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Background: Thoracic aortopathy associates with extracellular matrix remodeling and altered biomechanical properties. We sought to quantify the natural history of thoracic aortopathy in a common mouse model and to correlate measures of wall remodeling such as aortic dilatation or localized mural defects with evolving microstructural composition and biomechanical properties of the wall. Methods: We combined a high-resolution multimodality imaging approach (panoramic digital image correlation and optical coherence tomography) with histopathologic examinations and biaxial mechanical testing to correlate spatially, for the first time, macroscopic mural defects and medial degeneration within the ascending aorta with local changes in aortic wall composition and mechanical properties. Results: Findings revealed strong correlations between local decreases in elastic energy storage and increases in circumferential material stiffness with increasing proximal aortic diameter and especially mural defect size. Mural defects tended to exhibit a pronounced biomechanical dysfunction that is driven by an altered organization of collagen and elastic fibers. Conclusions: While aneurysmal dilatation is often observed within particular segments of the aorta, dissection and rupture initiate as highly localized mechanical failures. We show that wall composition and material properties are compromised in regions of local mural defects, which further increases the dilatation and overall structural vulnerability of the wall. Identification of therapies focused on promoting robust collagen accumulation may protect the wall from these vulnerabilities and limit the incidence of dissection and rupture.

Aortic Smooth Muscle Cells (SMCs) play a vital role in maintaining homeostasis in the aorta by sensing and responding to mechanical stimuli. However, the mechanisms that underlie the ability of SMCs to sense and respond to stiffness change in their environment are still partially unclear. In this study, we focus on the role of acto-myosin contractility in stiffness sensing and introduce a novel continuum mechanics approach based on the principles of thermal strains. Each stress fiber satisfies a universal stress-strain relationship driven by a Young’s modulus, a contraction coefficient scaling the fictitious thermal strain, a maximum contraction stress and a softening parameter describing the sliding effects between actin and myosin filaments. To account for the inherent variability of cellular responses, large populations of SMCs are modeled with the finite-element method, each cell having a random number and a random arrangement of stress fibers. Moreover, the level of myosin activation in each stress fiber satisfies a Weibull probability density function. Model predictions are compared to traction force measurements on different SMC lineages. It is demonstrated that the model not only predicts well the effects of substrate stiffness on cellular traction, but it can also successfully approximate the statistical variations of cellular tractions induced by intercellular variability. Finally, stresses in the nuclear envelope and in the nucleus are computed with the model, showing that the variations of cytoskeletal forces induced by substrate stiffness directly induce deformations of the nucleus which can potentially alter gene expression. The predictability of the model combined to its relative simplicity are promising assets for further investigation of stiffness sensing in 3D environments. Eventually, this could contribute to decipher the effects of mechanosensitivity impairment, which are known to be at the root of aortic aneurysms.

Objectives A biomechanical approach to the rupture risk of an abdominal aortic aneurysm (AAA) could be a solution to ensure a personalized estimate of this risk. It is still difficult to know in what conditions, the assumptions made by biomechanics, are valid. The objective of this work was to determine the individual biomechanical rupture threshold and to assess the correlation between their rupture sites and the locations of their maximum stress comparing two computed tomography scan (CT) before and at time of rupture. Materials and Methods We included 5 patients who had undergone two CT; one within the last 6 months period before rupture and a second CT scan just before the surgical procedure for the rupture. All DICOM data, both pre- and rupture, were processed following the same following steps: generation of a 3D geometry of the AAA, meshing and computational stress analysis using the finite element method. We used two different modelling scenarios to study the distribution of the stresses, a “wall” model without intraluminal thrombus (ILT) and a “thrombus” model with ILT. Results The average time between the pre-rupture and rupture CT scans was 44 days (22-97). The median of the maximum stresses applied to the wall between the pre-rupture and rupture states were 0.817 MPa (0.555-1.295) and 1.160 MPa (0.633-1.625) for the "wall" model; and 0.365 MPa (0.291-0.753) and 0.390 MPa (0.343-0.819) for the "thrombus" model. There was an agreement between the site of rupture and the location of maximum stress for only one patient, who was the only patient without ILT. Conclusion We observed a large variability of stress values at rupture sites between patients. The rupture threshold strongly varied between individuals depending on the intraluminal thrombus. The site of rupture did not correlate with the maximum stress except for one patient.

Les méthodes existantes de réparation endo-vasculaire aortique sont présentées. Neuf modèles synthétiques réalistes sont proposés, comportant des niveaux de sténose différents, et des conditions aux limites adaptées. Les simulations effectuées permettent de calculer débits, pressions et contraintes pariétales. Ces résultats pourront venir en aide au médecin afin de mieux appréhender la méthode optimale d'intervention.

