Computational modeling of hypertensive growth in the human carotid artery

Persistent non-homeostatic remodeling of aortic collagen following a brief episode of hypertension: A computational study

The healthy adult aorta exhibits a remarkable homeostatic ability to respond to sustained changes in hemodynamic loads under many circumstances, but this mechanical homeostasis can be compromised or lost in natural aging and diverse pathological processes. Herein, we investigate persistent non-homeostatic changes in the composition and mechanical properties of the thoracic aorta in adult wild-type mice following 14 days of angiotensin II-induced hypertension. We employ a multiscale computational model of arterial growth and remodeling driven by mechanosensitive and angiotensin II-related cell signaling pathways. We find that experimentally observed findings can only be recapitulated computationally if the collagen deposited during the transient period of hypertension has altered properties (deposition stretch, fiber angle, crosslinking) compared with the collagen produced in the original homeostatic state. Some of these changes are predicted to persist for at least six months after blood pressure is restored to normal levels, consistent with the experimental findings.

Soft-Tissue Material Properties and Mechanogenetics during Cardiovascular Development

During embryonic development, changes in the cardiovascular microstructure and material properties are essential for an integrated biomechanical understanding. This knowledge also enables realistic predictive computational tools, specifically targeting the formation of congenital heart defects. Material characterization of cardiovascular embryonic tissue at consequent embryonic stages is critical to understand growth, remodeling, and hemodynamic functions. Two biomechanical loading modes, which are wall shear stress and blood pressure, are associated with distinct molecular pathways and govern vascular morphology through microstructural remodeling. Dynamic embryonic tissues have complex signaling networks integrated with mechanical factors such as stress, strain, and stiffness. While the multiscale interplay between the mechanical loading modes and microstructural changes has been studied in animal models, mechanical characterization of early embryonic cardiovascular tissue is challenging due to the miniature sample sizes and active/passive vascular components. Accordingly, this comparative review focuses on the embryonic material characterization of developing cardiovascular systems and attempts to classify it for different species and embryonic timepoints. Key cardiovascular components including the great vessels, ventricles, heart valves, and the umbilical cord arteries are covered. A state-of-the-art review of experimental techniques for embryonic material characterization is provided along with the two novel methods developed to measure the residual and von Mises stress distributions in avian embryonic vessels noninvasively, for the first time in the literature. As attempted in this review, the compilation of embryonic mechanical properties will also contribute to our understanding of the mature cardiovascular system and possibly lead to new microstructural and genetic interventions to correct abnormal development.

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.

Multiscale simulations of left ventricular growth and remodeling

Cardiomyocytes can adapt their size, shape, and orientation in response to altered biomechanical or biochemical stimuli. The process by which the heart undergoes structural changes-affecting both geometry and material properties-in response to altered ventricular loading, altered hormonal levels, or mutant sarcomeric proteins is broadly known as cardiac growth and remodeling (G&R). Although it is likely that cardiac G&R initially occurs as an adaptive response of the heart to the underlying stimuli, prolonged pathological changes can lead to increased risk of atrial fibrillation, heart failure, and sudden death. During the past few decades, computational models have been extensively used to investigate the mechanisms of cardiac G&R, as a complement to experimental measurements. These models have provided an opportunity to quantitatively study the relationships between the underlying stimuli (primarily mechanical) and the adverse outcomes of cardiac G&R, i.e., alterations in ventricular size and function. State-of-the-art computational models have shown promise in predicting the progression of cardiac G&R. However, there are still limitations that need to be addressed in future works to advance the field. In this review, we first outline the current state of computational models of cardiac growth and myofiber remodeling. Then, we discuss the potential limitations of current models of cardiac G&R that need to be addressed before they can be utilized in clinical care. Finally, we briefly discuss the next feasible steps and future directions that could advance the field of cardiac G&R.

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.

