A strain energy function for arteries accounting for wall composition and structure

Nonlinear Elasticity of Blood Vessels and Vascular Grafts

The transplantation of vascular grafts has emerged as a prevailing approach to address vascular disorders. However, the development of small-diameter vascular grafts is still in progress, as they serve in a more complicated mechanical environment than their counterparts with larger diameters. The biocompatibility and functional characteristics of small-diameter vascular grafts have been well developed; however, mismatch in mechanical properties between the vascular grafts and native arteries has not been accomplished, which might facilitate the long-term patency of small-diameter vascular grafts. From a point of view in mechanics, mimicking the nonlinear elastic mechanical behavior exhibited by natural blood vessels might be the state-of-the-art in designing vascular grafts. This review centers on elucidating the nonlinear elastic behavior of natural blood vessels and vascular grafts. The biological functionality and limitations associated with as-reported vascular grafts are meticulously reviewed and the future trajectory for fabricating biomimetic small-diameter grafts is discussed. This review might provide a different insight from the traditional design and fabrication of artificial vascular grafts.

Review paper: The importance of consideration of collagen cross-links in computational models of collagen-based tissues

Collagen as the main protein in Extra Cellular Matrix (ECM) is the main load-bearing component of fibrous tissues. Nanostructure and architecture of collagen fibrils play an important role in mechanical behavior of these tissues. Extensive experimental and theoretical studies have so far been performed to capture these properties, but none of the current models realistically represent the complexity of network mechanics because still less is known about the collagen's inner structure and its effect on the mechanical properties of tissues. The goal of this review article is to emphasize the significance of cross-links in computational modeling of different collagen-based tissues, and to reveal the need for continuum models to consider cross-links properties to better reflect the mechanical behavior observed in experiments. In addition, this study outlines the limitations of current investigations and provides potential suggestions for the future work.

In Vivo Material Properties of Human Common Carotid Arteries: Trends and Sex Differences

INTRODUCTION

In vivo estimation of material properties of arterial tissue can provide essential insights into the development and progression of cardiovascular diseases. Furthermore, these properties can be used as an input to finite element simulations of potential medical treatments.

MATERIALS AND METHODS

This study uses non-invasively measured pressure, diameter and wall thickness of human common carotid arteries (CCAs) acquired in 103 healthy subjects. A non-linear optimization was performed to estimate material parameters of two different constitutive models: a phenomenological, isotropic model and a structural, anisotropic model. The effect of age, sex, body mass index and blood pressure on the parameters was investigated.

RESULTS AND CONCLUSION

Although both material models were able to model in vivo arterial behaviour, the structural model provided more realistic results in the supra-physiological domain. The phenomenological model predicted very high deformations for pressures above the systolic level. However, the phenomenological model has fewer parameters that were shown to be more robust. This is an advantage when only the physiological domain is of interest. The effect of stiffening with age, BMI and blood pressure was present for women, but not always for men. In general, sex had the biggest effect on the mechanical properties of CCAs. Stiffening trends with age, BMI and blood pressure were present but not very strong. The intersubject variability was high. Therefore, it can be concluded that finding a representative set of parameters for a certain age or BMI group would be very challenging. Instead, for purposes of patient-specific modelling of surgical procedures, we currently advise the use of patient-specific parameters.

Constituent-based quasi-linear viscoelasticity: a revised quasi-linear modelling framework to capture nonlinear viscoelasticity in arteries

Arteries exhibit fully nonlinear viscoelastic behaviours (i.e. both elastically and viscously nonlinear). While elastically nonlinear arterial models are well established, effective mathematical descriptions of nonlinear viscoelasticity are lacking. Quasi-linear viscoelasticity (QLV) offers a convenient way to mathematically describe viscoelasticity, but its viscous linearity assumption is unsuitable for whole-wall vascular applications. Conversely, application of fully nonlinear viscoelastic models, involving deformation-dependent viscous parameters, to experimental data is impractical and often reduces to identifying specific solutions for each tested loading condition. The present study aims to address this limitation: By applying QLV theory at the wall constituent rather than at the whole-wall level, the deformation-dependent relative contribution of the constituents allows to capture nonlinear viscoelasticity with a unique set of deformation-independent model parameters. Five murine common carotid arteries were subjected to a protocol of quasi-static and harmonic, pseudo-physiological biaxial loading conditions to characterise their viscoelastic behaviour. The arterial wall was modelled as a constrained mixture of an isotropic elastin matrix and four families of collagen fibres. Constituent-based QLV was implemented by assigning different relaxation functions to collagen- and elastin-borne parts of the wall stress. Nonlinearity in viscoelasticity was assessed via the pressure dependency of the dynamic-to-quasi-static stiffness ratio. The experimentally measured ratio increased with pressure, from 1.03 [Formula: see text] 0.03 (mean [Formula: see text] standard deviation) at 80-40 mmHg to 1.58 [Formula: see text] 0.22 at 160-120 mmHg. Constituent-based QLV captured well this trend by attributing the wall viscosity predominantly to collagen fibres, whose recruitment starts at physiological pressures. In conclusion, constituent-based QLV offers a practical and effective solution to model arterial viscoelasticity.

A review on the biomechanical behaviour of the aorta

Large aortic aneurysm and acute and chronic aortic dissection are pathologies of the aorta requiring surgery. Recent advances in medical intervention have improved patient outcomes; however, a clear understanding of the mechanisms leading to aortic failure and, hence, a better understanding of failure risk, is still missing. Biomechanical analysis of the aorta could provide insights into the development and progression of aortic abnormalities, giving clinicians a powerful tool in risk stratification. The complexity of the aortic system presents significant challenges for a biomechanical study and requires various approaches to analyse the aorta. To address this, here we present a holistic review of the biomechanical studies of the aorta by categorising articles into four broad approaches, namely theoretical, in vivo, experimental and combined investigations. Experimental studies that focus on identifying mechanical properties of the aortic tissue are also included. By reviewing the literature and discussing drawbacks, limitations and future challenges in each area, we hope to present a more complete picture of the state-of-the-art of aortic biomechanics to stimulate research on critical topics. Combining experimental modalities and computational approaches could lead to more comprehensive results in risk prediction for the aortic system.

Fluid-structure interaction study for biomechanics and risk factors in Stanford type A aortic dissection

Aortic dissection is a life-threatening condition with a rising prevalence in the elderly population, possibly as a consequence of the increasing population life expectancy. Untreated aortic dissection can lead to myocardial infarction, aortic branch malperfusion or occlusion, rupture, aneurysm formation and death. This study aims to assess the potential of a biomechanical model in predicting the risks of a non-dilated thoracic aorta with Stanford type A dissection. To achieve this, a fully coupled fluid-structure interaction model was developed under realistic blood flow conditions. This model of the aorta was developed by considering three-dimensional artery geometry, multiple artery layers, hyperelastic artery wall, in vivo-based physiological time-varying blood velocity profiles, and non-Newtonian blood behaviours. The results demonstrate that in a thoracic aorta with Stanford type A dissection, the wall shear stress (WSS) is significantly low in the ascending aorta and false lumen, leading to potential aortic dilation and thrombus formation. The results also reveal that the WSS is highly related to blood flow patterns. The aortic arch region near the brachiocephalic and left common carotid artery is prone to rupture, showing a good agreement with the clinical reports. The results have been translated into their potential clinical relevance by revealing the role of the stress state, WSS and flow characteristics as the main parameters affecting lesion progression, including rupture and aneurysm. The developed model can be tailored for patient-specific studies and utilised as a predictive tool to estimate aneurysm growth and initiation of wall rupture inside the human thoracic aorta.