Evolution of mechanical and structural properties in the Ascending Thoracic Aorta (ATA) is the results of complex mechanobiological processes. In this work, we address some numerical challenges in order to elaborate computational models of these processes. For that, we extend the state of the art of homogenized constrained mixture (hCM) models. In these models, prestretches are assigned to the mixed constituents in order to ensure local mechanical equilibrium macroscopically, and to maintain a homeostatic level of tension in collagen fibers microscopically. Although the initial prestretches were assumed as homogeneous in idealized straight tubes, more elaborate prestretch distributions need to be considered for curved geometrical models such as patient-specific ATA. Therefore, we introduce prestretches having a three-dimensional gradient across the ATA geometry in the homeostatic reference state. We test different schemes with the objective to ensure stable growth and remodeling (G&R) simulations on patient-specific curved vessels. In these simulations, aneurysm progression is triggered by tissue changes in the constituents such as mass degradation of intramural elastin. The results show that the initial prestretches are not only critical for the stability of numerical simulations, but they also affect the G&R response. Eventually, we submit that initial conditions required for G&R simulations need to be identified regionally for ensuring realistic patient-specific predictions of aneurysm progression.

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.

This work presents the development of a Hybrid Mock Circulatory Loop (HMCL) to simulate hemodynamics at patient-specific level in terms of both 3D geometry and inlet/outlet boundary conditions.Clinical data have been processed to define the morphological and functional patient-specific settings. A piston pump is used to impose a parametric flow rate profile at the inlet of the hemodynamic circuit. In order to guarantee the physiological pressure and flow conditions, a specific hybrid chamber system including a real-time control has been designed and implemented. The developed system was validated firstly in a single outlet branch model and, secondly, on a 3D printed patient-specific multi-branch phantom. Finally, for the 3D phantom, the outlet flow profiles were compared with the corresponding in-vivo flow data.Results showed that the root mean squared error between the prescribed setpoint and the measured pressures was always below 3 mmHg (about 2.5%) for all cases. The obtained flow profiles for the patient-specific model were in agreement with the related functional in-vivo data.The capability to reproduce physiological hemodynamics condition, with high-fidelity, plays a significant role in the cardiovascular research. The developed platform can be used to assess the performances of cardiovascular devices, to validate numerical simulations, and to test imaging systems.

This paper presents a method to derive the virtual fields for identifying constitutive model parameters using the Virtual Fields Method (VFM). The VFM is an approach to identify unknown constitutive parameters using deformation fields measured across a given volume of interest. The general principle for solving identification problems with the VFM is first to derive parametric stress field, where the stress components at any point depend on the unknown constitutive parameters, across the volume of interest from the measured deformation fields. Applying the principle of virtual work to the parametric stress fields, one can write scalar equations of the unknown parameters and solve the obtained system of equations to deduce the values of unknown parameters. However, no rules have been proposed to select the virtual fields in identification problems related to nonlinear elasticity and there are multiple strategies possible that can yield different results. In this work, we propose a systematic, robust and automatic approach to reconstruct the systems of scalar equations with the VFM. This approach is well suited to finite-element implementation and can be applied to any problem provided that full-field deformation data are available across a volume of interest. We also successfully demonstrate the feasibility of the novel approach by multiple numerical examples. Potential applications of the proposed approach are numerous in biomedical engineering where imaging techniques are commonly used to observe soft tissues and where alterations of material properties are markers of diseased states.List of symbols

Background The role of the plantar venous pump (PVP) on venous return is evident but the effects of the foot morphology have never been characterized properly. Method 52 healthy volunteers—26 with normal plantar arch (control) and 26 with dysmorphic plantar arch (in two subgroups: 13 flat feet, 13 hollow feet)—were included. Using Doppler ultrasound, we measured the diameter and the peak systolic velocity in the large veins of the lower limb after PVP stimulation by manual compression and bodyweight transfer. Result The mean peak systolic velocity of the studied veins varied from 12.2 cm/s to 41.7 cm/s in the control group and from 10.9 cm/s to 39.1 cm/s in the dysmorphic plantar group. The foot arch morphology did not affect significantly the venous blood flows, except in the great saphenous vein during manual compression. Conclusion The plantar morphology did not induce a significant increase of venous blood velocity resulting from PVP stimulation.

