Prior Distributions of Material Parameters for Bayesian Calibration of Growth and Remodeling Computational Model of Abdominal Aortic Wall

A biochemomechanical model of collagen turnover in arterial adaptations to hemodynamic loading

The production, removal, and remodeling of fibrillar collagen is fundamental to mechanical homeostasis in arteries, including dynamic morphological and microstructural changes that occur in response to sustained changes in blood flow and pressure under physiological conditions. These dynamic processes involve complex, coupled biological, chemical, and mechanical mechanisms that are not completely understood. Nevertheless, recent simulations using constrained mixture models with phenomenologically motivated constitutive relations have proven able to predict salient features of the progression of certain vascular adaptations as well as disease processes. Collagen turnover is modeled, in part, via stress-dependent changes in collagen half-life, typically within the range of 10-70 days. By contrast, in this work we introduce a biochemomechanical approach to model the cellular synthesis of procollagen as well as its transition from an intermediate state of assembled microfibrils to mature cross-linked fibers, with mechano-regulated removal. The resulting model can simulate temporal changes in geometry, composition, and stress during early vascular adaptation (weeks to months) for modest changes in blood flow or pressure. It is shown that these simulations capture salient features from data presented in the literature from different animal models.

Effect of aging on the biaxial mechanical behavior of human descending thoracic aorta: Experiments and constitutive modeling considering collagen crosslinking

Collagen crosslinking, an important contributor to the stiffness of soft tissues, was found to increase with aging in the aortic wall. Here we investigated the mechanical properties of human descending thoracic aorta with aging and the role of collagen crosslinking through a combined experimental and modeling approach. A total of 32 samples from 17 donors were collected and divided into three age groups: <40, 40-60 and > 60 years. Planar biaxial tensile tests were performed to characterize the anisotropic mechanical behavior of the aortic samples. A recently developed constitutive model incorporating collagen crosslinking into the two-fiber family model (Holzapfel and Ogden, 2020) was modified to accommodate biaxial deformation of the aorta, in which the extension and rotation kinematics of bonded fibers and crosslinks were decoupled. The mechanical testing results show that the aorta stiffens with aging with a more drastic change in the longitudinal direction, which results in altered aortic anisotropy. Our results demonstrate a good fitting capability of the constitutive model considering crosslinking for the biaxial aortic mechanics of all age groups. Furthermore, constitutive modeling results suggest an increased contribution of crosslinking and strain energy density to the biaxial stress-stretch behaviors with aging and point to excessive crosslinking as a prominent contributor to aortic stiffening.

A Biochemomechanical Model of Collagen Turnover in Arterial Adaptations to Hemodynamic Loading

The production, removal, and remodeling of fibrillar collagen is fundamental to arterial homeostasis, including dynamic morphological and microstructural changes that occur in response to sustained changes in blood flow and pressure under physiological conditions. These dynamic processes involve complex, coupled biological, chemical, and mechanical mechanisms that are not completely understood. Nevertheless, recent simulations using constrained mixture models with phenomenologically motivated constitutive relations have demonstrated a capability to predict salient features of the progression of certain vascular adaptations and disease processes. Collagen turnover is modeled, in part, via stress-dependent changes in collagen half-life, typically taken within the range of 10â€"70 days. By contrast, in this work we introduce a biochemomechanical approach to model the cellular synthesis of procollagen as well as its transition from an intermediate state of assembled microfibrils to mature cross-linked fibers, with mechano-regulated removal. The resulting model can simulate temporal changes in geometry, composition, and stress during early vascular adaptation (weeks to months) for modest changes in blood flow or pressure. It is shown that these simulations capture salient features from data presented in the literature from different animal models.

Computational modelling of multi-temporal ventricular-vascular interactions during the progression of pulmonary arterial hypertension

A computational framework is developed to consider the concurrent growth and remodelling (G&R) processes occurring in the large pulmonary artery (PA) and right ventricle (RV), as well as ventricular-vascular interactions during the progression of pulmonary arterial hypertension (PAH). This computational framework couples the RV and the proximal PA in a closed-loop circulatory system that operates in a short timescale of a cardiac cycle, and evolves over a long timescale due to G&R processes in the PA and RV. The framework predicts changes in haemodynamics (e.g. 68.2% increase in mean PA pressure), RV geometry (e.g. 38% increase in RV end-diastolic volume) and PA tissue microstructure (e.g. 90% increase in collagen mass) that are consistent with clinical and experimental measurements of PAH. The framework also predicts that a reduction in RV contractility is associated with long-term RV chamber dilation, a common biomarker observed in the late-stage PAH. Sensitivity analyses on the G&R rate constants show that large PA stiffening (both short and long term) is affected by RV remodelling more than the reverse. This framework can serve as a foundation for the future development of a more predictive and comprehensive cardiovascular G&R model with realistic heart and vascular geometries.