Modeling planar response of vascular tissues using quadratic functions of effective strain

Simulation-based studies of the cardiovascular structure such as aorta have become increasingly popular for many biomedical problems such as predictions of aneurysm rupture. A critical step in these simulations is the development of constitutive models that accurately describe the tissue's mechanical behavior. In this work, we present a new constitutive model, which explicitly accounts for the gradual recruitment of collagen fibers. The recruitment is considered using an effective stretch, which is a continuum-scale kinematic variable measuring the uncrimped stretch of the tissue in an average sense. The strain energy of a fiber bundle is described by a quadratic function of the effective strain. Constitutive models formulated in this manner are applied to describe the responses of ascending thoracic aortic aneurysm and porcine thoracic aorta tissues. The heterogeneous properties of the ATAA tissue are extracted from bulge inflation test data, and then used in finite element analysis to simulate the inflation test. The descriptive and predictive capabilities are further assessed using planar testing data of porcine thoracic aortic tissues. It is found that the constitutive model can accurately describe the stress-strain relations. In particular, the finite element simulation replicates the displacement, strain, and stress distributions with excellent fidelity.

Percutaneous delivery and degradation of a shape memory elastomer poly(glycerol dodecanedioate) in porcine pulmonary arteries

Shape memory biodegradable elastomers are an emergent class of biomaterials well-suited for percutaneous cardiovascular repair requiring nonlinear elastic materials with facile handling. We have previously developed a chemically crosslinked shape memory elastomer, poly (glycerol dodecanedioate) (PGD), exhibiting tunable transition temperatures around body temperature (34-38 °C), exhibiting nonlinear elastic properties approximating cardiac tissues, and favorable degradation rates in vitro. Degree of tissue coverage, degradation and consequent changes in polymer thermomechanical properties, and inflammatory response in preclinical animal models are unknown material attributes required for translating this material into cardiovascular devices. This study investigates changes in the polymer structure, tissue coverage, endothelialization, and inflammation of percutaneously implanted PGD patches (20 mm × 9 mm x 0.5 mm) into the branch pulmonary arteries of Yorkshire pigs for three months. After three months in vivo, 5/8 samples exhibited (100%) tissue coverage, 2/8 samples exhibited 85-95% tissue coverage, and 1/8 samples exhibited limited (<20%) tissue coverage with mild-moderate inflammation. PGD explants showed a (60-70%) volume loss and (25-30%) mass loss, and a reduction in polymer crosslinks. Lumenal and mural surfaces and the cross-section of the explant demonstrated evidence of degradation. This study validates PGD as an appropriate cardiovascular engineering material due to its propensity for rapid tissue coverage and uneventful inflammatory response in a preclinical animal model, establishing a precedent for consideration in cardiovascular repair applications.

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.

A discrete fiber network finite element model of arterial elastin network considering inter-fiber crosslinking property and density

Inter-fiber crosslinks within the extracellular matrix (ECM) play important roles in determining the mechanical properties of the fibrous network. Discrete fiber network (DFN) models have been used to study fibrous biological material, however the contribution of inter-fiber crosslinks to the mechanics of the ECM network is not well understood. In this study, a DFN model of arterial elastin network was developed based on measured structural features to study the contribution of inter-fiber crosslinking properties and density to the mechanics and fiber kinematics of the network. The DFN was generated by randomly placing line segments into a given domain following a fiber orientation distribution function obtained from multiphoton microscopy until a desired fiber areal fraction was reached. Intersections between the line segments were treated as crosslinks. The generated DFN model was then incorporated into an ABAQUS finite element model to simulate the network under equi- and nonequi-biaxial deformation. The inter-fiber crosslinks were modeled using connector elements with either zero (pin joint) or infinite (weld joint) rotational stiffness. Furthermore, inter-fiber crosslinking density was systematically reduced and its effect on both network- and fiber-level mechanics was studied. The DFN model showed good fitting and predicting capabilities of the stress-strain behavior of the elastin network. While the pin and weld joints do not seem to have noticeable effect on the network stress-strain behavior, the crosslinking properties can affect the local fiber mechanics and kinematics. Overall, our study suggests that inter-fiber crosslinking properties are important to the multiscale mechanics and fiber kinematics of the ECM network.

Fluid-structure interaction (FSI) simulation for studying the impact of atherosclerosis on hemodynamics, arterial tissue remodeling, and initiation risk of intracranial aneurysms

The biomechanical and hemodynamic effects of atherosclerosis on the initiation of intracranial aneurysms (IA) are not yet clearly discovered. Also, studies for the observation of hemodynamic variation due to atherosclerotic stenosis and its impact on arterial remodeling and aneurysm genesis remain a controversial field of vascular engineering. The majority of studies performed are relevant to computational fluid dynamic (CFD) simulations. CFD studies are limited in consideration of blood and arterial tissue interactions. In this work, the interaction of the blood and vessel tissue because of atherosclerotic occlusions is studied by developing a fluid and structure interaction (FSI) analysis for the first time. The FSI presents a semi-realistic simulation environment to observe how the blood and vessels' structural interactions can increase the accuracy of the biomechanical study results. In the first step, many different intracranial vessels are modeled for an investigation of the biomechanical and hemodynamic effects of atherosclerosis in arterial tissue remodeling. Three physiological conditions of an intact artery, the artery with intracranial atherosclerosis (ICAS), and an atherosclerotic aneurysm (ACA) are employed in the models with required assumptions. Finally, the obtained outputs are studied with comparative and statistical analyses according to the intact model in a normal physiological condition. The results show that existing occlusions in the cross-sectional area of the arteries play a determinative role in changing the hemodynamic behavior of the arterial segments. The undesirable variations in blood velocity and pressure throughout the vessels increase the risk of arterial tissue remodeling and aneurysm formation.

Remodeling of extracellular matrix in the urinary bladder of paraplegic rats results in increased compliance and delayed fiber recruitment 16 weeks after spinal cord injury

The ability of the urinary bladder to maintain low intravesical pressures while storing urine is key in ensuring proper organ function and highlights the key role that tissue mechanics plays in the lower urinary tract. Loss of supraspinal neuronal connections to the bladder after spinal cord injury can lead to remodeling of the structure of the bladder wall, which may alter its mechanical characteristics. In this study, we investigate if the morphology and mechanical properties of the bladder extracellular matrix are altered in rats 16 weeks after spinal cord injury as compared to animals who underwent sham surgery. We measured and quantified the changes in bladder geometry and mechanical behavior using histological analysis, tensile testing, and constitutive modeling. Our results suggest bladder compliance is increased in paraplegic animals 16 weeks post-injury. Furthermore, constitutive modeling showed that increased distensibility was driven by an increase in collagen fiber waviness, which altered the distribution of fiber recruitment during loading. STATEMENT OF SIGNIFICANCE: The ability of the urinary bladder to store urine under low pressure is key in ensuring proper organ function. This highlights the important role that mechanics plays in the lower urinary tract. Loss of control of neurologic connection to the bladder from spinal cord injury can lead to changes of the structure of the bladder wall, resulting in altered mechanical characteristics. We found that the bladder wall's microstructure in rats 16 weeks after spinal cord injury is more compliant than in healthy animals. This is significant since it is the longest time post-injury analyzed, to date. Understanding the extreme remodeling capabilities of the bladder in pathological conditions is key to inform new possible therapies.

