Growing matter: a review of growth in living systems

Living systems can grow, develop, adapt, and evolve. These phenomena are non-intuitive to traditional engineers and often difficult to understand. Yet, classical engineering tools can provide valuable insight into the mechanisms of growth in health and disease. Within the past decade, the concept of incompatible configurations has evolved as a powerful tool to model growing systems within the framework of nonlinear continuum mechanics. However, there is still a substantial disconnect between the individual disciplines, which explore the phenomenon of growth from different angles. Here we show that the nonlinear field theories of mechanics provide a unified concept to model finite growth by means of a single tensorial internal variable, the second order growth tensor. We review the literature and categorize existing growth models by means of two criteria: the microstructural appearance of growth, either isotropic or anisotropic; and the microenvironmental cues that drive the growth process, either chemical or mechanical. We demonstrate that this generic concept is applicable to a broad range of phenomena such as growing arteries, growing tumors, growing skin, growing airway walls, growing heart valve leaflets, growing skeletal muscle, growing plant stems, growing heart valve annuli, and growing cardiac muscle. The proposed approach has important biological and clinical applications in atherosclerosis, in-stent restenosis, tumor invasion, tissue expansion, chronic bronchitis, mitral regurgitation, limb lengthening, tendon tear, plant physiology, dilated and hypertrophic cardiomyopathy, and heart failure. Understanding the mechanisms of growth in these chronic conditions may open new avenues in medical device design and personalized medicine to surgically or pharmacologically manipulate development and alter, control, or revert disease progression.

Detection of bridging veins rupture and subdural haematoma onset using a finite element head model

BACKGROUND

One of the most severe traumatic brain injuries, the subdural haematoma, is related to damage and rupture of the bridging veins, generating an abnormal collection of blood between the dura mater and arachnoid mater. Current numerical models of these vessels rely on very simple geometries and material laws, limiting its accuracy and bio-fidelity.

METHODS

In this work, departing from an existing human head numerical model, a realistic geometry for the bridging veins was developed, devoting special attention to the finite elements type employed. A novel and adequate constitutive model including damage behavior was also successfully implemented.

FINDINGS

Results attest that vessel tearing onset was correctly captured, after comparison against experiments on cadavers.

INTERPRETATION

Doing so, the model allow to precisely predict the individual influence of kinematic parameters such as the pulse duration, linear and rotational accelerations in promoting vessel tearing.

Personalising left-ventricular biophysical models of the heart using parametric physics-informed neural networks

We present a parametric physics-informed neural network for the simulation of personalised left-ventricular biomechanics. The neural network is constrained to the biophysical problem in two ways: (i) the network output is restricted to a subspace built from radial basis functions capturing characteristic deformations of left ventricles and (ii) the cost function used for training is the energy potential functional specifically tailored for hyperelastic, anisotropic, nearly-incompressible active materials. The radial bases are generated from the results of a nonlinear Finite Element model coupled with an anatomical shape model derived from high-resolution cardiac images. We show that, by coupling the neural network with a simplified circulation model, we can efficiently generate computationally inexpensive estimations of cardiac mechanics. Our model is 30 times faster than the reference Finite Element model used, including training time, while yielding satisfactory average errors in the predictions of ejection fraction (-3%), peak systolic pressure (7%), stroke work (4%) and myocardial strains (14%). This physics-informed neural network is well suited to efficiently augment cardiac images with functional data and to generate large sets of synthetic cases for training deep network classifiers while it provides efficient personalization to the specific patient of interest with a high level of detail.

Equilibrated warping: Finite element image registration with finite strain equilibrium gap regularization

In this paper, we propose a novel continuum finite strain formulation of the equilibrium gap regularization for image registration. The equilibrium gap regularization essentially penalizes any deviation from the solution of a hyperelastic body in equilibrium with arbitrary loads prescribed at the boundary. It thus represents a regularization with strong mechanical basis, especially suited for cardiac image analysis. We describe the consistent linearization and discretization of the regularized image registration problem, in the framework of the finite elements method. The method is implemented using FEniCS & VTK, and distributed as a freely available python library. We show that the equilibrated warping method is effective and robust: regularization strength and image noise have minimal impact on motion tracking, especially when compared to strain-based regularization methods such as hyperelastic warping. We also show that equilibrated warping is able to extract main deformation features on both tagged and untagged cardiac magnetic resonance images.

Probabilistic Voxel-Fe model for single cell motility in 3D

BACKGROUND

Cells respond to a variety of external stimuli regulated by the environment conditions. Mechanical, chemical and biological factors are of great interest and have been deeply studied. Furthermore, mathematical and computational models have been rapidly growing over the past few years, permitting researches to run complex scenarios saving time and resources. Usually these models focus on specific features of cell migration, making them only suitable to study restricted phenomena.

METHODS

Here we present a versatile finite element (FE) cell-scale 3D migration model based on probabilities depending in turn on ECM mechanical properties, chemical, fluid and boundary conditions.

RESULTS

With this approach we are able to capture important outcomes of cell migration such as: velocities, trajectories, cell shape and aspect ratio, cell stress or ECM displacements.

CONCLUSIONS

The modular form of the model will allow us to constantly update and redefine it as advancements are made in clarifying how cellular events take place.

A biomechanical breast model evaluated with respect to MRI data collected in three different positions

BACKGROUND

Mammography is a specific type of breast imaging that uses low-dose X-rays to detect cancer in early stage. During the exam, the women breast is compressed between two plates in order to even out the breast thickness and to spread out the soft tissues. This technique improves exam quality but can be uncomfortable for the patient. The perceived discomfort can be assessed by the means of a breast biomechanical model. Alternative breast compression techniques may be computationally investigated trough finite elements simulations.

METHODS

The aim of this work is to develop and evaluate a new biomechanical Finite Element (FE) breast model. The complex breast anatomy is considered including adipose and glandular tissues, muscle, skin, suspensory ligaments and pectoral fascias. Material hyper-elasticity is modeled using the Neo-Hookean material models. The stress-free breast geometry and subject-specific constitutive models are derived using tissues deformations measurements from MR images.

FINDINGS

The breast geometry in three breast configurations were computed using the breast stress-free geometry together with the estimated set of equivalent Young's modulus (E_breast^r = 0.3 kPa, E_breast^l = 0.2 kPa, E_skin = 4 kPa, E_fascia = 120 kPa). The Hausdorff distance between estimated and measured breast geometries for prone, supine and supine tilted configurations is equal to 2.17 mm, 1.72 mm and 5.90 mm respectively.

INTERPRETATION

A subject-specific breast model allows a better characterization of breast mechanics. However, the model presents some limitations when estimating the supine tilted breast configuration. The results show clearly the difficulties to characterize soft tissues mechanics at large strain ranges with Neo-Hookean material models.

Numerical investigation of biomechanically coupled growth in cortical folding

Cortical folding-the process of forming the characteristic gyri (hills) and sulci (valleys) of the cortex-is a highly dynamic process that results from the interaction between gene expression, cellular mechanisms, and mechanical forces. Like many other cells, neurons are sensitive to their mechanical environment. Because of this, cortical growth may not happen uniformly throughout gyri and sulci after the onset of cortical folding, which is accompanied by patterns of tension and compression in the surrounding tissue. Here, as an extension of our previous work, we introduce a biomechanically coupled growth model to investigate the importance of interaction between biological growth and mechanical cues during brain development. Our earlier simulations of cortical growth consisted of a homogeneous growing cortex attached to an elastic subcortex. Here, we let the evolution of cortical growth depend on a geometrical quantity-the mean curvature of the cortex-to achieve preferential growth in either gyri or sulci. As opposed to the popular pre-patterning hypothesis, our model treats inhomogeneous cortical growth as the result of folding rather than the cause. The model is implemented numerically in a commercial finite element software Abaqus/Explicit in Abaqus reference manuals, Dassault Systemes Simulia, Providence (2019) by writing user-defined material subroutine (VUMAT). Our simulations show that gyral-sulcal thickness variations are a phenomenon particular to low stiffness ratios. In comparison with cortical thickness measurements of [Formula: see text] human brains via a consistent sampling scheme, our simulations with similar cortical and subcortical stiffnesses suggest that cortical growth is higher in gyri than in sulci.

