanted to undertake further training in pathology, I advised him of a vacant position at The London Hospital Medical College [later QMUL], which he took, and thus entered micro-anatomical and forensic research. When he removed to Melbourne, he established the renowned femur collection which enabled many international collaborators to access first class, well documented human bone research material. At UCL, we established a facility for determining the fabric level mineralisation density of bone at the sub-micron scale using quantitative backscattered electron imaging in an automated digital scanning electron microscopy system [qBSE-SEM]. We also introduced confocal scanning optical microscopy [CSLM] to bone studies and developed methods for marrying the information contents from these important methodologies. At the same time, Jim Elliott developed X-ray microtomography [XMT] at QMUL and we correlated all these methods.

John provided us several femur samples, which like most other research material at the time we embedded in PMMA, en route to smart imaging with SEM and CSLM. John, with David Thomas, took to XMT in Melbourne. Unable to compete with XMT for large volume 3D imaging for the vascular space compartment in bone, we took to casting aside the bone in our precious blocks by dissolving it with sequential treatments with HCl and NaOCl solutions, leaving a cast of the marrow spaces and the osteocyte lacunar-canalicular space. The latter was so abundant that it blocked visibility of the blood vessel canal spaces, so we destroyed it by ultrasonication to clean the residual cast. This was in earlier days coated with gold to give surface conductivity and an enhanced BSE signal, but latterly we have simply used uncoated samples at say 50Pa chamber pressure to circumvent charging problems.

The resin casts allow us to image the space compartment in bone at a resolution far superior to that obtainable by XMT, allowing new insights into growth, modelling and remodelling processes in compact bone tissue.

The recent decade our understand of the cellular organization of human bone remodeling have been revised, providing a new perspective on this process during physiological and pathophysiological conditions, and the critical remodeling steps contributing to bone loss. We know now that bone remodeling comprises three successive phases: (1) a short initial resorption phase by primary osteoclasts, (2) a longer reversal-resorption phase with intermixed reversal cells (osteoprogenitors) and secondary osteoclasts, and (3) a subsequent formation phase with mature bone-forming osteoblasts. Moreover, it is well established that trabecular bone remodeling events are separated from marrow cavity by canopy cells (osteoprogenitors), which is part of the bone marrow envelope enwrapping the marrow cavity.

In this study, we focus on the close interplay between osteoclasts and osteoprogenitors (bone lining cells, reversal cells and canopy cells), which play a critical role in coupling of bone resorption to the subsequent bone formation. During the reversal-resorption phase, the osteoprogenitors colonizing eroded surfaces gradually differentiate into bone-forming osteoblasts and expand to a critical density required for initiation of bone formation. Osteoclasts are in direct cell-cell contact with these osteoprogenitors (involving Semaphorin 4D - plexin B1 interaction) and secrete coupling factors that promote these osteoprogenitors (involving clastokines like LIF, PDGFB, TRAcP5b), which on the other hand express osteoclast-promoting RANKL and degrade the collagen debris left behind by the osteoclasts. These osteoprogenitors also interact with the mechanosensing osteocytes, and there is evidence supporting that mechanical conditions likely sensed by osteocytes may affect the interplay between osteoclasts and osteoprogenitors. Indeed, osteoclasts, osteoprogenitors and osteocytes form an overlook partnership, which is critical to the coupling of bone resorption and formation within each bone-remodeling event.

Tissue specific metabolic rates for various organs and organ systems are typically calculated for multiple organ tissues as given constants of kcal/kg expended per day. These constants (Kᵢ) are multiplied by an organ’s mass (Tᵢ) and add up to the whole body resting energy expenditure: REE = Σ(Kᵢ × Tᵢ).

Organ and tissue mass-specific metabolic rates are measured using a variety of techniques such as magnetic resonance imaging, calorimetry, or by a respirometer. Within the category of ‘residual mass’ in metabolic rate calculations often includes the skeleton, blood, skin, and other small tissues and organs. Problematically, skeletal tissue is lumped in with other organs and tissues for the metabolic rate constant of residual mass since it is not considered an expensive tissue with a high metabolic rate. But this ignores the exponential scaling of osteocyte density with body mass reported in mammals.

Metabolic rate scales at the ¾ power of body mass. This same scaling can be interpreted as a ratio of the average metabolic rate of a cell, Bc, to the average cell size, mc: B/M = Bc/mc. The average cellular metabolic rate to average cell size decreases as body size increases so that as body mass changes, there is a tradeoff between cell size and cell metabolic rate. However, osteocytes generally fall within the narrow range of 5-20 µm diameters, but comparative mammalian osteocyte density increases nonlinearly with body mass. Thus the tissue specific metabolic rate of bone must vary enormously across the Class.

Bone, unlike other organ tissues, is unique in that roughly 95% of its cells are trapped in an inorganic mineral matrix at densities per unit volume that depend upon growth rate, body mass, and thus also life history. In our intraspecific research on human bone, osteocyte density scales positively with body height, indicating that larger individuals have higher osteocyte densities for orchestrating bone formation and mineralization, which thus also have higher metabolic rates. It appears that the same increase in energetic efficiency observed in interspecific comparisons of the mass specific metabolic rate of bone at larger body sizes also characterizes body size categories among humans. Long period biological rhythms that regulate rates of cell proliferation explain some aspects of human body size variability.

Retrieving metabolic rates or rates of oxygen consumption from living organisms is a difficult task that has not been fully explored in bone. Our presentation will examine the scaling of osteocyte density and its implications for the mass-specific metabolic rate of bone.

Bone is a hierarchical, composite connective tissue that can adapt and change through the lifespan of an individual. Its mineralized matrix holds within it information about life history, functional adaptation, health and disease, leaving tell-tale signatures (e.g. in terms of tissue composition, distribution and orientation and the spaces within it) as a result of the dynamic processes of modeling and remodeling. Contributions from fields as varied as paleontology, forensic science, anthropology, orthopedics, materials science and engineering, combined with advances in imaging and analysis methodologies have resulted in a deeper understanding of this complex internal structure of bone and its relationship to attaining and maintaining bone quality and responsiveness to mechanical loading through the lifespan.

This presentation reviews multidisciplinary research that grew from collaborations with Dr. John Clement and the Melbourne Femur Collection, and expanded into other anatomical locations and samples with the aim of (1) quantifying patterned organization in cortical bone microstructure and properties through ontogeny and with aging using correlative light and electron microscopy as well as 3D techniques such as microCT, (2) relating this organization to the underlying processes of bone modeling, remodeling and establishment of bone morphology, and (3) applying these techniques to bioarchaeological and clinical contexts. The presentation will highlight how new methods of visualization at different length scales can enhance not only this kind of basic science research, but also be used in the education of future researchers and clinicians.

The fetal membranes are an important biological structure for pregnancy that surrounds and protects the fetus. They are layered structures, comprising the amnion, the chorion, and part of the maternal layer decidua. During gestation, they undergo complex microstructural changes, such as the weakening of the tissue in preparation for delivery. Little is known about the influence of the collagen fibers organization within the amnion in the rupture process of the fetal membranes. Non-crystalline X-ray diffraction (XRD) has been applied to study the collagen organization in some soft tissues, such as the cornea, breast, bone, cartilage, and, more recently, amnion. Some studies have suggested that the loss of the regular structure of the collagen fibers in the amnion may represent a contributing factor to PPROM. This work aims to analyze the biomechanics of fetal membranes under different off-plane collagen fibers within it through the potential of numerical analysis to understand whether it has a potential impact on preterm pre-labor rupture of the fetal membrane (PPROM).

A multilayer model of the fetal membrane was developed based on a robust inflation mechanical test dataset. In terms of constitutive models, the amnion was characterized by the modified version of the Buerzle-Mazza constitutive model (μo=2.4MPa, q=2.96, m5=0.463, m2=0.00228, m3=41.12, m4=1.27, N=32). The chorion (E=1MPa, υ=0.41) and the decidua (E=1MPa, υ=0.49) were characterized by elastic linear properties.

The evolution of the maximum principal stress curves with pressure in the amnion when the off-plane angle is set to 0° or 10° is different from the cases where the same parameter is set to 20° or 30°: for the first two values, the curves always increase throughout the entire simulation; for the 20° and 30° angles, the stress is 0 for smaller pressures and a rapid increase in stress is verified for higher pressures. The maximum principal stress is larger when the angle is changed from 0° to 10°, and from 30° to 20°. In the chorion layer, the maximum principal stress at the apex of the membrane increases with the off-plane angle.

Different off-plane fiber angles had a strong impact in terms of maximum principal stress in both layers, especially in the mechanical dominant layer amnion. In terms of PPROM, it is very likely that certain off-plane collagen fibers that lead to higher maximum principal stresses potentiate the rupture of the membrane. These results highlight the potential of our model to characterize the biomechanics of fetal membranes under different physiological conditions.

Pelvic floor disorders, including uterine prolapse and urinary incontinence, have a significant impact on women’s quality of life and well-being, affecting between one-third and one-half of all women [1]. For uterine prolapse, risk factors include advancing age, obesity, physical inactivity, and parity. The disease is caused by a weakening of pelvic floor musculature and other supporting anatomical structures, such as the uterine ligaments. Currently, tissue changes leading to the development and progression of uterine prolapse through mechanical and molecular alterations are understudied. Since aging and hormonal changes may affect components of the extracellular matrix, including collagen fibrils and their nanostructure (d-spacing) [2], it is crucial to investigate changes in the collagen backbone of the uterine support structures to gain a deeper understanding of the development and progression of uterine prolapse. As part of the uterine support structures, the broad ligament connects the uterus to the lateral pelvic walls and is often described as a double layer of peritoneum. Consequently, our aim was to investigate the characteristics and nanoscale behavior under loading of collagen in the broad ligament.

