A computational approach will be presented for the estimation of the in vivo magnitude and spatial distribution of mechanical material properties of organs and other soft tissues from standard clinical imaging data. To this end, a new shape-based objective function, quantifying the difference between the measured and predicted tissue mechanical response is introduced. By utilizing shape, rather than deformation or related quantity, standard clinical imaging data can be utilized (e.g., without tagging) without further manipulation to approximate such measures from the images first. This objective function can then be implemented into an optimization-based inverse solution approach to estimate mechanical properties of tissues from initial and final shapes derived from clinical imaging data. This approach is an extension of prior work by the authors that used a standard discretized version of the Hausdorff distance as an objective function in an iterative approach to material parameter estimation [1]. A key component of the new inverse approach is constructing the geometry of the region of interest using a signed distance function. As such, a novel level-set framework is introduced for the objective function that is easily differentiable, and thus, able to be implemented into an optimization framework to estimate the material parameters that minimize the objective function with respect to a target shape with relative computational efficiency. A set of simulated inverse problems was used to evaluate the inverse solution estimation procedure based on estimating the passive elasticity of human ventricular walls from standard cardiac imaging data and corresponding hemodynamic measurements. In evaluating the results, emphasis will be placed on not just the accuracy of the material parameter estimates, but also on the computational expense (e.g., number of forward finite element analyses) required to approximate the target response. Various levels of heterogeneity will be considered in terms of the effect on solution accuracy and/or need for regularization. Additionally, sensitivity to model error will be explored.

REFERENCES

[1] Xu, J., Wong, T.C., Simon, M.A., and Brigham, J.C. A Clinically Applicable Strategy to Estimate the In Vivo Distribution of Mechanical Material Properties of the Right Ventricular Wall. International Journal for Numerical Methods in Biomedical Engineering, (2021)

For physics-based simulations, forward (UQ) and inverse uncertainty propagation still generate challenges for computationally demanding, real-world applications, like the ones appearing in many scenarios in Bioengineering. Two main obstacles pertain to a high stochastic dimension and many necessary forward solver calls caused by the statistical nature of the underlying algorithms.

A high stochastic dimension usually precludes the reliable use of surrogate-based approaches to reduce computational costs. Instead, we propose a Bayesian multi-fidelity procedure that exploits conditional distributions between two or more model fidelities in a small data regime (100 to 300 high-fidelity evaluations are necessary to train the conditional). The required online sampling is entirely shifted to the low-fidelity models. The latter can, for example, use simplified physics and coarser numerical discretization and only need to share a (nonlinear) statistical relationship with the high-fidelity model, giving a high degree of flexibility in selecting and creating such low-fidelity models. In both cases, the forward UQ and the Bayesian inverse problem, our approach results in an accurate posterior distribution, despite the inaccurate and noisy information the low-fidelity models provide. In the case of forward UQ, we call our approach Bayesian Multi Fidelity Monte Carlo (BMFMC), and for the inverse problem Bayesian Multi-Fidelity Inverse Analysis (BMFIA).

Especially for the Bayesian inverse problem, BMFIA brings further advantages. It shifts the necessary derivative evaluations to the low-fidelity model, allowing the analyst to exploit adjoint implementations for simplified physical models. We then perform Bayesian inference with efficient stochastic variational methods, which require solely evaluations of the lower-fidelity model. If the low-fidelity models cannot provide model gradients, we propose new developments in sequential black box variational inference schemes. The latter poses the variational optimization problem without needing model gradients. The formulation is more efficient than gradient-free sampling schemes, such as sequential Monte Carlo or Markov Chain Monte Carlo methods. It gives reliable posterior approximations for moderate stochastic dimensions (up to 50) where surrogate approaches are already prohibitive.

Another possibility for some challenging problems in Bioengineering is to drastically reduce the number of forward model calls via approximating the log-likelihood by a surrogate model. The advantage of such a log-likelihood approximation over the outputs of the forward model is that instead of a potentially highly dimensional model output, only a scalar value has to be approximated. To allow the scalability of the approach to higher stochastic dimensions, the training samples of the surrogate are adaptively selected, and the uncertainties of the surrogate are taken into account.

In this presentation, we will show the proposed methods' essential aspects and their application to different challenging problems in Biomechanics.

Changes in our body that occur due to illness and disease also bring mechanical changes, which are often only observed by clinicians poking and prodding tissues. These present opportunities for new diagnosis and monitoring technologies. In our work we have taken a tissue biomechanics approach to study the wound healing process. This area is particularly important due to the large costs that wounds place on healthcare resources (>£4.7 billion in the UK annually) and pain experienced by patients.

To assess how wound healing relates to mechanical changes, we used a mouse model of acute wound healing. We made 4 mm diameter wounds in the skin using a biopsy punch and then the skin was allowed to recover with mechanical and histological assessment at days 1, 3, 7 and 14 post-wounding. These correlated with the stages of wound healing – haemostasis, inflammation, proliferation, and remodelling. We excised the tissue and undertook tensile testing for global properties, image-based local strain assessment using Digital Image Correlation (DIC), and Optical Coherence Topography Elastography (OCE) to characterise the material changes in the skin. We correlated these to histology with H&E and Picrosirius red staining for wound-staging and collagen fibre characterisation respectively. Concurrently we developed a finite element model to aid the mechanistic interpretation of the data.

Our tensile testing results showed no discernible change in the hyperelastic moduli/coefficients when a wound was present in skin, compared to intact skin. This contrasted with literature which had shown the opposite. We believe that this is due to the more physiologically relevant strains we used to test the tissue, rather than the “test to failure” approach of others. To understand this further, we measured the local in-plane strains in the skin during tension. We observed re-organisation of the tissue strains with a compliant ring which reduces stress on the wound. This mechanism during healing appears to ensure that wounds are protected whilst healing. When skin was simulated by finite element models it became clear that a bulk hyperelastic approach did not sufficiently account for these changes, and fibrous models would be required. Our histology data showed how the fibrous components in the skin vary during healing, which indicates models will require time-variant structural changes. Our analysis of the wound mechanics by OCE helps identify sub-surface mechanical changes and we will share our progress on this.

The changes that occur in tissues during physiological changes, presents a substantial opportunity for our bioengineering community but we need to have both experiments and models that reflect the reality of tissue changes. Our work has shown that the experimentally derived data is most useful for computational model development only if both global and local structural changes are considered. Furthermore, the need for a model that adapts to the time-variant changes during a disease’s progression become more central. These, set against a backdrop of a varied population, increase the challenge of accurate physiological modelling but present a huge opportunity for the computational and experimental communities to work together.

Considerable research efforts have been devoted to the development of microstructurally-based anisotropic continuum constitutive models of biological soft tissues. These formulations typically rely on the definition of one or more vector fields representing the local orientation of biological fibres (i.e. collagen fibres) within a tissue. Methods to incorporate such a structural information into anatomically realistic micromechanical finite element (FE) models of soft tissues such as skin are still lagging behind, particularly when it comes to models aiming to capture the complex local three-dimensional (3D) architecture of the collagen fibres network.

In order to improve the predictive power of the next generation of biophysical models of soft tissues it is essential to develop robust methods and methodologies to seamlessly integrate the microstructural characteristics of the collagen network. Here, we developed such an approach combining high-resolution imaging of human dermis, fibre orientation image analysis, voxel-based mesh generation and micromechanical FE analyses.

Fresh full-thickness abdominal skin extracted during a cosmetic surgery procedure from a 39 years-old female Caucasian patient was commercially obtained (TCS Cellworks, Buckingham, UK). The skin sample was cut into 1 mm slices and processed for serial block-face scanning electron microscopy using a high contrast fixation protocol (SBEM Protocol v7_01_10, https://ncmir.ucsd.edu/sbem-protocol) and embedded in Spurr resin (Agar Scientific, Stansted, UK). The tissue block was then trimmed, glued onto an aluminium pin, sputter coated in gold/palladium and imaged in the serial block-face imaging system 3View® (Gatan, Inc., Pleasanton, CA, USA) mounted inside a Zeiss Sigma VP field emission scanning electron microscope with variable pressure mode (Carl Zeiss Microscopy GmbH, Jena, Germany) and imaged at 2.5kV. The acquisition was done at a sampling XY resolutions of 2500 x 2500 pixels (i.e. 8 nm pixel size) every 50 nm, resulting in 376 images. For development purpose, and due to the large size of the data set, the original image stack was cropped to generate a sub-stack with a 600×600×50 voxel dimension. The stack of 50 images was processed using a 3D orientation analysis algorithm based on the calculation of local structure tensors. A series of Python and Fortran programmes were written to generate a voxel-based hexahedral FE mesh with the option to assign fibre vectors at node, element or integration point level, import it into the FE package Abaqus® (Simulia, Dassault Systèmes, Johnston, RI, USA), code constitutive equations for invariant-based anisotropic hyperelasticity via Abaqus® UMAT subroutines, assign material properties to matrix and fibre phases, and run numerical analyses to study the micromechanics of the dermis. The main objective of our analyses was to quantify and understand the effects of faithfully capturing collagen fibre orientation on the homogenised micromechanics of collagen assemblies, and compare our technique to approaches considering a uniform orientation of collagen fibres, with or without fibre dispersion. Uniaxial/biaxial extensions and shear tests were simulated. The results of our numerical analyses did not only demonstrate the criticality of accounting for local fibre orientation but also the importance of distinguishing between the matrix and fibre phases as spatially independent domains within a tissue block.

Cardiovascular diseases are the main cause of death worldwide. The myocardial bride is one of the congenital abnormalities while part of the coronary artery is placed under the myocardium instead of resting on top of it. The myocardial bridge can be asymptomatic during adult life or can cause many cardiovascular consequences such as angina, myocardial ischemia, acute coronary syndrome, left ventricular dysfunction, arrhythmia, and even sudden cardiac death. Therefore, the investigation of the presented abnormality can significantly influence its understanding.

The presented research focuses on the numerical modelling of the blood flow through the myocardial bridge section. Computer modelling is a useful tool to assess the risk factors influenced by blood flow disturbances in arteriosclerosis disease development. The mentioned factors are mainly connected with the low shear stress affected blood vessels accompanied by high oscillations of the blood flow in specific regions. In the case of the myocardial bridge, the blood vessel movement and its contraction can significantly influence the results of the flow calculations. Therefore, numerical models should include the simulated arteries' geometry changes, which is a challenging model development. It can be realized by the dynamic mesh approach accounting for the dynamic discretization of the investigated domain during the calculations. The presented research describes two methods of mesh motion defining in the commercial CFD software (ANSYS Fluent) extended by additional user defined functions. The first is based on the shape reconstruction from the camera records collected in in-vitro conditions on the blood vessel phantom. Results from the model and experimental campaign are compared including shape, pressures and flow in the blood vessel phantom. The pressure range was in this case at the level of approx. 120/80 mmHg. The consistency between those results was at a satisfactory level. The second mesh motion deformation was based on the patient's medical images collected in in-vivo conditions and processed by auxiliary software (ANTS) performing advanced image transformation based on diffeomorphism. The obtained results from those two methods pointed out the validity of the dynamic domain definition. The relevant volume change of the vessel during the heart cycle also influences the assumed boundary conditions introduced to solve governing equations covering specifically the mass conservation principle. The dynamic shape reconstruction in the CFD model was compared with the instant segmentation data showing satisfactory agreement.

CFD is a noninvasive technique that could be applied to clinical practice to predict the blood flow in the coronary arteries. Including the vessel shape dynamics from medical images in the CFD models increase those models' accuracy.

Acknowledgements: This research is supported by National Science Centre (Poland) project No. 2017/27/B/ST8/01046 and project No. 2019/34/H/ST8/00624. This help is gratefully acknowledged.

Coil embolization is performed to treat intracranial aneurysms. During the follow-up after coil embolization, a recurrence of the aneurysm called recanalization may occur due to blood inflow. Therefore, it is expected that risk prediction of aneurysmal recanalization will enable effective treatment planning. Recently, computational fluid dynamics (CFD) has been conducted to identify the risk factors of recanalization. Although most of the previous studies assumed that blood is a Newtonian fluid, actual blood is a non-Newtonian fluid. Especially, the shear rate in coil embolized aneurysms becomes so low that the effect of non-Newtonian fluid is considered to be significant. In this study, we conducted CFD and statistical analysis to investigate the effect of non-Newtonian fluid properties on the prediction of aneurysmal recanalization. Our target of the analysis was basilar tip aneurysms. We identified 31 aneurysms including 4 recanalized aneurysms and 27 stable aneurysms. In this study, we defined recanalization as the case that recanalized less than 2 years after the first coil embolization. On the other hand, aneurysms that remained stable for more than 2 years after the embolization were defined as stable. We applied Newtonian and non-Newtonian blood models for these cases in the CFD analysis. We modeled the non-Newtonian blood using a modified Casson model based on the results of viscosity measurements on 12 patients with aneurysms. A porous media model was applied to model the embolized coil mass. We defined 33 hemodynamic and 3 morphological parameters. For each hemodynamic parameter, the value before (BF) and after (AF) coil embolization was obtained, and their reduction ratio (RR) was also calculated. We focused in particular on the V_Neck and the V_Dome, which indicate the dimensionless velocity on the neck plane in the aneurysm, respectively. In addition, the spatial mean, maximum, and minimum values were denoted as Ave, Max, and Min, respectively. Univariate logistic regression analysis was performed to compare each parameter between recanalized and stable cases. In addition, ROC analysis was also performed for parameters that showed statistically significant differences (P < 0.05). The sensitivity, specificity, and area under the curve (AUC) were evaluated among the parameters. As a result, by considering non-Newtonian fluid properties, V_{Neck_Ave_RR}, V_{Neck_Max_RR}, and V_{Dome_Ave_RR} newly indicated statistically significant differences between the recanalized and stable cases (i.e., the parameters that showed statistically significant differences in the Newtonian fluid also showed statistically significant differences in the non-Newtonian fluid). In addition, although the highest sensitivity (=0.75) and AUC (=0.84) were obtained with the V_{Dome_Ave_RR} when we assumed Newtonian fluid, the higher sensitivity (=1.00) and AUC (=0.89) were achieved when the non-Newtonian model was applied. The results showed that considering the non-Newtonian properties increased the sensitivity and AUC of recanalization prediction. In conclusion, non-Newtonian fluid properties changed the parameters that showed statistically significant differences between recanalization and stable cases. Furthermore, the V_{Dome_Ave_RR} obtained the highest accuracy in all researched parameters assuming Newtonian and Non-Newtonian fluid. The present result implies that the introduction of non-Newtonian fluid properties can improve the prediction accuracy of recanalization in coil embolized aneurysms.

Understanding cardiac sympathovagal balance and its relationship to the degree of reinnervation after heart transplantation has been a longstanding challenge in medicine. While autonomic markers derived from cardiac rhythms are often used to assess cardiac sympathovagal balance, their relationship to reinnervation has not been fully explored. In this study, we used a mathematical model of the human cardiovascular system and its autonomic control to explore the influence of varying levels of vagal and sympathetic cardiac reinnervation on autonomic cardiac markers.

