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Combination Therapies and Personalized Medicine02:50

Combination Therapies and Personalized Medicine

Combining two or more treatment methods increases the life span of cancer patients while reducing damage to vital organs or tissue from the overuse of a single treatment. Combination therapy also targets different cancer-inducing pathways, thus reducing the chances of developing resistance to treatment.
The combination of the drug acetazolamide and sulforaphane is a good example of combination therapy to treat cancer. The cells in the interior of a large tumor often die due to the hypoxic and...

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Updated: Jun 26, 2026

Modeling Chemotherapy Resistant Leukemia In Vitro
08:41

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Published on: February 9, 2016

Modeling, Analysis, and Optimal Control of Leukemic Cell Population Dynamics Under Therapy.

Pauline Mazel1,2, Frédéric Grognard3, Thomas Stiehl4,5,6

  • 1Université Côte d'Azur, Inria, INRAE, CNRS, MACBES, Valbonne, France. pauline.mazel@inria.fr.

Bulletin of Mathematical Biology
|June 24, 2026
PubMed
Summary

This study extends a mathematical model of leukemia cell dynamics to include chemotherapy effects. The research optimizes anti-cancer strategies by minimizing leukemia stem cells and drug toxicity, revealing a complex system with potential for novel therapeutic approaches.

Keywords:
Acute myeloid leukemiaMathematical oncologyPontryagin’s Maximum PrincipleSensitivity analysisTrans-heteroclinic bifurcationTurnpike phenomena

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Published on: November 21, 2018

Area of Science:

  • Mathematical Biology
  • Computational Oncology
  • Systems Biology

Background:

  • Existing ordinary differential equation (ODE) models describe healthy and leukemic cell dynamics.
  • Chemotherapy's impact on these dynamics requires a more refined mathematical framework.

Purpose of the Study:

  • To extend an existing ODE model by incorporating a chemotherapy control variable.
  • To establish a mathematical basis for investigating anti-cancer strategies.
  • To optimize chemotherapy regimens for minimizing leukemia stem cells and drug toxicity.

Main Methods:

  • Stability analysis of system equilibria using clinical data.
  • Optimal control problem formulation using Pontryagin's Maximum Principle.
  • Direct numerical optimization and sensitivity analysis.

Main Results:

  • Identification of a complex equilibrium structure, including a continuum of coexistence states and bifurcation thresholds.
  • Demonstration of a turnpike phenomenon where dynamic trajectories approach ideal static structures over time.
  • Sensitivity analysis providing insights into biological mechanisms influencing optimal therapeutic outcomes.

Conclusions:

  • The extended framework offers a refined mathematical basis for anti-cancer strategy investigation.
  • The study highlights unconventional features in optimal control problems due to complex equilibria.
  • Findings suggest potential for improved chemotherapy optimization based on identified biological mechanisms.