Biaxial mechanics of thermally denaturing skin - Part 2: Modeling

Understanding the response of skin to superphysiological temperatures is critical to the diagnosis and prognosis of thermal injuries, and to the development of temperature-based medical therapeutics. Unfortunately, this understanding has been hindered by our incomplete knowledge about the nonlinear coupling between skin temperature and its mechanics. In Part I of this study we experimentally demonstrated a complex interdependence of time, temperature, direction, and load in skin's response to superphysiological temperatures. In Part II of our study, we test two different models of skin's thermo-mechanics to explain our observations. In both models we assume that skin's response to superphysiological temperatures is governed by the denaturation of its highly collageneous microstructure. Thus, we capture skin's native mechanics via a microstructurally-motivated strain energy function which includes probability distributions for collagen fiber orientation and waviness. In the first model, we capture skin's response to superphysiological temperatures as a transition between two states that link the kinetics of collagen fiber denaturation to fiber coiling and to the transformation of each fiber's constitutive behavior from purely elastic to viscoelastic. In the second model, we capture skin's response to superphysiological temperatures instead via three states in which a sequence of two reactions link the kinetics of collagen fiber denaturation to fiber coiling, followed by a state of fiber damage. Given the success of both models in qualitatively and quantitatively capturing our observations, we expect that our work will provide guidance for future experiments that could probe each model's assumptions toward a better understanding of skin's coupled thermo-mechanics and that our work will be used to guide the engineering design of heat treatment therapies. STATEMENT OF SIGNIFICANCE: Quantifying and modeling skin thermo-mechanics is critical to our understanding of skin physiology, pathophysiology, as well as heat-based treatments. This work addresses a lack of theoretical and computational models of the coupled thermo-mechanics of skin. Our model accounts for skin microstructure through modeling the probability of fiber orientation and fiber stress-free states. Denaturing induces changes in the stress-free configuration of collagen, as well as changes in fiber stiffness and viscoelastic properties. We propose two competing models that fit all of our experimental observations. These models will enable future developments of thermal-therapeutics, prevention and management of skin thermal injuries, and set a foundation for improved mechanistic models of skin thermo-mechanics.

Uniaxial properties of ascending aortic aneurysms in light of effective stretch

A constitutive model that explicitly considers the gradual recruitment of collagen fibers is applied to investigate the uniaxial properties of human ascending aortic aneurysms. The model uses an effective stretch, which is a continuum scale kinematic variable measuring the true stretch of the tissue, to formulate the fiber stress. The constitutive equation contains two shape parameters characterizing the stochastic distribution of fiber waviness, and two elastic parameters accounting for, respectively, the elastic properties of ground substance and the straightened collagen fibers. The model is applied to 156 sets of uniaxial stress-stretch data obtained from 52 aneurysm samples. Major findings include (1) the uniaxial response can be well described by a quadratic strain energy function of the effective strain; (2) the ultimate stretches, when measured in terms of the effective stretch, are closely clustered around 1.1, in contrast to a much wider range in the original stretch; and (3) the ultimate stress correlates positively with the fiber stiffness. The age dependence and directional differences of constitutive parameters are also investigated. Results indicate that only the waviness depends strongly on age; no clear alterations occur in elastic parameters. Further, the fibers are wavier and stiffer in the circumferential direction than in the longitudinal direction. No other parameters exhibit significant direction difference. STATEMENT OF SIGNIFICANCE: We introduced a constitutive model which explicitly accounts for collagen fiber recruitment to investigate the uniaxial properties of human ascending aortic aneurysm tissues. Uniaxial response data from 156 specimens were considered in the study. It was found that the seemingly dissimilar response curves are, in fact, similar if we measure the deformation using an effective stretch which factors out the uncrimping deformation. The rupture stretches in terms of the effective stretch are closely packed around 1.1. And the stress-stretch curves collapse to a canonical curve after a transformation.

Multiscale Computational Modeling of Vascular Adaptation: A Systems Biology Approach Using Agent-Based Models

The widespread incidence of cardiovascular diseases and associated mortality and morbidity, along with the advent of powerful computational resources, have fostered an extensive research in computational modeling of vascular pathophysiology field and promoted in-silico models as a support for biomedical research. Given the multiscale nature of biological systems, the integration of phenomena at different spatial and temporal scales has emerged to be essential in capturing mechanobiological mechanisms underlying vascular adaptation processes. In this regard, agent-based models have demonstrated to successfully embed the systems biology principles and capture the emergent behavior of cellular systems under different pathophysiological conditions. Furthermore, through their modular structure, agent-based models are suitable to be integrated with continuum-based models within a multiscale framework that can link the molecular pathways to the cell and tissue levels. This can allow improving existing therapies and/or developing new therapeutic strategies. The present review examines the multiscale computational frameworks of vascular adaptation with an emphasis on the integration of agent-based approaches with continuum models to describe vascular pathophysiology in a systems biology perspective. The state-of-the-art highlights the current gaps and limitations in the field, thus shedding light on new areas to be explored that may become the future research focus. The inclusion of molecular intracellular pathways (e.g., genomics or proteomics) within the multiscale agent-based modeling frameworks will certainly provide a great contribution to the promising personalized medicine. Efforts will be also needed to address the challenges encountered for the verification, uncertainty quantification, calibration and validation of these multiscale frameworks.

A Review of Biomechanics Analysis of the Umbilical-Placenta System With Regards to Diseases

Placenta is an important organ that is crucial for both fetal and maternal health. Abnormalities of the placenta, such as during intrauterine growth restriction (IUGR) and pre-eclampsia (PE) are common, and an improved understanding of these diseases is needed to improve medical care. Biomechanics analysis of the placenta is an under-explored area of investigation, which has demonstrated usefulness in contributing to our understanding of the placenta physiology. In this review, we introduce fundamental biomechanics concepts and discuss the findings of biomechanical analysis of the placenta and umbilical cord, including both tissue biomechanics and biofluid mechanics. The biomechanics of placenta ultrasound elastography and its potential in improving clinical detection of placenta diseases are also discussed. Finally, potential future work is listed.

