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$\bf{Purpose}$: To assess whether Growth & Remodeling (G&R) theory could explain staphyloma formation from a local scleral weakening. $\bf{Methods}$: A finite element model of a healthy eye was reconstructed, including the following connective tissues: the lamina cribrosa, the peripapillary sclera, and the peripheral sclera. The scleral shell was modelled as a constrained mixture, consisting of an isotropic ground matrix and two collagen fiber families (circumferential and meridional). The homogenized constrained mixture model was employed to simulate the adaptation of the sclera to alterations in its biomechanical environment over a duration of 13.7 years. G&R processes were triggered by reducing the shear stiffness of the ground matrix in the peripapillary sclera and lamina cribrosa by 85%. Three distinct G&R scenarios were investigated: (1) low mass turnover rate in combination with transmural volumetric growth; (2) high mass turnover rate in combination with transmural volumetric growth; and (3) high mass turnover rate in combination with mass density growth. $\bf{Results}$: In scenario 1, we observed a significant outpouching of the posterior pole, closely resembling the shape of a Type-III staphyloma. Additionally, we found a notable change in scleral curvature and a thinning of the peripapillary sclera by 84%. In contrast, scenarios 2 and 3 exhibited less drastic deformations, with stable posterior staphylomas after approximately 7 years. $\bf{Conclusions}$: Our framework suggests that local scleral weakening is sufficient to trigger staphyloma formation under normal intraocular pressure. With patient-specific scleral geometries (obtainable via wide-field optical coherence tomography), our framework could aid in identifying individuals at risk of developing posterior staphylomas.

OBJECTIVE: Assessing the biomechanical behaviour of the aortic wall in vivo can potentially improve the diagnosis and prognosis of patients with abdominal aortic aneurysms (AAA). With ultrasound, AAA wall stiffness can be estimated as the diameter change in response to blood pressure. However, this measurement has shown limited reproducibility, possibly influenced by the unknown effects of the highly variable ultrasound probe pressure. This study addressed this gap by analyzing time-resolved ultrasound sequences from AAA patients.METHOD: Two-dimensional ultrasound sequences were acquired from AAA patients, alternatively applying light and firm probe pressure. Diameter variations and stiffness were evaluated and compared. An in silico simulation was performed to support the in vivo observations.RESULTS: It was found that half of the AAAs were particularly responsive to the probe pressure: in these patients, the cyclic diameter variation between diastole and systole changed from 1% at light probe pressure to 5% at firm probe pressure and the estimated stiffness decreases by a factor of 6.3. Conversely, the other half of the patients were less responsive: diameter variations increased marginally and stiffness decreased by a factor of 1.5 when transitioning from light to firm probe pressure. Through numerical simulations, we were able to show that the rather counter-intuitive stiffness decrease observed in the responsive cohort is actually consistent with a biomechanical model.CONCLUSION: We conclude that probe pressure has an important effect on the estimation of AAA wall stiffness. Ultimately, our findings suggest potential implications for AAA mechanical characterization via ultrasound imaging.

Background and Objectives: The mechanics of the nucleus depends on cellular structures and architecture, and impact a number of diseases. Nuclear mechanics is yet rather complex due to heterogeneous distribution of dense heterochromatin and loose euchromatin domains, giving rise to spatially variable stiffness properties. Methods: In this study, we propose to use the adjoint-based inverse solver to identify for the first time the nonhomogeneous elastic property distribution of the nucleus. Inputs of the inverse solver are deformation fields measured with microscopic imaging in contracting cardiomyocytes. Results: The feasibility of the proposed method is first demonstrated using simulated data. Results indicate accurate identification of the assumed heterochromatin region, with a maximum relative error of less than 5%. We also investigate the influence of unknown Poisson's ratio on the reconstruction and find that variations of the Poisson's ratio in the range [0.3-0.5] result in uncertainties of less than 15% in the identified stiffness. Finally, we apply the inverse solver on actual deformation fields acquired within the nuclei of two cardiomyocytes. The obtained results are in good agreement with the density maps obtained from microscopy images. Conclusions: Overall, the proposed approach shows great potential for nuclear elastography, with promising value for emerging fields of mechanobiology and mechanogenetics.