To investigate this relationship, we applied a mathematical model of the human cardiovascular system and its autonomic control. The model integrates the chronotropic and inotropic effects of the arterial baroreflex and pulmonary stretch reflex, which are the main contributors to heart rate variability. The work focused on markers that are commonly used to assess cardiac sympathovagal balance, including resting heart rate, bradycardic and tachycardic heart rate response to the Valsalva maneuver, root mean square error of normalized RR-intervals (RMSDD), high-frequency (HF) power, low-frequency (LF) power, and total power of the heart rate variability spectrum. To evaluate the strength of the relationship between the level of cardiac reinnervation and the respective markers we calculated Spearman's rank correlation coefficients.

Results showed that for assessing vagal cardiac reinnervation levels above 20%, resting heart rate, RMSDD, and total spectral power may be equally suitable as the commonly used measure of HF power. The strength of the correlation between these markers and vagal reinnervation was found to be very high, with correlation coefficients of ρ=0.99, ρ=0.97, and ρ=0.89, respectively (all p<0.05). Concerning sympathetic reinnervation, simulations suggest that LF/HF-ratio and tachycardic response to the Valsalva maneuver may be more suitable than the regularly used measure of LF-power. The strength of the correlation between these markers and sympathetic reinnervation was high: ρ=0.88 and ρ=0.84, respectively (both p<0.05). These findings suggest that there are differences in the performance of cardiac autonomic markers in assessing vagal and sympathetic reinnervation and that some markers may be more suitable than others depending on the level of reinnervation.

The developed mathematical model can provide critical insights into the genesis of autonomic cardiac markers and their relationship to cardiac reinnervation. Furthermore, it suggests strategies for designing and interpreting future clinical studies, which would then provide clinical evidence for the current findings and allow more accurate evaluation of cardiac (re)innervation levels after heart transplantation. Overall, the findings of this model study might have important implications for the assessment and management of cardiovascular disease and highlight the potential of mathematical models to enhance our understanding of complex physiological systems.

This work was funded by the European Project H2020-EU.1.2.2. “A neuroprosthesis to restore the vagal-cardiac closed-loop connection after heart transplantation, NeuHeart” (Grant agreement ID: 824071).

Objectives: A standard treatment for severe Aortic Stenosis (AS) is surgical valve replacement with biological prostheses. Fluid-structure-interaction (FSI) simulations are a powerful tool for studying hemodynamic valve behavior and thus optimize function, geometry and durability particularly of prosthetic aortic valves. In this study, an FSI simulation of a bioprosthetic bovine pericardium aortic valve was established, which incorporated an anisotropic hyperelastic material model for the valve leaflets.

Methods: A valve-specific geometric model from a µCT scan (voxel size 31µm) of the 21 mm Avalus™ Bioprosthesis (Model 400, Medtronic, Ireland) was obtained. An anisotropic hyperelastic material model was used, a first order Ogden model for the isotropic matrix and an exponentially-based strain energy function for embedded hyperelastic fibers representing collagen fibers in circumferential leaflet direction. The valve structure was then coupled with a fluid domain consisting of a tube with 24mm diameter as inlet, the sinuses of Valsalva and a tube with 30mm diameter as outlet. Blood was assumed to be a Newtonian fluid. The inlet pressure boundary condition was chosen to represent a clinically determined transvalvular pressure gradient during a cardiac cycle, while the outlet pressure boundary condition was set to zero. The valve hemodynamic behavior was analyzed by determining the valve’s effective orifice area, leaflet fluttering dynamics during systole and fluid velocities.

Results: The composite valve model was successfully implemented in the FSI simulations performed on the Vienna Scientific Cluster supercomputer. The simulated effective orifice area at mid-systole was 1.6 cm². Systolic leaflet fluttering – which is associated with fatigue and failure of bioprosthetic leaflets over time – was most pronounced at beginning of systole, with amplitudes up to 2.5 mm. However, during the course of systole, the leaflets stabilized, resulting in smaller fluttering amplitudes but higher fluttering frequencies (up to the simulation output sampling rate of 200 Hz). Peak velocities in the free jet during systole went up to 3.0 m/s.

Conclusions: A hyperelastic anisotropic leaflet material was successfully integrated in an aortic valve model and used for FSI analysis. The model is being refined and validated with experimental flow tests. After validation the influence of differently sized valves on the valve hydrodynamics will be investigated together with correlations of simulation results with clinical outcomes.

An intracranial aneurysm is a cerebrovascular disease that swells of bulges abnormally in the wall of intracranial arteries. Rupture of aneurysms cause subarachnoid hemorrhage with high mortality. Unruptured aneurysms occasionally have Thin-Walled Regions (TWRs) where the wall thickness is thinner than the surrounding areas. Although TWRs in intracranial aneurysms have a risk of rupture, imaging modalities cannot evaluate the thickness of the aneurysm wall. The surgical treatment will be able to perform safely by identifying TWRs before the treatment. TWRs have been related to hemodynamic factors. Although Computational Fluid Dynamics (CFD) analysis has been applied to identify the hemodynamic characteristics around TWRs, few previous studies have focused on the difference in hemodynamic factors between TWRs and non-TWRs by quantitative definition of TWRs. The purpose of this study is to investigate the hemodynamic factors involved in TWRs by comparing the results in TWRs and non-TWRs by CFD and image analysis. We identified 100 aneurysms (middle cerebral artery: 78, anterior cerebral artery: 20, internal carotid artery: 2) treated with craniotomy and clipping. Unsteady CFD analysis was performed with the inlet boundary condition imposed on the mean mass flow pulsations measured from healthy adults, the outlet boundary condition fixed at a static pressure of 0 Pa, and the no-slip wall boundary. We evaluate the pressure difference (PD), wall shear stress (WSS), and wall shear stress divergence (WSSD) on the aneurysm wall. All parameters are normalized by the dynamic pressure at the aneurysm inlet. Since TWRs generally indicate intense red, the comprehensive Red (cR) value was defined by the RGB color model to evaluate the redness. The cR value was calculated for each pixel of the intraoperative images, and TWRs were defined using the cR value. We extracted the TWRs in the three-dimensional geometry of the aneurysm and the other region of the aneurysm wall was defined as non-TWRs. The mean values of each parameter in TWRs and non-TWRs were calculated and compared between the two groups using Mann-Whitney’s U test. As a result, the mean PD of all cases was 0.0688 in TWRs and -0.0278 in non-TWRs, the mean WSS was 0.0510 in TWRs and 0.0439 in non-TWRs, and the mean WSSD was 0.0162 in TWRs and 0.0014 in non-TWRs, respectively. These three parameters were statistically significantly higher for TWRs than non-TWRs (P<0.05). The higher PD of the TWRs is thought to be caused by the vertical stress on the aneurysm wall due to flow impingement on the aneurysm wall. We considered that high friction against the aneurysm wall is related to high WSS in the TWRs, resulting in a decrease the number of endothelial cells in the wall and the thin-wall. The WSSD was high in the TWRs because the tensile forces on the aneurysm wall may lead to the thin-wall. In conclusion, our results suggested that these hemodynamic parameters are related to TWRs. By conducting a CFD analysis on each patient and examining the areas with high PD, WSS, and WSSD values, it may be possible to identify TWRs before treatment.

