Cell signaling and tissue remodeling in the pulmonary autograft after the Ross procedure: A computational study.

In the Ross procedure, a patient's pulmonary valve is transplanted in the aortic position. Despite advantages of this surgery, reoperation is still needed in many cases due to excessive dilatation of the pulmonary autograft. To further understand the failure mechanisms, we propose a multiscale model predicting adaptive processes in the autograft at the cell and tissue scale. The cell-scale model consists of a network model, that includes important signaling pathways and relations between relevant transcription factors and their target genes. The resulting gene activity leads to changes in the mechanical properties of the tissue, modeled as a constrained mixture of collagen, elastin and smooth muscle. The multiscale model is calibrated with findings from experiments in which seven sheep underwent the Ross procedure. The model is then validated against a different set of sheep experiments, for which a qualitative agreement between model and experiment is found. Model outcomes at the cell scale, including the activity of genes and transcription factors, also match experimentally obtained transcriptomics data.

Hemodynamics and wall shear metrics in a pulmonary autograft: Comparing a fluid-structure interaction and computational fluid dynamics approach.

OBJECTIVE: In young patients, aortic valve disease is often treated by placement of a pulmonary autograft (PA) which adapts to its new environment through growth and remodeling. To better understand the hemodynamic forces acting on the highly distensible PA in the acute phase after surgery, we developed a fluid-structure interaction (FSI) framework and comprehensively compared hemodynamics and wall shear-stress (WSS) metrics with a computational fluid dynamic (CFD) simulation. METHODS: The FSI framework couples a prestressed non-linear hyperelastic arterial tissue model with a fluid model using the in-house coupling code CoCoNuT. Geometry, material parameters and boundary conditions are based on in-vivo measurements. Hemodynamics, time-averaged WSS (TAWSS), oscillatory shear index (OSI) and topological shear variation index (TSVI) are evaluated qualitatively and quantitatively for 3 different sheeps. RESULTS: Despite systolic-to-diastolic volumetric changes of the PA in the order of 20 %, the point-by-point correlation of TAWSS and OSI obtained through CFD and FSI remains high (r > 0.9, p < 0.01) for TAWSS and (r > 0.8, p < 0.01) for OSI). Instantaneous WSS divergence patterns qualitatively preserve similarities, but large deformations of the PA leads to a decrease of the correlation between FSI and CFD resolved TSVI (r < 0.7, p < 0.01). Moderate co-localization between FSI and CFD is observed for low thresholds of TAWSS and high thresholds of OSI and TSVI. CONCLUSION: FSI might be warranted if we were to use the TSVI as a mechano-biological driver for growth and remodeling of PA due to varying intra-vascular flow structures and near wall hemodynamics because of the large expansion of the PA.

Uncertainty quantification of the wall thickness and stiffness in an idealized dissected aorta.

Personalized treatment informed by computational models has the potential to markedly improve the outcome for patients with a type B aortic dissection. However, existing computational models of dissected walls significantly simplify the characteristic false lumen, tears and/or material behavior. Moreover, the patient-specific wall thickness and stiffness cannot be accurately captured non-invasively in clinical practice, which inevitably leads to assumptions in these wall models. It is important to evaluate the impact of the corresponding uncertainty on the predicted wall deformations and stress, which are both key outcome indicators for treatment optimization. Therefore, a physiology-inspired finite element framework was proposed to model the wall deformation and stress of a type B aortic dissection at diastolic and systolic pressure. Based on this framework, 300 finite element analyses, sampled with a Latin hypercube, were performed to assess the global uncertainty, introduced by 4 uncertain wall thickness and stiffness input parameters, on 4 displacement and stress output parameters. The specific impact of each input parameter was estimated using Gaussian process regression, as surrogate model of the finite element framework, and a δ moment-independent analysis. The global uncertainty analysis indicated minor differences between the uncertainty at diastolic and systolic pressure. For all output parameters, the 4th quartile contained the major fraction of the uncertainty. The parameter-specific uncertainty analysis elucidated that the material stiffness and relative thickness of the dissected membrane were the respective main determinants of the wall deformation and stress. The uncertainty analysis provides insight into the effect of uncertain wall thickness and stiffness parameters on the predicted deformation and stress. Moreover, it emphasizes the need for probabilistic rather than deterministic predictions for clinical decision making in aortic dissections.