Endoluminal reconstruction using flow diverters represents a novel paradigm for the minimally invasive treatment of intracranial aneurysms. The configuration assumed by these very dense braided stents once deployed within the parent vessel is not easily predictable and medical volumetric images alone may be insufficient to plan the treatment satisfactorily. Therefore, here we propose a fast and accurate machine learning and reduced order modelling framework, based on finite element simulations, to assist practitioners in the planning and interventional stages. It consists of a first classification step to determine a priori whether a simulation will be successful (good conformity between stent and vessel) or not from a clinical perspective, followed by a regression step that provides an approximated solution of the deployed stent configuration. The latter is achieved using a non-intrusive reduced order modelling scheme that combines the proper orthogonal decomposition algorithm and Gaussian process regression. The workflow was validated on an idealised intracranial artery with a saccular aneurysm and the effect of six geometrical and surgical parameters on the outcome of stent deployment was studied. The two-step workflow allows the classification of deployment conditions with up to 95% accuracy and real-time prediction of the stent deployed configuration with an average prediction error never greater than the spatial resolution of 3D rotational angiography (0.15 mm). These results are promising as they demonstrate the ability of these techniques to achieve simulations within a few milliseconds while retaining the mechanical realism and predictability of the stent deployed configuration.

High-fidelity biomechanical models usually involve the mechanical characterization of biological tissues using experimental methods based on optical measurements. In most experiments, strains are evaluated based on displacements of a few markers and represents an average within the region of interest (ROI). Full-field measurements may improve description of non-homogeneous materials such as soft tissues. The approach based on non-rigid Image Registration is proposed and compared with standard Digital Image Correlation (DIC) on a set of samples, including (i) complex heterogeneous deformations with sub-pixel displacement, (ii) a typical uniaxial tension test of aorta, and (iii) an indentation test on skin. The possibility to extend the ROI to the whole sample and the exploitation of a natural tissue pattern represents the main assets of the proposed method whereas the results show similar accuracy as standard DIC when analysing sub-pixel deformations. Therefore, displacement and strain fields measurement based on Image Registration is very promising to characterize heterogeneous specimens with irregular shapes and/or small dimensions, which are typical features of soft biological tissues.

Progressive aneurysmal dilatation is a well-recognized complication in patients with chronic type B aortic dissection (cTBAD), which may lead to a delayed rupture and create a life-threatening condition. However, our understanding of such aortic expansion in cTBAD remains weak. In the present paper, we propose to use numerical simulations to study the role of growth and remodeling (G\&R) in aneurysmal dilatation after cTBAD. We set up a 3D finite-element model of G\&R for aortic dissection within an open-source code. Constitutive equations, momentum balance equations, and equations related to the mechanobiology of the artery were formulated based on the homogenized constrained mixture theory. The model was first applied to idealized aortic geometries with cylindrical and toric shapes to demonstrate its feasibility and efficiency. The model was then applied to a patient-specific aortic segment to show its potential in more relevant and complex patient-specific clinical applications. It was found that the G\&R tends to naturally trigger the aneurysmal dilatation after dissection, in order to restore its tensional equilibrium. Our results indicated that the value of the gain parameter, related to collagen G\&R, plays an important role in the stability of aortic expansion after cTBAD. A small gain parameter will induce an excessive aneurysmal degeneration whilst a large gain parameter helps to recover a stabilized state of the artery after dissection. Finally, it was found that other mechanobiology-related parameters, such as the circumferential length of the dissection, as well as the pressure in the false lumen, may also be determinant for the stability of aneurysmal dilatation after cTBAD. Both a wide tear and an elevated false lumen pressure favor an unstable development of aortic expansion after cTBAD. As future work, the present model will be validated through predictions of aneurysmal dilatation in patient-specific clinical cases, in comparison with datasets followed over a significant period of time.

It is of great significance to identify the nonhomogeneous distribution of material properties in human tissues for different clinical and medical applications. This leads to the requirement of solving an inverse problem in elasticity. The virtual fields method (VFM) is a rather recent inverse method with remarkable computational efficiency compared with the optimization-based methods. In this study, we aim to identify nonhomogeneous hyperelastic material properties using the VFM. We propose two novel algorithms, RE-VFM and NO-VFM. In RE-VFM, the solid is partitioned in different regions and the elastic properties of each region are determined. In NO-VFM, 2 the distribution of elastic properties is completely reconstructed through the inverse problem without partitioning the solid. As the VFM requires to use virtual fields, we proposed an efficient way to construct them and implemented the approach in the FEniCS package. We validated the proposed methods on several examples, including a bilayer structure, a lamina cribosa (LC) model and a cube model embedded with a spherical inclusion. The numerical examples illustrate the feasibility of both RE-VFM and NO-VFM. Notably, the spatial variations of the Young's modulus distribution can be recovered accurately within only 5 iterations. The obtained results reveal the potential of the proposed methods for future clinical applications such as estimating the risk of vision loss related to glaucoma and detecting tumors., Comment: Advances in Software Engineering, In press

When they are damaged or injured, soft biological tissues are able to self-repair and heal. Mechanics is critical during the healing process, as the damaged extracellular matrix (ECM) tends to be replaced with a new undamaged ECM supporting homeostatic stresses. Computational modeling has been commonly used to simulate the healing process. However, there is a pressing need to have a unified thermodynamics theory for healing. From the viewpoint of continuum damage mechanics, some key parameters related to healing processes, for instance, the volume fraction of newly grown soft tissue and the growth deformation, can be regarded as internal variables and have related evolution equations. This paper is aiming to establish this unified framework inspired by thermodynamics for continuum damage models for the healing of soft biological tissues. The significant advantage of the proposed model is that no \textit{ad hoc} equations are required for describing the healing process. Therefore, this new model is more concise and offers a universal approach to simulate the healing process. Three numerical examples are provided to demonstrate the effectiveness of the proposed model, which is in good agreement with the existing works, including an application for balloon angioplasty in an arteriosclerotic artery with a fiber cap., Comment: 42 pages, 17 figures, 3 tables, submit to Journal of the Mechanics and Physics of Solids

In this paper we introduce a new method simulating stent graft deployment for assisting endovascular repair of abdominal aortic aneurysms. The method relies on intraoperative images coupled with mechanical models. A multi-step algorithm has been developed to increase the reliability of simulations. The first step predicts the position of the stent graft within the aorta. The second step is an axisymmetric geometric reconstruction of each individual stent. The third step minimizes the rotation of each stent around its main axis. Finally, the last step virtually deploys each stent within a deployment box extracted from the preoperative CT scan. A proof of concept is performed on a patient. The accuracy is compatible with the clinical threshold of 3 mm: the average distance between target and simulated stents is 1.73 $\pm$ 0.37 mm. Fenestrations of the stent-graft are reconstructed with a maximum error of less than 2.5 mm, which is enables a secure catheterization of secondary arteries. In summary, the method is able to assist EVAR practitioners by providing all necessary information for a fast and accurate stent graft positioning, combining intraoperative data and a mechanical model in a very low cost framework.

