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A Mathematical Model for the Quantitation of Tumor and Antibody-Forming Cell Populations within an Animal's Body¹

From The Department of Microbiology, University of Alabama Medical Center, Birmingham, Alabama 35233

Abstract

The application of a mathematical model described by Hege and Cole was tested by a murine myeloma model. The plasmacytoma MOPC 104E secretes an IgM antibody to bacterial dextran B-1355. By using this system the various parameters required in the equation could be quantitated. The model relates the number of tumor cells in the population to antibody produced under conditions of logarithmic growth. Experimental values of antibody measured and estimation of starting population (An) of tumor cells showed that 2.24 x 10⁶ cells grew when 3 x 10⁶ cells were injected. This indicates that approximately 75% of the cells grew when 3.0 x 10⁶ tumor cells were given i.p. into each mouse. The experimentally determined antibody levels were in agreement with the computer calculated values.

Footnotes

¹ This work was supported by Grant GB 13804 from the National Science Foundation and American Cancer Grant In-66J.