We propose a model mechanism for the initiation and spatial positioning of teeth primordia in the alligator, Alligator mississippiensis. Detailed embryological studies by Westergaard and Ferguson have shown that jaw growth plays a crucial role in the developmental patterning of the tooth initiation process. Based on biological data we develop a dynamic patterning mechanism, which crucially includes domain growth. The mechanism can reproduce the spatial pattern development of the first seven teeth primordia in each half jaw of A. mississippiensis. The (...) results for the precise spatio-temporal sequence compare well with experiment. Simulation of the model also predicts that certain transplantations can alter the spatial sequence of teeth primordia initiation. (shrink)

Endothelial cells, when cultured on gelled basement membrane matrix exert forces of tension through which they deform the matrix and at the same time they aggregate into clusters. The cells eventually form a network of cord-like structures connecting cell aggregates. In this network, almost all of the matrix has been pulled underneath the cell cords and cell clusters. This phenomenon has been proposed as a possible model for the growth and development of planar vascular systems in vitro. Our hypothesis is (...) that the matrix is reorganized and the cellular networks form as a result of traction forces exerted by the cells on the matrix and the latter's elasticity. We construct and analyze a mathematical model based on this hypothesis and examine conditions necessary for the formation of the pattern. We show cell migration is not necessary for pattern formation and that isotropic, strain-stimulated traction is sufficient to form the observed patterns. (shrink)

Gliomas are diffuse and invasive brain tumors with the nefarious ability to evade even seemingly draconian treatment measures. Here we introduce a simple mathematical model for drug delivery of chemotherapeutic agents to treat such a tumor. The model predicts that heterogeneity in drug delivery related to variability in vascular density throughout the brain results in an apparent tumor reduction based on imaging studies despite continual spread beyond the resolution of the imaging modality. We discuss a clinical example for which the (...) model-predicted scenario is relevant. The analysis and results suggest an explanation for the clinical problem of the long-standing confounding observation of shrinkage of the lesion in certain areas of the brain with continued growth in other areas. (shrink)