In its permanent quest of mechanobiological homeostasis, our vascula-ture significantly adapts across multiple length and time scales in various physiological and pathological conditions. Computational modeling of vascular growth and remodeling (G\&R) has significantly improved our insights of the mechanobio-logical processes of diseases such as hypertension or aneurysms. However, patient-specific computational modeling of ascending thoracic aortic aneurysm (ATAA) evolution, based on finite-element models (FEM), remains a challenging scientific problem with rare contributions, despite the major significance of this topic of research. Challenges are related to complex boundary conditions and geometries combined with layer-specific G\&R responses. To address these challenges, in the current paper, we employed the constrained mixture model (CMM) to model the arterial wall as a mixture of different constituents such as elastin, collagen fiber families and smooth muscle cells (SMCs). Implemented in Abaqus as a UMAT, this first patient-specific CMM-based FEM of G\&R in human ATAA was first validated for canonical problems such as single-layer thick-wall cylindrical and bi-layer thick-wall toric arterial geometries. Then it was used to predict ATAA evolution for a patient-specific aortic geometry, showing that the typical shape of an ATAA can be simply produced by elastin proteolysis localized in regions of deranged hemodymanics. The results indicate a transfer of stress to the adventitia by elastin loss and continuous adaptation of the stress distribution due to change of ATAA shape. Moreover, stress redistribution leads to collagen deposition where the maximum elastin mass is lost, which in turn leads to stiffening of the arterial wall. As future work, the predictions of this G\&R framework will be validated on datasets of patient-specific ATAA geometries followed up over a significant number of years.

Aortic Aneurysms are among the most critical cardiovascular diseases. The present study is focused on Ascending Thoracic Aortic Aneurysms (ATAA). The main causes of ATAA are commonly cardiac malformations like bicuspid aor-tic valve or genetic mutations. Research studies dedicated to ATAA tend more and more to invoke multifactorial eects. In the current review, we show that all these eects converge towards a single paradigm relying upon the crucial biome-chanical role played by smooth muscle cells (SMCs) in controlling the distribution of mechanical stresses across the aortic wall. The chapter is organized as follows. In section 6.2, we introduce the basics of arterial wall biomechanics and how the stresses are distributed across its dierent layers and among the main structural constituents: collagen, elastin, and SMCs. In section 6.3, we introduce the biome-chanical active role of SMCs and its main regulators. We show how SMCs actively regulate the distribution of stresses across the aortic wall and among the main structural constituents. In section 6.4, we review studies showing that SMCs tend to have a preferred homeostatic tension. We show that mechanosensing can be understood as a reaction to homeostasis unbalance of SMC tension. Through the use of layer-specic multiscale modeling of the arterial wall, it is revealed that the quantication of SMC homeostatic tension is crucial to predict numerically the initiation and development of ATAA.

Healing of soft biological tissue is the process of self-recovering or self-repairing the injured or damaged extracellular matrix (ECM). Healing is assumed to be stress-driven, with the objective of returning to a homeostatic stress metrics in the tissue after replacing the damaged ECM with new undamaged one. However, based on the existence of intrinsic length-scales in soft tissues, it is thought that computational models of healing should be non-local. In the present study, we introduce for the first time two gradient-enhanced con-stitutive healing models for soft tissues including non-local variables. The first model combines a continuum damage model with a temporally homogenized growth model, where the growth direction is determined according to local principal stress directions. The second one is based on a gradient-enhanced healing model with continuously recoverable damage variable. Both models are implemented in the finite-element package Abaqus by means of a user sub-routine UEL. Three two-dimensional situations simulating the healing process of soft tissues are modeled numerically with both models, and their application for simulation of balloon angioplasty is provided by illustrating the change of damage field and geometry in the media layer throughout the healing process.