Broad ligament samples were obtained according to local ethics regulations from women of different ages (66 ± 22 years) post mortem. Quadratic samples (15 × 15 mm²) were subjected to biaxial stretching with simultaneous microfocussed ultra-small-angle X-ray scattering (USAXS) to determine changes in collagen fiber orientation and d-spacing with deformation (MiNaXS beamline P03/PETRA III, DESY) [3]. Deformation was increased in a stepwise manner (0%, 5%, 10%, 15%, 20%). For each step, a map of 1 × 1mm² with 25 individual USAXS measurements was created. In addition, samples adjacent to the USAXS-samples were prepared for histological assessment of collagen orientation, elastin and proteoglycan content, and cellular properties. Slices were cut in frontal, sagittal, and horizontal orientation to allow collagen fiber assessment from different directions.

Radial integration of scattering data indicated the presence of two main orthogonal collagen fibril orientations. With increasing tissue strain, collagen d-spacing (an indicator of fibril strain) and fibril alignment increased while fibril thickness decreased (all p<0.05). Preliminary histological evaluation from slides with orthogonally oriented cuts confirmed the presence of multiple main collagen fiber orientations. Collagen fibers exhibited crimping. Further, the broad ligament samples were cell rich and included small vessels.

Histological evaluation confirmed the presence of multiple predominant fiber orientations as indicated by USAXS. This is in agreement with descriptions of fiber distribution in peritoneum [4]. Compared to reported fibril strains in tendons [5], the observed fibril strain in the broad ligament was smaller. This could be explained by the much higher alignment of collagen fibers to a unidirectional loading axis in tendons. The presented findings provide a more detailed understanding of collagen characteristics of the broad ligament and may contribute to the development of biomechanical models of the uterine support system.

References:

[1] MacLennan et al., 2000, DOI: 10.1111/j.1471-0528.2000.tb11669.x.

[2] Fang et al., 2012, DOI: 10.1038/jid.2012.47.

[3] Euchler et al., 2022, DOI: 10.1088/1742-6596/2380/1/012109.

[4] Liu et al., 2017, DOI: 10.1016/j.biomaterials.2016.11.041.

[5] Barreto et al., 2023, DOI: 10.1016/j.matbio.2022.11.006.

Childbirth trauma during the second stage of labor is a prevalent concern, affecting millions of women worldwide. Levator ani muscle (LAM) trauma, which can impact 6-40% of women undergoing vaginal delivery, particularly nulliparous individuals, is a prevalent injury arising from childbirth. LAM trauma can lead to persistent morbidity and the necessity of future surgical intervention for 10-20% of patients. However, predicting and diagnosing pelvic floor lesions can be challenging. To address this issue, biomechanical simulations have been used as a helpful tool to evaluate pelvic floor muscle (PFM) injuries. However, using the finite element method (FEM) for these simulations can be a time-consuming process. Thus, it is important to explore alternative techniques for applying these methods in a clinical setting. One promising approach is to use machine learning (ML) algorithms, which can leverage simulation data to offer faster results. The present study aims to develop a ML framework to predict stresses on the PFM during childbirth by training ML algorithms on FEM simulation data.

To generate the data, 2744 childbirth simulations were performed in Abaqus software, in which the material parameters of the constitutive model used to characterize the PFM were changed. The constitutive parameters varied between ranges of values ​​according to the literature, thus allowing to characterize the pelvic floor of most women. A total of 1715 simulations were successfully completed.

A dataset was created in which each observation corresponds to a node of the pelvic floor in one simulation. Specifically, 46 nodes located in the inferior portion of the PFM were selected, which is the region that undergoes the most stretching during childbirth. Features such as node number and position, initial coordinates, and material parameters were used for training. Four ML models, namely Random Forest (RF), Extreme Gradient Boosting (XGBT), Support Vector Regression (SVR), and Artificial Neural Networks (ANN), were chosen for the study. A training and test set were created with a 90/10 split, recurring to a stratification method to guarantee the same feature distribution in both sets. Subsequently, hyperparameter optimization with cross-validation was performed. The models' performance was measured by the mean squared error (MSE) and the mean absolute error (MAE).

The stress values were measured at the moment of maximum stretch, and ranged from 0 to 30 MPa. The results for predicting the maximum principal stresses showed that the ANN produced the best outcomes, with a MSE of 0.112 and a MAE of 0.191. Conversely, the SVR model had the highest error, with a MSE of 0.444 and a MAE of 0.356. Both tree-based algorithms performed reasonably well and were closer to the outcomes achieved by the ANN. The ANN is capable of making predictions in approximately 120 milliseconds, indicating its potential for real-time applications.

The current work represents an advance in the field of childbirth computational simulations using artificial intelligence tools. The ability to predict the stresses suffered by the woman on the pelvic floor immediately before or during childbirth could aid in medical decision-making and in the identification of non-visible injuries.

Tissue development in normal and pathological conditions is driven by a set of biological phenomena. Growth is characterized by a change of mass which might be positive (tissue growth) by cell division, cell enlargement, and extracellular matrix secretion, or negative (tissue atrophy) by cell death, cell shrinkage or resorption [1]. Cancer is a malignant pathology characterized by accelerated and uncontrolled cellular growth and proliferation [2]. In 2020, it was estimated 19.3 million newly diagnosed cases and almost 10.0 million cancer deaths, worldwide [3]. The development of solid tumors is a multi-factor biological process, as it is influenced by molecular and genetic factors, cell-cell and cell-extracellular interactions, and vascularization (in particular oxygen and nutrients supply) [4].

Several experimental and theoretical efforts have been taken to unravel the mechanisms of tumor growth. Constitutive mechanics models are one of these approaches as they can help describe mass changes and stress development during the events of tumor progression [4]. From a biomechanical perspective, solid tumors are hyperelastic, compressible, anisotropic materials with a mechanical behavior both space and time-dependent, whose mass varies over time [5]. In this work, the goal is to establish a computational framework to model tissue growth to be latter applied for solid tumors.

Initially, a constitutive model to describe the anisotropic growth of a solid mass is implemented [6] considering the multiplicative decomposition of the deformation gradient into an elastic and a growth contribution [7]. In this first attempt, anisotropic growth is considered a strain-driven process with a privileged direction for growth due to the presence of a micro-structure [8]. To ease the use of this model in more complex scenarios, the constitutive model is implemented into the finite element software Abaqus® using a user-defined subroutine (UMAT). To validate the UMAT subroutine, the numerical solution for a single unitary hexahedral finite element is computed for a set of deformation cases in the software ABAQUS® and compared to the analytical solution [6].

Finally, the UMAT is implemented in an in-silico model of a solid tumor surrounded by the extracellular matrix (simplified by a parallelepiped) and cyclic uniaxial and biaxial stretch scenarios are applied. The Cauchy stresses are recorded in the direction of the applied displacements as function of the stretch. At the unload final state, the embedded tumor presents a positive volume change as the tumor grows irreversibly in an anisotropic manner. Future steps include the incorporation of a tumor growth law derived by experimental evidence and the implementation of a stress-driven anisotropic growth evolution.

References

[1] Ambrosi D, Guana F. Stress-Modulated Growth. Mathematics and Mechanics of Solids 2007;12:319–42. https://doi.org/10.1177/1081286505059739.

[2] Ambrosi D, Amar M Ben, Cyron CJ, DeSimone A, Goriely A, Humphrey JD, et al. Growth and remodelling of living tissues: Perspectives, challenges and opportunities. J R Soc Interface 2019;16. https://doi.org/10.1098/rsif.2019.0233.

[3] Sung H, Ferlay J, Siegel RL, Laversanne M, Soerjomataram I, Jemal A, et al. Global Cancer Statistics 2020: GLOBOCAN Estimates of Incidence and Mortality Worldwide for 36 Cancers in 185 Countries. CA Cancer J Clin 2021;71:209–49. https://doi.org/https://doi.org/10.3322/caac.21660.

[4] Xue S-L, Li B, Feng X-Q, Gao H. Biochemomechanical poroelastic theory of avascular tumor growth. J Mech Phys Solids 2016;94:409–32. https://doi.org/10.1016/j.jmps.2016.05.011.

[5] Ramírez-Torres A, Rodríguez-Ramos R, Merodio J, Penta R, Bravo-Castillero J, Guinovart-Díaz R, et al. The influence of anisotropic growth and geometry on the stress of solid tumors. Int J Eng Sci 2017;119:40–9. https://doi.org/10.1016/j.ijengsci.2017.06.011.

[6] Vila Pouca MCP, Areias P, Göktepe S, Ashton-Miller JA, Natal Jorge RM, Parente MPL. Modeling permanent deformation during low-cycle fatigue: Application to the pelvic floor muscles during labor. J Mech Phys Solids 2022;164:104908. https://doi.org/10.1016/j.jmps.2022.104908.

[7] Rodriguez EK, Hoger A, McCulloch AD. Stress-dependent finite growth in soft elastic tissues. J Biomech 1994;27:455–67. https://doi.org/10.1016/0021-9290(94)90021-3.

[8] Soleimani M, Muthyala N, Marino M, Wriggers P. A novel stress-induced anisotropic growth model driven by nutrient diffusion: Theory, FEM implementation and applications in bio-mechanical problems. J Mech Phys Solids 2020;144:104097. https://doi.org/10.1016/j.jmps.2020.104097.

Acknowledgements: The authors gratefully acknowledge the support from the Portuguese Foundation of Science under the grant SFRH/BD/09480/2022 and the funding of the research project PTDC/EME-APL/1342/2020.

The Finite Element Method (FEM) is a powerful tool that enables the simulation of many complex engineering problems. In complex analysis, such as in the modelling of biological and biomechanical phenomena, it is necessary to specify the constitutive equations that describe the biomechanical behaviour of such materials.

Soft tissues and other biological materials subjected to large deformations present an extremely nonlinear behaviour, which makes the constitutive modelling of such materials a complex task and expensive in terms of time and computational resources. Alternatively, it is possible to use surrogate models, which consist of models that replace the traditional and expensive main models to overcome some computational limitations.

