On the Biomechanics of Cardiac S-Looping in the Chick: Insights From Modeling and Perturbation Studies.

Cardiac looping is an important embryonic developmental stage where the primitive heart tube (HT) twists into a configuration that more closely resembles the mature heart. Improper looping leads to congenital defects. Using the chick embryo as the experimental model, we study cardiac s-looping wherein the primitive ventricle, which lay superior to the atrium, now assumes its definitive position inferior to it. This process results in a heart loop that is no longer planar with the inflow and outflow tracts now lying in adjacent planes. We investigate the biomechanics of s-looping and use modeling to understand the nonlinear and time-variant morphogenetic shape changes. We developed physical and finite element models and validated the models using perturbation studies. The results from experiments and models show how force actuators such as bending of the embryonic dorsal wall (cervical flexure), rotation around the body axis (embryo torsion), and HT growth interact to produce the heart loop. Using model-based and experimental data, we present an improved hypothesis for early cardiac s-looping.

On the role of intrinsic and extrinsic forces in early cardiac S-looping.

BACKGROUND: Looping is a crucial phase during heart development when the initially straight heart tube is transformed into a shape that more closely resembles the mature heart. Although the genetic and biochemical pathways of cardiac looping have been well studied, the biophysical mechanisms that actually effect the looping process remain poorly understood. Using a combined experimental (chick embryo) and computational (finite element modeling) approach, we study the forces driving early s-looping when the primitive ventricle moves to its definitive position inferior to the common atrium. RESULTS: New results from our study indicate that the primitive heart has no intrinsic ability to form an s-loop and that extrinsic forces are necessary to effect early s-looping. They support previous studies that established an important role for cervical flexure in causing early cardiac s-looping. Our results also show that forces applied by the splanchnopleure cannot be ignored during early s-looping and shed light on the role of cardiac jelly. Using available experimental data and computer modeling, we successfully developed and tested a hypothesis for the force mechanisms driving s-loop formation. CONCLUSIONS: Forces external to the primitive heart tube are necessary in the later stages of cardiac looping. Experimental and model results support our proposed hypothesis for forces driving early s-looping.

On the Role of Autonomous Control in Organ Development.

Developmental biology ("development" for short) deals with how the mature animal or plant results from a single fertilized cell. This paper is concerned with one aspect of development, morphogenesis-the formation of complex shapes from simpler ones. In particular, this paper focuses on organ development and illustrates the central role that mechanical feedback plays in effecting the final shape of various organs. The first aim of this paper is to illustrate how self-governing autonomous control systems can lead to the development of organs such as the heart. Although feedback plays a key role in these processes, the field is largely unexplored by controls engineers; hence, the second aim of this paper is to introduce mechanical feedback during development to controls engineers and suggest avenues for future research.

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.

The role of mechanical forces in the torsional component of cardiac looping.

During early development, the initially straight heart tube (HT) bends and twists (loops) into a curved tube to lay out the basic plan of the mature heart. The physical mechanisms that drive and regulate looping are not yet completely understood. This paper reviews our recent studies of the mechanics of cardiac torsion during the first phase of looping (c-looping). Experiments and computational modeling show that torsion is primarily caused by forces exerted on the HT by the primitive atria and the splanchnopleure, a membrane that presses against the ventral surface of the heart. Experimental and numerical results are described and integrated to propose a hypothesis for cardiac torsion, and key aspects of our hypothesis are tested using experiments that perturb normal looping. For each perturbation, the models predict the correct qualitative response. These studies provide new insight into the mechanisms that drive and regulate cardiac looping.

On modeling morphogenesis of the looping heart following mechanical perturbations.

Looping is a crucial early phase during heart development, as the initially straight heart tube (HT) deforms into a curved tube to lay out the basic plan of the mature heart. This paper focuses on the first phase of looping, called c-looping, when the HT bends ventrally and twists dextrally (rightward) to create a c-shaped tube. Previous research has shown that bending is an intrinsic process, while dextral torsion is likely caused by external forces acting on the heart. However, the specific mechanisms that drive and regulate looping are not yet completely understood. Here, we present new experimental data and finite element models to help define these mechanisms for the torsional component of c-looping. First, with regions of growth and contraction specified according to experiments on chick embryos, a three-dimensional model exhibits morphogenetic deformation consistent with observations for normal looping. Next, the model is tested further using experiments in which looping is perturbed by removing structures that exert forces on the heart--a membrane (splanchnopleure (SPL)) that presses against the ventral surface of the heart and the left and right primitive atria. In all cases, the model predicts the correct qualitative behavior. Finally, a two-dimensional model of the HT cross section is used to study a feedback mechanism for stress-based regulation of looping. The model is tested using experiments in which the SPL is removed before, during, and after c-looping. In each simulation, the model predicts the correct response. Hence, these models provide new insight into the mechanical mechanisms that drive and regulate cardiac looping.

