Preliminary establishment and validation of the inversion method for growth and remodeling parameters of patient-specific abdominal aortic aneurysm

Traditional medical imaging and biomechanical studies have challenges in analyzing the long-term evolution process of abdominal aortic aneurysm (AAA). The homogenized constrained mixture theory (HCMT) allows for quantitative analysis of the changes in the multidimensional morphology and composition of AAA. However, the accuracy of HCMT still requires further clinical verification. This study aims to establish a patient-specific AAA growth model based on HCMT, simulate the long-term growth and remodeling (G&R) process of AAA, and validate the feasibility and accuracy of the method using two additional AAA cases with five follow-up datasets. The media and adventitia layers of AAA were modeled as mixtures composed of elastin, collagen fibers, and smooth muscle cells (SMCs). The strain energy function was used to describe the continuous deposition and degradation effect of the mixture during the AAA evolution. Multiple sets of growth parameters were applied to finite element simulations, and the simulation results were compared with the follow-up data for gradually selecting the optimal growth parameters. Two additional AAA patients with different growth rates were used for validating this method, the optimal growth parameters were obtained using the first two follow-up imaging data, and the growth model was applied to simulate the subsequent four time points. The differences between the simulated diameters and the follow-up diameters of AAA were compared to validate the accuracy of the mechanistic model. The growth parameters, especially the stress-mediated substance deposition gain factor, are highly related to the AAA G&R process. When setting the optimal growth parameters to simulate AAA growth, the proportion of simulation results within the distance of less than 0.5 mm from the baseline models is above 80%. For the validating cases, the mean difference rates between the simulated diameter and the real-world diameter are within 2.5%, which basically meets the clinical demand for quantitatively predicting the AAA growth in maximum diameters. This study simulated the growth process of AAA, and validated the accuracy of this mechanistic model. This method was proved to be used to predict the G&R process of AAA caused by dynamic changes in the mixtures of the AAA vessel wall during long-term, assisting accurately and quantitatively predicting the multidimensional morphological development and mixtures evolution process of AAA in the clinic.

Multi-scaled temporal modeling of cardiovascular disease progression: An illustration of proximal arteries in pulmonary hypertension

The progression of cardiovascular disease is intricately influenced by a complex interplay between physiological pathways, biochemical processes, and physical mechanisms. This study aimed to develop an in-silico physics-based approach to comprehensively model the multifaceted vascular pathophysiological adaptations. This approach focused on capturing the progression of proximal pulmonary arterial hypertension, which is significantly associated with the irreversible degradation of arterial walls and compensatory stress-induced growth and remodeling. This study incorporated critical characteristics related to the distinct time scales for the deformation, thus reflecting the impact of mean pressure on artery growth and tissue damage. The in-silico simulation of the progression of pulmonary hypertension was realized based on computational code combined with the finite element method (FEM) for the simulation of disease progression. The parametric studies further explored the consequences of these irreversible processes. This computational modeling approach may advance our understanding of pulmonary hypertension and its progression.

Hemodynamics and Wall Mechanics of Vascular Graft Failure

Blood vessels are subjected to complex biomechanical loads, primarily from pressure-driven blood flow. Abnormal loading associated with vascular grafts, arising from altered hemodynamics or wall mechanics, can cause acute and progressive vascular failure and end-organ dysfunction. Perturbations to mechanobiological stimuli experienced by vascular cells contribute to remodeling of the vascular wall via activation of mechanosensitive signaling pathways and subsequent changes in gene expression and associated turnover of cells and extracellular matrix. In this review, we outline experimental and computational tools used to quantify metrics of biomechanical loading in vascular grafts and highlight those that show potential in predicting graft failure for diverse disease contexts. We include metrics derived from both fluid and solid mechanics that drive feedback loops between mechanobiological processes and changes in the biomechanical state that govern the natural history of vascular grafts. As illustrative examples, we consider application-specific coronary artery bypass grafts, peripheral vascular grafts, and tissue-engineered vascular grafts for congenital heart surgery as each of these involves unique circulatory environments, loading magnitudes, and graft materials.