Introduction

Image-based computational models of cardiac electromechanics (EM) are a powerful tool to understand the
mechanisms underlying physiological and pathological conditions in cardiac function and to improve diagnosis and therapy planning. To realize such advanced applications methodological key challenges must be addressed. First, enhanced computational efficiency and robustness is crucial to facilitate model personalization and the simulation of prolonged observation periods under a broad range of conditions. Second, physiological completeness encompassing therapy-relevant mechanisms is needed to endow models with predictive capabilities beyond the mere replication of observations.​​

Methods

In this talk, we report on a universal cardiac EM modeling framework that builds on a flexible method for
coupling a 3D model of cardiac EM to the physiologically comprehensive 0D CircAdapt model representing
closed-loop circulation. Additionally, we present recent advances in EM cardiac model personalization. In
particular, we focus on the identification of passive cardiac properties. Here, we present a novel methodology to simultaneously perform an automated identification of in-vivo passive mechanical properties and an estimation of the unloaded reference configuration.

Results

We report on the efficiency, robustness, and accuracy of the numerical scheme and solver implementation and show the model’s ability to replicate physiological behaviors by simulating the transient response to alterations in loading conditions and contractility, as induced by experimental protocols used for assessing systolic and diastolic ventricular properties. Further, we demonstrate the applicability of the framework to several clinically relevant problems.

Conclusion

The mechanistic completeness and efficiency of the framework renders advanced EM modeling applications feasible. The model facilitates the efficient and robust exploration of parameter spaces over prolonged observation periods which is pivotal for personalizing models to closely match observations. Moreover, the model can be trusted to provide predictions of the acute transient response to interventions or therapies altering loading conditions and contractility.

Coronary artery disease is a chronic disease in which the blood vessels are blocked, as a result of the growth of atherosclerotic plaques inside the arteries. To treat atherosclerosis, different clinical treatments are employed, including percutaneous coronary intervention (PCI). PCI includes the insertion of a stent, a metallic scaffold, its placement and expansion inside the diseased artery and the restoration of the blood flow. For a stent to be released to the market, its performance in terms of safety and efficacy is initially tested and evaluated, in in vitro, animal studies and clinical trials. However, this process is time consuming and costly, and there are certain limitations, such as the onset of severe complications and adverse events during clinical studies, which can be addressed by the exploitation of the very promising in-silico approaches. The fast-emerging technology of in-silico technologies is considered as an effective means for providing answers to “What if” questions. Among the available computational methods, the application of finite element method has proven to be the “method of choice” in replicating the biomechanical response of stents, by modelling their deployment in diseased, idealized or realistic, arteries. Structural simulations of stent implantation allow the evaluation of quantities of interest which could be difficult or even impossible to be observed through other means. By using models of coronary arteries and different stents or stenting techniques, the analysis of several geometrical (e.g., size of atherosclerotic plaques, malapposition, stent cell size, minimum lumen area, etc.) and mechanical quantities (type of atherosclerotic plaques, stent stress/strain, arterial stress/strain, etc.) can be performed. Such models provide useful insights into several aspects of stent design, towards of a final stent configuration for optimal post-implantation outcomes. In this work, a finite element analysis is performed to simulate the deployment of a commercially available stent inside a reconstructed patient specific artery. In more detail, for the reconstruction of the arterial wall and the underlying atherosclerotic plaque components, Optical Coherence Tomography and Invasive Coronary Angiography imaging are used, and an in-house 3D reconstruction software tool is employed. The next step involves the design of the 3D stent and its positioning in the stenosed artery. Then by the application of appropriate boundary conditions in the arterial-stent model and the implementation of a pressure driven approach, the in-silico expansion of the stent is achieved. For the finite model, representative material properties and material models are used. This study focuses on investigating the effect of the material properties of the underlying arterial wall and atherosclerotic plaques (fibrous, lipid, calcified) for providing guidance in appropriate material selection in stent modeling approaches towards improving stent design and performance. In more detail, we investigate the stresses, strains and deformations caused in the scaffold and the arterial wall considering the calcified plaques stiffness variance.

The segmentation of computed tomography (CT) scans allows to define patient-specific computational models for the development of targeted tissue engineering applications. However, the segmentation of these images does not provide an accurate definition of the soft tissues. For cervical spine models, this problem is observed when rebuilding intervertebral discs (IVD), facet joints and ligaments, requiring adjustments on the geometry of these structures. In the literature, there is no consensual definition of the parameters that characterise these structures, as they provide different results when compared to the benchmark experimental data. Also, recent works use non-linear material properties to achieve a better physiological cervical spine mobility. The aim of this study was to define the role of the components of the cervical spine, on a linear finite element (FE) model, and how can a combination of modelling parameters be adapted to better represent cervical spine mobility and assist on enhancing new tissue engineering strategies. Adjustments on IVD geometry, ligaments insertion and material properties were taken to evaluate if a FE model could replicate experimental data mobility without requiring non-linear material properties.

Three subject-specific models were segmented and converted to FE models in ScanIP (Synopsys, Inc.,USA). The IVD design was based on vertebrae boundaries and experimental data volumes. The segmentation of the IVD was performed by the attribution of different material properties to the Nucleus Pulposus and the Annulus Fibrosus. On Abaqus (Dassault Systèmes, USA), the model was assembled with the cervical spine ligaments. For the ligaments, two parameters were studied: insertion area and number of elements. The range of motion (RoM) of the model, measured on the superior surface of each IVD, was compared with experimental mobility data conducted in Panjabi et al. (2001). Based on the RoM, the influence of patient-specific geometrical features was evaluated.

For validation, the FE model was conditioned to a simultaneous 50N compressive load and 1Nm moment in different directions. The FE model agreed well in flexion where motion for each segment was 7.97° at C4-C5, 5.58° at C5-C6 and 2.84° at C6-C7, as well as in extension where motion for each segment was 6.80° at C4-C5, 4.65° at C5-C6 and 1.67° at C6-C7 which are within the experimental findings. For lateral bending, motion for segment at C4-C5 was 7.92° and at C5-C6 was 5.59° were in accord with the experimental data, however motion for segment at C6-C7 was 2.15° which meant an underprediction by 153%. For axial rotation, motion for segment at C4-C5 was 9.48° and at C5-C6 was 7.35° which overpredicted by 29% and 28%, respectively. For segment at C6-C7 motion was 3.60° which is within the experimental data.

Adjustments on the cervical spine components produced favorable outcomes, when compared to the experimental mobility data. The workflow followed in this study ensured uniform segmentation of cervical spine finite element models and latter adaptations of parameters. Compared to non-linear FE models, this methodology presented similar mobility results with a facilitated segmentation process and linear material properties.

Bone tissue engineering (BTE) scaffolds are used in different situations when there is a need to replace or regenerate bone tissue, such as fractures, tumor resections or joint replacement. Among biocompatible materials bio-Ceramic scaffolds represent an effective solution for BTE applications since they stimulate the bone growth thanks to their affinity with the native bone tissue. The main drawback of ceramic materials is represented by their intrinsic brittleness that makes the failure unpredictable and catastrophic. One of the key challenges in tissue engineering is to design scaffolds with appropriate mechanical properties and pore structures that can carry the load and in the meantime support cell growth and differentiation. To this purpose, we developed a numerical tool able to generate bone-like architectures with tuneable morphometric properties based on stochastic approaches. In particular, the Voronoi tessellation was used to create the three-dimensional scaffold mimicking the natural structure of bone tissue. A predefined number of seeds have been randomly distributed in a cubic domain and the Voronoi tessellation have been created. According to a statistical probability function based on the orientation of the edge of the cells, faces and edges have been removed in order to get a fully interconnected porosity. Finally, the resulting structure have been dilated to get the scaffold architecture. Taking inspiration from the trabecular bone tissue, the model was forced to have a preferential orientation of the rod-like trabeculae along a prescribed direction, no more than four trabeculae converging in one node and control the ratio between rod-like and plate like trabeculae.

