Control of tumor growth distributions through kinetic methods

Area of Science:

• Mathematical Biology
• Statistical Physics
• Tumor Growth Dynamics

Background:

• Mathematical modeling of tumor growth is a long-standing challenge with various existing formulations.
• Tumor growth dynamics are complex, influenced by microscopic interactions and leading to specific equilibrium distributions.

Purpose of the Study:

• To develop a novel kinetic model for continuous tumor growth distribution using statistical physics tools.
• To design microscopic feedback control therapies for influencing tumor growth and mitigating risks in large tumors.

Main Methods:

• Utilized mathematical tools from statistical physics to formulate a novel kinetic growth model.
• Derived Fokker-Planck type equations for free and controlled tumor growth distributions.
• Analyzed steady-state solutions and the impact of feedback control on distribution tails.

Main Results:

• The novel kinetic model highlights the role of microscopic transitions in equilibrium distributions.
• Free tumor growth distributions exhibit generalized Gamma densities with fat tails.
• Feedback control therapies modify the drift operator, resulting in slim-tailed distributions and mitigated risk factors.

Conclusions:

• The mesoscopic description allows for precise microscopic feedback control therapies.
• Controlled tumor growth models show a marked mitigation of risk factors by producing slim-tailed size distributions.
• Numerical results validate the theoretical analysis of the developed models and therapies.