The identification of nonhomogeneous elastic property distributions has been traditionally achieved with well acknowledged optimization based inverse approaches, but when full-field displacement measurements are available, the virtual fields method (VFM) can be computationally more efficient by converting the large-scale optimization problem into multiple small-scale optimization problems. A possible downside of the VFM so far was not to take into account prior knowledge, which is often available and needed when there is a very large number of unknowns and the inverse problem is ill-posed. In this work, different approaches are proposed for introducing regularization into the VFM, aiming to penalize the local variations of identified stiffness properties in order to reduce the effects of uncertainty in the inverse problem resolution. The feasibility and accuracy of the regularized VFM are tested through several numerical and experimental datasets. It is shown that the main advantage of the novel VFM approaches is the low computational cost, as large-scale inverse problems with 10,000 unknown parameters can be solved within several seconds using a standard personal computer. Although the regularized VFM can successfully detect a stiff inclusion in a soft solid with high accuracy, regularization also introduces unexpected spurious effects in the results, blurring the interface between soft and stiff regions. We also observed that the regularization did not improve the smoothness significantly due to local effects of the small-scale optimization problem introduced in the proposed VFM method. Therefore, traditional regularization, which penalizes local variations of identified stiffness properties, can be combined with the VFM to solve inverse problems with a high computational efficiency, but supplemental regularization conditions will need to be adapted in the future to better delineate soft-stiff interfaces with this methodology.

Ascending Thoracic Aortic Aneurysm (ATAA) is a permanent dilatation of the aorta which is usually related to tissue degeneration, hemodynamic conditions, lifestyle, environmental and genetic factors. As the mechanical conditions can become critical in a dilated aorta, a patient-specific computational model can be very useful to assist clinical decisions in the management of ATAAs. In this article, we model the biomechanical conditions of ATAA by performing Fluid–Structure Interaction (FSI) simulations in the SimVascular open-source software package. The patient-specific geometric model is reconstructed from Computed Tomography scan (CT). The numerical implementation takes into account patient-specific outlet conditions and a temporal flow variation at the model inlet. We performed a mesh convergence analysis on a new mesh reconstruction method in SimVascular and showed that it can significantly reduce the computational cost without impacting the accuracy.

Previous studies have shown that the rupture properties of an ascending thoracic aortic aneurysm (ATAA) are strongly correlated with the pre-rupture response features. In this work, we present a two-step machine learning method to predict where the rupture is likely to occur in ATAA and what safety reserve the structure may have. The study was carried out using ATAA specimens from 15 patients who underwent surgical intervention. Through inflation test, full-field deformation data and post-rupture images were collected, from which the wall tension and surface strain distributions were computed. The tension-strain data in the pressure range of 9-18 kPa were fitted to a third-order polynomial to characterize the response properties. It is hypothesized that the region where rupture is prone to initiate is associated with a high level of tension buildup. A machine learning method is devised to predict the peak risk region. The predicted regions were found to match the actual rupture sites in 13 samples out of the total 15. In the second step, another machine learning model is utilized to predict the tissue's rupture strength in the peak risk region. Results suggest that the ATAA rupture risk can be reasonably predicted using tension-strain response in the physiological range. This may open a pathway for evaluating the ATAA rupture propensity using information of in vivo response.

Smooth muscle cells (SMCs) usually express a contractile phenotype in the healthy aorta. However, aortic SMCs have the ability to undergo profound changes in phenotype in response to changes in their extracellular environment, as occurs in ascending thoracic aortic aneurysms (ATAA). Accordingly, there is a pressing need to quantify the mechanobiological effects of these changes at single cell level. To address this need, we applied Traction Force Microscopy (TFM) on 759 cells coming from three primary healthy (AoPrim) human SMC lineages and three primary aneurysmal (AnevPrim) human SMC lineages, from age and gender matched donors. We measured the basal traction forces applied by each of these cells onto compliant hydrogels of different stiffness (4, 8, 12, 25 kPa). Although the range of force generation by SMCs suggested some heterogeneity, we observed that: 1. the traction forces were significantly larger on substrates of larger stiffness; 2. traction forces in AnevPrim were significantly higher than in AoPrim cells. We modelled computationally the dynamic force generation process in SMCs using the motor-clutch model and found that it accounts well for the stiffness-dependent traction forces. The existence of larger traction forces in the AnevPrim SMCs were related to the larger size of cells in these lineages. We conclude that phenotype changes occurring in ATAA, which were previously known to reduce the expression of elongated and contractile SMCs (rendering SMCs less responsive to vasoactive agents), tend also to induce stronger SMCs. Future work aims at understanding the causes of this alteration process in aortic aneurysms. Supplementary information The online version of this article (10.1007/s10237-020-01412-6) contains supplementary material, which is available to authorized users.