The study of border zone formation in ischemic heart using electro-chemical coupled computational model

Myocardial infarction (MI) is the most common cause of a heart failure, which occurs due to myocardial ischemia leading to left ventricular (LV) remodeling. LV remodeling particularly occurs at the ischemic area and the region surrounds it, known as the border zone. The role of the border zone in initiating LV remodeling process urges the investigation on the correlation between early border zone changes and remodeling outcome. Thus, this study aims to simulate a preliminary conceptual work of the border zone formation and evolution during onset of MI and its effect towards early LV remodeling processes by incorporating the oxygen concentration effect on the electrophysiology of an idealized three-dimensional LV through electro-chemical coupled mathematical model. The simulation result shows that the region of border zone, represented by the distribution of electrical conductivities, keeps expanding over time. Based on this result, the border zone is also proposed to consist of three sub-regions, namely mildly, moderately, and seriously impaired conductivity regions, which each region categorized depending on its electrical conductivities. This division could be used as a biomarker for classification of reversible and irreversible myocardial injury and will help to identify the different risks for the survival of patient. Larger ischemic size and complete occlusion of the coronary artery can be associated with an increased risk of developing irreversible injury, in particular if the reperfusion treatment is delayed. Increased irreversible injury area can be related with cardiovascular events and will further deteriorate the LV function over time.

The study of myocardial ischemia-reperfusion treatment through computational modelling

Reperfusion of the blood flow to ischemic myocardium is the standard treatment for patients suffering myocardial infarction. However, the reperfusion itself can also induce myocardial injury, in which the actual mechanism and its risk factors remain unclear. This work aims to study the mechanism of ischemia-reperfusion treatment using a three-dimensional (3D) oxygen diffusion model. An electrical model is then coupled to an oxygen model to identify the possible region of myocardial damage. Our findings show that the value of oxygen exceeds its optimum (>1.0) at the ischemic area during early reperfusion period. This complication was exacerbated in a longer ischemic period. While a longer reperfusion time causes a continuous excessive oxygen supply to the ischemic area throughout the reperfusion time. This work also suggests the use of less than 0.8 of initial oxygen concentration in the reperfusion treatment to prevent undesired upsurge at the early reperfusion period and further myocardial injury. We also found the region at risk for myocardial injury is confined in the ischemic vicinity revealed by its electrical conductivity impairment. Although there is a risk that reperfusion leads to myocardial injury for excessive oxygen accumulation, the reperfusion treatment is helpful in reducing the infarct size.

Computational modeling of cardiac growth and remodeling in pressure overloaded hearts-Linking microstructure to organ phenotype

Cardiac growth and remodeling (G&R) refers to structural changes in myocardial tissue in response to chronic alterations in loading conditions. One such condition is pressure overload where elevated wall stresses stimulate the growth in cardiomyocyte thickness, associated with a phenotype of concentric hypertrophy at the organ scale, and promote fibrosis. The initial hypertrophic response can be considered adaptive and beneficial by favoring myocyte survival, but over time if pressure overload conditions persist, maladaptive mechanisms favoring cell death and fibrosis start to dominate, ultimately mediating the transition towards an overt heart failure phenotype. The underlying mechanisms linking biological factors at the myocyte level to biomechanical factors at the systemic and organ level remain poorly understood. Computational models of G&R show high promise as a unique framework for providing a quantitative link between myocardial stresses and strains at the organ scale to biological regulatory processes at the cellular level which govern the hypertrophic response. However, microstructurally motivated, rigorously validated computational models of G&R are still in their infancy. This article provides an overview of the current state-of-the-art of computational models to study cardiac G&R. The microstructure and mechanosensing/mechanotransduction within cells of the myocardium is discussed and quantitative data from previous experimental and clinical studies is summarized. We conclude with a discussion of major challenges and possible directions of future research that can advance the current state of cardiac G&R computational modeling. STATEMENT OF SIGNIFICANCE: The mechanistic links between organ-scale biomechanics and biological factors at the cellular size scale remain poorly understood as these are largely elusive to investigations using experimental methodology alone. Computational G&R models show high promise to establish quantitative links which allow more mechanistic insight into adaptation mechanisms and may be used as a tool for stratifying the state and predict the progression of disease in the clinic. This review provides a comprehensive overview of research in this domain including a summary of experimental data. Thus, this study may serve as a basis for the further development of more advanced G&R models which are suitable for making clinical predictions on disease progression or for testing hypotheses on pathogenic mechanisms using in-silico models.

