On minimising tumoural growth under treatment resistance
Matthias M Fischer1, Nils Blüthgen1
1Institute for Theoretical Biology, Charité and Humboldt Universität zu Berlin, 10115 Berlin, Germany.
Abstract:
Drug resistance is a major challenge for curative cancer treatment, representing the main reason of death in patients. Evolutionary biology suggests pauses between treatment rounds as a way to delay or even avoid resistance emergence. Indeed, this approach has already shown promising preclinical and early clinical results, and stimulated the development of mathematical models for finding optimal treatment protocols. Due to their complexity, however, these models do not lend themself to a rigorous mathematical analysis, hence so far clinical recommendations generally relied on numerical simulations and ad-hoc heuristics. Here, we derive two mathematical models describing tumour growth under genetic and epigenetic treatment resistance, respectively, which are simple enough for a complete analytical investigation. First, we find key differences in response to treatment protocols between the two modes of resistance. Second, we identify the optimal treatment protocol which leads to the largest possible tumour shrinkage rate. Third, we fit the "epigenetic model" to previously published xenograft experiment data, finding excellent agreement, underscoring the biological validity of our approach. Finally, we use the fitted model to calculate the optimal treatment protocol for this specific experiment, which we demonstrate to cause curative treatment, making it superior to previous approaches which generally aimed at stabilising tumour burden. Overall, our approach underscores the usefulness of simple mathematical models and their analytical examination, and we anticipate our findings to guide future preclinical and, ultimately, clinical research in optimising treatment regimes.
Insights
Simple mathematical models reveal optimal cancer treatment pauses to overcome drug resistance. This approach leads to significant tumor shrinkage and potentially curative outcomes, guiding future clinical strategies.
Area of Science:
- Oncology
- Mathematical Biology
- Evolutionary Biology
Background:
- Drug resistance is a primary cause of cancer treatment failure and mortality.
- Evolutionary principles suggest treatment interruptions can delay or prevent resistance.
- Existing mathematical models are too complex for analytical study, limiting clinical application.
Purpose of the Study:
- To develop simple, analytically tractable mathematical models for tumor growth under genetic and epigenetic resistance.
- To identify optimal cancer treatment protocols that maximize tumor shrinkage rate.
- To validate the epigenetic model with experimental data and apply it for curative treatment strategies.
Main Methods:
- Derivation of two distinct mathematical models for genetic and epigenetic drug resistance.
- Analytical investigation of model behavior under various treatment protocols.
- Fitting the epigenetic model to published xenograft experiment data.
- Calculation of optimal treatment protocols based on the fitted model.
Main Results:
- Identified key differences in tumor response to treatment protocols based on resistance type (genetic vs. epigenetic).
- Determined optimal treatment strategies that maximize tumor shrinkage rate.
- Demonstrated excellent agreement between the epigenetic model and experimental xenograft data.
- Calculated a curative treatment protocol for the specific experiment, outperforming methods focused on tumor stabilization.
Conclusions:
- Simple mathematical models are valuable tools for analyzing complex cancer treatment dynamics.
- Analytical examination of these models can reveal optimal strategies for overcoming drug resistance.
- The derived epigenetic model shows biological validity and can guide the development of curative cancer therapies.
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