Mathematical modeling of vertebrate limb development

Yong-Tao Zhang, Mark S. Alber, Stuart A. Newman
2013 Mathematical Biosciences  
In this paper, we review several main mathematical and computational models of vertebrate limb development and their roles in accounting for different aspects of this process. The main aspects of limb development have been modeled, including outgrowth and shaping of the limb bud, establishment of molecular gradients within the bud, and formation of the skeleton. These processes occur interdependently during development, although (as described in this review), there are various interpretations
more » ... the biological relationships among them. A wide range of mathematical and computational methods have been used to study these processes, including ordinary and partial differential equation systems, cellular automata and discrete, stochastic models, finite difference methods, finite element methods, the immersed boundary method, and various combinations of the above. Multiscale mathematical modeling and associated computational simulation have become integrated into the study of limb morphogenesis and pattern formation to an extent with few parallels in the field of developmental biology. These methods have contributed to the design and analysis of experiments employing microsurgical and genetic manipulations, evaluation of alternative hypotheses for limb bud outgrowth, interpretation of the effects of natural mutations, and the formulation of scenarios for the origination and evolution of the limb skeleton.
doi:10.1016/j.mbs.2012.11.003 pmid:23219575 fatcat:p3w3rhokv5fj3i3cmkssw3sdpq