Am J Cancer Res 2012;2(2):204-213
Original Article
Predicting success or failure of immunotherapy for cancer:
insights from a clinically applicable mathematical model
Charles F. Babbs
Department of Basic Medical Sciences and Weldon School of Biomedical Engineering, Purdue University, West Lafayette,
Indiana, USA.
Received December 8, 2011; accepted December 26, 2011; Epub January, 2012; Published February 1, 2012
Abstract: The objective of this study was to create a clinically applicable mathematical model of immunotherapy for cancer and
use it to explore differences between successful and unsuccessful treatment scenarios. The simplified predator-prey model
includes four lumped parameters: tumor growth rate, g; immune cell killing efficiency, k; immune cell signaling factor, lamda;
and immune cell half-life decay, μ. The predator-prey equations as functions of time, t, for normalized tumor cell numbers, y, (the
prey) and immunocyte numbers, x, (the predators) are: dy/dt = gy – kx and dx/dt = lambdaxy – μx. A parameter estimation
procedure that capitalizes on available clinical data and the timing of clinically observable phenomena gives mid-range
benchmarks for parameters representing the unstable equilibrium case in which the tumor neither grows nor shrinks.
Departure from this equilibrium results in oscillations in tumor cell numbers and in many cases complete elimination of the
tumor. Several paradoxical phenomena are predicted, including increasing tumor cell numbers prior to a population crash,
apparent cure with late recurrence, one or more cycles of tumor growth prior to eventual tumor elimination, and improved tumor
killing with initially weaker immune parameters or smaller initial populations of immune cells. The model and the parameter
estimation techniques are easily adapted to various human cancers that evoke an immune response. They may help clinicians
understand and predict certain strange and unexpected effects in the world of tumor immunity and lead to the design of clinical
trials to test improved treatment protocols for patients. (AJCR0000097).
Keywords: Adoptive, basal cell carcinoma, imiquimod, immune modulation, Lotka-Volterra, lymphoma, melanoma, predator-
prey, tumor infiltrating lymphocytes
Address all correspondence to:
Charles F. Babbs, MD, PhD
Department of Basic Medical Sciences
1246 Lynn Hall
Purdue University
West Lafayette IN47907-1246, USA.
E-mail: babbs@purdue.edu
Original Article
Predicting success or failure of immunotherapy for cancer:
insights from a clinically applicable mathematical model
Charles F. Babbs
Department of Basic Medical Sciences and Weldon School of Biomedical Engineering, Purdue University, West Lafayette,
Indiana, USA.
Received December 8, 2011; accepted December 26, 2011; Epub January, 2012; Published February 1, 2012
Abstract: The objective of this study was to create a clinically applicable mathematical model of immunotherapy for cancer and
use it to explore differences between successful and unsuccessful treatment scenarios. The simplified predator-prey model
includes four lumped parameters: tumor growth rate, g; immune cell killing efficiency, k; immune cell signaling factor, lamda;
and immune cell half-life decay, μ. The predator-prey equations as functions of time, t, for normalized tumor cell numbers, y, (the
prey) and immunocyte numbers, x, (the predators) are: dy/dt = gy – kx and dx/dt = lambdaxy – μx. A parameter estimation
procedure that capitalizes on available clinical data and the timing of clinically observable phenomena gives mid-range
benchmarks for parameters representing the unstable equilibrium case in which the tumor neither grows nor shrinks.
Departure from this equilibrium results in oscillations in tumor cell numbers and in many cases complete elimination of the
tumor. Several paradoxical phenomena are predicted, including increasing tumor cell numbers prior to a population crash,
apparent cure with late recurrence, one or more cycles of tumor growth prior to eventual tumor elimination, and improved tumor
killing with initially weaker immune parameters or smaller initial populations of immune cells. The model and the parameter
estimation techniques are easily adapted to various human cancers that evoke an immune response. They may help clinicians
understand and predict certain strange and unexpected effects in the world of tumor immunity and lead to the design of clinical
trials to test improved treatment protocols for patients. (AJCR0000097).
Keywords: Adoptive, basal cell carcinoma, imiquimod, immune modulation, Lotka-Volterra, lymphoma, melanoma, predator-
prey, tumor infiltrating lymphocytes
Address all correspondence to:
Charles F. Babbs, MD, PhD
Department of Basic Medical Sciences
1246 Lynn Hall
Purdue University
West Lafayette IN47907-1246, USA.
E-mail: babbs@purdue.edu
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American Journal of Cancer Research
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