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A theoretical explanation of "concomitant resistance"
1Department of Biomathematics, Syntex Drug Discovery Research, Palo Alto, CA 94393, USA.
Bulletin of Mathematical Biology
|September 1, 1995
Summary
Concomitant resistance, a tumor growth dynamic, can be real or apparent. True resistance requires one tumor implant to become quiescent, necessitating a recruitment signal for regrowth upon removal of the inhibiting tumor.
Area of Science:
- Mathematical biology
- Tumor growth dynamics
- Cancer research
Background:
- Concomitant resistance is a tumor growth dynamic where a second tumor's growth is inhibited by a first.
- Previous models explored tumor growth with regenerating liver and tumor dormancy/recurrence.
Purpose of the Study:
- To extend previous modeling studies to the concomitant resistance phenomenon.
- To propose and analyze mathematical models for concomitant resistance.
Main Methods:
- Developed two interlocking mathematical models: one for interactive competition, another for proportional growth inhibition.
- Analyzed system equilibria and dynamics under constant coefficients for three parameter subcases.
Main Results:
- Concomitant resistance can be real or apparent.
- Constant model coefficients necessitate total tumor quiescence for true concomitant resistance.
- Regrowth of the inhibited tumor requires a non-constant recruitment signal if it enters quiescence.
Conclusions:
- Mathematical modeling provides insights into the mechanisms of concomitant resistance.
- The conditions for true concomitant resistance are specific and may require dynamic regulatory signals.