Growth and remodeling of the dissected membrane in an idealized dissected aorta model.

While transitioning from the acute to chronic phase, the wall of a dissected aorta often expands in diameter and adaptations in thickness and microstructure take place in the dissected membrane. Including the mechanisms, leading to these changes, in a computational model is expected to improve the accuracy of predictions of the long-term complications and optimal treatment timing of dissection patients. An idealized dissected wall was modeled to represent the elastin and collagen production and/or degradation imposed by stress- and inflammation-mediated growth and remodeling, using the homogenized constrained mixture theory. As no optimal growth and remodeling parameters have been defined for aortic dissections, a Latin hypercube sampling with 1000 parameter combinations was assessed for four inflammation patterns, with a varying spatial extent (full/local) and temporal evolution (permanent/transient). The dissected membrane thickening and microstructure was considered together with the diameter expansion over a period of 90 days. The highest success rate was found for the transient inflammation patterns, with about 15% of the samples leading to converged solutions after 90 days. Clinically observed thickening rates were found for 2-4% of the transient inflammation samples, which represented median total diameter expansion rates of about 5 mm/year. The dissected membrane microstructure showed an elastin decrease and, in most cases, a collagen increase. In conclusion, the model with the transient inflammation pattern allowed the reproduction of clinically observed dissected membrane thickening rates, diameter expansion rates and adaptations in microstructure, thus providing guidance in reducing the parameter space in growth and remodeling models of aortic dissections.

Drivers of vascular growth and remodeling: A computational framework to promote benign adaptation in the Ross procedure.

In the sixties, Dr Donald Ross designed a surgical solution for young patients with aortic valve disease by using the patients' own pulmonary valve. The Ross procedure is the only aortic valve replacement technique that can restore long-term survival and preserve quality of life. The main failure mode of the Ross procedure is wall dilatation, potentially leading to valve regurgitation and leakage. Dilatation occurs due to the inability of the pulmonary autograft to adapt to the sudden increase in loading when exposing to aortic pressures. Previous experimental data has shown that a permanent external support wrapped around the artery can prevent the acute dilatation of the arterial wall. However, the textile support leads to stress-shielding phenomena due to the loss of mechanical wall compliance. We present a pragmatic and modular computational framework of arterial growth and remodeling predicting the long-term outcomes of cardiovascular tissue adaptation, with and without textile wrapping. The model integrates mean, systolic and diastolic pressures and assumes the resulting wall stresses to drive the biological remodeling rules. Rather than a single mean pressure or stress deviation from the homeostatic state, we demonstrate that only pulsatile stresses can predict available experimental results. Therefore, we suggest that a biodegradable external support could induce benign remodeling in the Ross procedure. Indeed, a biodegradable textile wrapped around the autograft fulfills the trade-off between prevention of acute dilatation on the one hand and recovery of arterial wall compliance on the other hand. After further validation, the computational framework can set the basis for the development of an actual biodegradable external support for the Ross procedure with optimized polymer mechanical properties and degradation behavior.

How to implement constrained mixture growth and remodeling algorithms for soft biological tissues.

Biological soft tissues are constantly adapting to their mechanical environment and remodel to restore certain mechanobiological homeostatic conditions. These effects can be modeled using the constrained mixture theory, that assumes degradation of material over time and the gradual replacement of extant material by newly deposited material. While this theory presents an elegant way to grasp phenomena of growth and remodeling in soft biological tissues, implementation difficulties may arise. Therefore, we give a detailed overview of the mathematical description of the constrained mixture theory and its homogenized equivalent, and present practical suggestions to numerically implement the theories. These implementations are thoroughly tested with multiple example growth and remodeling models. Results show a good correspondence between both theories, with the homogenized theory favored in terms of time efficiency. Results of a step time convergence study show the importance of choosing a small enough time step, especially when using the classical theory.

Pulse wave velocity: A clinical measure to aid material parameter estimation in computational arterial biomechanics.