Three dimensional numerical analysis of hemodynamic of stenosed artery considering realistic outlet boundary conditions

BACKGROUND AND OBJECTIVE

Mortality rate increases globally among which one third is due to diseased blood vessels. Due to late diagnoses of the disease in vessels (severe stenoses), qualitative and rapid assessment becomes difficult. Earlier assessment of stenoses can lead to formulation of effective treatment protocol. It is often found that proliferation of secondary stenoses at downstream of a stenosed vessel depends on the degree of severity of primary stenoses. Numerical investigation of flow dynamics of blood in such condition helps in prediction of distributed field of secondarystenoses. This investigation also requires consideration of rigorous boundary conditions at inlet and outlet of defined flow domain.

METHODS

Patient-specific geometry of aortic arch with stenoses in descending aorta was considered for numerical estimation of biofluid dynamics. Boundary conditionsat inlet and outlet were extracted from time-resolved pulsed Doppler Ultrasound imaging at appropriate sections of the vessel. Womersley inlet flux was considered. Flow parameters like wall shear stress, oscillatory shear index, etc. were evaluated at upper and lower aortic arch of the vessel at different combinations of boundary conditions at inlet and four outlets respectively.

RESULTS

Effect of outlet boundary conditions were acknowledged for the progression of secondary stenoses. Severity of primary stenoses was found influencing the progression of secondary stenoses. It was found that the outlets Left Subclavian Artery and Left Common Carotid Artery greatly influence the flow dynamic structure within the stenosed aortic arch. Simultaneously, lower wall of aortic-arch had shown more affinity for secondary stenoses progression.

CONCLUSION

Aortic arch is a vital anatomical region of circulatory system which is vulnerable to progression of secondary stenoses in presence of primary stenoses in ascending or descending aorta. It also drives the author to speculate the influence of anurysm in descending aorta on this landmark of aortic arch.

Using machine learning to characterize heart failure across the scales

Heart failure is a progressive chronic condition in which the heart undergoes detrimental changes in structure and function across multiple scales in time and space. Multiscale models of cardiac growth can provide a patient-specific window into the progression of heart failure and guide personalized treatment planning. Yet, the predictive potential of cardiac growth models remains poorly understood. Here, we quantify predictive power of a stretch-driven growth model using a chronic porcine heart failure model, subject-specific multiscale simulation, and machine learning techniques. We combine hierarchical modeling, Bayesian inference, and Gaussian process regression to quantify the uncertainty of our experimental measurements during an 8-week long study of volume overload in six pigs. We then propagate the experimental uncertainties from the organ scale through our computational growth model and quantify the agreement between experimentally measured and computationally predicted alterations on the cellular scale. Our study suggests that stretch is the major stimulus for myocyte lengthening and demonstrates that a stretch-driven growth model alone can explain [Formula: see text] of the observed changes in myocyte morphology. We anticipate that our approach will allow us to design, calibrate, and validate a new generation of multiscale cardiac growth models to explore the interplay of various subcellular-, cellular-, and organ-level contributors to heart failure. Using machine learning in heart failure research has the potential to combine information from different sources, subjects, and scales to provide a more holistic picture of the failing heart and point toward new treatment strategies.

Gradient-enhanced continuum models of healing in damaged soft tissues

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

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).

Mathematical model of hypertension-induced arterial remodeling: A chemo-mechanical approach

The development of chronic hypertension is a poorly described process involving many chemical and structural changes to the artery. Typically, mathematical models of this disease focus primarily on the mechanical aspects such as arterial geometry, elasticity, and tissue content, or alternatively on the chemical drivers of vasoactivity such as nitric oxide and reactive oxygen species. This paper presents a model that considers the powerful interaction between mechanical and biochemical drivers of hypertension and arterial remodeling. Based on biological processes thought to be involved in the development of hypertension, we have built a system of algebraic, differential, and integral equations. Endothelial dysfunction, which is known to limit vasodilation, is explicitly considered in the model and plays a vital role in the development of chronic hypertension. Numerical solutions to the system are consistent with available experimental data for normal and spontaneously-hypertensive rats.