Knowledge of the mechanical properties of the aorta is essential as important concerns regarding the treatment of aortic pathologies, such as atherosclerosis, aneurysms and dissections, are fundamentally mechanobiological. A comprehensive review is presented in the current chapter. As the function of arteries is to carry blood to the peripheral organs, the main biomechanical properties of interest are elasticity and rupture properties. Regarding elastic properties, an essential parameter remains the physiological linearized elastic modulus in the circumferential direction, although sophisticated constitutive equations including hyperelasticity are available to model the complex coupled roles played by collagen, elastin and smooth muscle cells in the mechanics of the aorta. Regarding rupture properties, tensile strengths in the axial and circumferential directions are on the order of 1.5 MPa in the thoracic aorta and the radial strength, which is important regarding dissections, is about 0.1 MPa. All these properties may vary spatially and change with the adaptation of the aortic wall to different conditions through growth and remodelling. The progression of diseases, such as aneurysms and atherosclerosis, also manifests with alterations of these material properties. After presenting how the mechanical properties of elastic arteries, including the aorta, can be measured and how they can be used in models to predict the biomechanical response of same under different circumstances, a section will focus on the biomechanics of the ascending thoracic aorta and the chapter will end with current challenges regarding predictive numerical simulations for personalized medicine.

The mechanical integrity of arteries is of prime importance, for a proper oxygen and nutrients delivery to all organs. To optimize their mechanical properties, healthy arteries exhibit a complex hierarchical microstructure which ensures a sufficient compliance at low stresses and which stiffens at higher stresses, preventing over-dilatation. In this article, we propose a vast literature survey on how the mechanical properties of arteries are related to structural features. We first review the characteristics of arterial microstructure and composition and then we review the mechanical behavior of arteries. This allows evidencing, for the first time, the strong correlation existing between elastin and collagen contents within the arterial wall. However, bringing together most of the available mechanical tests on arterial walls shows the important variability of the mechanical arterial response. The presentation is organized at three different scales: at the tissue (macroscopic) scale, at the (micrometer) scale of the fiber networks, and at the (submicrometer) fibrillar and cellular scale. Glossary: Autoclave: pressure chamber used to carry out processes requiring elevated temperature and pressure different from ambient air pressure. In the sequel, autoclaving is used to separate soluble proteins (such as collagen) from non-soluble proteins (such as elastin). Constitutive relation: in mechanics, material-specific relation between stress and strain that characterizes the response of the material to an applied mechanical loading. In vivo pre stretch and pre stress: The in vivo state of the arterial tissue is not free of mechanical loading; in particular, it is subjected to an axial elongation and residual stresses. Staining: auxiliary technique used in microscopy to highlight structures in materials. For biological tissues, it involves the use of structure-specific dyes. Nomenclature: not needed

This paper discusses an important issue about the virtual fields method when it is used to identify nonhomogeneous shear moduli of nearly incompressible solids. From simulated examples, we observed that conventional virtual fields, which assign null displacements on the entire boundary, do not perform well on nonhomogeneous and nearly incompressible solids. Thus, these conventional virtual fields should not be used for such materials. We propose two novel types of virtual fields derived from either finite element analyses performed on the same domain with homogeneous properties or computing the curl of a potential vector field. From a variety of simulated and experimental examples, we observe that the proposed virtual fields significantly improve the accuracy of the estimated shear moduli of nonhomogeneous and nearly incompressible solids. Furthermore, the sensitivity to noise of the proposed approach is moderate and the approach can handle cases with unknown boundary conditions. Therefore, based on this careful and thorough analysis, it is concluded that the proposed approaches are a significant improvement of the VFM to identify nonhomogeneous shear moduli in nearly incompressible solids., Comment: International Journal of Solids and Structures, Elsevier, 2019

In this paper, the objective is to assess the histomechanical effects of collagen proteolysis in arteries under loading conditions reproducing in vivo environment. Thirteen segments of common porcine carotid arteries (8 proximal and 5 distal) were immersed in a bath of bacterial collagenase and tested with a pulsatile tension/inflation machine. Diameter, pressure and axial load were monitored throughout the tests and used to derive the stress-stretch curves and to determine the secant circumferential stiffness. Results were analyzed separately for proximal and distal segments, before and after 1, 2 and 3 hours of enzymatic degradation. A histological analysis was performed to relate the arterial microstructure to its mechanical behavior under collagen proteolysis. Control (before enzymatic degradation) and treated populations (after 1, 2 or 3 hours of enzymatic degradation) were found statistically incomparable, and histology confirmed the alteration of the fibrous structure of collagen bundles induced by the collagenase treatment. A decrease of the secant circumferential stiffness of the arterial wall was noticed mostly at the beginning of the treatment, and was less pronounced after 1 hour. These results constitute an important set of enzymatically damaged arteries that can be used to validate biomechanical computational models correlating structure and properties of blood vessels.

