Limiting spheroid size as a function of growth factor source location

✍ Scribed by J.A. Adam; K.Y. Ward

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 224 KB
• Volume: 10
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/s0893-9659(97)00032-3

✦ Synopsis

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 0, near which (i.e., as C --* 0-) mitosis, and hence spheroid growth, is generally strongly inhibited.