Renato Perucchio

Modeling Heart Development

Mechanics plays a major role in heart development. This paper reviews some of the mechanical aspects involved in theoretical modeling of the embryonic heart as it transforms from a single tube into a four-chambered pump. In particular, large deformations and significant alterations in structure lead to highly nonlinear boundary value problems. First, the biological background for the problem is discussed. Next, a modified elasticity theory is presented that includes active contraction and growth, and the theory is incorporated into a finite element analysis. Finally, models for the heart are presented to illustrate the developmental processes of growth, remodeling, and morphogenesis. Combining such models with appropriate experiments should shed light on the complex mechanisms involved in cardiac development.

A topology-preserving parallel 3D thinning algorithm for extracting the curve skeleton

We introduce a new topology-preserving 3D thinning procedure for deriving the curve voxel skeleton from 3D binary digital images. Based on a rigorously defined classification procedure, the algorithm consists of sequential thinning iterations each characterized by six parallel directional sub-iterations followed by a set of sequential sub-iterations. The algorithm is shown to produce concise and geometrically accurate 3D curve skeletons. The thinning algorithm is also insensitive to object rotation and only moderately sensitive to noise. Although this thinning procedure is valid for curve skeleton extraction of general elongated objects, in this paper, we specifically discuss its application to the orientation modeling of trabecular biological tissues.

Mechanical asymmetry in the embryonic chick heart during looping.

AbstractCardiac 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.

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.

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.

Domain Delaunay Tetrahedrization of arbitrarily shaped curved polyhedra defined in a solid modeling system

An algorithm is presented for constructing a topologically and geometrically valid Domain Delaunay Z’etrahedr.zatiorz (DDT) of an arbitrarily shaped solid model with quadric curved faces (including objects with holes and nonmanifold objects). The algorithm operates on the boundary representation (B-rep) of the solid, and makes extensive use of properties of the Delaunay triangulation. This algorithm also includes a mechanism for transferring neighborhood information from the solid model to the elements of the tetrahedral model. Neighborhood information is used for identifying tetrahedral to be included in the DDT, and — in combination with geometric criteria — for ensuring that the DDT approximates satisfactorily the curved faces of the solid.

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.

AN INTEGRATED BOUNDARY ELEMENT ANALYSIS SYSTEM WITH INTERACTIVE COMPUTER GRAPHICS FOR THREE-DIMENSIONAL LINEAR-ELASTIC FRACTURE MECHANICS

Abstract An analysis system for three-dimensional fracture mechanics based on an interactive computer graphic preprocessor and a linear-elastic boundary element code is described. The system is designed for virtual memory mini-computer operations and incorporates a multidomain modeling capability which allows the treatment of domains built up as a sequence of adjacent regions. In the application of the BEM to linear-elastic fracture mechanics, two issues are addressed: crack surface modeling and singularity representation. The multidomain option is used to separate numerically the two crack surfaces by including the crack plane within the interface of two adjoining subdomains. Quadratic, isoparametric elements are made to embody the correct crack tip displacement variation by repositioning side nodes at the quarter-point. The inclusion of the correct singular traction term is accomplished by multiplying the traction shape functions by an “ad hoc” shape function. The combined strength of BEM analysis and interactive preprocessing is demonstrated by the application of the integrated system to a variety of three-dimensional fracture mechanics problems.

Parallel fem algorithms based on recursive spatial decomposition—I. Automatic mesh generation

Abstract This paper discusses an automatic meshing scheme that is suitable for parallel processing. Meshes derived from solid models through recursive spatial decompositions inherit the hierarchical organization and the spatial addressability of the underlying grid. These two properties are exploited to design a meshing algorithm capable of operating in parallel (concurrent) processing environments. The concept of a meshing operator for parallel processing is defined and algorithms for various stages of the automatic meshing scheme are presented. A systematic simulation of fine- and coarse-grain parallel configurations is used to evaluate the performance of the meshing scheme. A companion paper focuses on parallel processing for the analysis of these automatically derived meshes via hierarchical substructuring.

Three-dimensional fatigue crack propagation analysis using the boundary element method

Abstract The boundary element method and interactive computer graphics together make possible the analysis of general, three-dimensional linear elastic crack propagation. A program called the Fracture Editor has been developed for this purpose. The pre-processing, post-processing and fracture prediction capabilities of this program make up a general purpose fracture propagation processor. The function of the Fracture Editor is described in detail. These functions include file management, fracture propagation prediction, automatic crack front updating, interactive remeshing, attribute editing, mesh inspection, and post-processing of results. An example problem, fatigue crack propagation in a crane runway girder, is included. Predictions concerning crack front shape and size as a function of number of cycles of applied load are made with the Fracture Editor.