Hemodynamic environments from opposing sides of human aortic valve leaflets evoke distinct endothelial phenotypes in vitro.

The regulation of valvular endothelial phenotypes by the hemodynamic environments of the human aortic valve is poorly understood. The nodular lesions of calcific aortic stenosis (CAS) develop predominantly beneath the aortic surface of the valve leaflets in the valvular fibrosa layer. However, the mechanisms of this regional localization remain poorly characterized. In this study, we combine numerical simulation with in vitro experimentation to investigate the hypothesis that the previously documented differences between valve endothelial phenotypes are linked to distinct hemodynamic environments characteristic of these individual anatomical locations. A finite-element model of the aortic valve was created, describing the dynamic motion of the valve cusps and blood in the valve throughout the cardiac cycle. A fluid mesh with high resolution on the fluid boundary was used to allow accurate computation of the wall shear stresses. This model was used to compute two distinct shear stress waveforms, one for the ventricular surface and one for the aortic surface. These waveforms were then applied experimentally to cultured human endothelial cells and the expression of several pathophysiological relevant genes was assessed. Compared to endothelial cells subjected to shear stress waveforms representative of the aortic face, the endothelial cells subjected to the ventricular waveform showed significantly increased expression of the "atheroprotective" transcription factor Kruppel-like factor 2 (KLF2) and the matricellular protein Nephroblastoma overexpressed (NOV), and suppressed expression of chemokine Monocyte-chemotactic protein-1 (MCP-1). Our observations suggest that the difference in shear stress waveforms between the two sides of the aortic valve leaflet may contribute to the documented differential side-specific gene expression, and may be relevant for the development and progression of CAS and the potential role of endothelial mechanotransduction in this disease.

On the multiscale modeling of heart valve biomechanics in health and disease.

Theoretical models of the human heart valves are useful tools for understanding and characterizing the dynamics of healthy and diseased valves. Enabled by advances in numerical modeling and in a range of disciplines within experimental biomechanics, recent models of the heart valves have become increasingly comprehensive and accurate. In this paper, we first review the fundamentals of native heart valve physiology, composition and mechanics in health and disease. We will then furnish an overview of the development of theoretical and experimental methods in modeling heart valve biomechanics over the past three decades. Next, we will emphasize the necessity of using multiscale modeling approaches in order to provide a comprehensive description of heart valve biomechanics able to capture general heart valve behavior. Finally, we will offer an outlook for the future of valve multiscale modeling, the potential directions for further developments and the challenges involved.

Functional endothelialized microvascular networks with circular cross-sections in a tissue culture substrate.

Functional endothelialized networks constitute a critical building block for vascularized replacement tissues, organ assist devices, and laboratory tools for in vitro discovery and evaluation of new therapeutic compounds. Progress towards realization of these functional artificial vasculatures has been gated by limitations associated with the mechanical and surface chemical properties of commonly used microfluidic substrate materials and by the geometry of the microchannels produced using conventional fabrication techniques. Here we report on a method for constructing microvascular networks from polystyrene substrates commonly used for tissue culture, built with circular cross-sections and smooth transitions at bifurcations. Silicon master molds are constructed using an electroplating process that results in semi-circular channel cross-sections with smoothly varying radii. These master molds are used to emboss polystyrene sheets which are then joined to form closed bifurcated channel networks with circular cross-sections. The mechanical and surface chemical properties of these polystyrene microvascular network structures enable culture of endothelial cells along the inner lumen. Endothelial cell viability was assessed, documenting nearly confluent monolayers within 3D microfabricated channel networks with rounded cross-sections.

A computational model of aging and calcification in the aortic heart valve.

The aortic heart valve undergoes geometric and mechanical changes over time. The cusps of a normal, healthy valve thicken and become less extensible over time. In the disease calcific aortic stenosis (CAS), calcified nodules progressively stiffen the cusps. The local mechanical changes in the cusps, due to either normal aging or pathological processes, affect overall function of the valve. In this paper, we propose a computational model for the aging aortic valve that connects local changes to overall valve function. We extend a previous model for the healthy valve to describe aging. To model normal/uncomplicated aging, leaflet thickness and extensibility are varied versus age according to experimental data. To model calcification, initial sites are defined and a simple growth law is assumed. The nodules then grow over time, so that the area of calcification increases from one model to the next model representing greater age. Overall valve function is recorded for each individual model to yield a single simulation of valve function over time. This simulation is the first theoretical tool to describe the temporal behavior of aortic valve calcification. The ability to better understand and predict disease progression will aid in design and timing of patient treatments for CAS.

A multiscale computational comparison of the bicuspid and tricuspid aortic valves in relation to calcific aortic stenosis.