Investigation of Fiber-Driven Mechanical Behavior of Human and Porcine Bladder Tissue Tested Under Identical Conditions

The urinary bladder is a highly dynamic organ that undergoes large deformations several times per day. Mechanical characteristics of the tissue are crucial in determining the function and dysfunction of the organ. Yet, literature reporting on the mechanical properties of human bladder tissue is scarce and, at times, contradictory. In this study, we focused on mechanically testing tissue from both human and pig bladders using identical protocols to validate the use of pigs as a model for the human bladder. Furthermore, we tested the effect of two treatments on tissue mechanical properties. Namely, elastase to digest elastin fibers, and oxybutynin to reduce smooth muscle cell spasticity. Additionally, mechanical properties based on the anatomical direction of testing were evaluated. We implemented two different material models to aid in the interpretation of the experimental results. We found that human tissue behaves similarly to pig tissue at high deformations (collagen-dominated behavior) while we detected differences between the species at low deformations (amorphous matrix-dominated behavior). Our results also suggest that elastin could play a role in determining the behavior of the fiber network. Finally, we confirmed the anisotropy of the tissue, which reached higher stresses in the transverse direction when compared to the longitudinal direction.

Incorporating fiber recruitment in hyperelastic modeling of vascular tissues by means of kinematic average

We present a framework for considering the gradual recruitment of collagen fibers in hyperelastic constitutive modeling. An effective stretch, which is a response variable representing the true stretch at the tissue-scale, is introduced. Properties of the effective stretch are discussed in detail. The effective stretch and strain invariants derived from it are used in selected hyperelastic constitutive models to describe the tissue response. This construction is investigated in conjunction with Holzapfel-Gasser-Ogden family strain energy functions. The ensuing models are validated against a large body of uniaxial and bi-axial stress-strain response data from human aortic aneurysm tissues. Both the descriptive and the predictive capabilities are examined. The former is evaluated by the quality of constitutive fitting, and the latter is assessed using finite element simulation. The models significantly improve the quality of fitting, and reproduce the experiment displacement, stress, and strain distributions with high fidelity in the finite element simulation.

Review of the Techniques Used for Investigating the Role Elastin and Collagen Play in Arterial Wall Mechanics

The arterial wall is characterised by a complex microstructure that impacts the mechanical properties of the vascular tissue. The main components consist of collagen and elastin fibres, proteoglycans, Vascular Smooth Muscle Cells (VSMCs) and ground matrix. While VSMCs play a key role in the active mechanical response of arteries, collagen and elastin determine the passive mechanics. Several experimental methods have been designed to investigate the role of these structural proteins in determining the passive mechanics of the arterial wall. Microscopy imaging of load-free or fixed samples provides useful information on the structure-function coupling of the vascular tissue, and mechanical testing provides information on the mechanical role of collagen and elastin networks. However, when these techniques are used separately, they fail to provide a full picture of the arterial micromechanics. More recently, advances in imaging techniques have allowed combining both methods, thus dynamically imaging the sample while loaded in a pseudo-physiological way, and overcoming the limitation of using either of the two methods separately. The present review aims at describing the techniques currently available to researchers for the investigation of the arterial wall micromechanics. This review also aims to elucidate the current understanding of arterial mechanics and identify some research gaps.

A COUPLED EXPERIMENTAL AND NUMERICAL APPROACH TO CHARACTERIZE THE ANISOTROPIC MECHANICAL BEHAVIOR OF AORTIC TISSUES

Nowadays, the investigation of aortic wall biomechanics is a fundamental tool in clinical research and vascular prosthesis design. This study aims at analyzing the biomechanical behavior of aortic tissues using a coupled experimental and computational approach. Considering the typical fiber-reinforced configuration of aortic tissues, uni-axial tensile tests along six different loading directions were performed on specimens from pig aorta. Starting from the obtained experimental data, a suitable constitutive framework was defined and a methodology for the identification of the constitutive parameters was developed using the inverse analysis of mechanical tests. Transversal stretch versus loading stretch and nominal stress versus loading stretch curves were evaluated, showing the anisotropic and nonlinear mechanical behavior determined by tissue conformation with fibers distributed along preferential directions. In detail, experimental data showed different mechanical responses between longitudinal and circumferential directions, with a greater tissue stiffness along the longitudinal one. The reliability of the developed constitutive framework was evaluated by the comparison between experimental data and model results. The mentioned analysis can be considered as a useful tool for the development of reliable computational models, which allow a better understanding of the pathophysiology of cardiovascular diseases and can be applied for a proper planning of surgical procedures.

Reduced stiffness and augmented traction force in type 2 diabetic coronary microvascular smooth muscle

Type 2 diabetic (T2DM) coronary resistance microvessels (CRMs) undergo inward hypertrophic remodeling associated with reduced stiffness and reduced coronary blood flow in both mice and pig models. Since reduced stiffness does not appear to be due to functional changes in the extracellular matrix, this study tested the hypothesis that decreased CRM stiffness in T2DM is due to reduced vascular smooth muscle cell (VSMC) stiffness, which impacts the traction force generated by VSMCs. Atomic force microscopy (AFM) and traction force microscopy (TFM) were conducted on primary low-passage CRM VSMCs from normal Db/db and T2DM db/db mice in addition to low-passage normal and T2DM deidentified human coronary VSMCs. Elastic modulus was reduced in T2DM mouse and human coronary VSMCs compared with normal (mouse: Db/db 6.84 ± 0.34 kPa vs. db/db 4.70 ± 0.19 kPa, P < 0.0001; human: normal 3.59 ± 0.38 kPa vs. T2DM 2.61 ± 0.35 kPa, P = 0.05). Both mouse and human T2DM coronary microvascular VSMCs were less adhesive to fibronectin compared with normal. T2DM db/db coronary VSMCs generated enhanced traction force by TFM (control 692 ± 67 Pa vs. db/db 1,507 ± 207 Pa; P < 0.01). Immunoblot analysis showed that T2DM human coronary VSMCs expressed reduced β₁-integrin and elevated β₃-integrin (control 1.00 ± 0.06 vs. T2DM 0.62 ± 0.14, P < 0.05 and control 1.00 ± 0.49 vs. T2DM 3.39 ± 1.05, P = 0.06, respectively). These data show that T2DM coronary VSMCs are less stiff and less adhesive to fibronectin but are able to generate enhanced force, corroborating previously published computational findings that decreasing cellular stiffness increases the cells' ability to generate higher traction force.NEW & NOTEWORTHY We show here that a potential causative factor for reduced diabetic coronary microvascular stiffness is the direct reduction in coronary vascular smooth muscle cell stiffness. These cells were also able to generate enhanced traction force, validating previously published computational models. Collectively, these data show that smooth muscle cell stiffness can be a contributor to overall tissue stiffness in the coronary microcirculation, and this may be a novel area of interest for therapeutic targets.

A Two-Dimensional Model of Hypertension-Induced Arterial Remodeling With Account for Stress Interaction Between Elastin and Collagen

We propose a novel structure-based two-dimensional (2D) mathematical model of hypertension-induced arterial remodeling. The model is built in the framework of the constrained mixture theory and global growth approach, utilizing a recently proposed structure-based constitutive model of arterial tissue that accounts for the individual natural configurations of and stress interaction between elastin and collagen. The basic novel predictive result is that provided remodeling causes a change in the elastin/collagen mass fraction ratio, it leads to a structural reorganization of collagen that manifests as an altered fiber undulation and a change in direction of the helically oriented fibers in the tissue natural state. Results obtained from the illustrative simulations for a porcine renal artery show that when remodeling is complete the collagen reorganization might have significant effects on the initial arterial geometry and mechanical properties of the arterial tissue. The proposed model has potential to describe and advance mechanistic understanding of adaptive arterial remodeling, promote the continual refinement of mathematical models of arterial remodeling, and provide motivation for new avenues of experimental investigation.