A Fluid-Solid-Growth Solver for Cardiovascular Modeling

We implement full, three-dimensional constrained mixture theory for vascular growth and remodeling into a finite element fluid-structure interaction (FSI) solver. The resulting "fluid-solid-growth" (FSG) solver allows long term, patient-specific predictions of changing hemodynamics, vessel wall morphology, tissue composition, and material properties. This extension from short term (FSI) to long term (FSG) simulations increases clinical relevance by enabling mechanobioloigcally-dependent studies of disease progression in complex domains.

Computer Model-Driven Design in Cardiovascular Regenerative Medicine

Continuing advances in genomics, molecular and cellular mechanobiology and immunobiology, including transcriptomics and proteomics, and biomechanics increasingly reveal the complexity underlying native tissue and organ structure and function. Identifying methods to repair, regenerate, or replace vital tissues and organs remains one of the greatest challenges of modern biomedical engineering, one that deserves our very best effort. Notwithstanding the continuing need for improving standard methods of investigation, including cell, organoid, and tissue culture, biomaterials development and fabrication, animal models, and clinical research, it is increasingly evident that modern computational methods should play increasingly greater roles in advancing the basic science, bioengineering, and clinical application of regenerative medicine. This brief review focuses on the development and application of computational models of tissue and organ mechanobiology and mechanics for purposes of designing tissue engineered constructs and understanding their development in vitro and in situ. Although the basic approaches are general, for illustrative purposes we describe two recent examples from cardiovascular medicine-tissue engineered heart valves (TEHVs) and tissue engineered vascular grafts (TEVGs)-to highlight current methods of approach as well as continuing needs.

Numerical analysis of biothermal-fluids and cardiac thermal pulse of abdominal aortic aneurysm

Abdominal aortic aneurysms are serious and difficult to detect, conditions can be deadly if they rupture. In this study, the heat transfer and flow physics of Abdominal Aortic Aneurysm (AAA) were discussed and associated with cardiac cycle to illustrate the cardiac thermal pulse (CTP) of AAA. A CTP and infrared thermography (IRT) evaluation-based on AAA and abdomen skin surface detection method was proposed, respectively. Infrared thermography (IRT) is a promising imaging technique that may detect AAA quicker and cheaper than other imaging techniques (as biomarker). From CFD rigid-wall and FSI Analysis, the transient bioheat transfer effect resulted in a distinct thermal signature (circular thermal elevation) on the temperature profile of midriff skin surface, at both regular body temperature and supine position, under normal clinical temperature. However, it is important to note that thermography is not a perfect technology, and it does have some limitations, such as lack of clinical trials. There is still work to be done to improve this imaging technique and make it a more viable and accurate method for detecting abdominal aortic aneurysms. However, thermography is currently one of the most convenient technologies in this field, and it has the potential to detect abdominal aortic aneurysms earlier than other techniques. CTP, on the other hand, was used to examine the thermal physics of AAA. In CFD rigid-wall Analysis, AAA had a CTP that only responded to systolic phase at regular body temperature. In contrast, a healthy abdominal aorta displayed a CTP that responded to the full cardiac cycle, including diastolic phase at all simulated cases. Besides, the findings from FSI Analysis suggest the influence of numerical simulation techniques on the prediction of thermal physics behaviours of AAA and abdominal skin surface. Lastly, this study correlated the relationship between natural convective heat transfer coefficient with AAA and provided reference for potential clinical diagnostic using IRT in clinical implications.