Region-dependent mechanical characterization of porcine thoracic aorta with a one-to-many correspondence method to create virtual datasets using uniaxial tensile tests

The simulation of the cardiovascular system and in silico clinical trials have garnered attention in the biomedical engineering field. Physics-based modeling is essential to associate with physical and clinical features. In physics-based constitutive modeling, the identification of the parameters and estimation of their ranges based on appropriate experiments are required. Uniaxial tests are commonly used in the field of vascular mechanics, but they have limitations in fully characterizing the regional mechanical behavior of the aorta. Therefore, this study is aimed at identifying a method to integrate constitutive models with experimental data to elucidate regional aortic behavior. To create a virtual two-dimensional dataset, a pair of uniaxial experimental datasets in the longitudinal and circumferential directions was combined using a one-to-many correspondence method such as bootstrap aggregation. The proposed approach is subsequently applied to three constitutive models, i.e., the Fung model, Holzapfel model, and constrained mixture model, to estimate the material parameters based on the four test regions of the porcine thoracic aorta. Finally, the regional difference in the mechanical behavior of the aorta, the correlation between the experimental characteristics and model parameters, and the inter-correlation of the material parameters are confirmed. This integrative approach will enhance the prediction capability of the model with respect to the regions of the aorta.

Inverse modeling framework for characterizing patient-specific microstructural changes in the pulmonary arteries

Microstructural changes in the pulmonary arteries associated with pulmonary arterial hypertension (PAH) is not well understood and characterized in humans. To address this issue, we developed and applied a patient-specific inverse finite element (FE) modeling framework to characterize mechanical and structural changes of the micro-constituents in the proximal pulmonary arteries using in-vivo pressure measurements and magnetic resonance images. The framework was applied using data acquired from a pediatric PAH patient and a heart transplant patient with normal pulmonary arterial pressure, which serves as control. Parameters of a constrained mixture model that are associated with the structure and mechanical properties of elastin, collagen fibers and smooth muscle cells were optimized to fit the patient-specific pressure-diameter responses of the main pulmonary artery. Based on the optimized parameters, individual stress and linearized stiffness resultants of the three tissue constituents, as well as their aggregated values, were estimated in the pulmonary artery. Aggregated stress resultant and stiffness are, respectively, 4.6 and 3.4 times higher in the PAH patient than the control subject. Stress and stiffness resultants of each tissue constituent are also higher in the PAH patient. Specifically, the mean stress resultant is highest in elastin (PAH: 69.96, control: 14.42 kPa-mm), followed by those in smooth muscle cell (PAH: 13.95, control: 4.016 kPa-mm) and collagen fibers (PAH: 13.19, control: 2.908 kPa-mm) in both the PAH patient and the control subject. This result implies that elastin may be the key load-bearing constituent in the pulmonary arteries of the PAH patient and the control subject.

Machine learning approaches to surrogate multifidelity Growth and Remodeling models for efficient abdominal aortic aneurysmal applications

Computational Growth and Remodeling (G&R) models have been widely used to capture the pathological development of arterial diseases and have shown promise for aiding clinical diagnosis, prognosis prediction, and staging classification. However, due to the high complexity of the arterial adaptation mechanism, high-fidelity arterial G&R simulation usually takes hours or even days, which hinders its application in clinical practice. To remedy this problem, we develop a computationally efficient arterial G&R simulation framework that comprehensively combines the physics-based G&R simulations and data-driven machine learning approaches. The proposed framework greatly enhances the computational efficiency of arterial G&R simulations, thereby enabling more time-consuming arterial applications, including personalized parameter estimation and arterial disease progression prediction. In particular, we achieve significant computational cost reduction mainly through two methods: (1) constructing a Multifidelity Surrogate (MFS) to approximate multifidelity G&R simulations by using a cokriging approach and (2) developing a novel iterative optimization algorithm for personalized parameter estimation. The proposed framework is demonstrated by estimating G&R model parameters and predicting individual aneurysm growth using follow-up CT images of Abdominal Aortic Aneurysms (AAAs) from 21 patients. Results show that the personalized parameters are satisfactorily estimated and the growth of AAAs is predicted within the clinically relevant time frame, i.e., less than 2 h, without a loss of accuracy.