Aortic smooth muscle cells (SMCs) play a vital role in maintaining mechanical homeostasis in the aorta. We recently found that SMCs of aneurysmal aortas apply larger traction forces than SMCs of healthy aortas. This result was explained by the significant increase of hypertrophic SMCs abundance in aneurysms. In this study, we investigate whether the cytoskeleton stiffness of SMCs may also be altered in aneurysmal aortas. For that, we use atomic force microscopy (AFM) nano-indentation with a specific mode that allows subcellular-resolution mapping of the local stiffness across a specified region of interest of the cell. Aortic SMCs from a commercial human lineage (AoSMCs, Lonza) and primary aneurysmal SMCs (AnevSMCs) are cultured in conditions promoting the development of their contractile apparatus, and seeded on hydrogels with stiffness properties of 12 kPa and 25 kPa. Results show that all SMCs exhibit globally a lognormal stiffness distribution, with medians in the range 10–30 kPa. The mean of stiffness distributions is 16 kPa in aneurysmal SMCs and 12 kPa in healthy cells, but the differences are not statistically significant due to the large dispersion of AFM nano-indentation stiffness. We conclude that the possible alterations previously found in aneurysmal SMCs do not affect significantly the AFM nano-indentation stiffness of their cytoskeleton.

With the rising popularity of endovascular aortic repair (EVAR) for aortic aneurysms and dissections, there is a crucial need for investigating the delayed appearance of post-EVAR complications such as stent-graft kinking, fracture and migration respectively. These complications have been noted to be influenced by the radial stiffness and bending flexibility attributes of stent-grafts. Auxetic designs with negative Poisson's ratio offer interesting advantages such as enhanced fracture toughness, superior indentation resistance and adaptive stiffness in response to intricate morphology for stenting applications over conventional stent designs. The objective of this study is to propose different auxetic stent candidates and to compare their mechanical performance with two conventional stent candidates for endovascular applications using numerical simulation through crimp/crushing tests for their radial stiffness and three-point bending/kinking tests for their flexibility, respectively. The results demonstrate that the novel hybrid auxetic designs (CRE and CSTAR) possess the best trade-off between radial stiffness and bending flexibility characteristics among all candidates for stent-graft applications.

Aneurysm shrinkage is clinically observed after successful endovascular aortic aneurysm repair (EVAR). However, global understanding of post-operative aneurysm evolutions remains weak. In this work, we propose to study these effects using numerical simulation. We set up a 3D finite-element model of post-EVAR vascular adaptation within an open-source finite-element code, which was initially developed for growth and remodeling (G&R). We modeled the endograft with a set of uniaxial prestrained springs that apply radial forces on the inner surface of the artery. Constitutive equations, momentum balance equations, and equations related to the mechanobiology of the artery were formulated based on the homogenized constrained mixture theory. We performed a sensitivity analysis by varying different selected parameters, namely oversizing and compliance of the stent-graft, gain parameters related to collagen G&R, and the residual pressure in the aneurysm sac. This permitted us to evaluate how each factor influences post-EVAR vascular adaptation. It was found that oversizing, compliance or gain parameters have a limited influence compared to that of the residual pressure in the aneurysm sac, which was found to play a critical role in the stability of aneurysm after stent-graft implantation. An excessive residual pressure larger than 50 mmHg can induce a continuous expansion of the aneurysm while a moderate residual pressure below this critical threshold yields continuous shrinkage of the aneurysm. Moreover, it was found that elderly patients, with relatively lower amounts of remnant elastin in the arterial wall, are more sensitive to the effect of residual pressure. Therefore, these results show that elderly patients may present a higher potential risk of aortic sac expansion due to intra-aneurysm sac pressure after EVAR than younger patients.

Growth and remodelling (G&R) of biological tissues are mechanisms which respectively involve a change in mass and material properties. In particular, arterial media calcification (AMC) is a patholo...

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.

Magnetic resonance imaging (MRI) is the preferred modality to assess hemodynamics in healthy and diseased blood vessels. As an affordable and non-invasive alternative, Color-Doppler imaging is a good candidate. Nevertheless, Color-Doppler acquisitions provide only partial information on the blood velocity within the vessel. We present a framework to reconstruct 2D velocity fields in the aorta. We generated 2D Color-Doppler-like images from patient-specific Computational Fluid Dynamics (CFD) models of abdominal aortas and evaluated the framework's performance. The 2D velocity field reconstruction is based on the minimization of a cost function, in which the reconstructed velocities are constrained to satisfy fluid dynamics principles. The numerical evaluations show that the reconstructed vector flow fields agree with ground-truth velocities, with an average magnitude error of less than 4% and an average angular error of less than 2