In vivo development of tissue engineered vascular grafts: a fluid-solid-growth model

Methods of tissue engineering continue to advance, and multiple clinical trials are underway evaluating tissue engineered vascular grafts (TEVGs). Whereas initial concerns focused on suture retention and burst pressure, there is now a pressing need to design grafts to have optimal performance, including an ability to grow and remodel in response to changing hemodynamic loads. Toward this end, there is similarly a need for computational methods that can describe and predict the evolution of TEVG geometry, composition, and material properties while accounting for changes in hemodynamics. Although the ultimate goal is a fluid-solid-growth (FSG) model incorporating fully 3D growth and remodeling and 3D hemodynamics, lower fidelity models having high computational efficiency promise to play important roles, especially in the design of candidate grafts. We introduce here an efficient FSG model of in vivo development of a TEVG based on two simplifying concepts: mechanobiologically equilibrated growth and remodeling of the graft and an embedded control volume analysis of the hemodynamics. Illustrative simulations for a model Fontan conduit reveal the utility of this approach, which promises to be particularly useful in initial design considerations involving formal methods of optimization which otherwise add considerably to the computational expense.

Plasticity and Enzymatic Degradation Coupled With Volumetric Growth in Pulmonary Hypertension Progression

Pulmonary hypertension (PH) is one of the least understood and highly elusive cardiovascular conditions associated with elevated pulmonary arterial pressure. Although the disease mechanisms are not completely understood, evidence has accumulated from human and animal studies that irreversible processes of pulmonary arterial wall damage, compensated by stress-mediated growth, play critical roles in eliciting the mechanisms of disease progression. The aim of this study is to develop a thermodynamic modeling structure of the pulmonary artery to consider coupled plastic-degradation-growth irreversible processes to investigate the mechanical roles of the dissipative phenomena in the disease progression. The proposed model performs a model parameter study of plastic deformation and degradation processes coupled with dissipative growth subjected to elevated pulmonary arterial pressure and computationally generates in silico simulations of PH progression using the clinical features of PH, found in human morphological and mechanical data. The results show that considering plastic deformation can provide a much better fitting of the ex vivo inflation tests than a widely used pure hyperelastic model in higher pressure conditions. In addition, the parameter sensitivity study illustrates that arterial damage and growth cause the increased stiffness, and the full simulation (combining elastic-plastic-degradation-growth models) reveals a key postpathological recovery process of compensating vessel damage by vascular adaptation by reducing the rate of vessel dilation and mediating vascular wall stress. Finally, the simulation results of luminal enlargement, arterial thickening, and arterial stiffness for an anisotropic growth are found to be close to the values from the literature.

Coupling hemodynamics with mechanobiology in patient-specific computational models of ascending thoracic aortic aneurysms

BACKGROUND AND OBJECTIVE

The prevention of ascending thoracic aortic aneurysms (ATAAs), which affect thousands of persons every year worldwide, remains a major issue. ATAAs may be caused by anything that weakens the aortic wall. Altered hemodynamics, which concerns a majority of patients with bicuspid aortic valves, has been shown to be related to such weakening and to contribute to ATAA development and progression. However the underlying mechanisms remain unclear and computational modeling in this field could help significantly to elucidate how hemodynamics and mechanobiology interact in ATAAs.

METHODS

Accordingly, we propose a numerical framework combining computational fluid dynamics and 4D flow magnetic resonance imaging (MRI) coupled with finite element (FE) analyses to simulate growth and remodeling (G&R) occurring in patient-specific aortas in relation with altered hemodynamics. The geometries and the blood velocities obtained from 4D flow MRI are used as boundary conditions for CFD simulations. CFD simulations provide an estimation of the wall shear stress (WSS) and relative residence time (RRT) distribution across the luminal surface of the wall. An initial insult is then applied to the FE model of the aortic wall, assuming that the magnitude of the insult correlates spatially with the normalized RRT distribution obtained from CFD simulations. G&R simulations are then performed. The material behavior of each Gauss point in these FE models is evolved continuously to compensate for the deviation of the actual wall stress distribution from the homeostatic state after the initial insult. The whole approach is illustrated on two healthy and two diseased subjects. The G&R parameters are calibrated against previously established statistical models of ATAA growth rates.

RESULTS

Among the variety of results provided by G&R simulations, the analysis focused especially on the evolution of the wall stiffness, which was shown to be a major risk factor for ATAAs. It was shown that the G&R parameters, such as for instance the rate of collagen production or cell mechanosensitivity, play a critical role in ATAA progression and remodeling.