Cortical bone mapping improves finite element strain prediction accuracy at the proximal femur

Despite evidence of the biomechanical role of cortical bone, current state of the art finite element models of the proximal femur built from clinical CT data lack a subject-specific representation of the bone cortex. Our main research hypothesis is that the subject-specific modelling of cortical bone layer from CT images, through a deconvolution procedure known as Cortical Bone Mapping (CBM, validated for cortical thickness and density estimates) can improve the accuracy of CT-based FE models of the proximal femur, currently limited by partial volume artefacts. Our secondary hypothesis is that a careful choice of cortical-specific density-elasticity relationship may improve model accuracy. We therefore: (i) implemented a procedure to include subject-specific CBM estimates of both cortical thickness and density in CT-based FE models. (ii) defined alternative models that included CBM estimates and featured a cortical-specific or an independently optimised density-elasticity relationship. (iii) tested our hypotheses in terms of elastic strain estimates and failure load and location prediction, by comparing with a published cohort of 14 femurs, where strain and strength in stance and fall loading configuration were experimentally measured, and estimated through reference FE models that did not explicitly model the cortical compartment. Our findings support the main hypothesis: an explicit modelling of the proximal femur cortical bone layer including CBM estimates of cortical bone thickness and density increased the FE strains prediction, mostly by reducing peak errors (average error reduced by 30%, maximum error and 95th percentile of error distribution halved) and especially when focusing on the femoral neck locations (all error metrics at least halved). We instead rejected the secondary hypothesis: changes in cortical density-elasticity relationship could not improve validation performances. From these improved baseline strain estimates, further work is needed to achieve accurate strength predictions, as models incorporating cortical thickness and density produced worse estimates of failure load and equivalent estimates of failure location when compared to reference models. In summary, we recommend including local estimates of cortical thickness and density in FE models to estimate bone strains in physiological conditions, and especially when designing exercise studies to promote bone strength.

On skin expansion

This article discusses skin expansion without considering cellular growth of the skin. An in vivo analysis was carried out that involved expansion at three different sites on one patient, allowing for the observation of the relaxation process. Those measurements were used to characterize the human skin of the thorax during the surgical process of skin expansion. A comparison between the in vivo results and the numerical finite elements model of the expansion was used to identify the material elastic parameters of the skin of the thorax of that patient. Delfino's constitutive equation was chosen to model the in vivo results. The skin is considered to be an isotropic, homogeneous, hyperelastic, and incompressible membrane. When the skin is extended, such as with expanders, the collagen fibers are also extended and cause stiffening in the skin, which results in increasing resistance to expansion or further stretching. We observed this phenomenon as an increase in the parameters as subsequent expansions continued. The number and shape of the skin expanders used in expansions were also studied, both mathematically and experimentally. The choice of the site where the expansion should be performed is discussed to enlighten problems that can lead to frustrated skin expansions. These results are very encouraging and provide insight into our understanding of the behavior of stretched skin by expansion. To our knowledge, this study has provided results that considerably improve our understanding of the behavior of human skin under expansion.

High-Frequency Fluctuations in Post-stenotic Patient Specific Carotid Stenosis Fluid Dynamics: A Computational Fluid Dynamics Strategy Study

Purpose

Screening of asymptomatic carotid stenoses is performed by auscultation of the carotid bruit, but the sensitivity is poor. Instead, it has been suggested to detect carotid bruit as neck’s skin vibrations. We here take a first step towards a computational fluid dynamics proof-of-concept study, and investigate the robustness of our numerical approach for capturing high-frequent fluctuations in the post-stenotic flow. The aim was to find an ideal solution strategy from a pragmatic point of view, balancing accuracy with computational cost comparing an under-resolved direct numerical simulation (DNS) approach vs. three common large eddy simulation (LES) models (static/dynamic Smagorinsky and Sigma).

