Xiaoguang Chen and G. Wayne Brodland

Department of Civil Engineering, University of Waterloo, Waterloo, ON, Canada N2L 3G1

E-mail: brodland@uwaterloo. ca


A finite element-based simulation of neurulation, a critical developmental event common to all vertebrates, is presented for an amphibian embryo. During this process, a sheet of tissue rolls up to form a tube, the precursor of the spinal cord and brain. Material property data for the simulation are based on the cellular fabric of the tissues and on tensile test data, and geometric data are obtained from three-dimensional reconstructions. A spatio-temporal correlation system is used to organize and correlate the data and to construct the finite element model. The simulations predict morphogenetic movements similar to those which occur in real embryos.

Keywords: mechanics of morphogenesis, finite element analysis; constitutive models; fabric evolution


During early embryo development, structured sheets of cells undergo dramatic self-driven changes of shape in order to form organs and other crucial structures (Fig. 1) [Alberts et al. 1989; Gilbert, 2003]. When anomalies occur in these motions, serious and debilitating malformation birth defects, such as spina bifida, can result. In order to develop effective new strategies for preventing malformation defects it is necessary to understand the mechanics that underlie these motions.

To investigate the mechanics of “morphogenetic movements” is challenging because large strains occur in the tissues and their small scale makes it difficult to obtain accurate geometric and mechanical property data. For example, during formation of the neural tube (Fig. 1), the precursor of the spinal cord and brain, certain tissues experience strains as high as several hundred percent. Direct measurement of the tensile properties of the tissues involved in this process is difficult because they are less than half a millimeter in size and are extremely fragile.


Neural fold



Figure 1. The process of neurulation

M. Pandey et al. (eds), Advances in Engineering Structures, Mechanics & Construction, 459-469. © 2006 Springer. Printed in the Netherlands.

Traditionally, embryological research has focused on identifying the molecular and genetic aspects of development [Huang and Ingber, 1999; Lecuit, 2003], and relatively little effort has been devoted to understanding the relevant mechanics. Recent work [Swartz, 2001; Stephanou, 2002; Chen, 2004; Robinson, 2004; Brodland, 2005; Moore et al, 2005] has shown, however, that mechanical processes must function in concert with chemical signal regulation and genetics to produce morphogenetic movements. In the present study, axolotls (Ambystoma mexicanum) embryos are used. Like a number of other amphibian embryos, they share important geometric similarities with human embryos and, for this reason, are often used as an animal model for neurulation.

This paper presents a whole-embryo finite element model of neurulation; the first of its kind. To capture the mechanical interactions that occur across cellular, tissue and whole-embryo scales, an advanced, multi-scale finite element approach is used. Cell-based simulations are used to construct a system of constitutive equations for embryonic tissues, and experimental data are used to determine the parameters in these equations. Images of live embryos and serial sections of fixed embryos provide the geometric data needed to complete the whole-embryo model.