CONCLUSIONS

These preliminary findings show that patient-specific computational modeling coupling hemodynamics with mechanobiology is a promising approach to explore aneurysm progression.

Machine Learning-Based Pulse Wave Analysis for Early Detection of Abdominal Aortic Aneurysms Using In Silico Pulse Waves

An abdominal aortic aneurysm (AAA) is usually asymptomatic until rupture, which is associated with extremely high mortality. Consequently, the early detection of AAAs is of paramount importance in reducing mortality; however, most AAAs are detected by medical imaging only incidentally. The aim of this study was to investigate the feasibility of machine learning-based pulse wave (PW) analysis for the early detection of AAAs using a database of in silico PWs. PWs in the large systemic arteries were simulated using one-dimensional blood flow modelling. A database of in silico PWs representative of subjects (aged 55, 65 and 75 years) with different AAA sizes was created by varying the AAA-related parameters with major impacts on PWs—identified by parameter sensitivity analysis—in an existing database of in silico PWs representative of subjects without AAAs. Then, a machine learning architecture for AAA detection was trained and tested using the new in silico PW database. The parameter sensitivity analysis revealed that the AAA maximum diameter and stiffness of the large systemic arteries were the dominant AAA-related biophysical properties considerably influencing the PWs. However, AAA detection by PW indexes was compromised by other non-AAA related cardiovascular parameters. The proposed machine learning model produced a sensitivity of 86.8 % and a specificity of 86.3 % in early detection of AAA from the photoplethysmogram PW signal measured in the digital artery with added random noise. The number of false positive and negative results increased with increasing age and decreasing AAA size, respectively. These findings suggest that machine learning-based PW analysis is a promising approach for AAA screening using PW signals acquired by wearable devices.

Computational modeling of vascular growth in patient-specific pulmonary arterial patch reconstructions

Recent progress in vascular growth mechanics has involved the use of computational algorithms to address clinical problems with the use of three-dimensional patient specific geometries. The objective of this study is to establish a predictive computational model for the volumetric growth of pulmonary arterial (PA) tissue following complex cardiovascular patch reconstructive surgeries for congenital heart disease patients. For the first time in the literature, the growth mechanics and performance of artificial cardiovascular patches in contact with the growing PA tissue domain is established. An elastic-growing material model was developed in the open source FEBio software suite to first examine the surgical patch reconstruction process for an idealized main PA anatomy as a benchmark model and then for the patient-specific PA of a newborn. Following patch reconstruction, high levels of stress and strain are compensated by growth on the arterial tissue. As this growth progresses, the arterial tissue is predicted to stiffen to limit elastic deformations. We simulated this arterial growth up to the age of 18 years, when somatic growth plateaus. Our research findings show that the non-growing patch material remains in a low strain state throughout the simulation timeline, while experiencing high stress hot-spots. Arterial tissue growth along the surgical stitch lines is triggered mainly due to PA geometry and blood pressure, rather than due to material property differences in the artificial and native tissue. Thus, non-uniform growth patterns are observed along the arterial tissue proximal to the sutured boundaries. This computational approach is effective for the pre-surgical planning of complex patch surgeries to quantify the unbalanced growth of native arteries and artificial non-growing materials to develop optimal patch biomechanics for improved postoperative outcomes.

Modeling intracranial aneurysm stability and growth: an integrative mechanobiological framework for clinical cases

We present a novel patient-specific fluid-solid-growth framework to model the mechanobiological state of clinically detected intracranial aneurysms (IAs) and their evolution. The artery and IA sac are modeled as thick-walled, non-linear elastic fiber-reinforced composites. We represent the undulation distribution of collagen fibers: the adventitia of the healthy artery is modeled as a protective sheath whereas the aneurysm sac is modeled to bear load within physiological range of pressures. Initially, we assume the detected IA is stable and then consider two flow-related mechanisms to drive enlargement: (1) low wall shear stress; (2) dysfunctional endothelium which is associated with regions of high oscillatory flow. Localized collagen degradation and remodelling gives rise to formation of secondary blebs on the aneurysm dome. Restabilization of blebs is achieved by remodelling of the homeostatic collagen fiber stretch distribution. This integrative mechanobiological modelling workflow provides a step towards a personalized risk-assessment and treatment of clinically detected IAs.