Patient-Specific Prediction of Abdominal Aortic Aneurysm Expansion Using Bayesian Calibration

Translating recent advances in abdominal aortic aneurysm (AAA) growth and remodeling (G&R) knowledge into a predictive, patient-specific clinical treatment tool requires a major paradigm shift in computational modeling. The objectives of this study are to develop a prediction framework that first calibrates the physical AAA G&R model using patient-specific serial computed tomography (CT) scan images, predicts the expansion of an AAA in the future, and quantifies the associated uncertainty in the prediction. We adopt a Bayesian calibration method to calibrate parameters in the G&R computational model and predict the magnitude of AAA expansion. The proposed Bayesian approach can take different sources of uncertainty; therefore, it is well suited to achieve our aims in predicting the AAA expansion process as well as in computing the propagated uncertainty. We demonstrate how to achieve the proposed aims by solving the formulated Bayesian calibration problems for cases with the synthetic G&R model output data and real medical patient-specific CT data. We compare and discuss the performance of predictions and computation time under different sampling cases of the model output data and patient data, both of which are simulated by the G&R computation. Furthermore, we apply our Bayesian calibration to real patient-specific serial CT data and validate our prediction. The accuracy and efficiency of the proposed method is promising, which appeals to computational and medical communities.

In Silico Tissue Engineering: A Coupled Agent-Based Finite Element Approach

Over the past two decades, the increase in prevalence of cardiovascular diseases and the limited availability of autologous blood vessels and saphenous vein grafts have motivated the development of tissue-engineered vascular grafts (TEVGs). However, compliance mismatch and poor mechanical properties of the TEVGs remain as two major issues that need to be addressed. Researchers have investigated the role of various culture conditions and mechanical conditioning in deposition and orientation of collagen fibers, which are the key structural components in the vascular wall; however, the intrinsic complexity of mechanobiological interactions demands implementing new engineering approaches that allow researchers to investigate various scenarios more efficiently. In this study, we utilized a coupled agent-based finite element analysis (AB-FEA) modeling approach to study the effect of various loading modes (uniaxial, biaxial, and equibiaxial), boundary conditions, stretch magnitudes, and growth factor concentrations on growth and remodeling of smooth muscle cell-populated TEVGs, with specific focus on collagen deposition and orientation. Our simulations (12 weeks of culture) showed that biaxial cyclic loading (and not uniaxial or equibiaxial) leads to alignment of collagen fibers in the physiological directions. Moreover, axial boundary conditions of the TEVG act as determinants of fiber orientations. Decreasing the serum concentration, from 10% to 5% or 1%, significantly decreased the growth and remodeling speed, but only affected the fiber orientation in the 1% serum case. In conclusion, in silico tissue engineering has the potential to evolve the future of tissue engineering, as it will allow researchers to conceptualize various interactions and investigate numerous scenarios with great speed. In this study, we were able to predict the orientation of collagen fibers in TEVGs using a coupled AB-FEA model in less than 8 h. Impact Statement Tissue-engineered vascular grafts (TEVGs) hold potential to replace the current gold standard of vascular grafting, saphenous vein grafts. However, developing TEVGs that mimic the mechanical performance of the native tissue remains a challenging task. We developed a computational model of the grafts' remodeling processes and studied the effects of various loading mechanisms and culture conditions on collagen fiber orientation, which is a key factor in mechanical performance of the grafts. We were able to predict the fiber orientations accurately and show that biaxial loading and axial boundary conditions are important factors in collagen fiber organization.

