Introduction: Quantifying the effect of a new drug in the presence of natural variability between individuals is a major challenge of drug development. For bone diseases, where mechanics is an important outcome, one approach is to apply a non-intrusive uncertainty quantification method such as Monte Carlo on finite element (FE) models of bones, but with the drawback that a large number of simulations are usually necessary [1]. In this study, a stochastic FE (sFE) solver was developed that uses an intrusive method to predict the variation in bone mechanics given the variability in bone tissue elastic properties.

Method: The sFE solver is developed based on ParOSol, an open-source matrix-free FE solver specialized in bone mechanics. ParOSol solves the system of equations without storing the calculated matrix, resulting in a minimum memory footprint. Developing the sFE solver necessitates significant development in different modules from pre-processing to post-processing using C++ and Python programming languages. The core of the sFE solver is written by C++ codes, and Python is used to facilitate pre-processing and post-processing steps and to carry out the stochastic analysis. Here, the polynomial chaos expansions (PCE) method is implemented to quantify the uncertainty of bone mechanics efficiently, and the stiffness matrix is calculated using Hermite polynomials [2]. The new system of equations is numerically solved using Jacobi’s smoother and preconditioned conjugate gradients method. In this study, multigrid and parallelization features are disabled. Young’s modulus and von Mises stress are considered uncertain input and output variables, respectively. Propagated uncertainty through von Mises stress is quantified using statistical analysis of PCE coefficients. The implementation was used to analyse a column with a square cross-section considered a simplified bone to evaluate the correctness of the implementation process. The column meshes using hexahedral elements with 3 elements in width and 10 elements in height. Here, Young’s modulus is homogeneous and normally distributed with mean value and coefficient of variation equal to 1000 MPa and 10%, respectively. Young’s modulus is estimated using a linear combination of two orders of Hermite polynomials. Poisson’s ratio is deterministic and homogeneous equal to 0.3. The bottom face of the column is fixed in the height direction, and the upper face is under displacement-controlled compression (10% of height). Also, rigid body motions are fixed.

Results: Since Young’s modulus is homogeneous and has identical variability through all the elements, it is expected that all stress components will vary identically (i.e. normally distributed with a 10% coefficient of variation). The propagated uncertainty through the predicted von Mises stress is quantified and found to be less than 0.1% different from the analytical result (with respect to mean and variance).

Conclusion: The present evaluation provides an initial demonstration of the correctness of sFE implementation.

Acknowledgements: This study was funded by the EPSRC New Investigator Award (Grant Reference Numbers: EP/V050346/1).

Reference:

[1] La Mattina AA. et al. Ann Biomed Eng 2023; 51:117-124.

[2] Xiu D, Princeton, NJ, USA:Princeton Univ. Press, (2010).

Our research presents a multidisciplinary bio-optical-mechanical approach for describing the three-dimensional (3D) motion of healthy and pathological sperm cells during a free swim in the human female reproductive system. Our novel method is based on a multidisciplinary mechanical-numerical-modeling and experimental-optical approach that combines prior knowledge of the sperm cell's internal structure, and a description of its flagellar beating patterns.

The interaction of human sperm cells with the female reproductive system significantly impacts fertilization. On average, a few dozen to hundreds of sperm cells reach the fertilization site, where only a single sperm cell fertilizes an oocyte. This may be one of the strictest selection processes created by evolution, but its design and role are not fully understood. The prospective correlation between sperm morphology, motility, and uterine interaction should affect the diagnosis and prognosis of male fertility, especially in pathological cases of abnormal sperm morphology and motility. In addition, such analysis may help obtain a more informed sperm selection for in vitro fertilization (IVF), where a male sperm cell fertilizes a female oocyte in a dish. Because the physiological mechanisms of the natural selection of sperm cells in the female body are bypassed in IVF, it is not possible to predict which individual sperm cell would be the one that is most likely to fertilize the oocyte naturally and result in a healthy child, especially in pathological cases. Moreover, the relationship between morphology, motility, cell–surface interaction, and fertilization potential is still not completely clear. Understanding sperm 3D motility while swimming inside the female reproductive tract may lead to improved sperm cell classification and sperm selection for IVF.