Fast, Rate-Independent, Finite Element Implementation of a 3D Constrained Mixture Model of Soft Tissue Growth and Remodeling

Constrained mixture models of soft tissue growth and remodeling can simulate many evolving conditions in health as well as in disease and its treatment, but they can be computationally expensive. In this paper, we derive a new fast, robust finite element implementation based on a concept of mechanobiological equilibrium that yields fully resolved solutions and allows computation of quasi-equilibrated evolutions when imposed perturbations are slow relative to the adaptive process. We demonstrate quadratic convergence and verify the model via comparisons with semi-analytical solutions for arterial mechanics. We further examine the enlargement of aortic aneurysms for which we identify new mechanobiological insights into factors that affect the nearby non-aneurysmal segment as it responds to the changing mechanics within the diseased segment. Because this new 3D approach can be implemented within many existing finite element solvers, constrained mixture models of growth and remodeling can now be used more widely.

Predictors of Abdominal Aortic Aneurysm Risks

Computational biomechanics via finite element analysis (FEA) has long promised a means of assessing patient-specific abdominal aortic aneurysm (AAA) rupture risk with greater efficacy than current clinically used size-based criteria. The pursuit stems from the notion that AAA rupture occurs when wall stress exceeds wall strength. Quantification of peak (maximum) wall stress (PWS) has been at the cornerstone of this research, with numerous studies having demonstrated that PWS better differentiates ruptured AAAs from non-ruptured AAAs. In contrast to wall stress models, which have become progressively more sophisticated, there has been relatively little progress in estimating patient-specific wall strength. This is because wall strength cannot be inferred non-invasively, and measurements from excised patient tissues show a large spectrum of wall strength values. In this review, we highlight studies that investigated the relationship between biomechanics and AAA rupture risk. We conclude that combining wall stress and wall strength approximations should provide better estimations of AAA rupture risk. However, before personalized biomechanical AAA risk assessment can become a reality, better methods for estimating patient-specific wall properties or surrogate markers of aortic wall degradation are needed. Artificial intelligence methods can be key in stratifying patients, leading to personalized AAA risk assessment.

Cardiovascular models for personalised medicine: Where now and where next?

The aim of this position paper is to provide a brief overview of the current status of cardiovascular modelling and of the processes required and some of the challenges to be addressed to see wider exploitation in both personal health management and clinical practice. In most branches of engineering the concept of the digital twin, informed by extensive and continuous monitoring and coupled with robust data assimilation and simulation techniques, is gaining traction: the Gartner Group listed it as one of the top ten digital trends in 2018. The cardiovascular modelling community is starting to develop a much more systematic approach to the combination of physics, mathematics, control theory, artificial intelligence, machine learning, computer science and advanced engineering methodology, as well as working more closely with the clinical community to better understand and exploit physiological measurements, and indeed to develop jointly better measurement protocols informed by model-based understanding. Developments in physiological modelling, model personalisation, model outcome uncertainty, and the role of models in clinical decision support are addressed and 'where-next' steps and challenges discussed.