Determining proper material parameters from clinical data remains a large, though unavoidable, challenge in patient-specific computational cardiovascular modeling. In an attempt to couple the clinical and modelling practice, this study investigated whether pulse wave velocity (PWV), a clinical arterial stiffness measure, can guide in determining appropriate parameter values for the Gasser-Ogden-Holzapfel (GOH) constitutive model. The reduction and uncertainty analysis was demonstrated on a cylindrical descending thoracic aorta model. Starting from discretized ranges of GOH parameters and using a full factorial design, the parameter sets yielding a physiological PWV (3.5-12.5 m/s) at diastolic pressure (80 mmHg; PWV80) were selected and their PWV at dicrotic notch pressure (110 mmHg; PWV110) was determined. These PWV measures were applied to determine the reduction of the 7D GOH parameter space, the 2D subspaces and the remaining uncertainty in case only PWV80 or both measurements are available. The resulting 12,032 parameter sets lead to a 7D parameter space reduction of ≥ 82.5 % using PWV80, which increased to 96.0 % when including PWV110, in particular at 3.5-8.5 m/s. A similar trend was observed for the remaining uncertainty and the 2D subspaces comprised of medial collagen fiber parameters, while scarce reductions were found for the adventitial and elastin parameters. In conclusion, PWV80 and PWV110 are complementary measures with the potential to reduce the GOH parameter space in arterial models, in particular for media- and collagen-related parameters. Moreover, this approach has the advantage that it allows the estimation of the remaining uncertainty after parameter space reduction.

Computational modeling reveals inflammation-driven dilatation of the pulmonary autograft in aortic position.

The pulmonary autograft in the Ross procedure, where the aortic valve is replaced by the patient's own pulmonary valve, is prone to failure due to dilatation. This is likely caused by tissue degradation and maladaptation, triggered by the higher experienced mechanical loads in aortic position. In order to further grasp the causes of dilatation, this study presents a model for tissue growth and remodeling of the pulmonary autograft, using the homogenized constrained mixture theory and equations for immuno- and mechano-mediated mass turnover. The model outcomes, compared to experimental data from an animal model of the pulmonary autograft in aortic position, show that inflammation likely plays an important role in the mass turnover of the tissue constituents and therefore in the autograft dilatation over time. We show a better match and prediction of long-term outcomes assuming immuno-mediated mass turnover, and show that there is no linear correlation between the stress-state of the material and mass production. Therefore, not only mechanobiological homeostatic adaption should be taken into account in the development of growth and remodeling models for arterial tissue in similar applications, but also inflammatory processes.

Layer-specific fiber distribution in arterial tissue modeled as a constrained mixture.

Collagen fibers and their orientation greatly influence an artery's mechanical characteristics, determining its transversely isotropic behavior. It is generally assumed that these fibers are deposited along a preferred direction to maximize the load bearing capacity of the vessel wall. This implies a large spatial variation in collagen orientation which can be reconstructed in numerical models using so-called reorientation algorithms. Until now, these algorithms have used the classical continuum mechanics modeling framework which requires knowledge of tissue-level parameters and the artery's stress-free reference state, which is inaccessible in a clinical context. We present an algorithm to compute the preferred fiber distribution compatible with the constrained mixture theory, which orients two collagen fiber families according to the loading experienced by the isotropic non-collagenous extracellular matrix, without requiring prior knowledge of the stress-free state. Because consensus is lacking whether stress or stretch is the determining factor behind the preferred fiber distribution, we implemented both approaches and compared the results with experimental microstructural data of an abdominal aorta. The stress-based algorithm was able to describe several experimentally observed transitions of the fiber distribution across the intima, media and adventitia.

Stiffness matters: Improved failure risk assessment of ascending thoracic aortic aneurysms.

Objectives: Rupture and dissection are feared complications of ascending thoracic aortic aneurysms caused by mechanical failure of the wall. The current method of using the aortic diameter to predict the risk of wall failure and to determine the need for surgical resection lacks accuracy. Therefore, this study aims to identify reliable and clinically measurable predictors for aneurysm rupture or dissection by performing a personalized failure risk analysis, including clinical, geometrical, histologic, and mechanical data. Methods: The study cohort consisted of 33 patients diagnosed with ascending aortic aneurysms without genetic syndromes. Uniaxial tensile tests until failure were performed to determine the wall strength. Material parameters were fitted against ex vivo planar biaxial data and in vivo pressure-diameter relationships at diastole and systole, which were derived from multiphasic computed tomography (CT) scans. Using the resulting material properties and in vivo data, the maximal in vivo stress at systole was calculated, assuming a thin-walled axisymmetric geometry. The retrospective failure risk was calculated by comparing the peak wall stress at suprasystolic pressure with the wall strength. Results: The distensibility coefficient, reflecting aortic compliance and derived from blood pressure measurements and multiphasic CT scans, outperformed predictors solely based on geometrical features in assessing the risk of aneurysm failure. Conclusions: In a clinical setting, multiphasic CT scans followed by the calculation of the distensibility coefficient are of added benefit in patient-specific, clinical decision-making. The distensibility derived from the aneurysm volume change has the best predictive power, as it also takes the axial stretch into account.