Such surrogates can learn the behaviour of the soft tissue when trained on previously acquired data and then replace the expensive numerical models. To develop the surrogates, Artificial Neural Networks (ANNs) will be trained from a large dataset with the deformations (inputs) and the corresponding stresses (outputs). Then, the weights and biases of the trained model will be used to write the forward pass equations in Fortran to implement a general user material subroutine (UMAT) for the Finite Element software ABAQUS. The surrogate models will be tested under homogeneous deformation cases and under more complex examples, where it is shown the values of the maximum principal stress obtained with a conventional UMAT and with the ANN. In the future, this data driven approach is going to be applied to soft tissues, such as the pelvic floor muscles.

The female pelvic cavity is a very complex anatomical region. Pelvic dysfunction, especially pelvic organ prolapse (POP) and urinary incontinence (UI), have a negative impact on women's lives, and it happens when the support mechanisms of the pelvic cavity become fragile. UI has a prevalence of a up to 28%, with stress urinary incontinence (SUI) being the most common form [1,2], characterized by involuntary urinary leakage during physical strain, coughing or an increase in intra-abdominal pressure (IAP). Existing treatments for these disorders are divided into conservative and invasive. The last ones consist of surgical interventions and should be used in patients in whom the first treatments did not work, or when the severity of the dysfunction is high.

SUI occurs when the intravesical pressure exceeds urethral resistance at which the urethra has the ability to remain closed [2]. Furthermore, it comes to a point when neither the pubourethral ligaments (PULs) [3] and the arcus tendineous fasciae pelvis (ATFP) [4] can stabilize the bladder neck (BN) [5]. Assessment of BN mobility in patients with SUI is essentially clinical, however, the imaging techniques such as ultrasound (US) and magnetic resonance imaging (MRI) are used as a method for evaluating this characteristic. The outcomes of radiographic images have been crucial and used as input for numerical methods.

The aim of the present study was to establish the IAP values and the in vivo biomechanical properties of the bladder tissue for two distinct groups (continent women and women with SUI). The numerical simulations of Valsalva maneuver were performed, applying the Ogden hyperelastic constitutive model to the bladder and also the inverse finite element analysis (FEA).

This study focuses on adapting an inverse FEA to estimate the in vivo properties of the bladder, using a constitutive model of the female pelvic cavity and MR images acquired at rest and during the Valsalva maneuver, for two distinct groups (continent and incontinent women). The bladder neck’s displacements were compared between computational simulation and MR images.

The results of the FEA showed that the bladder tissue of incontinent women have the highest stiffness approximately 47% higher when compared to continent women.

References

1. Jansson MH, et al. Stress and urgency urinary incontinence one year after a first birth—prevalence and risk factors. A prospective cohort study. Acta Obstetricia et Gynecologica Scandinavica 2021; 100(12):2193–2201.

2. Falah-Hassani K, et al. The pathophysiology of stress urinary incontinence: a systematic review and meta-analysis. International Urogynecology Journal 2021; 32(3):501–552.

3. Kefer JC, et al. Pubo-urethral ligament transection causes stress urinary incontinence in the female rat: A novel animal model of stress urinary incontinence. Journal of Urology 2008; 179(2):775–778.

4. Iyer J, et al. Introduction and Epidemiology of Pelvic Floor Dysfunction. In: Rane A, Rane A, Durrant J, Tamilselvi A, Sandhya G, eds. Ambulatory Urology and Urogynaecology. Wiley Online Library; 2021.

5. Occelli B, et al. Anatomic study of arcus tendineus fasciae pelvis. European Journal of Obstetrics and Gynecology and Reproductive Biology 2001; 97(2):213–219.

Tumour growth is a force-sensitive process, regulated in part by mechanical feedback from surrounding tissue [1]. Such mechano-responsiveness can govern tissue-specific risk and progression of cancer. However, the underlying biomechanisms by which mechanical loading influences cellular growth and proliferation have not yet been uncovered. In this work, we propose a novel computational framework to determine how the feedback between growth, mechanical loading, and cell-cell exchange flow could restrict tumour cell proliferation.

Non-cycling cell volume is regulated by an interplay between energy-consuming pumps, mechanosensitive ion channels, and actomyosin tension that coordinate to manipulate cellular osmotic pressure. Growth may be induced by impermeable solute synthesis and associated increases in osmotic pressure, which drives water intake. Through a combination of novel finite element analyses (FEA) and agent-based modelling (ABM), we investigate how internal and external stresses arising from active cell tension and mechanical loading could oppose limit cell division by restricting growth below a critical mitotic volume.

Our model predictions for osmotic control of division indicate that cell cycle synthesis drives growth, and that compressive loading can limit the potential for a cell to surpass the size checkpoint for division. Simulations further suggest that exchange flow through gap junctions in connected cells can restrict osmotically-regulated cell growth and subsequently restrict proliferation. Using our integrated FEA-ABM modelling framework to characterize multicellular interactions and matrix loading, simulations reveal that increasing matrix stiffness reduces the rate of cell proliferation in tumour spheroids, due to the emergent stress-sensitivity of cell growth and division. Mean cell pressure is predicted to converge to a critical value, independent of matrix stiffness, at which proliferation is inhibited. Cells at the tumour core are revealed to experience higher stress than peripheral cells, as supported by data from excised tumours [2]. Overall, simulations suggest that tumour spheroid size reduces with increasing matrix stiffness in a stress-dependent manner, supported by our experiments of tumour spheroid growth in hydrogel.

Our analyses suggest that stress-dependent tumour growth emerges from a constraint on osmotically regulated cell growth, whereby cells cannot obtain a critical mitotic volume due to external loading. Simulation of multicellular proliferation with coupled finite element and agent-based models provides unique insight into the evolution of macro-scale tissue behavior and mechanosensitive growth, with broad applications to patient-specific cancer diagnosis.

References

1. M. Kalli and T. Stylianopoulos. Front. Oncol. 8 (2018)

2. H.T. Nia, et al. Nat. Biomed. Eng. 1 (2017).

One of the crucial steps of cancer metastasis is the extravasation of cancer cells from the vascular network into the neighbouring organs. The endothelial cells, which form the inner lining of blood vessels, develop homophilic bonds with neighbouring cells with the help of VE-cadherin proteins and form a preventive barrier against extravasation. But there is strong evidence of such cell-cell bonds abruptly broken in cancer patients that helps the trans-endothelial migration of cancer cells [1]. A diseased state leads to the abnormal dynamic behaviour of VE-cadherin junctions resulting in a larger gap size between cells and altering the frequency of their opening, a state termed hyperpermeability. Chemical cues such as Thrombin, along with mechanical properties of the cell and extracellular matrix (ECM) are known to affect permeability by regulating the actin-cytoskeleton machinery of endothelial cells. But details of how the coupled mechano-chemical stimuli affect endothelial permeability are not yet understood completely.

We have developed a continuum-level mathematical model to study the dynamics of such gap formation. The model considers the mechanical equilibrium of the cell by coupling the VE-cadherin to Actin-cytoskeleton. Taking inspiration from contact mechanics, we model VE-cadherin as a cohesive surface with damage following a traction-separation law. Actin cytoskeleton follows the tensegrity principle and is coupled with microtubules following non-linear material laws. Cells are modelled in 3D and hence we can study the behaviour of micro-vessels, which are hard to study experimentally. The ECM-cell interaction also follows a traction-separation law, allowing us to understand the role of ECM stiffness in cell-cell interactions. We use a non-linear finite element solver to solve the mechano-chemical coupled system of equations.

Numerical simulations showed that micro-vessels exhibit higher permeability than their planar monolayer counterparts. In-silico studies show that the permeability of micro-vessels increases with the stiffness of the extracellular matrix. Interestingly, it was observed that shear between cells is responsible for variation in permeability between bi-cellular and tri-cellular junctions, explaining the phenotypic differences observed in experiments. Simulations also show that permeability is higher in those regions of micro-vessels with high shear stress fluctuations, matching the observations that atherosclerotic plaques are usually formed in regions where blood flow is disturbed. The novel mathematical modelling framework is capable of simulating already known results along with developing several testable hypotheses. The versatile model can thus be used in a variety of studies, from the role of VE-cadherin in the extravasation of cancer cells to understanding the effect of nanoparticles in effective drug delivery.

1. T Tomita et al., “Regulation of vascular permeability in cancer metastasis”, Cancer Sci, 2021

Cell mechanics of living cells are vital for many cell functions, including mechanotransduction , migration, and differentiation. It is known that changes in cell mechanics are often correlated with disease progression. Cell-matrix adhesion is important for the patterning, integrity and homeostasis of tissues and may provide a target for therapy, for example in cancer metastasis. Cell mechanics and adhesion between cells and the matrix are also important for tissue engineering. Therefore, it is important to study cell mechanics and cell-to-material adhesion. However, simultaneous characterization of the cell-to-material adhesion and viscoelastic properties of the same cell is challenging. In this study, we present a new approach to simultaneously determine these properties for single cells, using Microfluidics-based Atomic Force Microscopy.

During the approach period, the cantilever touches the cell and rests for a few seconds, where the cell relaxation curve is recorded. Then, negative pressure is applied to the cell through the cantilever, and the hollow cantilever grabs the cell and pulls it away from the materials surfaces. During the relaxation period, the viscoelastic properties of the cell can be determined where the contact area between cell and the cantilever can be visualized and measured. The adhesive force and adhesive energy for cell-to-material can be determined based on the detachment curve when pulling the cell away from the substrate.

To explore the correlation between cell-materials adhesion and cell migration, the single cell tracking method was adopted. ImageJ with TrackMate plug-in was employed to identify the cells and then analyse their path. The mean migration speed is calculated by dividing the displacement of the cell between each frame by the time between frames to obtain the velocity of the cell moving between those two frames, and then averaging the movement velocity over the entire motion trajectory.