The homogenized elastic properties of the scaffolds were characterized using finite element analysis on cubic domains by using the solver ParOSol. A damage-based iterative procedure has been used to assess the macroscopic strength of the scaffold.

The proposed model offers a versatile and effective method for designing ceramic scaffolds for tissue engineering applications. The ability to control the scaffold properties through the Voronoi tessellation allows for the development of customized and patient-specific scaffolds with enhanced mechanical properties, potentially leading to more effective tissue regeneration and repair. In particular, through this model we were able to control the amount of plate-like trabeculae and rod-like trabeculae, their orientation and detect their effect on the macroscopic strength of the scaffold.

In the field of bone tissue engineering (BTE), porous scaffolds gained attention due to their capability to promote tissue regeneration. Recently, triply periodic minimal surfaces (TPMS) scaffolding method became a promising candidate to aid bone tissue renewal. TPMS scaffolds allow tuning of several designing parameters, so the aim of this study was to understand the role of geometry, porosity degree and material non-linearity in the overall mechanical response of the scaffold. For this purpose, different building materials for TPMS scaffolds were simulated using the finite element (FE) method.

The TMPS scaffolds derived from a combination between geometry, Diamond (SD), Gyroid (SG) or Primitive (SP); and porosity, 60%, 70% or 80%. The nine different scaffolds (SD60, SD70, SD80, SG60, SG70, SG80, SP60, SP70 and SP80) were modelled on Abaqus (Dassault systems Simulia Corp., USA). The FE models were generated by the repetition of a cubic structural unit (1 mm side) on a 2x2x4 units configuration and modelled using two materials: VisiJet^® M3 Crystal (approximated as linear elastic, with E=1.46 GPa and ν=0.35), and a viscoelastic gelatin hydrogel (Kalyanam et al., 2009). On a first stage, the mechanical behaviour of the 16-units FE model was compared to a previous study that used FE models of 2-units (Castro et al., 2020). Preliminary results showed different mechanical behaviour on the maximum value and location of von-Mises stress, between 16- and 2- units. Thus, the 16-units scaffolds were considered for the following analysis. The mechanical loading was performed as a displacement-controlled compression along the z-direction of the FE model, applying a compression amplitude (measured along the z-direction) of up to 10% for the linear material and 2% for the hydrogel.

The scaffolds built with the linear elastic material showed a linear trend for each combination of geometry and porosity (R² coefficient from 0.99466 for SP80 to 0.99994 for SD80), in terms of equivalent strain/stress curves, revealing the absence of non-linear behaviour coming from the changes in scaffold geometry. In terms of equivalent stiffness, for each geometry, the Young’s modulus decreases with an increase in porosity, as expected. Furthermore, the SD and SP geometry corresponded to the highest and lowest Young’s Modulus, respectively, for each porosity level. The computational equivalent stiffness was compared with the stiffness values obtained from experimental tests (3D printed scaffolds in Crystal) and homogenisation method, showing considerable differences for the SD geometry and minor variations for SG and SP. However, the homogenisation method assumes an infinite periodicity of units, which probably means that, by increasing the number of units on the FE model, the outputs from these two methods could be closer.

The use of computational FE models allowed to study the mechanical behaviour under compression of TPMS scaffolds. The current outputs suggest that the non-linearities on the mechanical behaviour of TMPS scaffold are not introduced by the scaffold geometry, allowing for the exploration of non-linear building materials. Further work will include experimental tests of stress relaxation, to investigate the effect of geometry on the time-dependent behaviour of these scaffolds.

The application of computational methods to the design and testing process of Bone Tissue Engineering scaffolds is a valuable but complex approach, as the number of structures and materials that can be utilized to create these structures is constantly increasing and with it the time and costs required to accurately assess scaffold properties.

Among the different parameters that need to be defined, the macroscopic strength and the fracture mechanisms are of particular importance for ceramic-based scaffolds, as they are characterized by brittle-like failure and can undergo abrupt rupture processes. Proper assessment of scaffold strength and fracture patterns can aid the design and optimization process and therefore needs to be accurately implemented in the scaffold testing process.

Different crack propagation models exist nowadays, allowing for the computational evaluation of scaffold strength. Explicit methods can be characterized by stability issues, as convergence is conditionally achievable, and tends to limit its analyses to short transient processes. The phase-field approach, which is based on an implicit approach, models crack propagation as a gradient of element damage, allowing for the evaluation of brittle fracture as a quasi-static process. Furthermore, its versatility allows for the implementation of different phenomena, such as corrosion.

The staggered phase-field model created by Molnár et al. for modelling brittle failure was tested on hydroxyapatite-based scaffolds produced with the Robocasting technique. The results of this starting algorithm highlighted discrepancies in the failure mechanism when compared to finite element method results. While the latter displayed vertical cracks along the compression direction, suggesting that tensile stress is the dominating factor for fracture generation, the phase-field results were characterised by diagonally oriented cracks, highlighting a shear-dominated fracture process. This particular failure mode is owed to the specific function assumed for onset and progression of localised damage.

In this work, an alternative form of damage propagation is proposed with the purpose of better simulate the fracture mode observed in ceramic scaffolds subjected to compressive loads.

The aim of this alternative formulation is to account for a higher resistance of the material to shear stresses, and a much higher resistance to compression.

The final crack pattern formation more closely resembles the expected pattern and is therefore able to model the material’s behaviour more accurately, paving the way to the application of the phase-field model on bone tissue engineering scaffolds characterized by structural continuity between different layers along the loading direction, where compression stresses are transferred directly along said direction.

Skin is the body’s largest organ, composed of three layers that vary in properties across its structure and exhibit directional-dependent physical properties. Despite its exceptional healing capacity, the skin is very susceptible to full-thickness wounds that require specialized dressings to promote tissue regeneration. While there are various commercial skin grafting solutions available, they all have limitations that can result in non-native scar formation, for instance, highlighting the need for further investigation in the field. In this study, we investigate the use of fiber scaffolds with micro-scale auxetic geometries for skin tissue engineering applications. Auxetic structures are known to expand in multiple directions when stretched, enabling them to conform to different wound shapes and promote wound healing [1]. By altering the micro-geometry design, these structures can be tuned to provide tailored mechanical properties that match the unique needs of each patient’s wound, which may vary based on location of the wound or patient’s age or gender [2].

We have investigated two types of scaffold micro-scale designs, both comprising interwoven fiber networks to achieve auxetic behavior. These designs are categorized as re-entrant and chiral and exhibit distinct mechanical properties that are determined by the arrangement of interconnections between the fibers. Numerical finite element simulations of these fibrous structures were conducted to predict their mechanical behaviour prior to fabrication by means of a parametric study of each auxetic design. These simulations were generated, calculated and post-processed with a Python script-based software tool developed to automate this process. After numerical analysis, some designs were selected for fabrication and mechanical characterization with uniaxial and biaxial tensile tests to validate the numerical models. Polycaprolactone fiber scaffolds were fabricated using an in-house built melt electro-writing set-up. The multilayer structures were printed with fiber diameters of approximately 20 microns (with pore size around 300 microns) with the aim of developing microstructures that could provide adequate mechanical environment for cells.

Both numerical simulations and experimental tests have revealed that the mechanical behaviour of the printed scaffolds matches the mechanical properties [3] and behavior of skin (J-shaped stress-strain curve), as well as its auxetic behaviour [4]. Mimicking native tissue properties is essential for tissue engineering. Furthermore, comparative analysis of the results revealed differences in stiffness and auxeticity depending on the auxetic design, allowing us to tailor their properties via geometrical changes.