Understanding stress-strain relationships in arteries is important for fundamental investigations in mechanobiology. Here we demonstrate the essential role of chemoelasticity in determining the mechanical properties of arterial tissues. Stepwise stress-relaxation uniaxial tensile tests were carried out on samples of porcine thoracic aortas immersed in a hyperosmotic solution. The tissue deformations were tracked using optical coherence tomography (OCT) during the tensile tests and digital volume correlation (DVC) was used to obtain measurements of depth-resolved strains across the whole thickness of the tested aortas. The hyperosmotic solution exacerbated chemoelastic effects, and we were able to measure different manifestations of these chemoelastic effects: swelling of the media inducing a modification of its optical properties, existence of a transverse tensile strain. For the first time ever to our best knowledge, 3D strains induced by chemoelastic effects in soft tissues were quantified thanks to the OCT-DVC method. Without doubt, chemoelasticity plays an essential role in arterial mechanobiology in vivo and future work should focus on characterizing chemoelastic effects in arterial walls under physiological and disease conditions. Statement of significance: Chemoelasticity, coupling osmotic phenomena and mechanical stresses, is essential in soft tissue mechanobiology. For the first time ever, we measure and analyze 3D strain fields induced by these chemoelastic effects thanks to the unique combination of OCT imaging and digital volume correlation., Comment: Acta Biomaterialia, Elsevier, 2019, in press

Purpose. It has been reported clinically that rupture or dissections in thoracic aortic aneurysms (TAA) often occur due to hypertension which may be modelled with sudden increase of peripheral resistance, inducing acute changes of blood volumes in the aorta. There is clinical evidence that more compliant aneurysms are less prone to rupture as they can sustain such changes of volume. The aim of the current paper is to verify this paradigm by evaluating computationally the role played by the variation of peripheral resistance and the impact of aortic stiffness onto peak wall stress in ascending TAA. Methods. Fluid-Structure Interaction (FSI) analyses were performed using patient-specific geometries and boundary conditions derived from 4D MRI datasets acquired on a patient. Blood was assumed incompressible and was treated as a non-Newtonian fluid using the Carreau model while the wall mechanical properties were obtained from the bulge inflation tests carried out in vitro after surgical repair. The Navier Stokes equations were solved in ANSYS Fluent. The Arbitrary Lagrangian Eulerian formulation was used to account for the wall deformations. At the interface between the solid domain and the fluid domain, the fluid pressure was transferred to the wall and the displacement of the wall was transferred to the fluid. The two systems were connected by the System Coupling component which controls the solver execution of fluid and solid simulations in ANSYS. Fluid and solid domains were solved sequentially starting from the fluid simulations. Results. Distributions of blood flow, wall shear stress and wall stress were evaluated in the ascending thoracic aorta using the FSI analyses. We always observed a significant flow eccentricity in the simulations, in very good agreement with velocity profiles measured using 4D MRI. The results also showed significant increase of peak wall stress due to the increase of peripheral resistance and aortic stiffness. In the worst case scenario, the largest peripheral resistance (10 10 kg.s.m-4) and stiffness (10 MPa) resulted in a maximal principal stress equal to 702 kPa, whereas it was only 77 kPa in normal conditions. Conclusions. This is the first time that the risk of rupture of an aTAA is quantified in case of the combined effects of hypertension and aortic stiffness increase. Our findings suggest that a stiffer TAA may have the most altered distribution of wall stress and an acute change of peripheral vascular resistance could significantly increase the risk of rupture for a stiffer aneurysm.