We developed a dynamic 3D mechanical finite-element numerical model of sperm cell swimming inside the human female reproductive system and scored the pathological cells according to their chances of reaching the oocyte site. The sperm-cell models, including the full 3D sperm geometry, were preliminary constructed based on experimentally acquired dynamic 3D refractive index profiles of sperm cells swimming freely in vitro as imaged by high-resolution optical diffraction tomography, and then further developed. We numerically stimulated hundreds of cells swimming in a dish and in the female body, with normal and abnormal morphology. We verified that the number of normal sperm cells that succeeded in reaching the fallopian tube sites is greater than the number of abnormal sperm cells. Hence, besides the cell morphology influence, swimming under the female body’s environmental conditions significantly affects the behavior of sperm cells, especially abnormal sperm cells. Moreover, both cell 3D morphology and motility in the complicated geometry of the uterus are significant factors for filtering pathological sperm cells until they reach the oocyte site. Our method may lead to changes in sperm cell classification and evaluation and to new biophysical analysis tools to fill in the gaps from previous studies. Specifically, understanding the migration of normal and pathological human sperm cells inside the female reproductive system can improve the strategies of human sperm cell selection in IVF and fertility evaluation.

Connective tissue is one of the basic tissue types of the body. One of these connective tissues is fascia which is surrounding and interpenetrating skeletal muscle, joints, organs, nerves, and vascular beds. It serves several important functions including transmission of mechanical forces between muscles, tendons, ligaments and bones, protection of organs forming a barrier, regulation of mechanical stress by adsorbing, storing and releasing kinetic energy.

Concerning the mechanical behavior, fascia, is an incompressible, hyperelastic, non-linear and anisotropic material. Anisotropic behavior is given by the spatial orientation of the collagen fibers, which changes along the sheet to ensure a properly response to mechanical demands. As soft tissue, fascia also exhibits viscoelastic properties.

Today, computational simulation is a very powerful tool for the study and analysis of pathologies, treatments and surgeries. To do it correctly, it is necessary an exhaustive characterization and the use of an adequate constitutive model with the ability to predict the behavior of tissues, such as fascia. The present work aims to investigate in depth the mechanical behavior of deep fascia by means of a multidimensional characterization which includes uniaxial (UT), biaxial (BxT) and planar tension (PT) tests. Besides, a constitutive model is proposed to fit tests and obtain material parameters.

Tests were carried out with fascia from sheep. Different shapes were used for testing: dog bone for UT with a central region of interest of 25x5 mm (5:1 aspect ratio), being 25 mm the distance between clamps, rectangular for PT 35x15 mm (width x large), and cruciform shape for BxT with a central region of interest of 15x15 mm. Two directions were defined based on punch orientation with respect to the fibers: longitudinal which has the sample’s axial direction parallel to fibers, and transverse, which has it perpendicular. Testing protocols were defined based on literature and on our own previous tests. For UT and PT three strain levels (2,5%, 5% y 7,5%) are considered performing five cycles in each of them with a strain rate of 10%/min, for BxT case, a 10% strain level is defined undergoing the sample to five cycles and five ratios of one direction to the other, strain rate of 20%/min. Strain measurements and displacements were obtained using GOM Correlate, a digital image correlation software.

To obtain the material parameters by test fitting, a coupled and uncoupled exponential type energy function (SEF) are proposed that consider two perpendicular fiber directions following Stecco 2009.

Results show stress values like to those found in literature that used animal model for testing. For UT, in longitudinal direction, mean stress value was 3,96 MPa, and in transverse 0,6; PT shows for longitudinal and transverse 0,43 and 0,11 MPa respectively; finally, for BxT in case of 1:1 ratio, mean stresses were 3,16 and 1,2 MPa longitudinal to the transverse.

The fitting results show that an uncoupled exponential type function is be able to fit the UT or the equibiaxial experimental data, however fails to predict using the fitting parameters other experiments. On the contrary, the coupled exponential SEF shows good results during the fitting and prediction processes.

Introduction: Microdamage accumulated by cyclic loading or single overloading events contributes to bone fragility through a reduction in stiffness and strength [1]. QCT-based computational modelling cannot incorporate existing in vivo microdamage due to limited resolution. MR imaging on the other hand, is sensitive to pathophysiological changes to adjacent bone marrow that is ‘hidden’ to clinical CT imaging. In the case of repetitive trauma, signal hyperintensity in fluid sensitive sequences is indicative of a stress response where edema, haemorrhage and hyperaemia are present alongside microdamage [2]. Here, we aim to quantify this signal hyperintensity and use it to derive a pre-existing damage variable that represents the underlying tissue damage prior to overloading. We incorporate this variable into a constitutive model to investigate its influence on material and whole bone stiffness and strength.

