Visualizing the stress distribution within vascular tissues using intravascular ultrasound elastography: a preliminary investigation.

A methodology for computing the stress distribution of vascular tissue using finite element-based, intravascular ultrasound (IVUS) reconstruction elastography is described. This information could help cardiologists detect life-threatening atherosclerotic plaques and predict their propensity to rupture. The calculation of vessel stresses requires the measurement of strain from the ultrasound images, a calibrating pressure measurement and additional model assumptions. In this work, we conducted simulation studies to investigate the effect of varying the model assumptions, specifically Poisson's ratio and the outer boundary conditions, on the resulting stress fields. In both simulation and phantom studies, we created vessel geometries with two fibrous cap thicknesses to determine if we could detect a difference in peak stress (spatially) between the two. The results revealed that (i) Poisson's ratios had negligible impact on the accuracy of stress elastograms, (ii) the outer boundary condition assumption had the greatest effect on the resulting modulus and stress distributions and (iii) in simulation and in phantom experiments, our stress imaging technique was able to detect an increased peak stress for the vessel geometry with the smaller cap thickness. This work is a first step toward understanding and creating a robust stress measurement technique for evaluating atherosclerotic plaques using IVUS elastography.

Bending and twisting the embryonic heart: a computational model for c-looping based on realistic geometry.

The morphogenetic process of cardiac looping transforms the straight heart tube into a curved tube that resembles the shape of the future four-chambered heart. Although great progress has been made in identifying the molecular and genetic factors involved in looping, the physical mechanisms that drive this process have remained poorly understood. Recent work, however, has shed new light on this complicated problem. After briefly reviewing the current state of knowledge, we propose a relatively comprehensive hypothesis for the mechanics of the first phase of looping, termed c-looping, as the straight heart tube deforms into a c-shaped tube. According to this hypothesis, differential hypertrophic growth in the myocardium supplies the main forces that cause the heart tube to bend ventrally, while regional growth and cytoskeletal contraction in the omphalomesenteric veins (primitive atria) and compressive loads exerted by the splanchnopleuric membrane drive rightward torsion. A computational model based on realistic embryonic heart geometry is used to test the physical plausibility of this hypothesis. The behavior of the model is in reasonable agreement with available experimental data from control and perturbed embryos, offering support for our hypothesis. The results also suggest, however, that several other mechanisms contribute secondarily to normal looping, and we speculate that these mechanisms play backup roles when looping is perturbed. Finally, some outstanding questions are discussed for future study.

Viscoelastic material properties of the myocardium and cardiac jelly in the looping chick heart.

Accurate material properties of developing embryonic tissues are a crucial factor in studies of the mechanics of morphogenesis. In the present work, we characterize the viscoelastic material properties of the looping heart tube in the chick embryo through nonlinear finite element modeling and microindentation experiments. Both hysteresis and ramp-hold experiments were performed on the intact heart and isolated cardiac jelly (extracellular matrix). An inverse computational method was used to determine the constitutive relations for the myocardium and cardiac jelly. With both layers assumed to be quasilinear viscoelastic, material coefficients for an Ogden type strain-energy density function combined with Prony series of two terms or less were determined by fitting numerical results from a simplified model of a heart segment to experimental data. The experimental and modeling techniques can be applied generally for determining viscoelastic material properties of embryonic tissues.

Automatic generation of user material subroutines for biomechanical growth analysis.