Method

We found a reference solution by performing a spatial and temporal refinement study of a stenosed carotid bifurcation with constant flow rate. The reference solution \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\Delta x = 1.92 \times 10^{ - 4} \;{\text{m}},\; \Delta t = 5 \times 10^{ - 5} \;{\text{s}}} \right)$$\end{document}Δx=1.92×10-4m,Δt=5×10-5s was compared against LES for both a constant and pulsatile flow.

Results

Only the Sigma and Dynamic Smagorinsky models were able to replicate the flow field of the reference solution for a pulsatile simulation, however the computational cost of the Sigma model was lower. However, none of the sub-grid scale models were able to replicate the high-frequent flow in the peak-systolic constant flow rate simulations, which had a higher mean Reynolds number.

Conclusions

The Sigma model was the best combination between accuracy and cost for simulating the pulsatile post-stenotic flow field, whereas for the constant flow rate, the under-resolved DNS approach was better. These results can be used as a reference for future studies investigating high-frequent flow features.

Modelling actin polymerization: the effect on confined cell migration

The aim of this work is to model cell motility under conditions of mechanical confinement. This cell migration mode may occur in extravasation of tumour and neutrophil-like cells. Cell migration is the result of the complex action of different forces exerted by the interplay between myosin contractility forces and actin processes. Here, we propose and implement a finite element model of the confined migration of a single cell. In this model, we consider the effects of actin and myosin in cell motility. Both filament and globular actin are modelled. We model the cell considering cytoplasm and nucleus with different mechanical properties. The migration speed in the simulation is around 0.1 μm/min, which is in agreement with existing literature. From our simulation, we observe that the nucleus size has an important role in cell migration inside the channel. In the simulation the cell moves further when the nucleus is smaller. However, this speed is less sensitive to nucleus stiffness. The results show that the cell displacement is lower when the nucleus is stiffer. The degree of adhesion between the channel walls and the cell is also very important in confined migration. We observe an increment of cell velocity when the friction coefficient is higher.

Bioengineering Approaches for Placental Research

Research into the human placenta's complex functioning is complicated by a lack of suitable physiological in vivo models. Two complementary approaches have emerged recently to address these gaps in understanding, computational in silico techniques, including multi-scale modeling of placental blood flow and oxygen transport, and cellular in vitro approaches, including organoids, tissue engineering, and organ-on-a-chip models. Following a brief introduction to the placenta's structure and function and its influence on the substantial clinical problem of preterm birth, these different bioengineering approaches are reviewed. The cellular techniques allow for investigation of early first-trimester implantation and placental development, including critical biological processes such as trophoblast invasion and trophoblast fusion, that are otherwise very difficult to study. Similarly, computational models of the placenta and the pregnant pelvis at later-term gestation allow for investigations relevant to complications that occur when the placenta has fully developed. To fully understand clinical conditions associated with the placenta, including those with roots in early processes but that only manifest clinically at full-term, a holistic approach to the study of this fascinating, temporary but critical organ is required.

Multiscale modelling of palisade formation in gliobastoma multiforme

Palisades are characteristic tissue aberrations that arise in glioblastomas. Observation of palisades is considered as a clinical indicator of the transition from a noninvasive to an invasive tumour. In this paper we propose a computational model to study the influence of the hypoxic switch in palisade formation. For this we produced three-dimensional realistic simulations, based on a multiscale hybrid model, coupling the evolution of tumour cells and the oxygen diffusion in tissue, that depict the shape of palisades during its formation. Our results can be summarized as follows: (1) the presented simulations can provide clinicians and biologists with a better understanding of three-dimensional structure of palisades as well as of glioblastomas growth dynamics; (2) we show that heterogeneity in cell response to hypoxia is a relevant factor in palisade and pseudopalisade formation; (3) we show how selective processes based on the hypoxia switch influence the tumour proliferation.