Computational modeling of morphogenesis regulated by mechanical feedback.

Mechanical forces cause changes in form during embryogenesis and likely play a role in regulating these changes. This paper explores the idea that changes in homeostatic tissue stress (target stress), possibly modulated by genes, drive some morphogenetic processes. Computational models are presented to illustrate how regional variations in target stress can cause a range of complex behaviors involving the bending of epithelia. These models include growth and cytoskeletal contraction regulated by stress-based mechanical feedback. All simulations were carried out using the commercial finite element code ABAQUS, with growth and contraction included by modifying the zero-stress state in the material constitutive relations. Results presented for bending of bilayered beams and invagination of cylindrical and spherical shells provide insight into some of the mechanical aspects that must be considered in studying morphogenetic mechanisms.

Computational model for early cardiac looping.

Looping is a vital event during early cardiac morphogenesis, as the initially straight heart tube bends and twists into a curved tube, laying out the basic pattern of the future four-chambered heart. Despite intensive study for almost a century, the biophysical mechanisms that drive this process are not well understood. To explore a recently proposed hypothesis for looping, we constructed a finite element model for the embryonic chick heart during the first phase of looping, called c-looping. The model includes the main structures of the early heart (heart tube, omphalomesenteric veins, and dorsal mesocardium), and the analysis features realistic three-dimensional geometry, nonlinear passive and active material properties, and anisotropic growth. As per our earlier hypothesis for c-looping, actin-based morpho-genetic processes (active cell shape change, cytoskeletal contraction, and cell migration) are simulated in specific regions of the model. The model correctly predicts the initial gross morphological shape changes of the heart, as well as distributions of morphogenetic stresses and strains measured in embryonic chick hearts. The model was tested further in studies that perturbed normal cardiac morphogenesis. The model, taken together with the new experimental data, supports our hypothesis for the mechanisms that drive early looping.

Morphogenetic adaptation of the looping embryonic heart to altered mechanical loads.

The biophysical mechanisms that drive and regulate cardiac looping are not well understood, but mechanical forces likely play a central role. Previous studies have shown that cardiac torsion, which defines left-right directionality, is caused largely by forces exerted on the heart tube by a membrane called the splanchnopleure (SPL). Here we show that, when the SPL is removed from the embryonic chick heart, torsion is initially suppressed. Several hours later, however, normal torsion is restored. This delayed torsion coincides with increased myocardial stiffness, especially on the right side of the heart. Exposure to the myosin inhibitor Y-27632 suppressed both responses, suggesting that the delayed torsion is caused by an abnormal cytoskeletal contraction. This hypothesis is supported further by computational modeling. These results suggest that the looping embryonic heart has the ability to adapt to changes in the mechanical environment, which may play a regulatory role during morphogenesis.

Role of actin polymerization in bending of the early heart tube.

During cardiac c-looping, the heart transforms from a straight tube into a c-shaped tube, presenting the first evidence of left-right asymmetry in the embryo. C-looping consists of two primary deformation components: ventral bending and dextral rotation. This study examines the role of actin polymerization in bending of the heart tube. Exposure of stage 9-11 chick embryos to low concentrations of the actin polymerization inhibitors cytochalasin D (5 nM-2.0 microM) and latrunculin A (LA; 25 nM-2.0 microM) suppressed looping in a stage- and concentration-dependent manner in both whole embryos and isolated hearts. Local exposure of either the dorsal or ventral sides of isolated hearts to LA also inhibited looping, but less than global exposure, indicating that both sides contribute to the bending mechanism. Taken together, these data suggest that ongoing actin polymerization is required for the bending component of cardiac c-looping, and we speculate that polymerization-driven myocardial cell shape changes cause this deformation.