Fluid-Structure Interaction Simulation of Blood Flow and Cerebral Aneurysm: Effect of Partly Blocked Vessel

In this study, using fluid-structure interaction (FSI), 3-dimensional blood flow in an aneurysm in the circle of Willis - which is located in the middle cerebral artery (MCA) - has been simulated. The purpose of this study is to evaluate the effect of a partly blocked vessel on an aneurysm. To achieve this purpose, two cases have been investigated using the FSI method: in the first case, an ideal geometry of aneurysm in the MCA has been simulated; in the second case, modeling is performed for an ideal geometry of the aneurysm in the MCA with a partly blocked vessel. All boundary conditions, properties and modeling methods were considered the same for both cases. The only difference between the two cases was that part of the MCA parent artery was blocked in the second case. In order to consider the hyperelastic property of the wall and the non-Newtonian properties of the blood, the Mooney-Rivlin model and the Carreau model have been used, respectively. In the second case, the Von Mises stress in the peak systole is 26% higher than in the first case. With regard to the high amount of Von Mises stress, the risk of rupture of the aneurysm is higher in this case. In the second case, the maximum wall shear stress (WSS) is 12% higher than in the first case. And maximum displacement in the second case is also higher than in the first. So, the risk of growth of the aneurysm is higher in cases with a partly blocked vessel.

Elastic Fibers and Large Artery Mechanics in Animal Models of Development and Disease

Development of a closed circulatory system requires that large arteries adapt to the mechanical demands of high, pulsatile pressure. Elastin and collagen uniquely address these design criteria in the low and high stress regimes, resulting in a nonlinear mechanical response. Elastin is the core component of elastic fibers, which provide the artery wall with energy storage and recoil. The integrity of the elastic fiber network is affected by component insufficiency or disorganization, leading to an array of vascular pathologies and compromised mechanical behavior. In this review, we discuss how elastic fibers are formed and how they adapt in development and disease. We discuss elastic fiber contributions to arterial mechanical behavior and remodeling. We primarily present data from mouse models with elastic fiber deficiencies, but suggest that alternate small animal models may have unique experimental advantages and the potential to provide new insights. Advanced ultrastructural and biomechanical data are constantly being used to update computational models of arterial mechanics. We discuss the progression from early phenomenological models to microstructurally motivated strain energy functions for both collagen and elastic fiber networks. Although many current models individually account for arterial adaptation, complex geometries, and fluid-solid interactions (FSIs), future models will need to include an even greater number of factors and interactions in the complex system. Among these factors, we identify the need to revisit the role of time dependence and axial growth and remodeling in large artery mechanics, especially in cardiovascular diseases that affect the mechanical integrity of the elastic fibers.

Synchrotron-based visualization and segmentation of elastic lamellae in the mouse carotid artery during quasi-static pressure inflation

In computational aortic biomechanics, aortic and arterial tissue are typically modelled as a homogeneous layer, making abstraction not only of the layered structure of intima, media and adventitia but also of the microstructure that exists within these layers. Here, we present a novel method to visualize the microstructure of the tunica media along the entire circumference of the vessel. To that end, we developed a pressure-inflation device that is compatible with synchrotron-based phase-contrast imaging. Using freshly excised left common carotid arteries from n = 12 mice, we visualized how the lamellae and interlamellar layers inflate as the luminal pressure is increased from 0 to 120 mm Hg in quasi-static steps. A graph-based segmentation algorithm subsequently allowed us to automatically segment each of the three lamellae, resulting in a three-dimensional geometry that represents lamellae, interlamellar layers and adventitia at nine different pressure levels. Our results demonstrate that the three elastic lamellae unfold and stretch simultaneously as luminal pressure is increased. In the long term, we believe that the results presented in this work can be a first step towards a better understanding of the mechanics of the arterial microstructure.

Constituent-specific material behavior of soft biological tissue: experimental quantification and numerical identification for lung parenchyma

In this study, we present a method to experimentally quantify and numerically identify the constituent-specific material behavior of soft biological tissues. This allows the clear identification of the individual contributions of major load-bearing constituents and their interactions in the constitutive law. While the overall approach is applicable for many tissues, here it will be presented for the identification of a sophisticated constituent-specific material model of viable lung parenchyma. This material model will help to better model the effects of various lung diseases that feature altered fiber content in the lungs, such as emphysema or fibrosis. To experimentally quantify the mechanical properties of collagen, elastin, collagen-elastin-fiber interactions, and ground substance, we examined 18 collagenase and elastase treated rat lung parenchymal slices. The mechanical contributions of the collagen and elastin fibers in the living tissue were inferred from uniaxial tension tests comparing the behavior before and after the selective digestion of the respective fibers. In order to also obtain the mechanical influence of the ground substance, we consecutively treated the samples with both proteases. Collagen and elastin fibers are morphologically interconnected. Thus, a mechanical interaction between these fibers appears likely, but has not yet been experimentally verified. In this paper, we propose an experimental method to quantitatively assess the mechanical behavior of these collagen-elastin-fiber interactions. Based on our experiments, we have identified individual material models within a nonlinear continuum mechanics framework for each load-bearing component via an inverse analysis. The proposed constituent-specific material law can be incorporated into computational models of the respiratory system to simulate and even predict the behavior and alteration of the individual constituents and their effect on the whole respiratory system during normal and artificial breathing, in particular in the case of diseases that alter the fibers in the tissue.

The influence of the nylon balloon stiffness on the efficiency of the intra-aortic balloon occlusion

In interventional procedures, the balloon inflation is used to occlude the artery and thus reduce bleeding. There is no practically accepted measure of the procedure efficiency. A finite element method model with state-of-the-art modelling techniques was built in order to predict the occlusion levels under the influence of different balloon inflation and its material stiffness. The geometries of a healthy human thoracic aorta and an occlusion balloon were idealized. The non-linear constitutive material of Gasser-Ogden-Holzapfel model was employed for the thoracic aorta; the balloon was model as the hyperelastic model. The realistic physiological blood pressure and the balloon inflation pressures were applied to simulate the different occlusion levels. The final outcome shows an important influence of the material stiffness on the balloon deformation and thus the occlusion efficiency.

Numerical Study of the Blood Flow in a Deformable Human Aorta

In this work, we present a numerical investigation of blood flow in a portion of the human vascular system. More precisely, the present work analyzed the blood flow in the upper portion of the aorta. The aorta and its ramified blood vessels are surrounded by the cardiac muscle. The blood flow generates pressure on the internal surfaces of the artery and its ramifications, thereby causing deformation of the cardiac muscle. The numerical analysis used the Navier–Stokes equations as the governing equations of blood flow for the calculation of the velocity field and pressure distribution in the blood. The neo-Hookean hyperelastic model was used for the description of the behavior of the vessel walls. The velocity and pressure distributions were analyzed. The deformation of the vessel was also investigated. The numerical results could be used to better understand and predict the factors that trigger cardiovascular diseases and distortions of the aorta and as a diagnostic tool in clinical applications.