To reveal if the mechanical properties of biomaterials may affect the biomechanics of the breast cancer cells (MCF-7 cells), typical biomaterials Polydimethylsiloxane (PDMS) were used. The curing agent-to-base ratio was varied to yield PDMS with different stiffness. These PDMS samples were treated with Ozone to change the surface wetting properties to enable better cell attachment and proliferation.

The elastic modulus for MCF-7 cells on petri dish, determined here, is consistent with what was reported in literature. We have also demonstrated that both elastic cell moduli and viscosity of breast cancer cells (MCF-7 cells) can be affected by the mechanical properties of PDMS with different stiffness. The individual cell, which has stronger adhesion to the materials, appears to be stiffer. The cells seem to have stronger adhesion and slower migration when interfacing with stiffer materials.

According to the World Health Organization (WHO), prostate cancer (PCa) is the second most common cause of cancer worldwide¹.

Accurate risk stratification is crucial in treating prostate cancer. However, distinguishing high-risk from low-risk cases represents a significant challenge. Current diagnostic tools, such as blood-based prostate specific antigen (PSA) tests, digital rectal examination findings, and biopsies, often fail to differentiate the aggressiveness of cancer, leading to misclassification and under/over treatment². Consequently, new tools are urgently needed to predict outcomes and improve clinical decision-making to prevent unnecessary invasive treatments and associated morbidity³.

Therefore, the aim of this study is to develop an in-silico model of PCa tumour growth or degrowth that will predict prostate cancer outcome and provide an improved prognosis.

For the simulation of PCa tumour growth, a multispecies model of partial differential reaction-diffusion equations coupled with the mechanics of continuous media is here utilised. This multispecies model represents the phenomenological behaviour of PCa and its cellular processes, including proliferation, differentiation, and apoptosis. From these processes, the model simulates the evolution of the geometry, the distribution of tumour and healthy cells and stroma in the entire prostate. The model is implemented via the Finite Element Method. Magnetic Resonance Images (MRIs) are available to reconstruct the geometry of the prostate in a patient-specific manner. These images provide in-depth knowledge of the level of cellularity (DWI sequences) and vascularization (DCE sequences) of the tissue, which serve as input data to the model⁴. Real patient data are available for the validation of the model at a later time point.

The model has been tested on two clinical cases, showing promising preliminary results. The distribution of cellularity and PSA evolution are compared. Over time, the cellularity of the prostate obtained from the simulations reproduces closely the clinical values, with a similar spatial distribution. Furthermore, quantification of global cellularity does not give relative errors greater than 7%. On the other hand, the results obtained from the simulation of the PSA evolution suggest a close correlation with the observed clinical evolution, and the model can accurately predict the PSA's increase or decrease. However, further refinement of the model is necessary to improve its predictive capacity.

A patient specific model has been applied to simulate tumour growth in PCa. Moreover, this model can give predictions of the evolution of the PSA, which is the principal biomarker used by clinicians for the PCa follow-up. In future developments, different treatments will be incorporated which will allow for a better prognosis. Finally, the model will be further validated with additional patient-specific clinical data.

Acknowledgements

This publication is part of the project PLEC2021-007709 (ProCanAid), funded by MCIN/AEI/10.13039/501100011033/ and by the European Union NextGenerationEU/PRT and in collaboration with IISLAFE and QUIBIM. SHR was supported by the Government of Aragon (2019-23).

References

[1] Rebello, R.J., et al. Nat Rev Dis Primers. 7, 2021.

[2] Elwenspoek, M. et al. JAMA Netw open. 2:198427-198427, 2019.

[3] Moore, C.M. et al. Eur Urol, 64:544-52, 2013.

[4] Saiz-DeMena, D. et al. Eng Comput 3849–3865, 2022.

Tumour growth is usually hampered by poor blood supply when the tumour reaches a critical size. Under these circumstances, the process of growth tends to stall. When this supply is not verified, tumour cells may begin to secrete angiogenic growth factors that activate the process of angiogenesis, which is characterized by the formation of new blood vessels towards the tumour. Understanding this mechanism is one of the keys to comprehending tumour progression. To help in achieving this objective, computational models to describe angiogenesis in this context have emerged and have shown their potential to aid in this goal. Numerical methods are usually associated with these models, and numerous ones are documented in the literature. One of the most famous is Smoothed Particle Hydrodynamics (SPH).

The objective of this work was to enhance a 3D algorithm created by the authors, which simulates cell proliferation using the SPH algorithm along with the process of angiogenesis. In this algorithm, angiogenesis is triggered by VEGF concentration, and to test it, different concentrations and locations for the focus of concentration were considered.

The proposed algorithm uses SPH, and so the domain is discretized by particles with no connections between them. Through the particles, the approximation functions are derived, and the field function is approximated. Moreover, cell, extracellular matrix, boundary, and blood vessel particles are considered, and the initial velocity, internal pressure, and acceleration of all particles are calculated once the process of proliferation starts. Only one cell was initially considered and was allowed to grow and divide, following an exponential growth. Throughout the whole domain, a VEGF gradient was also defined, and firstly, the highest focus of VEGF was imposed near the cell. As the cells proliferate, a vessel is allowed to grow following the highest VEGF concentration.

Different simulations were run to see the viability of this new feature of the algorithm and to ensure that the generated vessel followed an appropriate path. In every simulation, the vessel grew towards the cluster of cells, which was considered a VEGF source. The growth was also regulated by the cell proliferation process to minimize excessive vessel growth. When this feature was validated, different values of concentration and different points of the focus of concentration were analysed to determine their impact on angiogenesis. Again, in all scenarios, the vessel growth followed the highest concentrations of VEGF, which corresponded to the different focus of concentration in each simulation.

The proposed algorithm was capable of combining the processes of cell proliferation and angiogenesis. As mentioned and reported in the literature, this new feature of the algorithm is dependent on the location of the source of VEGF, which is the factor that triggers the process, and on the cell proliferation process. The vessel growth followed the focus of concentration, as desired and anticipated. Despite the initial phase of the algorithm, the obtained results were reasonable and adequate.

Acknowledgements
The authors acknowledge the funding provided by Ministério da Ciência, Tecnologia e Ensino Superior – Fundação para a Ciência e a Tecnologia (Portugal), under the grant: SFRH/BD/146272/2019, and by LAETA, under the project UIDB/50022/2020.

Neuroblastoma (NB) is the most frequent solid cancer of early childhood. It is a type of cancer that is highly representative of the cancer disease itself, since NB is strongly heterogeneous with very diverse clinical courses that may vary from an indolent disease causing little or no harm and exhibiting spontaneous regression, to an aggressive disease with fatal progression. For these reasons, NB is considered a paradigm of cancer disease and an excellent context of application for the validation of novel developments which have the ambition to be of potential application in a large variety of solid cancers.

NB tumours consist of two main cell populations, neuroblasts and Schwann cells, and the current neuroblastoma classification is based on histological criteria, e. g. the quantity of Schwannian stroma. Neuroblasts and Schwann cells are primary interest herein for contribute directly to the mechanical properties of the tissue through the proliferation and death processes. Extracellular matrix also have a principal role in the cell-microenvironmental cross-talk therefore the tumour can promote to a better stage or keep growing.

We here present a phenomenological model which takes into account as detail as possible to better mimic the real tumour behaviour. Our hypothesis proposes that tumour evolution can be attributed to three distinct processes: growth, shrinkage, and remodelling. The biomechanical model is based on the mass and cellular balance equations coupled with elasticity. The multispecies model simulates the effect of the cellular processes that occur during tumour growth and shrinkage, namely proliferation and death.

The biomechanical finite element model of NB tumour growth starts from imaging data derived mainly from MRI sequences. This data comprises the geometry, the initial cellularity distribution and the tumour vasculature evaluation. At the end of the simulation, the results obtained are validated with a second set of imaging data obtained after treatment.

The study simulates three-month chemotherapy using real patient cases, and presents two distinct outcomes: in one of them, the tumour volume was reduced 20% and in the other one, the volume decreased 90%. One of the patients was classified as low-risk, following the International Neuroblastoma Risk Group (INRG) system, whereas the other was classified as intermediate-risk.
Differences appeared in the histology analysis, which reveal one tumour with a higher concentration of tumoural cells, and in the radiomic data obtained after image analysis. The model effectively reproduces these varying outcomes following the application of chemotherapy, facilitating the identification of cases in which the treatment may be effective.

Acknowledgments

The authors were supported by PRIMAGE (PRedictive In-silico Multiscale Analytics to support cancer personalized diaGnosis and prognosis, empowered by imaging biomarkers), a Horizon 2020 RIA project (Topic SC1-DTH-07-2018), grant agreement no: 826494.
SHR would like to thank the support of the Government of Aragon (Grant no 2019-23).
This work was supported by Grant PID2021-124271OB-I00 and PID2021-122409OB-C21 founded by MCIN/AEI/10.13039/501100011033 and ERDF A way of making Europe.

The Finite Element Method (FEM) has been used in a number of different areas of research, such as orthopedic implant design. Numerical analyses of hip implants and their surface topographies provide important information that can indicate if the connection between bone and implant is good. Although this approach requires less time compared to traditional in vivo studies, it is still time-consuming in situations when a large number of different models need to be created and analyzed. This is the situation with the analysis of a variety of surface topographies, which is needed to better understand the influence of each parameter on shear stress distribution. It is known that higher shear stress values lead to loosening of the contact between femoral bone and hip implant and additional surgical procedures. In order to perform shear stress classification, four algorithms have been considered. Those algorithms were: Support Vector Machines (SVM), K - Nearest Neighbor (KNN), Decision Tree (DT), and Random Forest (RF). A total of 10 model parameters have been used with the previously mentioned classification algorithms in order to obtain information if the shear stress value for the implant will be below the user-defined threshold value (0 – above threshold; 1 – below threshold). The considered parameters were: Number of different radius values (1 or 2); Radius 1 value (>0); Radius 2 value (≥0); Number of half-cylinders lengthwise (>1); Distance between half-cylinders lengthwise (≥0); Number of half-cylinder rows (≥0); Distance between half cylinders rows (≥0); Distance of the first half-cylinder from the edge where loading is defined (≥0); Distance of the last half-cylinder from the edge without loading (≥0); Half cylinder orientation (0 – half-.cylinder follows model length; 1 – half-cylinder follows model width). The database consisted of 60 models, which is the main limitation of this study. The obtained results show that classification algorithms can be useful as a way to have preliminary indications of models that should be further analyzed with FEM. SVM and RF have shown the best results out of the four considered algorithms. For those two algorithms, the following results were obtained: SVM: Precision - 93%; Recall - 92%; F1 score – 92%; RF: Precision - 90%; Recall - 86%; F1 score – 86%. KNN and DT have obtained significantly lower results.

Acknowledgment

This research is supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 952603 - SGABU. This article reflects only the author’s The Commission is not responsible for any use that may be made of the information it contains. The research was funded by the Ministry of Education, Science and Technological Development of the Republic of Serbia, contract number [451-03-68/2022-14/200107 (Faculty of Engineering, University of Kragujevac)].

Digital image processing has become increasingly widespread in biological and medical research as microscopy and screening images have become more complex. Automatic image processing plays an important role in increasing the comprehensibility of imaging data inference and reducing the amount of time and manual labor required to fulfill such tasks. One of such tasks requiring digital image processing is Traction Force Microscopy (TFM). Cells adhere to the extracellular matrix (ECM) and exert traction forces to probe the environment, migrate, maintain tissue integrity and form more complex multicellular structures. TFM has become the preferred methodology to quantify exerted forces at the cell–matrix interface and thereby provide quantitative information on cellular mechanics. Before TFM can be utilized, image processing is necessary in multiple phases of data preparation. Data used in this research was acquired from an in vitro model of sprouting angiogenesis in which Human Umbilical Vein Endothelial Cells (HUVECs) invade a polyethylene glycol (PEG) hydrogel. The data is represented as raw 3-dimensional volumes of cells before and after inhibiting their mechanical activity by means of Cytochalasin D. Currently the image processing for TFM required time consuming manual tuning of image denoising filters and tuning of an image segmentation threshold. The dataset was composed of 125 3D volumes of varying sizes, in height and width as well as in depth. These volumes consisted of 9126 total 2D slices, of which 20% was used as the test set, while 80% was used for neural network training.

In this paper we propose a methodology for automatic image segmentation which alleviates most of the manual labor required from the user. The aforementioned stacks of images contained noise caused by either the equipment used or the environment. This noise had to be reduced for the purpose of increasing the quality of training images and segmentation accuracy. The individual 2D slices of each image stack were introduced into the convolutional neural network, while the previously manually segmented images were used as training masks. The segmentation model is based on the U-Net architecture which was modified for this purpose. The model provides 2D segmented images which are concatenated into a 3D stack to reconstruct the 3D input volume. The model achieved admirable results showed by the intersection over union metric, which is greater than 80%. Future research will focus on the improvement of segmentation results through the creation of new image filtering mechanisms and the introduction of more data.

Acknowledgements: The research was funded by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia, contract number [451-03-47/2023-01/200378 (Institute for Information Technologies, University of Kragujevac)]. This research is also supported by the project that has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 952603 (SGABU project). J.B-F. acknowledges the support from the Research Foundation Flanders (FW) grant n. 1259223N. This article reflects only the author's view. The Commission is not responsible for any use that may be made of the information it contains.

In the era of personalized medicine, early and accurate prediction of individuals at high risk of severe consequences of carotid artery stenosis (CAS) which is caused by the atherosclerotic plaque deposition and progression, would allow preventive, therapeutic, or surgical measures before any of life-threatening events take place. It is therefore important to integrate machine learning techniques and computational modeling that can automatically and objectively segment and afterwards mesh the carotid arteries from image data. Among various diagnostic techniques, the US is usually initially recommended CAS diagnostic examination. The US images are used in this study as this diagnostic procedure is low-cost and present at the first level of clinical care, while its improvement in view of image processing and extracted features can be beneficial for more detailed and faster analysis of patients.

Comparing with traditional Computer-Aided Diagnosis (CAD) systems where feature selection and extraction are important steps, deep learning replaces generic imaging features with processing layers that are more complex and more specific to the data. In this study, we have investigated a deep learning approach, which does not require intensity thresholds and imaging features, leading to an optimal use of information and improved prediction power. The automatic carotid artery segmentation was done using U-Net based deep convolutional network (CNN). Deep learning is combined with meshing techniques to perform 3D reconstruction of patient-specific carotid bifurcation, including extraction of atherosclerotic plaque within the arterial wall. The clinical dataset of US anonymized images was used to train and validate the U-Net CNN in automatic segmentation of carotid components (lumen, arterial wall, atherosclerotic plaque) taking into account all three arterial branches (common, internal and external carotid artery). Common classification metrics are considered for one-vs-all quantitative evaluation, including precision (P), recall (R) and F1-score. Results on the test dataset for lumen: P= 0.89, R=0.78, F1=0.83; and for wall: P=0.82 R=0.91, F1=0.85. The results of segmentation are coupled with the reconstruction software to perform a full 3D reconstruction of carotid bifurcation and generate patient-specific 3D mesh. Using the reconstruction software, it is possible to obtain 3D volume information and perform the visualization of carotid structures in different planes and from different angles.

In summary, the automatic extraction of US features related to atherosclerotic carotid artery gives the specific segmentation of individual patient-specific anatomy and can be efficiently integrated with 3D reconstruction. The obtained 3D models can be used for further computational simulations and analyses of individual patients. Integration of deep learning techniques and computer-based modelling can contribute to better risk stratification and assessment of asymptomatic patients with carotid atherosclerotic disease.

Acknowledgements: This paper is supported by the European Union’s Horizon 2020 research and innovation programme TAXINOMISIS (Grant Agreement 755320). This article reflects only the author's view. The Commission is not responsible for any use that may be made of the information it contains. The research is also funded by Serbian Ministry of Education, Science, and Technological Development, grants [451-03-47/2023-01/200378 (Institute for Information Technologies, University of Kragujevac)] and [451-03-47/2023-01/200107 (Faculty of Engineering, University of Kragujevac)].

Mathematical models for multiscale phenomena are typically based on the deduction of a set of differential equations relating the behavior at different involved scales. The number of necessary parameters and the complexity of the equations are crucial in developing effective, predictive models.

A large scientific effort in deducing sophisticated numerical techniques, in particular neural network approaches, characterized the recent literature in the field. This is due to the availability in different fields and in material science of large new data sets down to the nanoscales. New sophisticated approaches exhibit an incredible ability of fitting experimental data even when strongly multiscale nonlinear behavior is observed. The important drawback of these approaches is that typically they are based on statistical based analysis without explicit causal relations, resulting in a poor physical insight.

In this perspective, we propose the adoption of symbolic data modelling techniques, that generate mathematical expressions to fit set of data points using the evolutionary process of Genetic Programming (GP). It is ``Evolutionary Polynomial Regression’’ (EPR) approach integrating regression capability and GP paradigm.

As a result, we obtain explicit analytic formulas that represent the multiscale phenomenon model, elucidating the role of dependent and independent variables, with the important possibility to minimize the complexity of the model in a classical Pareto front.

Specifically, by focusing on the important case of hierarchical biological materials, in this work we deduce numerical techniques that recognize the role of variables in multiscale modelling. Based on a recent set of data at the micro, meso and macroscale of spider silks of different spider species, by means the EPR approach we obtained a set of equations deducing the dependence of the macroscopic thermo-hygro-mechanical behavior from low scales parameters. This set of equations
represents the multiscale model, obtained from data modelling, that we propose to describe the spider silk behavior. Such material behavior constitutes a prototypical example of a physical phenomenon deeply based on a hierarchical behavior and on a complex energetic exchange among different scales. Spider silk is an incredible example on how, based on very `weak’ material components and chemical bonds at the micro scales, it is possible to obtain material behaviors unattained by artificial materials. This is interesting not only for biological aspects, but also in the field of designing new bioinspired materials.

We propose a preliminary analysis of the possibility of adopting such techniques in material science, that in our opinion can represent an important extension of presently adopted numerical methods. As we show, this can be fundamental to gain new physical and modelling insight based on the availability of large new data sets down to the nanoscales. Moreover, we suggest that, due to the generality of our results, the proposed approach can be of interest for many other different fields where multiscale phenomena underly the observed behavior.

In recent years, the use of Artificial Intelligence (AI) models that are informed by physics has become a popular approach for creating data-efficient models in fields such as computational physics, biomedicine, and biomechanics. At the heart of these applications is the complex and adaptable nature of living matter. The adaptations occurring in living systems, such as inflammation, or mechanical changes like growth and remodeling are governed by complex cell-signaling regulatory networks and occur on multiple spatial and temporal scales.

Mechanical modeling of changes in living systems such as peripheral artery plaque progression involves constructing computational models that simulate the development and progression of plaque in the arteries. While these models offer the potential to improve understanding of the underlying mechanisms of plaque formation and to predict the progression of the disease, there are several bottlenecks that can limit their accuracy and effectiveness.

One of the primary challenges is the limited availability of high-quality clinical data including measurements of arterial geometry, blood flow characteristics, and properties of the arterial wall and plaque, all necessary for constructing high quality models. Obtaining this data is often difficult and time-consuming, thus limiting the accuracy and validity of the resulting models.

Creating models that accurately represent complex interactions such as fluid dynamics, solid mechanics, and cellular processes of biological phenomena can be challenging, and models that are too simplistic may fail to capture key aspects of the disease process. In addition, the behavior of arterial plaque is highly variable between patients, and this makes it difficult to develop models that accurately capture the full range of possible disease trajectories.

Finally, creating and running accurate models requires significant computing resources, which can limit the number of simulations that can be performed and can make it difficult to perform sensitivity analyses and explore the effects of different input parameters.

AI has the potential to significantly enhance the accuracy of peripheral artery plaque progression models. The choice of AI method depends on the specific task, available data, and considerations around patient privacy and data security. Machine learning (ML) techniques, including both supervised and unsupervised learning, can be used to predict plaque progression and identify underlying patterns in the data. Genetic Algorithms optimize model parameters for individual patient characteristics and reinforcement learning can determine optimal treatment plans, learning to maximize the reward of minimizing plaque progression. Natural Language Processing (NLP) can be used to extract relevant clinical information from unstructured data, such as clinical notes. Bayesian Networks infer the likelihood of plaque progression based on various patient features. Artificial Neural Networks (ANNs) can model complex relationships between multiple variables, while convolutional and recurrent neural networks, can analyze images or sequential data related to plaque progression.

Acknowledgements

This paper is supported by the DECODE project (www.decodeitn.eu) that has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 956470. This article reflects only the author's view. The Commission is not responsible for any use that may be made of the information it contains.

We simulate biophysical processes at various spatial and temporal scales in order to investigate muscle activity. Multiscale simulations, where Huxley's muscle contraction model defines the microscopic scale material properties of muscle, and continuum muscle mechanics is modeled using the finite element approach, can require a significant amount of computational power. The computations performed at the microscale are the most time-consuming component in these simulations. In our work, we developed a computationally more efficient surrogate model to replace the actual Huxley muscle model in order to reduce the computational demands of the simulations.

Instead of solving Huxley’s muscle contraction equation via a method of characteristics, we train a physics-informed neural network to give an approximate solution. Physics-informed neural networks can produce solutions faster than traditional numerical solvers, although these solutions can be less reliable. Once the neural network is successfully trained we use it in multi-scale simulation instead of the traditional method of characteristics. The neural network takes as an input the position of the nearest available actin-binding site relative to the equilibrium position of the myosin head, time, activation, current and previous stretch and produces the probability of cross-bridge formation. For each of the integration points within the finite element model, a large number of positions of available actin sites are observed and stresses are calculated by summing all of the calculated probabilities of the cross-bridge formation.

In our work, we also present the interface between finite elements, at the macro level, and physics-informed neural network at the micro level. The neural network architecture and weights are loaded at the beginning of the finite element simulation, along with the initialization of the neural network input tensor. The size of the neural network input tensor is dependent on the number of integration points in the model and division along the axis at which the positions of the nearest available acting sites are observed. Values of the observed positions are constant during finite element simulation, so only the values for time, activation, and stretches are changed inside the neural network input tensor. To lower time consumption, values for all of the integration points are filled-in, before the neural network’s prediction. Once the tensors are filled-in, the neural network predicts output values for all the integration points in the model. After the neural network has made its prediction, stresses are calculated based on the probabilities of the attached myosin heads, and the finite element procedure continues with the next iteration or next time step. Our physics-informed surrogate model is around two times faster than the original Huxley model solved by the method of characteristics.

This research was supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 952603 (http://sgabu.eu/). This article reflects only the author's view. The Commission is not responsible for any use that may be made of the information it contains. Research was also supported by the SILICOFCM project that has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 777204. This article reflects only the authors’ views. The European Commission is not responsible for any use that may be made of the information the article contains. The research was also funded by the Ministry of Education, Science and Technological Development of the Republic of Serbia, contract numbers [451-03-68/2022-14/200107 (Faculty of Engineering, University of Kragujevac) and 451-03-68/2022-14/200378 (Institute for Information Technologies Kragujevac, University of Kragujevac)].

Restenosis refers to the uncontrolled growth of tissue in vessel walls as part of an inflammatory response that follows cardiovascular interventional procedures including balloon angioplasty and stent implantation. Although the risk of restenosis has reduced with the advent of drug-eluting stents, it is not completely eliminated. An in silico replication of neointimal hyperplasia, the mechanism behind restenosis, shall therefore provide the necessary means to derive insights about the biochemical and cellular interactions within the vessel wall, and eventually address the risks of restenosis in a patient-specific manner. In this regard, six important biochemical species in the vessel wall are modeled within the scope of this work: platelet-derived growth factor (PDGF), transforming growth factor (TGF)-β, extracellular matrix (ECM), endothelial cells (ECs), drug (rapamycin) and smooth muscle cells (SMCs). This is considered an extension of the work presented by the authors in [1]. The intricate interactions between these species are then coupled to a continuum mechanical finite growth theory, where the local SMC density drives the growth process and the local ECM (hence collagen) concentration controls the compliance of the vessel wall. Multiphysics-based frameworks for modeling damage-driven growth and remodeling have been presented in several earlier works (e.g. [2]), but the presented model specifically addresses the inflammatory response due to endothelium denudation in addition to the pharmacological influences of the rapamycin-based drugs embedded in modern drug-eluting stents.

[1] Manjunatha, K., Behr, M., Vogt, F., Reese, S., “A multiphysics modeling approach for in-stent restenosis: Theoretical aspects and finite element implementation”, Computers in Biology and Medicine, 150:106166, (2022).

[2] Escuer, J., Martinez, M. A., McGinty, S., and Pena, E., “Mathematical modelling of the restenosis process after stent implantation”, J. R. Soc. Interface, 16:20190313, (2019).

Aortic Dissection is a severe medical condition that can lead to fatality if not treated early. Aortic Dissection begins when a tear occurs in the aortic wall's inner layer (intima). Moreover, a second blood-filled channel called a false lumen is created where thrombosis most probably will happen. In type B Aortic Dissection, severe complications, such as malperfusion or rupture in the aorta, can occur in the first seven days, resulting in high mortality rates. The optimal treatment for type B Aortic Dissection remains a topic of debate, leading to an interest in computational methods to aid in decision-making for treatment.
To obtain a macroscopic model the Theory of Porous Media is chosen to modell the multiphasic structure of the thrombus. The whole aggregate is divided into solid, liquid, and nutrient constituents. As usual in the theory of porous media, all three phases occupy each material point simultaneously. The constituents are assumed to be materially incompressible, under isothermal conditions, and the entire aggregate is fully saturated. Darcy's law is used to describe the flow of fluid phases, i.e., the liquid and the nutrient phase. The constituents' balance equations have coupling terms that account for the interactions between the different phases. The essential coupling term for the growth process is the mass exchange term in the volume balances. Due to the incompressibility assumption the volume fractions can be used to define the constituents. Therefore, the regions with thrombus are determined using the solid volume fraction.
Initially, a set of equations for thrombosis in type B Aortic Dissection is presented. The respective variational form is approximated with finite elements and implemented in PANDAS, a finite element package used for solving strongly coupled multiphase porous media problems. However, the model's description is challenging due to the need for detailed knowledge and parameters to quantify the influence of different factors. Nevertheless, the effects of blood velocity and nutrients on thrombus growth are well researched. Therefore, a velocity and nutrient concentration induced growth model is proposed within the Theory of Porous Media. The effects of various parameters are studied using a realistic 2D geometry of the false lumen, and reasonable parameters for thrombus growth are selected. We present the model's features in agreement with the Virchow triad and its usefulness in actual cases. The simulations show that the thrombus grows in the low-velocity regions of the blood. The proposed model provides a reasonable approach for the numerical simulation of thrombosis.

Endovascular coil embolization is one of the primary methods for the treatment of a ruptured or unruptured cerebral aneurysm. Though being a well accepted and minimally invasive method, it bears the risk of suboptimal coil placement, which can lead to incomplete occlusion of the aneurysm, causing a degenerate healing process or in the worst case even aneurysm recurrence.

Our study investigates factors that lead to a suboptimal placement when a coil is deployed in an aneurysm. To this end, we use a mathematical model that simulates the embolization process of the coil in patient specific three-dimensional aneurysm geometries. One of the key features of coils is that they have an imprinted rest shape, which helps to safely fix them inside aneurysms. We consider the latter property by introducing bending and torsional forces into our model of the coil. In order to differentiate optimal from suboptimal placements, we use measures like the local packing density, which is connected to the quality of the subsequent healing process.

We model the coil as a one dimensional discrete space curve with the dynamics of a mass spring system. For this purpose, we include stretching, bending and torsional springs. The aimed for deflected rest shape is accounted for by penalizing deviations from it within the individual spring energies. To obtain the forces that act on the coil, we differentiate the total elastic energy of the spring mass system by algorithmic differentiation with respect to the material points. Collisions between coil segments and the aneurysm-wall are taken into account by an efficient contact algorithm, such that only a fraction of the possible contact partners have to be evaluated. The numerical solution of the model is obtained by a first order accurate time stepping scheme.

We then carry out a sensitivity study that shows how process parameters like the insertion point or the angle of insertion affect the shape of the deployed coil in the aneurysm. We further show how other medical tools such as, for example, stents or hyper-elastic balloons can support the coil-placement process. Finally, we investigate the sensitivity of our model with respect to the material parameters and rest shape of the coil.

Our model can be easily incorporated into blood-flow simulations of embolized aneurysms. It is our goal to eventually provide a simulation tool that will provide new insight into the behavior of coils and allow medical professionals to better plan coil embolization procedures and hence assist them in their practice.

Left ventricular (LV) hemodynamics are hypothesized to serve as an early indicator for the manifestation of cardiovascular diseases. In the analysis of hemodynamics, computational fluid dynamics (CFD) can complement medical imaging methods for in-depth flow investigations. To obtain information about individual conditions, a high level of patient-specific input into the model is required. Considering the variety of data sources, medical imaging modalities, and the range of data quality, this leads to demanding case processing with a lot of manual effort.