Computational and experimental study of the mechanics of embryonic wound healing

Wounds in the embryo show a remarkable ability to heal quickly without leaving a scar. Previous studies have found that an actomyosin ring (purse string) forms around the wound perimeter and contracts to close the wound over the course of several dozens of minutes. Here, we report experiments that reveal an even faster mechanism which remarkably closes wounds by more than 50% within the first 30s. Circular and elliptical wounds (~100μm in size) were made in the blastoderm of early chick embryos and allowed to heal, with wound area and shape characterized as functions of time. The closure rate displayed a biphasic behavior, with rapid constriction lasting about a minute, followed by a period of more gradual closure to complete healing. Fluorescent staining suggests that both healing phases are driven by actomyosin contraction, with relatively rapid contraction of fibers at cell borders within a relatively thick ring of tissue (several cells wide) around the wound followed by slower contraction of a thin supracellular actomyosin ring along the margin, consistent with a purse string mechanism. Finite-element modeling showed that this idea is biophysically plausible, with relatively isotropic contraction within the thick ring giving way to tangential contraction in the thin ring. In addition, consistent with experimental results, simulated elliptical wounds heal with little change in aspect ratio, and decreased membrane tension can cause these wounds to open briefly before going on to heal. These results provide new insight into the healing mechanism in embryonic epithelia.

A mechano-chemo-biological model for bone remodeling with a new mechano-chemo-transduction approach

Bone remodeling is a fundamental biological process that develops in bone tissue along its whole lifetime. It refers to a continuous bone transformation with new bone formation and old bone resorption that changes the internal microstructure and composition of the tissue. The main objectives of bone remodeling are: repair of the internal microcracks; adaptation of the macroscopic stiffness and strength to the actual changing mechanical demands; and control of the calcium homeostasis. Understanding this process and predicting its evolution is critical to reduce the effects of long-term disuse as happens during periods of reduced mobility. It is also important in the design of bone implants to avoid long-term stress shielding. Many mathematical models have been proposed from the earliest purely phenomenological to the latest that include biological knowledge. However, there still exists a lack of connection between the mechanical driving force and the biochemical and cell processes it triggers. Here, and following previous works that model independently the mechanobiological and biochemical processes in bone remodeling, we present a more complete model, useful for both cortical and trabecular bone, that uses a new mechanotransduction approach based on the effect of strains onto the bonding-unbonding rate of RANK/RANKL/OPG receptor-ligand reactions. We compare the results of this model with previous ones, showing a good agreement in similar conditions. We also apply it to realistic situations such as a femoral bone after implantation of a hip prosthesis, getting similar results to the clinical ones in the final bone density distribution. Finally, we extend this approach to the anisotropic case, getting not only the mean density, but also the directional homogenization of the microstructure. This biochemical approach permits, not only to predict the bone evolution under changes in the mechanical loads, but also, to consider anabolic and catabolic drugs to control bone density, such as those used in osteoporosis.

Growth of the flat bones of the membranous neurocranium: a computational model

This article assumes two stages in the formation of the bones in the calvaria, the first one takes into account the formation of the primary centers of ossification. This step counts on the differentiation from mesenchymal cells into osteoblasts. A molecular mechanism is used based on a system of reaction-diffusion between two antagonistic molecules, which are BMP2 and Noggin. To this effect we used equations whose behavior allows finding Turing patterns that determine the location of the primary centers. In the second step of the model we used a molecule that is expressed by osteoblasts, called Dxl5 and that is expressed from the osteoblasts of each flat bone. This molecule allows bone growth through its borders through cell differentiation adjacent to each bone of the skull. The model has been implemented numerically using the finite element method. The results allow us to observe a good approximation of the formation of flat bones of the membranous skull as well as the formation of fontanelles and sutures.

A patient-specific model of total knee arthroplasty to estimate patellar strain: A case study

BACKGROUND

Inappropriate patellar cut during total knee arthroplasty can lead to patellar complications due to increased bone strain. In this study, we evaluated patellar bone strain of a patient who had a deeper patellar cut than the recommended.

METHODS

A patient-specific model based on patient preoperative data was created. The model was decoupled into two levels: knee and patella. The knee model predicted kinematics and forces on the patella during squat movement. The patella model used these values to predict bone strain after total knee arthroplasty. Mechanical properties of the patellar bone were identified with micro-finite element modeling testing of cadaveric samples. The model was validated with a robotic knee simulator and postoperative X-rays. For this patient, we compared the deeper patellar cut depth to the recommended one, and evaluated patellar bone volume with octahedral shear strain above 1%.