Constitutive interpretation of arterial stiffness in clinical studies: a methodological review

Clinical assessment of arterial stiffness relies on noninvasive measurements of regional pulse wave velocity or local distensibility. However, arterial stiffness measures do not discriminate underlying changes in arterial wall constituent properties (e.g., in collagen, elastin, or smooth muscle), which is highly relevant for development and monitoring of treatment. In arterial stiffness in recent clinical-epidemiological studies, we systematically review clinical-epidemiological studies (2012–) that interpreted arterial stiffness changes in terms of changes in arterial wall constituent properties (63 studies included of 514 studies found). Most studies that did so were association studies (52 of 63 studies) providing limited causal evidence. Intervention studies (11 of 63 studies) addressed changes in arterial stiffness through the modulation of extracellular matrix integrity (5 of 11 studies) or smooth muscle tone (6 of 11 studies). A handful of studies (3 of 63 studies) used mathematical modeling to discriminate between extracellular matrix components. Overall, there exists a notable gap in the mechanistic interpretation of stiffness findings. In constitutive model-based interpretation, we first introduce constitutive-based modeling and use it to illustrate the relationship between constituent properties and stiffness measurements (“forward” approach). We then review all literature on modeling approaches for the constitutive interpretation of clinical arterial stiffness data (“inverse” approach), which are aimed at estimation of constitutive properties from arterial stiffness measurements to benefit treatment development and monitoring. Importantly, any modeling approach requires a tradeoff between model complexity and measurable data. Therefore, the feasibility of changing in vivo the biaxial mechanics and/or vascular smooth muscle tone should be explored. The effectiveness of modeling approaches should be confirmed using uncertainty quantification and sensitivity analysis. Taken together, constitutive modeling can significantly improve clinical interpretation of arterial stiffness findings.

Contributions of Glycosaminoglycans to Collagen Fiber Recruitment in Constitutive Modeling of Arterial Mechanics

The contribution of glycosaminoglycans (GAGs) to the biological and mechanical functions of biological tissue has emerged as an important area of research. GAGs provide structural basis for the organization and assembly of extracellular matrix (ECM). The mechanics of tissue with low GAG content can be indirectly affected by the interaction of GAGs with collagen fibers, which have long been known to be one of the primary contributors to soft tissue mechanics. Our earlier study showed that enzymatic GAG depletion results in straighter collagen fibers that are recruited at lower levels of stretch, and a corresponding shift in earlier arterial stiffening (Mattson et al., 2016). In this study, the effect of GAGs on collagen fiber recruitment was studied through a structure-based constitutive model. The model incorporates structural information, such as fiber orientation distribution, content, and recruitment of medial elastin, medial collagen, and adventitial collagen fibers. The model was first used to study planar biaxial tensile stress-stretch behavior of porcine descending thoracic aorta. Changes in elastin and collagen fiber orientation distribution, and collagen fiber recruitment were then incorporated into the model in order to predict the stress-stretch behavior of GAG depleted tissue. Our study shows that incorporating early collagen fiber recruitment into the model predicts the stress-stretch response of GAG depleted tissue reasonably well (rms = 0.141); considering further changes of fiber orientation distribution does not improve the predicting capability (rms = 0.149). Our study suggests an important role of GAGs in arterial mechanics that should be considered in developing constitutive models.

Biomechanical relevance of the microstructure in artery walls with a focus on passive and active components

The microstructure of arteries, consisting, in particular, of collagen, elastin, and vascular smooth muscle cells, plays a very significant role in their biomechanical response during a cardiac cycle. In this article, we highlight the microstructure and the contributions of each of its components to the overall mechanical behavior. We also describe the changes of the microstructure that occur as a result of abdominal aortic aneurysms and disease, such as atherosclerosis. We also focus on how the passive and active constituents are incorporated into a mathematical model without going into detail of the mathematical formulation. We conclude by mentioning open problems toward a better characterization of the biomechanical aspects of arteries that will be beneficial for a better understanding of cardiovascular pathophysiology.

Modelling of Soft Connective Tissues to Investigate Female Pelvic Floor Dysfunctions

After menopause, decreased levels of estrogen and progesterone remodel the collagen of the soft tissues thereby reducing their stiffness. Stress urinary incontinence is associated with involuntary urine leakage due to pathological movement of the pelvic organs resulting from lax suspension system, fasciae, and ligaments. This study compares the changes in the orientation and position of the female pelvic organs due to weakened fasciae, ligaments, and their combined laxity. A mixture theory weighted by respective volume fraction of elastin-collagen fibre compound (5%), adipose tissue (85%), and smooth muscle (5%) is adopted to characterize the mechanical behaviour of the fascia. The load carrying response (other than the functional response to the pelvic organs) of each fascia component, pelvic organs, muscles, and ligaments are assumed to be isotropic, hyperelastic, and incompressible. Finite element simulations are conducted during Valsalva manoeuvre with weakened tissues modelled by reduced tissue stiffness. A significant dislocation of the urethrovesical junction is observed due to weakness of the fascia (13.89 mm) compared to the ligaments (5.47 mm). The dynamics of the pelvic floor observed in this study during Valsalva manoeuvre is associated with urethral-bladder hypermobility, greater levator plate angulation, and positive Q-tip test which are observed in incontinent females.

Numerical Approximation of Elasticity Tensor Associated With Green-Naghdi Rate

Objective stress rates are often used in commercial finite element (FE) programs. However, deriving a consistent tangent modulus tensor (also known as elasticity tensor or material Jacobian) associated with the objective stress rates is challenging when complex material models are utilized. In this paper, an approximation method for the tangent modulus tensor associated with the Green-Naghdi rate of the Kirchhoff stress is employed to simplify the evaluation process. The effectiveness of the approach is demonstrated through the implementation of two user-defined fiber-reinforced hyperelastic material models. Comparisons between the approximation method and the closed-form analytical method demonstrate that the former can simplify the material Jacobian evaluation with satisfactory accuracy while retaining its computational efficiency. Moreover, since the approximation method is independent of material models, it can facilitate the implementation of complex material models in FE analysis using shell/membrane elements in abaqus.

Failure of the Porcine Ascending Aorta: Multidirectional Experiments and a Unifying Microstructural Model

The ascending thoracic aorta is poorly understood mechanically, especially its risk of dissection. To make better predictions of dissection risk, more information about the multidimensional failure behavior of the tissue is needed, and this information must be incorporated into an appropriate theoretical/computational model. Toward the creation of such a model, uniaxial, equibiaxial, peel, and shear lap tests were performed on healthy porcine ascending aorta samples. Uniaxial and equibiaxial tests showed anisotropy with greater stiffness and strength in the circumferential direction. Shear lap tests showed catastrophic failure at shear stresses (150-200 kPa) much lower than uniaxial tests (750-2500 kPa), consistent with the low peel tension (∼60 mN/mm). A novel multiscale computational model, including both prefailure and failure mechanics of the aorta, was developed. The microstructural part of the model included contributions from a collagen-reinforced elastin sheet and interlamellar connections representing fibrillin and smooth muscle. Components were represented as nonlinear fibers that failed at a critical stretch. Multiscale simulations of the different experiments were performed, and the model, appropriately specified, agreed well with all experimental data, representing a uniquely complete structure-based description of aorta mechanics. In addition, our experiments and model demonstrate the very low strength of the aorta in radial shear, suggesting an important possible mechanism for aortic dissection.