To target this issue, we standardized the workflow by coupling the patient-individual anatomical representation in form of a statistical shape model (SSM) with a fluid structure interaction (FSI) workflow. Thereby, we obtain a high degree of individuality in our simulations while keeping the case-specific effort involved at an acceptable level. Furthermore, the workflow allows usage of all common cardiac imaging modalities, namely computed tomography (CT), magnetic resonance imaging (MRI), and ultrasound (US).
To test the simulation pipeline, we processed data of healthy volunteers by comparing the FSI-computed flow results to measured velocity fields from 4D flow MRI. Further applications of the workflow were tested with simulations of patients showing isolated or combined aortic stenosis and mitral regurgitation. For patients with ventricle aneurysms after myocardial infarction, we compared pre- and post-treatment situations.

Imaging data of the healthy volunteers included 4D flow MRI and cine MRI sequences. While the latter served as model input, the flow data was used to check the results of computed hemodynamics for plausibility. Simulations of mitral regurgitation patients revealed characteristics of altered kinetic energy and specific energy dissipation during diastole. These results correspond well with findings of previous clinical MRI studies. Simulations of the pre- and post-surgical hemodynamics of left ventricular aneurysms showed significantly improved flow conditions after surgery. Although, the flow results cannot quantitatively be compared to clinical data because no MRI was acquired, results show improved flow patterns and align well with the improvement of the medical conditions patients showed after surgery.

To conclude, we could prove that our workflow is robust and easy to use while including a lot of patient-specific details. This allows for representation of individual flow features, which can perspectively be used in the clinical routine to support diagnostics, therapy planning, and outcome prediction. A profound validation study must be performed to test the approach on a sufficient amount of data. However, the availability of such comprehensive data is rare and prospective studies are very costly.

The left atrial appendage (LAA) is a small, finger-like structure in the heart's left atrium. Despite its small size, the LAA has been shown to affect cardiovascular health significantly. One of the challenges associated with the LAA is that it is its location, an area of the heart with poor blood flow, which can lead to blood stagnation. Patients with atrial fibrillation often experience insufficient contraction of the left atrium, predisposing the LAA morphology to hemostasis and thrombus formation, resulting in an increased risk of cardioembolic events. To prevent these pathologies, oral anticoagulation therapy is typically used as the primary treatment option for patients. However, not all patients are eligible for long-term oral anticoagulation therapy, which can cause complications such as bleeding. These circumstances led to the development of alternative treatment options, such as percutaneous occlusion devices. However, several drawbacks remain. Peri-implant leakage and device-related thrombosis are common complications in LAA closure procedures. Efforts have been made to reduce these risks, but interpatient heterogeneity remains challenging. Ongoing research aims to develop better treatment options for patients with atrial fibrillation and other cardiovascular conditions. One area of innovation is additive manufacturing (AM), also known as 3D printing, which can improve the accuracy of the selection of LAA closure devices. AM allows for the creation of complex and precise structures with high levels of customization, making it an attractive tool for personalized medicine. AM can generate personalized LAA used in medical practice device simulations, reducing the risk of device-anatomy mismatch and improving the procedure's success rate. Additionally, numerical simulation techniques are being employed to model the behavior of LAA, allowing researchers to optimize device performance and minimize the risk of complications.

This study presents a structural numerical approach for analyzing the optimal material for 3D printing a personalized LAA through finite element analysis (FEA). A 3D model of an LAA was obtained from an actual patient's computerized tomography (CT) scan and subsequently modeled numerically. The material selection for computational analysis is crucial to mimic human tissue's mechanical behavior accurately. When designing a cardiovascular training model, the chosen material for the LAA model must withstand the LAA pressures of device implantation. Higher radial resistance often correlates with higher tensile resistance in materials. Mechanical tensile tests were performed to evaluate the radial resistance of multiple materials. Thermoplastic polyurethane (TPU) material exhibited significant deformation during the tests, reaching 40% without breaking, which indicates its potential as a suitable material for replicating the biological tissue of the LAA. The ADINA® software was employed to perform the finite element analysis (FEA). The study yielded a maximum displacement of 0.4 millimeters for the LAA model, demonstrating a close resemblance to a real LAA in FA condition. Therefore, it was possible to conclude that TPU is a potential material to produce the LAA model for pre-procedural occlusion planning. By reducing the risk of complications associated with percutaneous occlusion devices, these innovations can improve the outcomes and quality of life for patients with AF and other cardiovascular conditions.

The range of materials available for 3D printing has been expanding rapidly in recent years. However, for very specific requirements, such as an anatomical model, there is not always a suitable material available. In particular, the design of gradients in elasticity, color, or surface properties is not truly represented by pure materials. Material jetting allows 3D printing of multiple materials simultaneously, resulting in composite materials with new properties. This study investigated and compared the mechanical properties of pure and composite materials and the possibilities of predicting composite properties by knowing the proportions of the pure materials used.

Samples of commercially available materials (VeroClear, RGD8530, Stratasys Ltd., Minnesota, USA) in their pure and mixed matrix inclusion forms were produced using material jetting (Connex3, Stratasys Ltd., Minnesota, USA). The composites had 1mm³ unit cells, including a cubic inclusion with a volume fraction of f_inc=10%, 30% or 45% RGD8530 in a VeroClear matrix. They were mechanically characterized by uniaxial tensile testing according to ISO 527 for Young’s modulus and Poisson’s ratio. In order to find and validate a method for predicting the properties of the multimaterials, multimaterial homogenization and finite element (FE) modelling were evaluated and compared with the measurement results. Inclusion size and geometry were characterized by optical coherence tomography (OCT) and digital microscopy.

The materials had Young's moduli ranging from 800MPa to 2.5GPa. Multimaterial composites were never as stiff as the primary materials' volume weighted average (26.5±2.7% softer for 45% inclusion volume). OCT scans revealed deviations from the digital design, more specifically a rounding of the inclusion edge, as well as blurred material interfaces within the polyjetted layers.

Models that assume ideal interface conditions, such as multimaterial homogenization or conventional FE simulation, are not capable of producing the measured Young’s moduli. A functional simulation model to predict the uniaxial Young’s modulus, can be established using FE simulation and considering a contact stiffness of F_A=2.2TN/m³ and an inclusion edge radius of r=220, as seen in the OCT data.

In conclusion, matrix-inclusion composites have a non-trivial behavior of elastic properties, which needs an adapted model to predict. The established FE model incorporates the interface stiffness between the individual materials used and the geometric deviations from the digital design that occur during the 3D printing process. This enables more complex parts to be produced using less primary material by predicting, designing and 3D printing structures with precisely defined mechanical properties and gradients that are required to mimic biological structures.

Background

Three-dimensional (3D) digital and additively manufactured models are increasingly used for pre-operative planning, especially for orthopaedics applications. However, the size of the model’s minimal detectable features in clinical CT imaging has not been determined, hence it remains unknown which features might remain undetected. Furthermore, it is crucial to identify potential error sources during CT imaging and image processing, quantify their effect on the 3D model accuracy, and develop an optimized workflow to allow for the reliable use of 3D models in the clinical routine. This study aimed to investigate the minimal detectable bone feature size in CT images and corresponding digital 3D models and to determine the errors attributed to different CT technologies, scanners, scan protocols (clinical versus high dosage for improved model quality), segmentation algorithms, as well as specimen orientation and consequently quantify the resulting geometrical deviations on a defined bone fracture model.

Materials and Methods

Incisions in the diaphyseal radii with 200 and 400 μm width, and bone lamellae (bony displacements) with 100, 200, 300, and 400 μm width were generated in twenty paired forearm anatomic specimens (age: 78 ± 8 years (5 male and female, each)). Additionally, a throughout osteotomy was performed in the diaphysis, held in place with additively manufactured guides to simulate a complete 100 μm wide fracture. Specimens were scanned with different CT scanners and corresponding digital 3D models were created. The effects of CT technologies/scanners, specimen positionings, scan and segmentation protocols, and image post-processing settings on feature detectability were assessed. Furthermore, the intra-and inter-operator variabilities were assessed for the segmentation threshold and 3D model accuracy. Three-dimensional reconstructions of surface scans of the physical specimens were used as ground truth to compute the specific geometry deviation.

Results

In CT images, fracture gaps of 100 μm, and bone lamellae of 300 μm and 400 μm were identified at a rate of 80 to 100%, respectively, independent of the investigated settings. In contrast, only 400 μm incisions and bony displacements were visible in digital 3D CT models. Hereby, the detection rate was independent of the scan settings but dependent on the selected CT technology. image segmentation and post-processing algorithms. Intra- and inter-operator variability were fair to excellent for 3D model accuracy (intra-class correlation of 0.43 to 0.92) and mean 3D deviation was < 0.16 mm on average for all operators, using a simple global segmentation threshold and minimal post-processing.

Conclusion

This first systematic investigation of the effect of multiple variables affecting 3D model accuracy demonstrated that sub-voxel imaging resolution was achieved for all variables. Thus, state-of-the-art CT imaging allows for the detection of bone features down to 100 μm. Corresponding digital 3D models still enable the identification of 400 μm features but require verification with the original CT image series.

Acknowledgements

This work has been partially supported by the Austrian Research Promotion Agency with the project “Additive Manufacturing for Medical Research, M3dRES (nr: 858060).

Hallux Valgus, also called a bunion, is a deformation of the metatarsophalangeal joint, more common in adults, with an estimated prevalence of 23% in the 18-65 age group and 35.7% over 65 years. There is a 3:1 relation for females, tending to increase with age [1]. Several reasons contribute to this type of deformity associated with tight shoes and high heels [2]. One of the theories is based on the idea that a continuous overload leads to deformation of the first metatarsal, with stretching of the capsule. The resulting imbalance of the first metatarsal phalangeal joint leads to increased deformity. The condition worsens, forming a bulge on the medial side [3].