An improved parameter fitting approach of a planar biaxial test including the experimental prestretch.

Planar biaxial testing is a popular experimental technique for characterizing and comparing biological soft tissues. A correct identification of the different stress states of the tissue sample is therefore essential. However, the difference between the zero-stress reference state and the sample state prior to the loading cycle caused by the mounting, preconditioning and preloading is often not considered. The importance of this difference, caused by prestretch, is investigated by simulating virtual planar biaxial experiments, either assuming an ideal test with a single deformation gradient or using finite element modeling to simulate a rake-based experiment. Multiple parameter fitting methods are used to estimate the material properties based on the available experimental data. These methods vary based on how they approximate the zero-stress state: either the prestretch is ignored, or the loads are zeroed after the preload has been reached, or the unknown prestretch values are included into the optimization function. The results reveal the high necessity of assessing the stress-free state when analyzing a planar biaxial test. The material fitting including the prestretch outperforms the other methods in terms of correctly describing the mechanical behavior of the tested material. It can be extended to correct for the boundary effects induced by the gripping mechanisms, providing a more accurate, yet more computationally expensive estimate of the material properties.

Growth and remodeling in the pulmonary autograft: Computational evaluation using kinematic growth models and constrained mixture theory.

Computational investigations of how soft tissues grow and remodel are gaining more and more interest and several growth and remodeling theories have been developed. Roughly, two main groups of theories for soft tissues can be distinguished: kinematic-based growth theory and theories based on constrained mixture theory. Our goal was to apply these two theories on the same experimental data. Within the experiment, a pulmonary artery was exposed to systemic conditions. The change in diameter was followed-up over time. A mechanical and microstructural analysis of native pulmonary artery and pulmonary autograft was conducted. Whereas the kinematic-based growth theory is able to accurately capture the growth of the tissue, it does not account for the mechanobiological processes causing this growth. The constrained mixture theory takes into account the mechanobiological processes including removal, deposition and adaptation of all structural constituents, allowing us to simulate a changing microstructure and mechanical behavior.

A homogenized constrained mixture model of restenosis and vascular remodelling after balloon angioplasty.

Restenosis is one of the main adverse effects of the treatment of atherosclerosis through balloon angioplasty or stenting. During the intervention, the arterial wall is overstretched, causing a cascade of cellular events and subsequent neointima formation. This mechanical stimulus and its mechanobiological effects can be reproduced in biomechanical simulations. The aim of these models is to predict the long-term outcome of these procedures, to help increase the understanding of restenosis formation and to allow for in silico optimization of the treatment. We propose a predictive finite-element model of restenosis, using the homogenized constrained mixture modelling framework designed to model growth and remodelling in soft tissues. We compare the results with clinical observations in human coronary arteries and experimental findings in non-human primate models. We also explore the model's clinical relevance by testing its response to different balloon loads and to the use of drug-eluting balloons. The comparison of the results with experimental data shows the relevance of the model. We show its ability to predict both inward and outward remodelling as observed in vivo and we show the importance of an improved understanding of restenosis formation from a biomechanical point of view.

How to implement user-defined fiber-reinforced hyperelastic materials in finite element software.