Microstructure-based constitutive model of coronary artery with active smooth muscle contraction

Currently, there is no full three-dimensional (3D) microstructural mechanical model of coronary artery based on measured microstructure including elastin, collagen and smooth muscle cells. Many structural models employ mean values of vessel microstructure, rather than continuous distributions of microstructure, to predict the mechanical properties of blood vessels. Although some models show good agreements on macroscopic vessel responses, they result in a lower elastin stiffness and earlier collagen recruitment. Hence, a full microstructural constitutive model is required for better understanding vascular biomechanics in health and disease. Here, a 3D microstructural model that accounts for all constituent microstructure is proposed to predict macroscopic and microscopic responses of coronary arteries. Coronary artery microstructural parameters were determined based on previous statistical measurements while mechanical testing of arteries (n = 5) were performed in this study to validate the computational predictions. The proposed model not only provides predictions of active and passive stress distributions of vessel wall, but also enables reliable estimations of material parameters of individual fibers and cells and thus predicts microstructural stresses. The validated microstructural model of coronary artery sheds light on vascular biomechanics and can be extend to diseased vessels for better understanding of initiation, progression and clinical treatment of vascular disease.

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).

On arterial fiber dispersion and auxetic effect

There are two polar contemporary approaches to the constitutive modeling of arterial wall with anisotropy induced by collagen fibers. The first one is based on the angular integration (AI) of the strain energy on a unit sphere for the analytically defined fiber dispersion. The second one is based on the introduction of the generalized structure tensors (GST). AI approach is very involved computationally while GST approach requires somewhat complicated procedure for the exclusion of compressed fibers. We present some middle ground models, which are based on the use of 16 and 8 structure tensors. These models are moderately involved computationally and they allow excluding compressed fibers easily. We use the proposed models to study the role of the fiber dispersion in the constitutive modeling of the arterial wall. Particularly, we study the auxetic effect which can appear in anisotropic materials. The effect means thickening of the tissue in the direction perpendicular to its stretching. Such an effect was not observed in experiments while some simple anisotropic models do predict it. We show that more accurate account of the fiber dispersion suppresses the auxetic effect in a qualitative agreement with experimental observations.

Transmural variation in elastin fiber orientation distribution in the arterial wall

The complex three-dimensional elastin network is a major load-bearing extracellular matrix (ECM) component of an artery. Despite the reported anisotropic behavior of arterial elastin network, it is usually treated as an isotropic material in constitutive models. Our recent multiphoton microscopy study reported a relatively uniform elastin fiber orientation distribution in porcine thoracic aorta when imaging from the intima side (Chow et al., 2014). However it is questionable whether the fiber orientation distribution obtained from a small depth is representative of the elastin network structure in the arterial wall, especially when developing structure-based constitutive models. To date, the structural basis for the anisotropic mechanical behavior of elastin is still not fully understood. In this study, we examined the transmural variation in elastin fiber orientation distribution in porcine thoracic aorta and its association with elastin anisotropy. Using multi-photon microscopy, we observed that the elastin fibers orientation changes from a relatively uniform distribution in regions close to the luminal surface to a more circumferential distribution in regions that dominate the media, then to a longitudinal distribution in regions close to the outer media. Planar biaxial tensile test was performed to characterize the anisotropic behavior of elastin network. A new structure-based constitutive model of elastin network was developed to incorporate the transmural variation in fiber orientation distribution. The new model well captures the anisotropic mechanical behavior of elastin network under both equi- and nonequi-biaxial loading and showed improvements in both fitting and predicting capabilities when compared to a model that only considers the fiber orientation distribution from the intima side. We submit that the transmural variation in fiber orientation distribution is important in characterizing the anisotropic mechanical behavior of elastin network and should be considered in constitutive modeling of an artery.

An agent-based model of leukocyte transendothelial migration during atherogenesis

A vast amount of work has been dedicated to the effects of hemodynamics and cytokines on leukocyte adhesion and trans-endothelial migration (TEM) and subsequent accumulation of leukocyte-derived foam cells in the artery wall. However, a comprehensive mechanobiological model to capture these spatiotemporal events and predict the growth and remodeling of an atherosclerotic artery is still lacking. Here, we present a multiscale model of leukocyte TEM and plaque evolution in the left anterior descending (LAD) coronary artery. The approach integrates cellular behaviors via agent-based modeling (ABM) and hemodynamic effects via computational fluid dynamics (CFD). In this computational framework, the ABM implements the diffusion kinetics of key biological proteins, namely Low Density Lipoprotein (LDL), Tissue Necrosis Factor alpha (TNF-α), Interlukin-10 (IL-10) and Interlukin-1 beta (IL-1β), to predict chemotactic driven leukocyte migration into and within the artery wall. The ABM also considers wall shear stress (WSS) dependent leukocyte TEM and compensatory arterial remodeling obeying Glagov's phenomenon. Interestingly, using fully developed steady blood flow does not result in a representative number of leukocyte TEM as compared to pulsatile flow, whereas passing WSS at peak systole of the pulsatile flow waveform does. Moreover, using the model, we have found leukocyte TEM increases monotonically with decreases in luminal volume. At critical plaque shapes the WSS changes rapidly resulting in sudden increases in leukocyte TEM suggesting lumen volumes that will give rise to rapid plaque growth rates if left untreated. Overall this multi-scale and multi-physics approach appropriately captures and integrates the spatiotemporal events occurring at the cellular level in order to predict leukocyte transmigration and plaque evolution.

A Combination of Constitutive Damage Model and Artificial Neural Networks to Characterize the Mechanical Properties of the Healthy and Atherosclerotic Human Coronary Arteries

It has been indicated that the content and structure of the elastin and collagen of the arterial wall can subject to a significant alteration due to the atherosclerosis. Consequently, a high tissue stiffness, stress, and even damage/rupture are triggered in the arterial wall. Although many studies so far have been conducted to quantify the mechanical properties of the coronary arteries, none of them consider the role of collagen damage of the healthy and atherosclerotic human coronary arterial walls. Recently, a fiber family-based constitutive equation was proposed to capture the anisotropic mechanical response of the healthy and atherosclerotic human coronary arteries via both the histostructural and uniaxial data. In this study, experimental mechanical measurements along with histological data of the healthy and atherosclerotic arterial walls were employed to determine the constitutive damage parameters and remodeling of the collagen fibers. To do this, the preconditioned arterial tissues were excised from human cadavers within 5-h postmortem, and the mean angle of their collagen fibers was precisely determined. Thereafter, a group of quasistatic axial and circumferential loadings were applied to the arterial walls, and the constrained nonlinear minimization method was employed to identify the arterial parameters according to the axial and circumferential extension data. The remodeling of the collagen fibers during the tensile test was also predicted via Artificial Neural Networks algorithm. Regardless of loading direction, the results presented a noteworthy load-bearing capability and stiffness of the atherosclerotic arteries compared to the healthy ones (P < 0.005). Theoretical fiber angles were found to be consistent with the experimental histological data with less than 2 and 5° difference for the healthy and atherosclerotic arterial walls, respectively. The pseudoelastic damage model data were also compared with that of the experimental data, and interestingly, the arterial mechanical behavior for both the primary loading (up to the elastic region) and the discontinuous softening (up to the ultimate stress) was well addressed. The proposed model predicted well the mechanical response of the arterial tissue considering the damage of collagen fibers for both the healthy and atherosclerotic arterial walls.