The corrective treatment of the Hallux Valgus deformity usually involves surgery, with several surgical procedures reported. However, the Chevron Osteotomy is the procedure usually followed in this type of treatment, consisting of translating a distal portion containing the head of the first metatarsal, produced by the cut in the sagittal plane of a 60º angle of the distal apex. The resulting central exostosis is excised, with subsequent plication of the medial capsule [4]. This surgical procedure is performed manually, without support systems, depending on the result of the surgeon's experience.

This work proposes a new fixation device that allows the blade's positioning, stabilization, and guidance to guarantee precision in the cutting procedures in the Chevron Osteotomy. The development of the device involved the identification of the criteria for positioning the blade and necessary positional adjustments to ensure the best alignment and stabilization of the cutting blade to perform the Osteotomy. The methodology starts with the geometry of foot bones, obtained from a computed tomography scan using the Mimics Innovation Suite^Ò software. Based on the geometry, a modular support device was conceived and 3D modelled (with Solidworks^Ò software) to be anchored in two Kirschen wires to be applied, one in the first metatarsal and the other in the first proximal phalanx.

The device was prototyped, and a protocol for the experimental tests was defined. Artificial bones were produced from the geometry of the bones, considering the cortical and trabecular components. The tests were conducted in the laboratory with an experimental simulation of the Chevron Osteotomy, varying the positional adjustments associated with the technique. The obtained results demonstrate the device's effectiveness with well-defined cuts.

References

[1] Nix S., Smith M., & Vicenzino B. Prevalence of hallux valgus in the general population: a systematic review and meta-analysis. Journal of foot and ankle research, 3, 21. https://doi.org/10.1186/1757-1146-3-21, 2010.

[2] Sharma J, Arora A, Gupta S. Disorders of the toe - Hallux valgus. Textbook of Orthopaedics & Trauma, Vol. 4. Jaypee Brothers Publishers, 2019.

[3] Lerat J-L. Cheville-Pied: L’Hallux Valgus. Traumatologie Orthopedie. Centre Hospitalier Lyon-Sud, Service de Chirurgie Orthopedique et de Medecine du sport, Cap. 6, 2011.

[4] McKean J., Park J. Hallux Valgus. Lineage Medical, Inc. https://www.orthobullets.com/foot-and-ankle/7008/hallux- valgus, janeiro 2023.

Acoustic waves propagation in biological tissues has been studied usually in the context of diagnostic methods, such as the elastography. In microfluidic devices, nonlinear acoustic phenomena, namely the acoustic radiation, acoustic streaming are employed to manipulate particles and actuate fluid flow. These principles have attracted much interest of the research focused on developing new tissue engineering technologies since the acoustic wave are highly biocompatible, providing a non-contact controlable handle to manipulate bioparticles, or cells.
The paper reports on development of multiscale models of the acoustic waves and related phenomena in porous fluid saturated structures representing perfused tissues, or biomaterial structures intended for fluid suspensions and particle transport due to acoustic power, taking into account nonlinear interactions between to deforming pores and particles.
We focus on modelling two important phenomena induced in porous structures by acoustic waves: the peristaltic deformation and the acoustic streaming. Both can propel the fluid and particle transport, influencing interaction between particles and pore walls. This problem is motivated by the recellularization in decellularized tissue scaffolds, an important progressive tissue engineering technology .
The fluid-structure interaction problem is imposed in elastic scaffolds. To capture both the peristaltic deformation and acoustic streaming in response to propagating acoustic wave, nonlinearities originating in the divergence of the Reynolds stress, the advection acceleration term in the Navier Stokes equation, and the nonlinearity generated deforming pore geometry must be retained. The perturbation with respect to a small parameter proportional to the inverse Strouhal number is applied. This yields the first and the second order sub-problem enabling to linearize the Navier-Stokes equations governing the barotropic viscous fluid dynamics in periodic scaffolds. Subsequent treatment by the asymptotic homogenization leads to a two scale problem where the macroscopic model of the porous medium describes the acoustic streaming. The vibro-acoustic analysis of the first order problem yields the streaming source term for the second order problem which attains the form of the Biot-type medium.
To respect the peristaltic deformation wave in the homogenized model derived in the fixed reference configuration, influence of the deforming channel geometry on the homogenized coefficients must be considered. We use the linear expansions of the permeability and other poroelastic coefficients of the homogenized model; these are based on the sensitivity analysis of the homogenized coefficients with respect to macroscopic strain and pressure which determine the deformation of local microconfigurations.
To account for the acoustic waves influence on the propulsion of cells in the tissue scaffolds, we consider microstructures with trains of inclusions flowing in pores. Using simplified assumption and additional kinematic constraints, the contact of cells with pore walls is avoided. The two-scale homogenization-based modelling provides analytical and computational tools to simulate the influence of the bulk acoustic waves on the microflow of the biological fluids in tissues. In particular, the presented research is aimed at providing a computational feedback to experimental studies of the acoustic waves impact on the tissue scaffolds recellularization. The models are implemented in our in-house developed finite element based software SfePy. Numerical illustrations are presented.

Many liver diseases display an increasing incidence, whereby hepatocellular carcinoma rank 4^th in mortality among cancers. A deep understanding of liver functioning and disease requires to study the complex orchestration of processes at many levels of organization, which favor a systems medicine approach, where experiments, clinical data acquisition and computational modeling are integrated.

The computational models are able to verify or falsify hypothesized mechanisms and already led to the identification of unrecognized mechanisms that could be used to propose new therapeutic strategies [Ghallab et. al., J. Hepat. 2016]. Along the same line of argument, a systems medicine approach recently questioned the consensus mechanism of bile transport by flow in bile canaliculi, the smallest bile conduits in the liver [Vartak et. al. Hepatology 2020], and demonstrated that novel experimental results were compatible with diffusive transport alone. The latter work focused on transport in the bile canaliculi network but did not take into account the entire pathway of bile salts from the liver entrance into the liver capillaries (sinusoids), through the hepatocytes, their excretion into the bile canaliculi and then their flux to the bile ducts from where they are transported to the gall bladder.

Here we will present the necessary modeling components for such a model at the level of liver tissue micro-architecture, from which some have recently been established, as, e.g., blood hemodynamics in sinusoids [Boissier et. al. 2021], and flux of metabolites into and out of hepatocytes [Dichamp et. al., 2023]. The works vary a number of parameters, e.g., in [Boissier et. al.] different numerical algorithms are compared with regard to accuracy and computational efficiency. For clinical relevance, such an entire circulation model shall study the effect of heterogeneity, and permit scalability.

Given the complexity, these requirements may make such models computationally inefficient or even infeasible. To overcome this, various model reduction techniques can be applied, that partially depend on the nature of available data.

We present recent research and first steps towards a proof-of concept model of fluorescent marker transport in the blood-hepatocyte-bile system at the level of liver micro-architecture displaying each individual cell. Starting from general 3D model of mixture flow and transport in each part of the system, we present a strategy for reducing the governing equations into 1D. We then follow by formulating a mathematical description of exchanges occurring at compartment interfaces. Numerical solutions of the model are presented for cases corresponding to used experimental setups. Even with the rather oversimplified assumption on the system geometry (1D) in the prototype model, we are able to capture qualitatively the zonation features that are observed experimentally in mice.

In the future, this model will be refined to explain image data on vascular and biliary networks obtained in intravital imaging. An extension towards upscaling could start from interpreting the parameters of the model at cellular resolution as effective values of their real-world counterparts and go to more complex techniques, such as homogenization (cf. Rohan et al. [2021a], Rohan et al. [2021b]).

The flexoelectricity corresponds to the couplings between the electric polarization of a solid and strain gradient. Identified in the sixties, this nanoscopic electromechanical interaction presents two main attractive features. Firstly, this phenomenon may exist in materials with centrosymmetry, contrary to the piezoelectric effect. Secondly, strain gradient effects being inversely proportional to the medium size, the scale of flexoelectricity is then rather large. Flexoelectricity still presents challenging experimental and theoretical issues [1] and offers promising avenues of research and promises as new therapies in the context of regenerative medicine [2]. Up to now, recent advances in the understanding of bone physiology point out the possible relevance of flexoelectricity effects in bone. Indeed, putting forward the seminal studies of Williams [3], Vasquez-Sancho et al. [4] experimentally showed that part of bone electricity may be due to the bone’s mineral flexoelectric property in addition to already described collagen’s piezoelectricity and stress-generated streaming potentials. This may explain the in vitro observation of osteoblasts (bone forming cells) activity near a crack in pure hydroxyapatite (HAP), without the presence of collagen (COL) [5]. Since this electrical polarization and its consequences in interstitial fluid flow within bone is a key issue in its adaptation and repair [6,7], the high potential of smart flexoelectric tailored biomaterials in the highly competitive osteo-articular tissue engineering domain has to be investigated.

In this context, this study aims at correlating the crack-induced flexoelectric effect combined to collagen piezoelectricity on the bone cell behaviour in its fluid environment. It is thus necessary to connect the microscopic phenomena in the vicinity of bone cells to bone tissue structures. Thus, a trans-scale approach (homogenization) is carried out to propagate nanoscopic electromechanical consequences at the upper scale where the bone modelling units (BMU) activity occurs. In particular, we derive from this multiscale approach the coupled phenomena governing the osteocytic sensing and cell-to-cell communication known to drive BMU. This study potentially may have in a longer term a great technological impact with the design of novel biomaterials and technological solutions to stimulate bone repair.

[1] Chae et al., ACS Appl Bio Mater, 1: 936, 2018.

[2] Wang et al., Prog Mat Sci, 106:100570, 2019.

[3] Williams & Breger, J. Biomech, 8:407, 1975.

[4] Vasquez-Sancho et al., Adv Mater, 30:1705316, 2018.

[5] Shu et al., Mater Sci Eng C, 44:191, 2014.

[6] Lemaire et al., J Mech B Biomed Mat, 4:909, 2011.

[7] Lemaire et al., Int J Num Meth Biomed Eng, 29:1223, 2013.