Quantification of the regional bioarchitecture in the human aorta

Regional variance in human aortic bioarchitecture responsible for the elasticity of the vessel is poorly understood. The current study quantifies the elements responsible for aortic compliance, namely, elastin, collagen and smooth muscle cells, using histological and stereological techniques on human tissue with a focus on regional heterogeneity. Using donated cadaveric tissue, a series of samples were excised between the proximal ascending aorta and the distal abdominal aorta, for five cadavers, each of which underwent various staining procedures to enhance specific constituents of the wall. Using polarised light microscopy techniques, the orientation of collagen fibres was studied for each location and each tunical layer of the aorta. Significant transmural and longitudinal heterogeneity in collagen fibre orientations were uncovered throughout the vessel. It is shown that a von Mises mixture model is required accurately to fit the complex collagen fibre distributions that exist along the aorta. Additionally, collagen and smooth muscle cell density was observed to increase with increasing distance from the heart, whereas elastin density decreased. Evidence clearly demonstrates that the aorta is a highly heterogeneous vessel which cannot be simplistically represented by a single compliance value. The quantification and fitting of the regional aortic bioarchitectural data, although not without its limitations, including mean cohort age of 77.6 years, facilitates the development of next-generation finite element models that can potentially simulate the influence of regional aortic composition and microstructure on vessel biomechanics.

Anisotropic stiffness and tensional homeostasis induce a natural anisotropy of volumetric growth and remodeling in soft biological tissues

Growth in soft biological tissues in general results in anisotropic changes of the tissue geometry. It remains a key challenge in biomechanics to understand, quantify, and predict this anisotropy. In this paper, we demonstrate that anisotropic tissue stiffness and the well-known mechanism of tensional homeostasis induce a natural anisotropy of the geometric changes resulting from volumetric growth in soft biological tissues. As a rule of thumb, this natural anisotropy makes differential tissue volume elements dilate mainly in the direction(s) of lowest stiffness. This simple principle is shown to explain the experimentally observed growth behavior in a host of different soft biological tissues without relying on any additional heuristic assumptions or quantities (such as ad hoc defined growth tensors).

In vivo quantification of regional circumferential Green strain in the thoracic and abdominal aorta by 2D spiral cine DENSE MRI

INTRODUCTION

Regional tissue mechanics play a fundamental role in patient-specific cardiovascular function. Nevertheless, regional assessments of aortic kinematics remain lacking due to the challenge of imaging the thin aortic wall. Herein, we present a novel application of DENSE (Displacement Encoding with Stimulated Echoes) MRI to quantify the circumferential Green strain of the thoracic and abdominal aorta.

METHODS

2D spiral cine DENSE and steady-state free procession (SSFP) cine images were acquired at 3T at the infrarenal aorta (IAA), descending thoracic aorta (DTA), or distal aortic arch (DAA) in a pilot study of 6 healthy volunteers. DENSE data was processed with multiple custom noise-reduction techniques to calculate circumferential Green strain across 16 equispaced sectors around the aorta. Each volunteer was scanned twice to evaluate interstudy repeatability.

RESULTS

Circumferential strain was heterogeneously distributed in all volunteers and locations. Spatial heterogeneity index by location was 0.37 (IAA), 0.28 (DTA), and 0.59 (DAA). Mean peak strain by DENSE for each cross-section was consistent with the homogenized linearized strain estimated from SSFP cine. The mean difference in peak strain across all sectors following repeat imaging was -0.1±2.2%, with a mean absolute difference of 1.7%.

CONCLUSIONS

Aortic cine DENSE MRI is a viable non-invasive technique for quantifying heterogeneous regional aortic wall strain and has significant potential to improve patient-specific clinical assessments of numerous aortopathies, as well as to provide the lacking spatiotemporal data required to refine computational models of aortic growth and remodeling.

Prediction of Abdominal Aortic Aneurysm Growth Using Dynamical Gaussian Process Implicit Surface

OBJECTIVE

We propose a novel approach to predict the Abdominal Aortic Aneurysm (AAA) growth in future time, using longitudinal computer tomography (CT) scans of AAAs that are captured at different times in a patient-specific way.

METHODS

We adopt a formulation that considers a surface of the AAA as a manifold embedded in a scalar field over the three dimensional (3D) space. For this formulation, we develop our Dynamical Gaussian Process Implicit Surface (DGPIS) model based on observed surfaces of 3D AAAs as visible variables while the scalar fields are hidden. In particular, we use Gaussian process regression to construct the field as an observation model from CT training image data. We then learn a dynamic model to represent the evolution of the field. Finally, we derive the predicted AAA surface from the predicted field along with uncertainty quantified in future time.