Microstructure and mechanics of human resistance arteries

Vascular diseases such as diabetes and hypertension cause changes to the vasculature that can lead to vessel stiffening and the loss of vasoactivity. The microstructural bases of these changes are not presently fully understood. We present a new methodology for stain-free visualization, at a microscopic scale, of the morphology of the main passive components of the walls of unfixed resistance arteries and their response to changes in transmural pressure. Human resistance arteries were dissected from subcutaneous fat biopsies, mounted on a perfusion myograph, and imaged at varying transmural pressures using a multimodal nonlinear microscope. High-resolution three-dimensional images of elastic fibers, collagen, and cell nuclei were constructed. The honeycomb structure of the elastic fibers comprising the internal elastic layer became visible at a transmural pressure of 30 mmHg. The adventitia, comprising wavy collagen fibers punctuated by straight elastic fibers, thinned under pressure as the collagen network straightened and pulled taut. Quantitative measurements of fiber orientation were made as a function of pressure. A multilayer analytical model was used to calculate the stiffness and stress in each layer. The adventitia was calculated to be up to 10 times as stiff as the media and experienced up to 8 times the stress, depending on lumen diameter. This work reveals that pressure-induced reorganization of fibrous proteins gives rise to very high local strain fields and highlights the unique mechanical roles of both fibrous networks. It thereby provides a basis for understanding the micromechanical significance of structural changes that occur with age and disease.

Inferring spatial variations of microstructural properties from macroscopic mechanical response

Disease alters tissue microstructure, which in turn affects the macroscopic mechanical properties of tissue. In elasticity imaging, the macroscopic response is measured and is used to infer the spatial distribution of the elastic constitutive parameters. When an empirical constitutive model is used, these parameters cannot be linked to the microstructure. However, when the constitutive model is derived from a microstructural representation of the material, it allows for the possibility of inferring the local averages of the spatial distribution of the microstructural parameters. This idea forms the basis of this study. In particular, we first derive a constitutive model by homogenizing the mechanical response of a network of elastic, tortuous fibers. Thereafter, we use this model in an inverse problem to determine the spatial distribution of the microstructural parameters. We solve the inverse problem as a constrained minimization problem and develop efficient methods for solving it. We apply these methods to displacement fields obtained by deforming gelatin-agar co-gels and determine the spatial distribution of agar concentration and fiber tortuosity, thereby demonstrating that it is possible to image local averages of microstructural parameters from macroscopic measurements of deformation.

A combination of experimental and numerical methods to investigate the role of strain rate on the mechanical properties and collagen fiber orientations of the healthy and atherosclerotic human coronary arteries

Atherosclerosis enables to alter not only the microstructural but also the physical properties of the arterial walls by plaque forming. Few studies so far have been conducted to calculate the isotropic or anisotropic mechanical properties of the healthy and atherosclerotic human coronary arteries. To date there is a paucity of knowledge on the mechanical response of the arteries under different strain rates. Therefore, the objective of the concurrent research was to comprehend whether the alteration in the strain rates of the human atherosclerotic arteries in comparison with the healthy ones contribute to the biomechanical behaviors. To do this, healthy and atherosclerotic human coronary arteries were removed from 18 individuals during autopsy. Histological analyses by both an expert histopathologist and an imaged-based recognizer software were performed to figure out the average angle of collagen fibers in the healthy and atherosclerotic arterial walls. Thereafter, the samples were subjected to 3 diverse strain rates, i.e., 5, 20, and 50 mm/min, until the material failure occurs. The stress-strain diagrams of the arterial tissues were calculated in order to capture their linear elastic and nonlinear hyperelastic mechanical properties. In addition, Artificial Neural Networks (ANNs) was employed to predict the alteration of mean angle of collagen fibers during load bearing up to failure. The findings suggest that strain rate has a significant (p < 0.05) role in the linear elastic and nonlinear hyperelastic mechanical properties as well as the mean angle of collagen fibers of the atherosclerotic arteries, whereas no specific impact on the healthy ones. Furthermore, the mean angle of collagen fibers during the load bearing up to the failure at each strain rate was well predicted by the proposed ANNs code.

Microstructure-based biomechanics of coronary arteries in health and disease

Coronary atherosclerosis is the major cause of mortality and disability in developed nations. A deeper understanding of mechanical properties of coronary arteries and hence their mechanical response to stress is significant for clinical prevention and treatment. Microstructure-based models of blood vessels can provide predictions of arterial mechanical response at the macro- and micro-mechanical level for each constituent structure. Such models must be based on quantitative data of structural parameters (constituent content, orientation angle and dimension) and mechanical properties of individual adventitia and media layers of normal arteries as well as change of structural and mechanical properties of atherosclerotic arteries. The microstructural constitutive models of healthy coronary arteries consist of three major mechanical components: collagen, elastin, and smooth muscle cells, while the models of atherosclerotic arteries should account for additional constituents including intima, fibrous plaque, lipid, calcification, etc. This review surveys the literature on morphology, mechanical properties, and microstructural constitutive models of normal and atherosclerotic coronary arteries. It also provides an overview of current gaps in knowledge that must be filed in order to advance this important area of research for understanding initiation, progression and clinical treatment of vascular disease. Patient-specific structural models are highlighted to provide diagnosis, virtual planning of therapy and prognosis when realistic patient-specific geometries and material properties of diseased vessels can be acquired by advanced imaging techniques.

A validated 3D microstructure-based constitutive model of coronary artery adventitia

A structure-based model that accurately predicts micro- or macromechanical behavior of blood vessels is necessary to understand vascular physiology. Based on recently measured microstructural data, we propose a three-dimensional microstructural model of coronary adventitia that incorporates the elastin and collagen distributions throughout the wall. The role of ground substance was found to be negligible under physiological axial stretch λz = 1.3, based on enzyme degradation of glycosaminoglycans in swine coronary adventitia (n = 5). The thick collagen bundles of outer adventitia (n = 4) were found to be undulated and unengaged at physiological loads, whereas the inner adventitia consisted of multiple sublayers of entangled fibers that bear the majority of load at higher pressures. The microstructural model was validated against biaxial (inflation and extension) experiments of coronary adventitia (n = 5). The model accurately predicted the nonlinear responses of the adventitia, even at high axial force (axial stretch ratio λz = 1.5). The model also enabled a reliable estimation of material parameters of individual fibers that were physically reasonable. A sensitivity analysis was performed to assess the effect of using mean values of the distributions for fiber orientation and waviness as opposed to the full distributions. The simplified mean analysis affects the fiber stress-strain relation, resulting in incorrect estimation of mechanical parameters, which underscores the need for measurements of fiber distribution for a rigorous analysis of fiber mechanics. The validated structure-based model of coronary adventitia provides a deeper understanding of vascular mechanics in health and can be extended to disease conditions.