FINDINGS

Model predictions were consistent with experimental measurements of the robotic knee simulator and postoperative X-rays. Compared to the recommended cut, the deeper cut increased the critical strain bone volume, but by less than 3% of total patellar volume.

INTERPRETATION

We thus conclude that the predicted increase in patellar strain should be within an acceptable range, since this patient had no complaints 8 months after surgery. This validated patient-specific model will later be used to address other questions on groups of patients, to eventually improve surgical planning and outcome of total knee arthroplasty.

Diffusion MRI simulation of realistic neurons with SpinDoctor and the Neuron Module

The diffusion MRI signal arising from neurons can be numerically simulated by solving the Bloch-Torrey partial differential equation. In this paper we present the Neuron Module that we implemented within the Matlab-based diffusion MRI simulation toolbox SpinDoctor. SpinDoctor uses finite element discretization and adaptive time integration to solve the Bloch-Torrey partial differential equation for general diffusion-encoding sequences, at multiple b-values and in multiple diffusion directions. In order to facilitate the diffusion MRI simulation of realistic neurons by the research community, we constructed finite element meshes for a group of 36 pyramidal neurons and a group of 29 spindle neurons whose morphological descriptions were found in the publicly available neuron repository NeuroMorpho.Org. These finite elements meshes range from having 15,163 nodes to 622,553 nodes. We also broke the neurons into the soma and dendrite branches and created finite elements meshes for these cell components. Through the Neuron Module, these neuron and cell components finite element meshes can be seamlessly coupled with the functionalities of SpinDoctor to provide the diffusion MRI signal attributable to spins inside neurons. We make these meshes and the source code of the Neuron Module available to the public as an open-source package. To illustrate some potential uses of the Neuron Module, we show numerical examples of the simulated diffusion MRI signals in multiple diffusion directions from whole neurons as well as from the soma and dendrite branches, and include a comparison of the high b-value behavior between dendrite branches and whole neurons. In addition, we demonstrate that the neuron meshes can be used to perform Monte-Carlo diffusion MRI simulations as well. We show that at equivalent accuracy, if only one gradient direction needs to be simulated, SpinDoctor is faster than a GPU implementation of Monte-Carlo, but if many gradient directions need to be simulated, there is a break-even point when the GPU implementation of Monte-Carlo becomes faster than SpinDoctor. Furthermore, we numerically compute the eigenfunctions and the eigenvalues of the Bloch-Torrey and the Laplace operators on the neuron geometries using a finite elements discretization, in order to give guidance in the choice of the space and time discretization parameters for both finite elements and Monte-Carlo approaches. Finally, we perform a statistical study on the set of 65 neurons to test some candidate biomakers that can potentially indicate the soma size. This preliminary study exemplifies the possible research that can be conducted using the Neuron Module.

A computational model for understanding the micro-mechanics of collagen fiber network in the tunica adventitia

Abdominal aortic aneurysm is a prevalent cardiovascular disease with high mortality rates. The mechanical response of the arterial wall relies on the organizational and structural behavior of its microstructural components, and thus, a detailed understanding of the microscopic mechanical response of the arterial wall layers at loads ranging up to rupture is necessary to improve diagnostic techniques and possibly treatments. Following the common notion that adventitia is the ultimate barrier at loads close to rupture, in the present study, a finite element model of adventitial collagen network was developed to study the mechanical state at the fiber level under uniaxial loading. Image stacks of the rabbit carotid adventitial tissue at rest and under uniaxial tension obtained using multi-photon microscopy were used in this study, as well as the force-displacement curves obtained from previously published experiments. Morphological parameters like fiber orientation distribution, waviness, and volume fraction were extracted for one sample from the confocal image stacks. An inverse random sampling approach combined with a random walk algorithm was employed to reconstruct the collagen network for numerical simulation. The model was then verified using experimental stress-stretch curves. The model shows the remarkable capacity of collagen fibers to uncrimp and reorient in the loading direction. These results further show that at high stretches, collagen network behaves in a highly non-affine manner, which was quantified for each sample. A comprehensive parameter study to understand the relationship between structural parameters and their influence on mechanical behavior is presented. Through this study, the model was used to conclude important structure-function relationships that control the mechanical response. Our results also show that at loads close to rupture, the probability of failure occurring at the fiber level is up to 2%. Uncertainties in usually employed rupture risk indicators and the stochastic nature of the event of rupture combined with limited knowledge on the microscopic determinants motivate the development of such an analysis. Moreover, this study will advance the study of coupling microscopic mechanisms to rupture of the artery as a whole.

