Estimating and determining the effect of a therapy on tumor dynamics by means of a modified Gompertz diffusion...

Area of Science:

• Mathematical Biology
• Biostatistics
• Pharmacodynamics

Background:

• Tumor growth dynamics are complex and influenced by various factors, including therapeutic interventions.
• Modeling tumor progression requires understanding the interplay between cell proliferation and death rates.
• Existing models may not fully capture the nuanced effects of combined therapies on tumor dynamics.

Purpose of the Study:

• To develop a methodology for estimating time-dependent therapy effects on tumor dynamics using a modified Gompertz diffusion process.
• To enable the estimation of individual therapy functions when combined treatment data is available.
• To determine the predominant in vivo effect (growth or death) of a single therapeutic agent.

Main Methods:

• Utilized a modified Gompertz diffusion process incorporating non-homogeneous terms for therapy effects.
• Proposed a method to estimate time-dependent functions representing therapy impact on birth and death parameters.
• Employed Kullback-Leibler divergence (relative entropy) as a criterion for analyzing therapy effects.

Main Results:

• Successfully developed a methodology to estimate therapy-induced changes in tumor growth and death rates.
• Demonstrated the ability to infer individual therapy effects from data of combined treatments or control groups.
• The Kullback-Leibler divergence criterion proved effective in distinguishing therapy impacts.

Conclusions:

• The proposed methodology offers a robust framework for analyzing tumor dynamics under therapeutic intervention.
• This approach facilitates the characterization of single-agent therapy effects in vivo.
• The study provides valuable tools for pharmacodynamic modeling and treatment optimization.