Evaluation of microstructurally motivated constitutive models to describe age-dependent tendon healing

Tendon injuries are common to all ages. Injured tendons typically do not recover full functionality. The amount and organization of tendon constituents dictate their mechanical properties. The impact of changes in these constituents during (patho)physiologic processes (e.g., aging and healing) are not fully understood. Toward this end, microstructurally motivated strain energy functions (SEFs) offer insight into underlying mechanisms of age-dependent healing. Several SEFs have been adapted for tendon; however, most are phenomenological. Therefore, the aims of this study are: (1) evaluate the descriptive capability of SEFs in age-dependent murine patellar tendon healing and (2) identify a SEF for implementation in a growth and remodeling (G&R) model. To accomplish these aims, models were fitted to patellar tendon tensile data from multiple age groups and post-injury timepoints. Model sensitivity to parameters and the determinability of the parameters were assessed. A two-way analysis of variance was used to identify changes in parameters and the feasibility of implementing each model into a G&R model is discussed. The evaluated SEFs exhibited adequate descriptive capability. Parameter determinability and sensitivity analysis, however, highlighted the need for additional data to inform and validate the models to increase physiologic relevance and enable G&R model formulation to determine underlying mechanisms of age-dependent healing. This work, as a first, evaluated changes in tendon mechanical properties both as functions of age and injury in an age-dependent manner using microstructurally motivated models, highlights inherent dependencies between parameters of widely used hyperelastic models, and identified unique post-injury behavior by the aging group compared to the mature and aged groups.

Mechanobiological model of arterial growth and remodeling

A coupled agent-based model (ABM) and finite element analysis (FEA) computational framework is developed to study the interplay of bio-chemo-mechanical factors in blood vessels and their role in maintaining homeostasis. The agent-based model implements the power of REPAST Simphony libraries and adapts its environment for biological simulations. Coupling a continuum-level model (FEA) to a cellular-level model (ABM) has enabled this computational framework to capture the response of blood vessels to increased or decreased levels of growth factors, proteases and other signaling molecules (on the micro scale) as well as altered blood pressure. Performance of the model is assessed by simulating porcine left anterior descending artery under normotensive conditions and transient increases in blood pressure and by analyzing sensitivity of the model to variations in the rule parameters of the ABM. These simulations proved that the model is stable under normotensive conditions and can recover from transient increases in blood pressure. Sensitivity studies revealed that the model is most sensitive to variations in the concentration of growth factors that affect cellular proliferation and regulate extracellular matrix composition (mainly collagen).

Growth and Remodeling of Load-Bearing Biological Soft Tissues

The past two decades reveal a growing role of continuum biomechanics in understanding homeostasis, adaptation, and disease progression in soft tissues. In this paper, we briefly review the two primary theoretical approaches for describing mechano-regulated soft tissue growth and remodeling on the continuum level as well as hybrid approaches that attempt to combine the advantages of these two approaches while avoiding their disadvantages. We also discuss emerging concepts, including that of mechanobiological stability. Moreover, to motivate and put into context the different theoretical approaches, we briefly review findings from mechanobiology that show the importance of mass turnover and the prestressing of both extant and new extracellular matrix in most cases of growth and remodeling. For illustrative purposes, these concepts and findings are discussed, in large part, within the context of two load-bearing, collagen dominated soft tissues - tendons/ligaments and blood vessels. We conclude by emphasizing further examples, needs, and opportunities in this exciting field of modeling soft tissues.