Patients with bicuspid aortic valve (BAV) are more likely to develop a calcific aortic stenosis (CAS), as well as a number of other ailments, as compared to their cohorts with normal tricuspid aortic valves (TAV). It is currently unknown whether the increase in risk of CAS is caused by the geometric differences between the tricuspid and bicuspid valves or whether the increase in risk is caused by the same underlying factors that produce the geometric difference. CAS progression is understood to be a multiscale process, mediated at the cell level. In this study, we employ multiscale finite-element simulations of the valves. We isolate the effect of one geometric factor, the number of cusps, in order to explore its effect on multiscale valve mechanics, particularly in relation to CAS. The BAV and TAV are modeled by a set of simulations describing the cell, tissue, and organ length scales. These simulations are linked across the length scales to create a coherent multiscale model. At each scale, the models are three-dimensional, dynamic, and incorporate accurate nonlinear constitutive models of the valve leaflet tissue. We compare results between the TAV and BAV at each length scale. At the cell-scale, our region of interest is the location where calcification develops, near the aortic-facing surface of the leaflet. Our simulations show the observed differences between the tricuspid and bicuspid valves at the organ scale: the bicuspid valve shows greater flexure in the solid phase and stronger jet formation in the fluid phase relative to the tricuspid. At the cell-scale, however, we show that the region of interest is shielded against strain by the wrinkling of the fibrosa. Thus, the cellular deformations are not significantly different between the TAV and BAV in the calcification-prone region. This result supports the assertion that the difference in calcification observed in the BAV versus TAV may be due primarily to factors other than the simple geometric difference between the two valves.

In vitro analysis of a hepatic device with intrinsic microvascular-based channels.

A novel microfluidics-based bilayer device with a discrete parenchymal chamber modeled upon hepatic organ architecture is described. The microfluidics network was designed using computational models to provide appropriate flow behavior based on physiological data from human microvasculature. Patterned silicon wafer molds were used to generate films with the vascular-based microfluidics network design and parenchymal chamber by soft lithography. The assembled device harbors hepatocytes behind a nanoporous membrane that permits transport of metabolites and small proteins while protecting them from the effects of shear stress. The device can sustain both human hepatoma cells and primary rat hepatocytes by continuous in vitro perfusion of medium, allowing proliferation and maintaining hepatic functions such as serum protein synthesis and metabolism. The design and fabrication processes are scalable, enabling the device concept to serve as both a platform technology for drug discovery and toxicity, and for the continuing development of an improved liver-assist device.

Transient, three-dimensional, multiscale simulations of the human aortic valve.

A set of multiscale simulations has been created to examine the dynamic behavior of the human aortic valve (AV) at the cell, tissue, and organ length scales. Each model is fully three-dimensional and includes appropriate nonlinear, anisotropic material models. The organ-scale model is a dynamic fluid-structure interaction that predicts the motion of the blood, cusps, and aortic root throughout the full cycle of opening and closing. The tissue-scale model simulates the behavior of the AV cusp tissue including the sub-millimeter features of multiple layers and undulated geometry. The cell-scale model predicts cellular deformations of individual cells within the cusps. Each simulation is verified against experimental data. The three simulations are linked: deformations from the organ-scale model are applied as boundary conditions to the tissue-scale model, and the same is done between the tissue and cell scales. This set of simulations is a major advance in the study of the AV as it allows analysis of transient, three-dimensional behavior of the AV over the range of length scales from cell to organ.

Microfabrication of three-dimensional engineered scaffolds.

One of the principal challenges facing the field of tissue engineering over the past 2 decades has been the requirement for large-scale engineered constructs comprising precisely organized cellular microenvironments. For vital organ assist and replacement devices, microfluidic-based systems such as the microcirculation, biliary, or renal filtration and resorption systems and other functional elements containing multiple cell types must be generated to provide for viable engineered tissues and clinical benefit. Over the last several years, microfabrication technology has emerged as a versatile and powerful approach for generating precisely engineered scaffolds for engineered tissues. Fabrication process tools such as photolithography, etching, molding, and lamination have been established for applications involving a range of biocompatible and biodegradable polymeric scaffolding materials. Computational fluid dynamic designs have been used to generate scaffold designs suitable for microvasculature and a number of organ-specific constructs; these designs have been translated into 3-dimensional scaffolding using microfabrication processes. Here a brief overview of the fundamental microfabrication technologies used for tissue engineering will be presented, along with a summary of progress in a number of applications, including the liver and kidney.

A finite shell element for heart mitral valve leaflet mechanics, with large deformations and 3D constitutive material model.

This paper presents a shell finite element formulation appropriate for simulating the heart valve leaflet mechanics, including three-dimensional (3D) stress and strain effects. A 4-node mixed-interpolation shell is formulated in convected coordinates. This shell model is made capable of handling arbitrary 3D material models by use of an algorithm that satisfies the shell stress assumption at every element integration point. A method for tracking the fiber direction is incorporated. The resulting shell element operates under the same conditions as a standard 4-node shell element with 5 degrees of freedom per node, but extends the modeling capabilities to handle large-deformation and anisotropic behavior.

A large-strain finite element formulation for biological tissues with application to mitral valve leaflet tissue mechanics.

This paper presents a finite element formulation suitable for large-strain modeling of biological tissues and uses this formulation to implement an accurate finite element model for mitral valve leaflet tissue. First, an experimentally derived strain energy function is obtained from literature. This function is implemented in finite elements using the mixed pressure-displacement formulation. A modification is made to aid in maintaining positive definiteness of the stiffness matrix at low strains. The numerical implementation is shown to be accurate in representing the analytical model of material behavior. The mixed formulation is useful for modeling of soft biological tissues in general, and the model presented here is applicable to finite element simulation of mitral valve mechanics.