G. W. Brodland Departments of Civil Engineering and Biology, University of Waterloo, Waterloo, ON N2L 3G1 Mem. ASME D. A. Clausi Department of Systems Design Engineering, University of Waterloo, Waterloo, ON N2L 3G1 Embryonic Tissue Morphogenesis Modeled by F E i A three-dimensional, large-strain finite element formulation for the simulation of morphogenetic behaviors in embryonic tissues is presented. It is used to investigate aspects of invagination, neural tube morphogenesis, contraction wave propagation and mechanical pattern formation. The simulations show that the spacing ofpatterns and the shapes produced by certain morphogenetic movements in epithelial sheets depend only slightly on the properties of the materials which underlie these sheets. Simulations of neural tube closure show that numerous, experimentally-observed features can be produced by contraction of apical microfilament bundles alone. That certain systems offorces are mechanically equivalent and that certain patterns of deformations are equivalent set practical limits on what can be inferred from the simulations. Introduction A variety of intriguing processes are critical to early em- bryogenesis (Alberts et al., 1989). Observers have, for millen- nia, attempted to identify the essential phenomena responsible for each of these processes. Although it is known that electrical, biochemical, and mechanical phenomena can be involved, the specific causes of many embryonic processes which seem el- ementary are still unknown. Mathematical models and computer simulations which com- plement physical experiments have been important to the test- ing of hypotheses about the forces and other factors which drive morphogenetic processes. Specifically, they have helped distinguish between factors which are causal and those which are not. Computer simulations have also demonstrated the relationship between local and global shape changes (Jacobson and Gordon, 1976; Hilfer and Hilfer, 1983) and confirmed hypotheses about the forces required to produce observed shape changes (Odell et al., 1981; Weliky and Oster, 1990; Dunnett et al., 1991; Clausi, 1991; Clausi and Brodland, 1993). These studies have firmly established computer simulations as a sci- entific tool for the study of morphogenetic processes. At the same time these studies have made us aware of the need for additional and more detailed simulations (Jacobson, 1980; Albrecht-Buehler, 1990; Koehl, 1990). Koehl writes ". . .it is critical that we complement the popular molecular and biochemical approaches to the control of morphogenesis with nuts-and-bolts analyses of the physics of how morpho- genetic processes occur." Here, a set of criteria is presented for the modeling of mor- phogenetic mechanical behaviors in embryonic tissue. The es- sential features of a finite element formulation which satisfies these criteria is outlined. The formulation is then used to dem- onstrate how mechanical interactions can give rise to a variety of biological phenomena. Aspects of tissue invagination, neural Contributed by the Bioengineering Division for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received by the Bioengineering Division July 14, 1992; revised manuscript received July 6, 1993. Associate Technical Editor: R. M. Hochmuth. tube formation, mechanical pattern formation, and contrac- tion wave propagation are investigated. What Drives Morphogenetic Movements? Many morphogenetic movements are driven by forces pro- duced in the epithelium, the outer-most layer of tissue. These forces are typically generated by cytoskeletal components and by various kinds of inter-cellular forces. Considerable debate continues about the possible involvement of other force gen- erators and about the role of subjacent tissue layers in specific morphogenetic processes. Various lines of evidence, including finite element simulations, however, suggest that many mor- phogenetic shape changes are driven by cytoskeletal compo- nents, especially microfilaments, in the epithelial layer (Clausi and Brodland, 1993). Typical components of an epithelial cell sheet which may be of mechanical importance are shown in Fig. 1. To quantitate the mechanical properties of substructural components such as microfilaments, microtubules, cytoplasm and other struc- tures is difficult, at best. In vivo, these components are subject to complex mechanical interactions with other components and with other cells, and their mechanical behavior can be highly dependent on biomechanical factors (Nakamura and Hira- Apical Microtubule Microfilament Bundle Cytoplasm Cell Membrane Fig. 1 Sub-cellular components which may be of mechanical impor- tance 146 /Vol. 116, MAY 1994 Transactions of the ASME Copyright © 1994 by ASME Downloaded 12 Jul 2011 to 129.97.72.149. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm