Applied Mathematics Letters
Solutions C(r) of the time-independent nonhomogeneous diffusion equation for three different piecewise-uniform source terms are used to examine the limiting size of multicell spheroids using a simple model which reproduces concentration-dependent mitotic behavior. A condition is derived under which nontrivial solutions do not exist (in all three cases), and a condition for the existence of a unique nontrivial solution is established for the case of growth-modifying factor (GMF) production throughout the spheroid. Qualitative behavior of the limiting size is established as a function of various physiological parameters. Of fundamental importance is the assumed GMF concentration threshold θ, near which (i.e., as C → θ−) mitosis, and hence spheroid growth, is generally strongly inhibited.
Original Publication Citation
Adam, J. A., & Ward, K. Y. (1997). Limiting spheroid size as a function of growth factor source location. Applied Mathematics Letters, 10(3), 43-46. doi:10.1016/s0893-9659(97)00032-3
Adam, J. A. and Ward, K. Y., "Limiting Spheroid Size as a Function of Growth Factor Source Location" (1997). Mathematics & Statistics Faculty Publications. 125.