RESULTS

A dataset of 7 subjects (4-7 scans) was collected and used to evaluate the proposed method by comparing its prediction Hausdorff distance errors against those of simple extrapolation. In addition, we evaluate the prediction results with respect to a conventional shape analysis technique such as Principal Component Analysis (PCA). All comparative results show the superior prediction performance of the proposed approach.

CONCLUSION

We introduce a novel approach to predict the AAA growth and its predicted uncertainty in future time, using longitudinal CT scans in a patient-specific fashion.

SIGNIFICANCE

The capability to predict the AAA shape and its confidence region by our approach establish the potential for guiding clinicians with informed decision in conducting medical treatment and monitoring of AAAs.

Structural modelling of the cardiovascular system

Computational modelling of the cardiovascular system offers much promise, but represents a truly interdisciplinary challenge, requiring knowledge of physiology, mechanics of materials, fluid dynamics and biochemistry. This paper aims to provide a summary of the recent advances in cardiovascular structural modelling, including the numerical methods, main constitutive models and modelling procedures developed to represent cardiovascular structures and pathologies across a broad range of length and timescales; serving as an accessible point of reference to newcomers to the field. The class of so-called hyperelastic materials provides the theoretical foundation for the modelling of how these materials deform under load, and so an overview of these models is provided; comparing classical to application-specific phenomenological models. The physiology is split into components and pathologies of the cardiovascular system and linked back to constitutive modelling developments, identifying current state of the art in modelling procedures from both clinical and engineering sources. Models which have originally been derived for one application and scale are shown to be used for an increasing range and for similar applications. The trend for such approaches is discussed in the context of increasing availability of high performance computing resources, where in some cases computer hardware can impact the choice of modelling approach used.

Growth Description for Vessel Wall Adaptation: A Thick-Walled Mixture Model of Abdominal Aortic Aneurysm Evolution

(1) Background: Vascular tissue seems to adapt towards stable homeostatic mechanical conditions, however, failure of reaching homeostasis may result in pathologies. Current vascular tissue adaptation models use many ad hoc assumptions, the implications of which are far from being fully understood; (2) Methods: The present study investigates the plausibility of different growth kinematics in modeling Abdominal Aortic Aneurysm (AAA) evolution in time. A structurally motivated constitutive description for the vessel wall is coupled to multi-constituent tissue growth descriptions; Constituent deposition preserved either the constituent’s density or its volume, and Isotropic Volume Growth (IVG), in-Plane Volume Growth (PVG), in-Thickness Volume Growth (TVG) and No Volume Growth (NVG) describe the kinematics of the growing vessel wall. The sensitivity of key modeling parameters is explored, and predictions are assessed for their plausibility; (3) Results: AAA development based on TVG and NVG kinematics provided not only quantitatively, but also qualitatively different results compared to IVG and PVG kinematics. Specifically, for IVG and PVG kinematics, increasing collagen mass production accelerated AAA expansion which seems counterintuitive. In addition, TVG and NVG kinematics showed less sensitivity to the initial constituent volume fractions, than predictions based on IVG and PVG; (4) Conclusions: The choice of tissue growth kinematics is of crucial importance when modeling AAA growth. Much more interdisciplinary experimental work is required to develop and validate vascular tissue adaption models, before such models can be of any practical use.

Hemodynamic assessments of the ascending thoracic aortic aneurysm using fluid-structure interaction approach

Current assessment and management of ascending thoracic aortic aneurysm (ATAA) rely heavily on the diameter of the ATAA and blood pressure rather than biomechanical and hemodynamic parameters such as arterial wall deformation or wall shear stress. The objective of the current study was to develop an accurate computational method for modeling the mechanical responses of the ATAA to provide additional information in patient evaluations. Fully coupled fluid structure interaction simulations were conducted using data from cases with ATAA with measured geometrical parameters in order to evaluate and analyze the change in biomechanical responses under normotensive and hypertensive conditions. Anisotropic hyperelastic material property estimates were applied to the ATAA data which represented three different geometrical configurations of ATAAs. The resulting analysis showed significant variations in maximum wall shear stress despite minimal differences in flow velocity between two blood pressure conditions. Additionally, the three different ATAA conditions identified different aortic expansions that were not uniform under pulsatile pressure. The elevated wall stress with hypertension was also geometry-dependent. The developed models suggest that ATTA cases have unique characteristic in biomechanical and hemodynamic evaluations that can be useful in risk management.