Materials and Methods: We use the equine athlete as a model for microdamage induced stress fracture where high-speed exercise induces subchondral microdamage. Distal metacarpals (MC3) from n=5 Thoroughbred racehorses were scanned by clinical QCT (0.3 mm voxel size), calibrated to bone mineral density (BMD) and converted to bone volume fraction (BV/TV). MR images (T1w, STIR) were acquired at 3T (0.3 mm voxel size) and registered to the QCT data. Regions of ‘dense’ or ‘sclerotic’ subchondral bone, where microdamage coalesces [3], were segmented from T1w images. Patch-based similarity [4] was used to generate pseudoCT (pCT) images from STIR images. A relative increase in STIR intensity in the dense subchondral bone returned a lower pCT-derived BMD than QCT. This reflects the presence of underlying porosities such as microdamage and increased vasculature [2]. We derived a pre-existing damage variable (D^pex) which affects stiffness and strength and incorporated it into an isotropic, asymmetric BV/TV-dependent elasto-viscoplastic material model (UMAT, Abaqus v6.16) [5,6,7]. Voxel based FEA was used to compress MC3 condyles in silico before (D^pex=0) and after the inclusion of accumulated ‘hidden’ porosity (D^pex>0) to investigate its influence on whole bone mechanical properties.

Results: pCT BMD in dense subchondral bone was lower in all MC3 bones. Incorporating resulted in a median reduction of material stiffness and strength of 20.3% and 20.9% in tension and compression. Inclusion of D^pex reduced whole bone stiffness and strength, and their reduction correlated with D^pex (R²=0.74, R²=0.89). Previous experimental results support our interpretation [8,9].

Discussion: We propose a methodology for incorporating MRI signal hyperintensity into QCT-based FE models to include pre-existing porosities that cannot be detected by clinical CT. Our results illustrate the value of multimodal imaging to potentially capture existing microdamage in vivo. As we use clinical imaging techniques, our results may also aid research in diseases such as osteoarthritis and bone cancer.

References: [1] Seref-Ferlengez, BoneKEy Rep., 4:1, 2015; [2] Taljanovic, Skeletal Radiol., 37:423, 2008; [3] Muir, Bone., 38:342, 2006; [4] Andreasen Med. Phys., 42:1596, 2015; [5] Schwiedrzik & Zysset. BMMB, 12:201, 2013; [6] Schwiedrzik BMMB, 12:1155, 2013; [7] Mirzaali JMBBM, 49:355, 2015. [8] Schwiedrzik Nature Materials 13:740, 2014; [9] Mirzaali Bone 93:196, 2016

Acknowledgements: HBLB VET/CS/027, Siemens Project IPA 42, Leverhulme Trust RPG-2020-215, EPSRC EP/P005756/1.

Neuromusculoskeletal computational models are useful for biomechanical simulations, allowing the analysis of human movement, development of protocols for rehabilitation, physical exercises and training, as well as the development of assistive devices, such as orthoses and prostheses. One of the several types of movements that can be simulated using neuromusculoskeletal models is the sit-to-stand, which is frequently requested during the performance of various activities of daily life of any individual. Despite the importance of simulating such a movement, whether for understanding its execution, analyzing ergonomic aspects, developing assistive devices or identifying possible causes of injury, there is a lack of neuromusculoskeletal computational models dedicated to this type of simulation and that can represent well the biomechanics of a bipedal individual. The OpenSim, an open-source and freely available environment for modeling, simulation and analyzing of the human movement, provides a neuromusculoskeletal model dedicated to squat-to-stand, but such model is not bipedal, which requires the simplification that the individual simulated performs the movement with complete homogeneity in both legs, which does not always happen, especially in cases of hemiparesis, a condition of muscle weakness on only one side of the body due to neuromotor disease (e.g. stroke). Thus, the objective of this work was to develop a bipedal neuromusculoskeletal model capable of representing the human biomechanics of the lower limbs and dedicated to sit-to-stand or squat-to-stand movement simulations. For the development of such a model, we started from the already validated and well accepted model gait10dof18musc freely available by OpenSim. Such model contains 10 degrees of freedom, being able to move in the sagittal plane, and 18 muscles responsible for the execution of the movements. However, such a model is not dedicated to the sit-to-stand movement, being initially designed only for gait. To obtain the model dedicated to the sit-to-stand movement proposed in this work, Hunt-Crossley contact force elements were added between the foot and the ground and kinematic and dynamic constraints were elaborated. In order to test the model obtained for the proposed movement, a predictive simulation was conducted, with the model starting in a sitting position, performing the sit-to-stand and standing stably. Joint movements (hips, knees and ankles) and muscle activations were analyzed. It was verified that the proposed model can perform the sit-to-stand movement well, in a stable way, generating coherent kinematic and dynamic results. The main limitation of the model is related to the foot-to-ground contact, which does not always have enough static for a stable movement, a point that will be improved in later works. In the future, it is intended to improve the model, adding contact force between the hamstrings and a platform capable of representing a seat, improving the foot-to-ground contact ratio and testing it under conditions of hemiparesis.