Bayesian inference of constitutive model parameters from uncertain uniaxial experiments on murine tendons

Constitutive models for biological tissue are typically formulated as a mixture of constituents and the overall response is then assembled by superposition or compatibility. This ensures the stress response of the biological tissue to be in the range of a given constitutive relationship, guaranteeing that at least one parameter combination exists so that an experimental response can be sufficiently well captured. Another, perhaps more challenging, problem is to use constitutive models as a proxy to infer the structure/function of a biological tissue from experiments. In other words, we determine the optimal set of parameters by solving an inverse problem and use these parameters to infer the integrity of the tissue constituents. In previous studies, we focused on the mechanical stress-stretch response of the murine patellar tendon at various age and healing timepoints and solved the inverse problem using three constitutive models, i.e., the Freed-Rajagopal, Gasser-Ogden-Holzapfel and Shearer in order of increasing microstructural detail. Herein, we extend this work by adopting a Bayesian perspective on parameter estimation and implement the constitutive relations in the tulip library for uncertainty analysis, critically analyzing parameter marginals, correlations, identifiability and sensitivity. Our results show the importance of investigating the variability of parameter estimates and that results from optimization may be misleading, particularly for models with many parameters inferred from limited experimental evidence. In our study, we show that different age and healing conditions do not correspond to statistically significant separation among the Gasser-Ogden-Holzapfel and Shearer model parameters, while the phenomenological Freed-Rajagopal model is instead characterized by better indentifiability and parameter learning. Use of the complete experimental observations rather than averaged stress-stretch responses appears to positively constrain inference and results appear to be invariant with respect to the scaling of the experimental uncertainty.

An in vivo parameter identification method for arteries: numerical validation for the human abdominal aorta

A method for identifying mechanical properties of arterial tissue in vivo is proposed in this paper and it is numerically validated for the human abdominal aorta. Supplied with pressure-radius data, the method determines six parameters representing relevant mechanical properties of an artery. In order to validate the method, 22 finite element arteries are created using published data for the human abdominal aorta. With these in silico abdominal aortas, which serve as mock experiments with exactly known material properties and boundary conditions, pressure-radius data sets are generated and the mechanical properties are identified using the proposed parameter identification method. By comparing the identified and pre-defined parameters, the method is quantitatively validated. For healthy abdominal aortas, the parameters show good agreement for the material constant associated with elastin and the radius of the stress-free state over a large range of values. Slightly larger discrepancies occur for the material constants associated with collagen, and the largest relative difference is obtained for the in situ axial prestretch. For pathological abdominal aortas incorrect parameters are identified, but the identification method reveals the presence of diseased aortas. The numerical validation indicates that the proposed parameter identification method is able to identify adequate parameters for healthy abdominal aortas and reveals pathological aortas from in vivo-like data.

Reactive Constrained Mixtures for Modeling the Solid Matrix of Biological Tissues

This article illustrates our approach for modeling the solid matrix of biological tissues using reactive constrained mixtures. Several examples are presented to highlight the potential benefits of this approach, showing that seemingly disparate fields of mechanics and chemical kinetics are actually closely interrelated and may be elegantly expressed in a unified framework. Thus, constrained mixture models recover classical theories for fibrous materials with bundles oriented in different directions or having different reference configurations, that produce characteristic fiber recruitment patterns under loading. Reactions that exchange mass among various constituents of a mixture may be used to describe tissue growth and remodeling, which may also alter the material's anisotropy. Similarly, reactions that describe the breaking and reforming of bonds may be used to model free energy dissipation in a viscoelastic material. Therefore, this framework is particularly well suited for modeling biological tissues.

Empirically Determined Vascular Smooth Muscle Cell Mechano-Adaptation Law

Cardiovascular disease can alter the mechanical environment of the vascular system, leading to mechano-adaptive growth and remodeling. Predictive models of arterial mechano-adaptation could improve patient treatments and outcomes in cardiovascular disease. Vessel-scale mechano-adaptation includes remodeling of both the cells and extracellular matrix. Here, we aimed to experimentally measure and characterize a phenomenological mechano-adaptation law for vascular smooth muscle cells (VSMCs) within an artery. To do this, we developed a highly controlled and reproducible system for applying a chronic step-change in strain to individual VSMCs with in vivo like architecture and tracked the temporal cellular stress evolution. We found that a simple linear growth law was able to capture the dynamic stress evolution of VSMCs in response to this mechanical perturbation. These results provide an initial framework for development of clinically relevant models of vascular remodeling that include VSMC adaptation.