A mathematical model of aortic aneurysm formation

Abdominal aortic aneurysm (AAA) is a localized enlargement of the abdominal aorta, such that the diameter exceeds 3 cm. The natural history of AAA is progressive growth leading to rupture, an event that carries up to 90% risk of mortality. Hence there is a need to predict the growth of the diameter of the aorta based on the diameter of a patient’s aneurysm at initial screening and aided by non-invasive biomarkers. IL-6 is overexpressed in AAA and was suggested as a prognostic marker for the risk in AAA. The present paper develops a mathematical model which relates the growth of the abdominal aorta to the serum concentration of IL-6. Given the initial diameter of the aorta and the serum concentration of IL-6, the model predicts the growth of the diameter at subsequent times. Such a prediction can provide guidance to how closely the patient’s abdominal aorta should be monitored. The mathematical model is represented by a system of partial differential equations taking place in the aortic wall, where the media is assumed to have the constituency of an hyperelastic material.

A novel chemo-mechano-biological model of arterial tissue growth and remodelling

Arterial growth and remodelling (G&R) is mediated by vascular cells in response to their chemical and mechanical environment. To date, mechanical and biochemical stimuli tend to be modelled separately, however this ignores their complex interplay. Here, we present a novel mathematical model of arterial chemo-mechano-biology. We illustrate its application to the development of an inflammatory aneurysm in the descending human aorta. The arterial wall is modelled as a bilayer cylindrical non-linear elastic membrane, which is internally pressurised and axially stretched. The medial degradation that accompanies aneurysm development is driven by an inflammatory response. Collagen remodelling is simulated by adaption of the natural reference configuration of constituents; growth is simulated by changes in normalised mass-densities. We account for the distribution of attachment stretches that collagen fibres are configured to the matrix and, innovatively, allow this distribution to remodel. This enables the changing functional role of the adventitia to be simulated. Fibroblast-mediated collagen growth is represented using a biochemical pathway model: a system of coupled non-linear ODEs governs the evolution of fibroblast properties and levels of key biomolecules under the regulation of Transforming Growth Factor (TGF)-β, a key promoter of matrix deposition. Given physiologically realistic targets, different modes of aneurysm development can be captured, while the predicted evolution of biochemical variables is qualitatively consistent with trends observed experimentally. Interestingly, we observe that increasing the levels of collagen-promoting TGF-β results in arrest of aneurysm growth, which seems to be consistent with experimental evidence. We conclude that this novel Chemo-Mechano-Biological (CMB) mathematical model has the potential to provide new mechanobiological insight into vascular disease progression and therapy.

Cell-matrix interaction during strain-dependent remodelling of simulated collagen networks

The importance of tissue remodelling is widely accepted, but the mechanism by which the remodelling process occurs remains poorly understood. At the tissue scale, the concept of tensional homeostasis, in which there exists a target stress for a cell and remodelling functions to move the cell stress towards that target, is an important foundation for much theoretical work. We present here a theoretical model of a cell in parallel with a network to study what factors of the remodelling process help the cell move towards mechanical stability. The cell-network system was deformed and kept at constant stress. Remodelling was modelled by simulating strain-dependent degradation of collagen fibres and four different cases of collagen addition. The model did not lead to complete tensional homeostasis in the range of conditions studied, but it showed how different expressions for deposition and removal of collagen in a fibre network can interact to modulate the cell's ability to shield itself from an imposed stress by remodelling the surroundings. This study also showed how delicate the balance between deposition and removal rates is and how sensitive the remodelling process is to small changes in the remodelling rules.