Computational modeling of acute myocardial infarction

Myocardial infarction, commonly known as heart attack, is caused by reduced blood supply and damages the heart muscle because of a lack of oxygen. Myocardial infarction initiates a cascade of biochemical and mechanical events. In the early stages, cardiomyocytes death, wall thinning, collagen degradation, and ventricular dilation are the immediate consequences of myocardial infarction. In the later stages, collagenous scar formation in the infarcted zone and hypertrophy of the non-infarcted zone are auto-regulatory mechanisms to partly correct for these events. Here we propose a computational model for the short-term adaptation after myocardial infarction using the continuum theory of multiplicative growth. Our model captures the effects of cell death initiating wall thinning, and collagen degradation initiating ventricular dilation. Our simulations agree well with clinical observations in early myocardial infarction. They represent a first step toward simulating the progression of myocardial infarction with the ultimate goal to predict the propensity toward heart failure as a function of infarct intensity, location, and size.

Patient-Specific Airway Wall Remodeling in Chronic Lung Disease

Chronic lung disease affects more than a quarter of the adult population; yet, the mechanics of the airways are poorly understood. The pathophysiology of chronic lung disease is commonly characterized by mucosal growth and smooth muscle contraction of the airways, which initiate an inward folding of the mucosal layer and progressive airflow obstruction. Since the degree of obstruction is closely correlated with the number of folds, mucosal folding has been extensively studied in idealized circular cross sections. However, airflow obstruction has never been studied in real airway geometries; the behavior of imperfect, non-cylindrical, continuously branching airways remains unknown. Here we model the effects of chronic lung disease using the nonlinear field theories of mechanics supplemented by the theory of finite growth. We perform finite element analysis of patient-specific Y-branch segments created from magnetic resonance images. We demonstrate that the mucosal folding pattern is insensitive to the specific airway geometry, but that it critically depends on the mucosal and submucosal stiffness, thickness, and loading mechanism. Our results suggests that patient-specific airway models with inherent geometric imperfections are more sensitive to obstruction than idealized circular models. Our models help to explain the pathophysiology of airway obstruction in chronic lung disease and hold promise to improve the diagnostics and treatment of asthma, bronchitis, chronic obstructive pulmonary disease, and respiratory failure.

Computational model of collagen turnover in carotid arteries during hypertension

It is well known that biological tissues adapt their properties because of different mechanical and chemical stimuli. The goal of this work is to study the collagen turnover in the arterial tissue of hypertensive patients through a coupled computational mechano-chemical model. Although it has been widely studied experimentally, computational models dealing with the mechano-chemical approach are not. The present approach can be extended easily to study other aspects of bone remodeling or collagen degradation in heart diseases. The model can be divided into three different stages. First, we study the smooth muscle cell synthesis of different biological substances due to over-stretching during hypertension. Next, we study the mass-transport of these substances along the arterial wall. The last step is to compute the turnover of collagen based on the amount of these substances in the arterial wall which interact with each other to modify the turnover rate of collagen. We simulate this process in a finite element model of a real human carotid artery. The final results show the well-known stiffening of the arterial wall due to the increase in the collagen content.

On the Role of Mechanics in Chronic Lung Disease

Progressive airflow obstruction is a classical hallmark of chronic lung disease, affecting more than one fourth of the adult population. As the disease progresses, the inner layer of the airway wall grows, folds inwards, and narrows the lumen. The critical failure conditions for airway folding have been studied intensely for idealized circular cross-sections. However, the role of airway branching during this process is unknown. Here, we show that the geometry of the bronchial tree plays a crucial role in chronic airway obstruction and that critical failure conditions vary significantly along a branching airway segment. We perform systematic parametric studies for varying airway cross-sections using a computational model for mucosal thickening based on the theory of finite growth. Our simulations indicate that smaller airways are at a higher risk of narrowing than larger airways and that regions away from a branch narrow more drastically than regions close to a branch. These results agree with clinical observations and could help explain the underlying mechanisms of progressive airway obstruction. Understanding growth-induced instabilities in constrained geometries has immediate biomedical applications beyond asthma and chronic bronchitis in the diagnostics and treatment of chronic gastritis, obstructive sleep apnea and breast cancer.