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A Quasi Birth-and-Death model for tumor recurrence
Leonardo M Santana1, Shridar Ganesan2, Gyan Bhanot3
1Department of Physics & Astronomy, Rutgers University, Piscataway, NJ 08854, USA.
Journal of Theoretical Biology
|August 3, 2019
Summary
This study introduces a mathematical model to predict cancer recurrence after chemotherapy. Extending chemotherapy duration can reduce recurrence probability and increase time to recurrence, aiding treatment optimization.
Area of Science:
- Mathematical Oncology
- Cancer Dynamics Modeling
Background:
- Chemoresistance and tumor recurrence stem from dormant cancer cells surviving treatment.
- Predicting and preventing cancer regrowth after therapy is a critical clinical challenge.
Purpose of the Study:
- To develop a mathematical model simulating tumor growth, dormancy, and recurrence dynamics.
- To analyze the impact of chemotherapy duration on recurrence probability and timing.
- To provide a framework for optimizing cancer treatment strategies.
Main Methods:
- Utilized a Quasi Birth-and-Death (QBD) model derived from a discrete-state master equation.
- Employed a continuum-limit approach to analyze undetectable residual tumor growth.
- Derived analytical solutions for recurrence probability and mean recurrence time using Kolmogorov equations and first-passage time formalism.
Main Results:
- Developed an exact formula for the probability of recurrence, revealing a phase transition.
- Obtained a drift-diffusion equation for mean recurrence time, solved analytically.
- Model parameters successfully fitted ovarian cancer recurrence-free survival data.
- Simulations confirmed that longer chemotherapy extends recurrence time and reduces long-term recurrence probability.
Conclusions:
- The proposed QBD model accurately predicts tumor recurrence dynamics and is applicable to clinical data.
- Optimizing chemotherapy duration is a viable strategy to improve patient outcomes, particularly for cancers lacking targeted therapies.
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