Triple-Spiked Zones in Cell Surface Tessellations: Model for Malignant Growth
Grace F. Kao MD; Maryland Health Care System; Lawrence A. Brown MD; Maryland Health Care System; Grover M. Hutchins MD; The Johns Hopkins Medical Institutions; G. William Moore MD, PhD; Maryland Health Care System; Raimond A. Struble PhD; Maryland Health Care System;
Content:
Tumors of surface epithelium are among the most common human malignancies. In benign surface epithelium, the cell surface exhibits a regular, repeated packing of cells, or tessellation, resembling a collection of equal cylinders resting side-by-side. Malignant transformation involves variably-sized cells, a disorganized surface, and the tendency to invade surrounding tissues.
Technology:
Ordinary and synthetic geometry.
Design:
Mathematically, a tessellation is a periodic tiling of the plane by polygons, or space by polyhedra. A cell tessellation is a surface of nearly-circular cell-apices. The triple-spiked zone is the region inside each triple of tangent circles. Each tangent cell-triple has an inscribed circle, tangent to the triple-spiked zone, that forms a circular communication zone among the original tangent circles.
Results:
It is demonstrated that a cell-triple communicates maximally if and only if all three cell-radii are equal.
Conclusion:
Malignant surface cells are characterized by more size variation and less balanced packing. In this model, unequal cell size and cell miscommunication are geometric features of the same underlying process. Therapy for the communication process might possibly control the cell-size process. Mathematical models can be used to explore alternatives to classical hypotheses in pathology, and explore general paradigms. Related URL: http://netautopsy.org/triplspk.htm