The combination of numerical simulations with a high-end fiber printing process and mechanical testing has enabled us to develop a platform for designing structured fiber scaffolds with tunable mechanical properties for skin tissue regeneration.

References

1. Kim et al, Materials (Basel), 14(22):6821, 2021.
2. Luebberding et al, Skin Res Technol, 20(2):127-35, 2014.
3. Joodaki et al, Proc Inst Mech Eng H, 232(4):323-343, 2018.
4. Dwivedi et al, R Soc Open Sci, 9(3):211301, 2022

Acknowledgements

The authors acknowledge the project LMP 176_21 funded by the Department of Science, University and Knowledge Society of the Government of Aragon.

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).

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.

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.

Chiral molecules form a plethora of liquid-crystalline phases, even in equilibrium. Liquid-crystalline phases formed by chiral and active agents have features that are even more counterintuitive. For instance, while in passive matter, chirality tends to cloak itself from the long-wavelength elastic and hydrodynamic properties, activity reveals its effect in cholesteric and chiral columnar phases, leading to unique forms of odd elastic behaviours. Specifically, cholesteric phases display a unique odd elastic force density tangential to the contours of the constant mean curvature of layer undulation. This ultimately leads to the formation of an antiferromagnetically organised, columnar, vortex-lattice array in extensile active cholesteric fluids. Columnar materials which are both polar and chiral surprisingly display two-dimensional odd elasticity, even though the system is three-dimensional. The interplay of this odd elasticity with three-dimensional Stokesian hydrodynamics leads to an oscillatory optical mode.
The interplay of chirality and activity also leads to liquid-crystalline phases without a passive analogue, such as time liquid crystals. In this phase, planar-chiral active elements — spinners — that tend to align with each other trade in rotation symmetry breaking for time-translation symmetry breaking. That is, in these spontaneously rotating aligned states, rotation symmetry is restored in a time-averaged sense. Therefore, while such states are aligned, they escape the celebrated Simha-Ramaswamy instability that plagues uniaxial active suspensions by spinning out of unstable configurations. In my talk, I will discuss both new phases of chiral active liquid crystals and their properties and the effect of activity on classical chiral liquid crystalline phases. I will specifically highlight how the interplay of chirality and activity allows the former to affect dynamic and static properties of ordered states to a much greater degree than in passive soft materials, as summarised above.
Given that most biomaterials are chiral, biological systems ranging in scales from subcellular to all the way to organisms are the natural domain for detecting chiral active liquid crystalline organisations and their effect. Indeed, some of the phases that I will describe in my talk were subsequently observed in in vitro experiments with properties consistent with my predictions. Furthermore, given chiral active liquid crystals have material properties that can, in principle, make them useful for engineering applications, a further important avenue of research will involve synthesising them artificially.

Whether one considers swarming insects, flocking birds, or bacterial colonies, collective motion arises from the coordination of individuals and entails the adjustment of their respective velocities. In particular, in close confinement, such as those encountered by dense cell populations during development or regeneration, collective migration can only arise coordinately. Yet, how individuals unify their velocities is often not understood. Focusing on a finite number of cells in circular confinements, we identify waves of polymerizing actin that function as a pacemaker governing the speed of individual cells. We show that the onset of collective motion coincides with the synchronization of the wave nucleation frequencies across the population. Employing a simpler and more readily accessible mechanical model system of active spheres, we identify the synchronization of the individuals' internal oscillators as one of the essential requirements to reach the corresponding collective state. The mechanical 'toy' experiment illustrates that the global synchronous state is achieved by nearest neighbor coupling. We suggest by analogy that local coupling and the synchronization of actin waves are essential for emergent, self-organized motion of cell collectives.

In this talk, I will describe two biologically inspired systems that can be described using the same geometrical Hamiltonian formalism. The first is ATP synthase proteins which rotate in a biological membrane. The second is swimming micro-organisms such as bacteria or algae confined to a 2D film. I will show that in both cases, the active systems self-assemble into distinct structural states - the rotating proteins rearrange into a hexagonal lattice, whereas the micro-swimmers evolve into sharp lines with a particular tilt. While the two systems differ both on the microscopic, local interaction, as well as the emerging, global structure, I will show that their dynamics originate from similar geometrical conservation laws dictated by a Hamiltonian formalism applicable to a broad class of fluid flows.

Many active biological particles, such as swimming microorganisms or motor-proteins, do work on their environment by going though a periodic sequence of shapes. Interactions between particles can lead to the phase-synchronization of their duty cycles. We consider collective dynamics in a suspension of
such active particles coupled through hydrodynamics. We demonstrate that the emergent non-equilibrium states feature stationary patterned flows and robust unidirectional pumping states under confinement. Moreover the phase-synchronized state of the suspension exhibits spatially robust chimera patterns in which synchronized and phase-isotropic regions coexist within the same system. These findings demonstrate a new route to pattern formation and could guide the design of new active materials. An extension of the same theory for treating ciliated surfaces quantitatively captures the instabilities and flow pupmping behaviour of ciliated carpets and metachronal waves.

The expression "Hierarchical fibre bundles" indicates structures with one principal direction. The structure is composed of multiple fibrillar elements, i.e. with one principal direction. Interfaces may or may not be present between the fibrillar elements. Finally, each fibrillar element is itself defined as a fibre bundle, made of fibrils with different mechanical and geometrical properties. The properties of each scale arise from the properties of the lower scale.
Hierarchical fibre bundles are abundant in nature across a variety of anisotropic biological materials, such as tendons, muscles and silk. These structures often exhibit exceptional fracture properties with outstanding toughness, thanks to the presence of structural proteins and/or to bio-mineralisation and their arrangement across different scales.
Analysing the fracture behaviour of complex fibre-based structures is still a challenging task, even when using advanced computational tools. Current numerical models often require a set of assumptions and (over-)simplifications. In particular, many models require the knowledge a priori of the fracture path. Biological materials, however, are characterised by complex internal structures with random features; moreover, for nano- and micro-bundles, it is often impossible to capture the fracture phenomenon empirically. The fracture path is thus often unknown, and it is one of the open questions which needs to be addressed using mechanical models. Here, we propose an alternative solution to model the fracture mechanics of fibre-based materials, which combines the mathematical Fibre Bundle Model (FBM) and Finite Element (FE) methods.
The Fibre Bundle model is a general theory of failure based on the statistical distribution of the critical elongations of the fibres forming the bundle. FBM assumes the bundle as a system of parallel one-dimensional elements, being clamped at their extremities and undergoing external forces along their main direction. Being a mathematical tool, the FBM is based on analytical formulations and thus it can be computed at practically instantaneous speed using computational solvers. In this work, we use the FBM to obtain general properties of the fracture behaviour of a fibre bundle undergoing elongation along its main axis, and to describe the stress-strain curves characterising the fibrils in the structure. The non-linear stress-strain curve obtained is utilised as an input for an FE approach, which aids us in comprehending the deformation and fracture behaviour of the fibrils and the interaction between different fibrils and the eventual surrounding interfaces.
We demonstrate the utility of the approach by applying it to spider-silk threads and bio-polymeric fibre bundles that are known for their non-linear properties. The enhanced numerical approach to the fracture mechanics of mixed fibre bundles will improve our understanding of the function of biological structures and bio-inspired materials across scales.