The analysis of the biomechanics of growth and remodeling in soft tissues requires the formulation of specialized pseudoelastic constitutive relations. The nonlinear finite element analysis package ABAQUS allows the user to implement such specialized material responses through the coding of a user material subroutine called UMAT. However, hand coding UMAT subroutines is a challenge even for simple pseudoelastic materials and requires substantial time to debug and test the code. To resolve this issue, we develop an automatic UMAT code generation procedure for pseudoelastic materials using the symbolic mathematics package MATHEMATICA and extend the UMAT generator to include continuum growth. The performance of the automatically coded UMAT is tested by simulating the stress-stretch response of a material defined by a Fung-orthotropic strain energy function, subject to uniaxial stretching, equibiaxial stretching, and simple shear in ABAQUS. The MATHEMATICA UMAT generator is then extended to include continuum growth by adding a growth subroutine to the automatically generated UMAT. The MATHEMATICA UMAT generator correctly derives the variables required in the UMAT code, quickly providing a ready-to-use UMAT. In turn, the UMAT accurately simulates the pseudoelastic response. In order to test the growth UMAT, we simulate the growth-based bending of a bilayered bar with differing fiber directions in a nongrowing passive layer. The anisotropic passive layer, being topologically tied to the growing isotropic layer, causes the bending bar to twist laterally. The results of simulations demonstrate the validity of the automatically coded UMAT, used in both standardized tests of hyperelastic materials and for a biomechanical growth analysis.

Patterns of muscular strain in the embryonic heart wall.

The hypothesis that inner layers of contracting muscular tubes undergo greater strain than concentric outer layers was tested by numerical modeling and by confocal microscopy of strain within the wall of the early chick heart. We modeled the looped heart as a thin muscular shell surrounding an inner layer of sponge-like trabeculae by two methods: calculation within a two-dimensional three-variable lumped model and simulated expansion of a three-dimensional, four-layer mesh of finite elements. Analysis of both models, and correlative microscopy of chamber dimensions, sarcomere spacing, and membrane leaks, indicate a gradient of strain decreasing across the wall from highest strain along inner layers. Prediction of wall thickening during expansion was confirmed by ultrasonography of beating hearts. Degree of stretch determined by radial position may thus contribute to observed patterns of regional myocardial conditioning and slowed proliferation, as well as to the morphogenesis of ventricular trabeculae and conduction fascicles. Developmental Dynamics 238:1535-1546, 2009. (c) 2009 Wiley-Liss, Inc.

Computational model for the transition from peristaltic to pulsatile flow in the embryonic heart tube.

Early in development, the heart is a single muscle-wrapped tube without formed valves. Yet survival of the embryo depends on the ability of this tube to pump blood at steadily increasing rates and pressures. Developmental biologists historically have speculated that the heart tube pumps via a peristaltic mechanism, with a wave of contraction propagating from the inflow to the outflow end. Physiological measurements, however, have shown that the flow becomes pulsatile in character quite early in development, before the valves form. Here, we use a computational model for flow though the embryonic heart to explore the pumping mechanism. Results from the model show that endocardial cushions, which are valve primordia arising near the ends of the tube, induce a transition from peristaltic to pulsatile flow. Comparison of numerical results with published experimental data shows reasonably good agreement for various pressure and flow parameters. This study illustrates the interrelationship between form and function in the early embryonic heart.

Mechanical asymmetry in the embryonic chick heart during looping.

Cardiac looping, which begins with ventral bending and rightward rotation of the primitive heart tube, is an essential morphogenetic event that occurs early in vertebrate development. The biophysical mechanism that drives this process is unknown. It has been speculated that increased stiffness along the dorsal side of the ventricle combined with an intrinsic cardiac force causes the heart to bend. There is no experimental support for this hypothesis, however, since little is known about regional mechanical properties of the heart during looping. We directly measured diastolic stiffness of the inner curvature (IC), outer curvature (OC), and dorsal-ventral sides of the stage 12 chick heart by microindentation. The IC of intact hearts was found to be significantly stiffer than either the OC or the sides. which were of similar stiffness. Isolated cardiac jelly, which is a thick, extracellular matrix compartment underlying the myocardium, was approximately an order of magnitude softer than intact hearts. The results of a computational model simulating the indentation experiments, combined with the stiffness measurements, suggests the regional variation in stiffness is due to the material properties of the myocardium. A second model shows that a relatively stiff IC may facilitate bending of the heart tube during looping.