Finite element modeling is often used in biomechanical engineering to evaluate medical devices, treatments and diagnostic tools. Using an adequate material model that describes the mechanical behavior of biological tissues is essential for a reliable outcome of the simulation. Pre-programmed material models for biological tissues are available in many finite element software packages. However, since these pre-programmed models are presented to the user as a black box, without the possibility to modify the material description, many researchers turn to implementing their own material formulations. This is a complex undertaking, requiring extensive knowledge while documentation is limited. This paper provides a detailed description, at the level of the biomedical engineer, of the implementation of a nonlinear hyperelastic material model using user subroutines in Abaqus®, in casuUANISOHYPER_INV and UMAT. The Gasser-Ogden-Holzapfel material model is used as an example, resulting in four implementation variations: the built-in implementation, a UANISOHYPER_INV formulation, a UMAT with analytical tangent stiffness formulation and a UMAT with numerical tangent stiffness formulation. In addition, three different element formulations are used: a continuum compressible, a continuum incompressible and a plane stress incompressible. All cases are thoroughly verified by applying a series of deformations on a single cube element and by simulating an extension-inflation experiment with non-homogeneous deformations and multiple elements. In these test cases, stresses, displacements, reaction forces, the required number of iterations and the total CPU time were compared. The results show that the four implementation variations are very similar, with total relative errors between 10-3 and 10-15, number of iterations that varied by maximum one iteration, and a comparable CPU time. In addition to this detailed overview, the user subroutines are added as supplementary material to this tutorial, which can be used as the ideal starting point for biomechanical engineers to implement their own material models at different levels of complexity.

A Chemomechanobiological Model of the Long-Term Healing Response of Arterial Tissue to a Clamping Injury.

Vascular clamping often causes injury to arterial tissue, leading to a cascade of cellular and extracellular events. A reliable in silico prediction of these processes following vascular injury could help us to increase our understanding thereof, and eventually optimize surgical techniques or drug delivery to minimize the amount of long-term damage. However, the complexity and interdependency of these events make translation into constitutive laws and their numerical implementation particularly challenging. We introduce a finite element simulation of arterial clamping taking into account acute endothelial denudation, damage to extracellular matrix, and smooth muscle cell loss. The model captures how this causes tissue inflammation and deviation from mechanical homeostasis, both triggering vascular remodeling. A number of cellular processes are modeled, aiming at restoring this homeostasis, i.e., smooth muscle cell phenotype switching, proliferation, migration, and the production of extracellular matrix. We calibrated these damage and remodeling laws by comparing our numerical results to in vivo experimental data of clamping and healing experiments. In these same experiments, the functional integrity of the tissue was assessed through myograph tests, which were also reproduced in the present study through a novel model for vasodilator and -constrictor dependent smooth muscle contraction. The simulation results show a good agreement with the in vivo experiments. The computational model was then also used to simulate healing beyond the duration of the experiments in order to exploit the benefits of computational model predictions. These results showed a significant sensitivity to model parameters related to smooth muscle cell phenotypes, highlighting the pressing need to further elucidate the biological processes of smooth muscle cell phenotypic switching in the future.

Constrained mixture modeling affects material parameter identification from planar biaxial tests.

The constrained mixture theory is an elegant way to incorporate the phenomenon of residual stresses in patient-specific finite element models of arteries. This theory assumes an in vivo reference geometry, obtained from medical imaging, and constituent-specific deposition stretches in the assumed reference state. It allows to model residual stresses and prestretches in arteries without the need for a stress-free reference configuration, most often unknown in patient-specific modeling. A finite element (FE) model requires material parameters, which are classically obtained by fitting the constitutive model to experimental data. The characterization of arterial tissue is often based on planar biaxial test data, to which nonlinear elastic fiber-reinforced material parameters are fitted. However, the introduction of the constrained mixture theory requires an adapted approach to parameter fitting. Therefore, we introduce an iterative fitting method, alternating between nonlinear least squares parameter optimization and an FE prestressing algorithm to obtain the correct constrained mixture material state during the mechanical test. We verify the method based on numerically constructed planar biaxial test data sets, containing ground truth sets of material parameters. The results show that the method converges to the correct parameter sets in just a few iterations. Next, the iterative fitting approach is applied to planar biaxial test data of ovine pulmonary artery tissue. The obtained results demonstrate a convergence towards constrained mixture compatible parameters, which differ significantly from classically obtained parameters. We show that this new modeling approach yields in vivo wall stresses similar to when using classically obtained parameters. However, due to the numerous advantages of constrained mixture modeling, our fitting method is relevant to obtain compatible material parameters, that may not be confused with parameters obtained in a classical way.