Constant demand for improvement of cardiovascular treatments and necessity for better understanding of soft tissue behaviour is frequently tackled with finite element (FE) modelling. The accuracy of FE simulations considerably depends on precise and reliable material parameters. They are obtained through the process of material characterization that consists of experimental testing and subsequent data analysis. When it comes to soft tissue, planar biaxial tensile tests are widely applied because they resemble in vivo conditions fairly well and material is assumed as anisotropic. In spite of planar biaxial tensile tests being the go-to type of experiment, they are still not standardized. The possible variations are numerous, from specimen size and different gripping mechanisms to the choice of preconditioning stretches, experimental protocols, and optimization procedures during data analysis. Limited availability of soft tissue requires simple and tiny square specimens. Before the start of experiment, specimens are mounted with hooks, rakes, or sutures and slightly preloaded to avoid the specimen hanging and to ensure that its orientation is perpendicular to loading axes. Application of the initial loads reflects in a different stress state compared to the reference configuration. This pre-stretching of the specimen cannot be measured due to the nature of experiment. Thus, measured initial force results in zero stretches during the material parameter estimation. However, these occurrences are mostly neglected. Either existing pre-stretches are disregarded or initial forces are annulled manually. Obviously, neither of the cases corresponds to real stress state.

In this work we developed the procedure to calculate mounting pre-stretches and consequently material parameters are determined more accurately. Standard optimization procedure is based on minimizing the least squares difference between experimental and model Cauchy stresses. Errors induced while calculating experimental Cauchy stresses lead to inaccurate material parameters. To avoid such errors, additional deformation gradient that represents mounted specimen in a state prior to experiment, has to be introduced. Since mounting pre-stretches are not measured, a new data fitting process is established with supplementary nested loop that will iteratively correct pre-stretches to satisfy equilibrium between initial experimental and model stresses. The procedures were first applied on the series of simulated virtual planar biaxial experiments where the exact material parameters can be set and compared to the obtained ones. Holzapfel-Gasser-Ogden strain energy function was used in virtual experiments while material parameters were based on the literature. Furthermore, data fitting procedures were applied to data gathered from biaxial experiments on aortic tissue samples. The analysis has shown significant difference between obtained material parameters, especially in cases where HGO structural parameters such as fibre family angle and in-plane dispersion are considered as fitting parameters. The rate of error increases with the amount of applied pre-stretches and also decreases with increase of maximum achieved experimental stretches. Finally, annulling initial force proved to be better approach if only standard optimization is to be applied.

The dura mater is the outermost layer of the meninges, a layered membrane that covers and protects the brain and spinal cord. It is a dense and fibrous connective tissue that is composed of collagen and elastin fibers, proteoglycans, and other extracellular matrix components [1]. The dura mater plays an important role in maintaining the stability and integrity of the brain and spinal cord, as well as in regulating the cerebrospinal fluid dynamics and protecting the neural tissue from mechanical stress and injury [2]. Despite its important role in, e.g., traumatic brain injury pathology it is frequently neglected in computational and physical human head models. Until now, the biomechanical failure tests have not yielded information about the anisotropic mechanical behavior of various locations of the human dura mater under physiological conditions. Additionally, limited data exists on the orientation of collagen fibers, which has not been thoroughly quantified.

Therefore, this study aimed to investigate the mechanical and structural anisotropy of different locations of the human dura mater and to correlate mechanical data with the quantification of the orientation of collagen fibers. To achieve this objective, sixty samples from six donors were subjected to quasi-static, uniaxial extension tests until failure in a heated tissue bath, utilizing a Z020 torsion multi-axis testing system (ZwickRoell AG, Ulm, Germany) together with an Aramis image correlation system (GOM, Braunschweig, Germany). Additionally, the collagen microstructure of samples from four donors was analyzed using second-harmonic generation imaging.

The data obtained were used to determine the failure stress and strain, E-moduli, and a microstructurally motivated material model was employed to examine local differences in both structure and mechanics. Among others, significant differences in both collagen fiber dispersion and main fiber orientation were found. The structural parameters obtained from only four out of six donors yielded good fitting results to the structurally motivated mechanical model for the remaining two donors in all directions. This study establishes a foundation for further research on the microstructure and mechanical properties of the human dura mater, enabling realistic modeling and prediction of tissue failure.

References

[1] J. T. Maikos, R. A. Elias, and D. I. Shreiber, "Mechanical properties of dura mater from the rat brain and spinal cord," J Neurotrauma, vol. 25, no. 1, pp. 38-51, Jan 2008, doi: 10.1089/neu.2007.0348.

[2] D. J. Patin, E. C. Eckstein, K. Harum, and V. S. Pallares, "Anatomic and biomechanical properties of human lumbar dura mater," Anesth Analg, vol. 76, no. 3, pp. 535-40, Mar 1993, doi: 10.1213/00000539-199303000-00014

Cardiovascular diseases are still one of the major cause of death worldwide. They are responsible for significant morbidity and therefore both noninvasive and especially invasive treatments are still being developed. Our research group is working in the field of new materials for cardiovascular surgery.

There are several procedures in the field of cardiovascular surgery which are based on the mechanical interaction of the arterial wall and the external support. A typical example is Pulmonary Artery Banding (PAB) in infant patients. PAB is a palliative procedure that reduces pulmonary over-circulation in neonates suffering from certain congenital heart diseases and constitutes the first stage of intervention prior to the complete repair of cardiac defects. The principle of PAB consists in the implantation of a band around the pulmonary artery, which results in the reduction of blood flow.

Our goal is to develop resorbable fabric based on composite material consisting of a polylactide and polycaprolactone (PLA/PCL) copolymer nanofibrous reinforcement combined with a collagen matrix for use in cardiovascular surgery as the pulmonary artery banding material. The resulting composite composed of these polymers prepared by electrospinning followed by the impregnation of the layers with collagen (type I) dispersion is then collagen-poly[L-lactide/caprolactone] (COLL-PLCL). This compound is bioresorbable and gives the advantage of PAB as a one-step procedure.

In our work, we present the results of the comparison of the mechanical properties of our COLL-PLCL material with two kinds of commercially available Gore material that can be used in pulmonary artery banding. They are the Gore Pericardial Membrane and the Gore Cardiovascular Patch, and both materials are chemically based on the form of polytetrafluoroethylene (PTFE).

The strips of all three materials underwent uniaxial tensile tests. In the case of the COLL-PLCL material, it was a monotonic tensile test, whereas the Gore materials were tested cyclically. The COLL-PLCL materials were tested in the hydrated state.

The results of our experiments show that all three materials exhibit an approximately linear mechanical response under primary loading. Cyclic loading led to so called preconditioned state, in which the Gore materials exhibited some non-linearities in their response. The preconditioned Gore-Tex materials were also considerably stiffer than those in the pristine state. Gore materials showed higher stress at failure than COLL-PLCL material whereas strain at failure was approximately the same. What is significant is that the COLL-PLCL material was much more compliant than Gore. We hypothesize that it will therefore cause a less mechanobiological response to compliance mismatch during banding.

Although the biomechanics of the circulatory system is a very dynamically developing field, the study of venous aneurysms is somewhat outside the mainstream. Although aneurysm, a bulge of the blood vessel wall, is mainly known as a disease of the arteries, it can also be encountered in veins. It occurs mainly at the site of an arterio-venous shunt, which is artificially created as a so-called vascular access for hemodialysis. Other venous aneurysms are quite rare. However, the number of patients for dialysis is increasing, so the need to study tissue biomechanics in vascular access is a current scientific problem.

The exact mechanism of arterio-venous shunt aneurysm formation, apart from the rather vague claim that it is a consequence of altered hemodynamic conditions, is still unknown. The same applies to the constitutive models and their parameters found for such affected vein walls. However, it should be emphasized that not only the change in hemodynamics due to arterialization of the vein, but also the repeated needling of the tissue during the hemodialysis procedure are involved in the formation of the arteriovenous shunt aneurysm. These lead to significant scarring of the vessel wall, which results in a change in mechanical properties compared to healthy vein. As with any scar, we should expect a significant increase in connective tissue content.

The long-term goal of our study is to experimentally identify material models for pathologically affected veins and compare them with the behavior of healthy tissue. We then intend to use the constitutive models for the arterio-venous shunt aneurysm tissue in computational fluid dynamics simulations with a deformable wall to determine the changes that occur in the hemodynamics of the aneurysm at the vascular access.

As a first step in our study, we perform tensile experiments with vein wall samples, both healthy ones and veins with a created arteriovenous shunt. We chose to model the tissue behavior as elastic after preconditioning. The constitutive model used for the vein wall is adopted from the work of Gasser Holzapfel and Ogden (2006), or we model the vein wall as an incompressible, anisotropic, hyperelastic material that exhibits significant material nonlinearity. Because aneurysmal vein wall samples are collected during surgery from living patients, it is not possible to compare them with other donor veins, as they are not naturally available. Comparisons will be made against the characteristics of veins taken to create an aorto-coronary bypass graft. The number of experimentally measured samples in both groups is not yet large enough to achieve significant population differences. Therefore, our present results should be considered as preliminary.

Tissue fibrosis, classically associated with excessive accumulation of extracellular matrix (ECM) by activated fibroblasts, can occur in several pathological conditions. Fibroblasts are mechanosensitive cells and increased stiffness of the ECM activates fibrotic pathways [1]. To mimic the three-dimensional cell microenvironment in vitro, fibroblasts are cultured in 3D spheroids. Mechanical assessment of cell spheroids is accomplished via parallel plate compression and mechanical properties in a continuum sense are determined from force vs displacement (F-δ) curves. Current analysis methods are often limited to Hertzian theory and its modifications, that only account for small deformations [2]. However, spheroids exhibit low stiffness, thus undergoing large deformations at small external forces, and therefore current contact mechanics models fail to describe such behavior [3,4]. Here, we use the Tatara model, which considers both nonlinear elasticity and large deformations to describe the mechanics of cell spheroids under parallel-plate compression.

Cell spheroids consisting of primary human fibroblasts cultured for four days were subjected to parallel-plate compression testing (MicroSquisher, CellScale) fitted with a round tungsten cantilever and accompanying SquisherJoy V5.23 software (CellScale, Ontario, Canada). The fluid bath test chamber was filled with sterile phosphate buffered saline (pH=7.4). Stage and optics were calibrated according to manufacturer’s instructions. Samples were compressed up to 50% apparent linear strain at different displacement rates. F–δ data was fitted using linear least squares regression on the Hertz and Tatara model and its extended version (custom MATLAB code) with fully constrained contact points (F =0, δ =0). Images were captured via two digital cameras during compression and static states to determine contact radius and lateral expansion of cell spheroids over a range of deformations.

The dependence of compression modulus on the displacement rate was examined. The Hertzian (and extended) theory was successfully applied to the small strain regime of F-δ curves to extract the compression modulus. In contrast to the Hertzian theory, for compressive displacements over 10-25% (depending on displacement rate), where the force follows the third and fifth power of the displacement, the Tatara numerical analysis theory better described the non-linear behavior of cell spheroids. The predicted contact radius of cell spheroids was found to be in good agreement with the data obtained from image analysis. However, the lateral expansion was underestimated by the Tatara model, a difference which may arise from the adopted constant-volume assumption.

The Hertzian theory and its modifications can be applied for strain in the range of 10%-25% while, for larger deformations (above 25% strain), the extended Tatara model better describes the deformation behavior of cell spheroids also providing their lateral expansion. While Hertzian contact theory and its modifications is applicable for small deformations, hyperelastic and nonlinear elasticity theory should be employed to better describe the data at larger deformations.

1. M. Jones et al, eLife, 7 :1-24, 2018

2. Y. Efremov et al, Scientific Reports, 7:1-14, 2017.

3. Y Tatara et al, JSME INT A-SOLID M, 36:190-196, 1993.

4. K. Liu et al, J. Phys. D, 31 :294-303, 1998

Background. Despite biomechanical factors playing a pivotal role in the onset and development of disease [1], little is known concerning the fracture behaviour of most biological tissues. Most experimental testing techniques fail to acquire data for the mechanical fracture characterisation of soft tissues. Therefore, we propose the novel symmetry-constraint Compact Tension (symconCT) test for aortic tissue fracture testing. It allows for stable crack propagation and the in-depth exploration of fracture processes. Finite Element Method (FEM) modelling was combined with Digital Image Correlation (DIC) to identify the specimen-specific constitutive properties.

Material and Methods. The classical CT test was augmented with an elastic metal beam connecting the two clamps [2]. It pre-strained the 30x35 mm² specimens and forced the fracture to develop in the middle of the specimen. Specimens with a 10 mm pre-notch were obtained from the intima-media compound of the porcine abdominal aorta. Tensile loading, either in the axial or circumferential direction, was applied orthogonal to the pre-notch at 3 mm min^-1 (ADMET eXpert 4000 Universal Testing System). 2D FEM models were developed (Abaqus 2019) for six specimens (representing mean ± standard deviation of recorded symconCT data sets), incorporating a viscoelastic Yeoh model and an isotropic bilinear cohesive zone model. Whilst the viscous properties were fixed, the two elastic Yeoh coefficients, c₁ and c₂, were calibrated against the clamp force and DIC-based Green-Lagrange strains. The cohesive strength and the fracture energy were also calibrated against the force.

Results. Given the load aligned with the main collagen fibre direction in the media, circumferentially loaded specimens reached higher forces, with a mean of 5.76 ± 0.69 N against 3.89 ± 0.57 N of the axially loaded specimens (t-test, p<0.05). Whilst circumferential loading resulted in a zig-zag crack, axial loading provoked a straight fracture. The DIC showed the maximum principal strain being orthogonal to the crack tip. The identified elastic properties were c₁ = 34.70 ± 1.52 kPa and c₂ = 98.70 ± 5.63 kPa under circumferential loading and c₁ = 14.54 ± 5.24 kPa and c₂ = 67.34 ± 6.65 kPa under axial loading. The cohesive strength resulted in 235.62 ± 24.04 kPa and 242.40±72.48 kPa, the fracture energy in 1.57 ± 0.82 kJ m² and 0.96 ± 0.34 kJ m² under circumferential and axial loading, respectively. Given the calibrated FEM models, the FEM crack extensions closely matched the experimental ones.

Conclusions. The symconCT test allowed for stable crack propagation, permitting the exploration of the fracture behaviour ahead of the crack tip. The DIC-based principal strains revealed mode-I failure dominating the fracture in both loading conditions. The FEM models accurately simulated the tissue fracture. Although inertial effects were overaccelerated (mass-scaling), good agreement with the experimental recordings was observed. Additionally, the vessel wall shows anisotropic mechanical properties [3], characteristics which could have further improved our results.

References.

[1] N. Baeyens, M. A. Schwartz, Mol. Biol. Cell, vol. 27, pp. 7-11, 2016.

[2] M. Alloisio, M. Chatziefraimidou, J. Roy, T. Gasser, Acta Biomaterialia (under review).

[3] T.C. Gasser, Vascular Biomechanics, ISBN: 978-3-030-70965-5. Springer 2021.