A 3D fluid-solid interaction model of the air puff test in the human cornea

We present a numerical model of a contactless test commonly used to assess the biomechanics of the human cornea. The test, consisting in a rapid air jet applied to the anterior surface of the cornea, is controversial. Although the numerous studies documented in the literature have not been able yet to clarify its relevance as a diagnostic tool, the test has the potential to be combined with inverse analysis procedures to characterize the parameters of numerical models of the cornea. With the final goal of employing the air puff test in advanced material identification algorithms, here we propose to model the cornea with standard finite elements and the fluids filling the anterior chamber of the eye with a meshfree discretization. The interaction between moving fluids and deforming cornea is accounted for by modifying the interface boundary conditions of both fluid and solid. The proposed model represents the first fully 3D example of an aqueous-cornea fluid-solid interaction analysis which uses a robust meshfree approach for the fluid. Although we restrict our scope to isotropic nonlinear materials, numerical results confirm the undeniable importance of including internal fluids in the simulation of the air puff test. Thus the proposed approach stands as a procedural paradigm for the identification of the mechanical parameters of the human cornea.

Finite Element Models of Osteocytes and Their Load-Induced Activation

PURPOSE OF REVIEW

Osteocytes are the conductors of bone adaptation and remodelling. Buried inside the calcified matrix, they sense mechanical cues and signal osteoclasts in case of low activity, and osteoblasts when stresses are high. How do osteocytes detect mechanical stress? What physical signal do they perceive? Finite element analysis is a useful tool to address these questions as it allows calculating stresses, strains and fluid flow where they cannot be measured. The purpose of this review is to evaluate the capabilities and challenges of finite element models of bone, in particular the osteocytes and load-induced activation mechanisms.

RECENT FINDINGS

High-resolution imaging and increased computational power allow ever more detailed modelling of osteocytes, either in isolation or embedded within the mineralised matrix. Over the years, homogeneous models of bone and osteocytes got replaced by heterogeneous and microstructural models, including, e.g. the lacuno-canalicular network and the cytoskeleton. The lacuno-canalicular network induces strain amplifications and the osteocyte protrusions seem to be stimulated much more than the cell body, both by strain and fluid flow. More realistic cell geometries, like minute constrictions of the canaliculi, increase this effect. Microstructural osteocyte models describe the transduction of external stimuli to the nucleus. Supracellular multiscale models (e.g. of a tunnelling osteon) allow to study differential loading of osteocytes and to distinguish between strain and fluid flow as the pivotal stimulatory cue. In the future, the finite element models may be enhanced by including chemical transport and intercellular communication between osteocytes, osteoclasts and osteoblasts.

Influence of an auxiliary facet system on intervertebral discs and adjacent facet joints

BACKGROUND CONTEXT

Facet supplementation stabilizes after facetectomy and undercutting laminectomy. It is indicated in degenerative spondylolisthesis with moderate disc degeneration and dynamic stenosis.

PURPOSE

To determine the influence of an auxiliary facet system (AFS) on the instrumented disc, adjacent levels' discs, and facet joints and to compare it with fusion.

STUDY DESIGN

Finite element study.

METHODS

L3-L4, L4-L5, and L5-S1 were studied using a validated finite element model with prescribed displacements for an intact spine, lesion by facetectomy and undercutting laminectomy, AFS, and fusion at L4-L5. The distribution of segmental range of motion (ROM) and applied moments, von Mises stress at the annulus, and facet joint contact forces were calculated with rotations in all planes. Institutional support for implant evaluation and modeling was received by Clariance.

RESULTS

In flexion-extension and lateral bending, fusion decreased L4-L5 ROM and increased adjacent levels' ROM. Range of motion was similarly distributed with intact lesion and AFS. In axial rotation, L4-L5 ROM represented 33% with intact, 55% after lesion, 25% with AFS, and 21% with fusion. Fusion increased annulus stress at adjacent levels in flexion-extension and lateral bending, but decreased stress at L4-L5 compared with AFS. In axial rotation, von Mises stress was similar with fusion and AFS. Facet loading increased in extension and lateral bending with fusion. It was comparable for fusion and AFS in axial rotation.

CONCLUSIONS

This study suggests that the AFS stabilizes L4-L5 in axial rotation after facetectomy and undercutting laminectomy as fusion does. This is because of the cross-link that generates an increased annulus stress in axial rotation at adjacent levels. With imposed displacements, without in vivo compensation of the hips, the solicitation at adjacent levels' discs and facet joints is higher with fusion compared with AFS. Fusion decreases intradiscal stress at the instrumented level.

FE Analyses of Hyperelastic Solids under Large Bending: The Role of the Searle Parameter and Eulerian Slenderness

A theoretical model concerning the finite bending of a prismatic hyperelastic solid has been recently proposed. Such a model provides the 3D kinematics and the stress field, taking into account the anticlastic effects arising in the transverse cross sections also. That model has been used later to extend the Elastica in the framework of finite elasticity. In the present work, Finite Element (FE) analyses of some basic structural systems subjected to finite bending have been carried out and the results have been compared with those provided by the theoretical model performed previously. In the theoretical formulation, the governing equation is the nonlinear local relationship between the bending moment and the curvature of the longitudinal axis of the bent beam. Such a relation has been provided in dimensionless form as a function of the Mooney-Rivlin constitutive constants and two kinematic dimensionless parameters termed Eulerian slenderness and compactness index of the cross section. Such parameters take relevance as they are involved in the well-known Searle parameter for bent solids. Two significant study cases have been investigated in detail. The results point out that the theoretical model leads to reliable results provided that the Eulerian slenderness and the compactness index of the cross sections do not exceed fixed threshold values.

Detailed simulation of viral propagation in the built environment

A summary is given of the mechanical characteristics of virus contaminants and the transmission via droplets and aerosols. The ordinary and partial differential equations describing the physics of these processes with high fidelity are presented, as well as appropriate numerical schemes to solve them. Several examples taken from recent evaluations of the built environment are shown, as well as the optimal placement of sensors.

Comparative analysis of the biomechanical behavior of anterograde/retrograde nailing in supracondylar femoral fractures

Supracondylar femoral fractures account for a noticeable percentage of the femoral shaft fractures, affecting two etiological groups: high energy trauma in young men, with good bone quality, and older women with osteoporotic femur. Surgical treatment of those kind of fractures remains controversial, with different surgical options such as plate and sliding barrel locking condylar plate, less invasive stabilization system (LISS) or intramedullary nailing, which has emerged as a new fixation choice in the treatment of that type of fractures. The present work performs a comparative study about the biomechanical behavior of anterograde and retrograde nailing in supracondylar femoral fractures type A, in order to determine the best choice of nailing and locking configuration. A three-dimensional finite element model of the femur was developed, modeling femoral supracondylar fracture and different nailing configurations, both for anterograde and retrograde nails. The study was focused on the immediately post-operative stage, verifying the appropriate stability of the osteosynthesis. The obtained results show a better biomechanical behavior for anterograde nails, providing a better stability from the point of view of global movements, lower stresses in screws, and less stress concentration in cortical bone. So, for the analyzed fractures and osteosyntheses types, anterograde nailing has demonstrated to be a better surgical option, being an excellent indication in supracondylar fractures of femur, with clear benefits compared to retrograde nailing, providing a better stabilization which enables for a more satisfactory fracture healing.