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Estimation of Tumor Size Evolution Using Particle Filters.

Jose M J Costa1,2, Helcio R B Orlande1, Haroldo F Campos Velho3

  • 11 Department of Mechanical Engineering, Federal University of Rio de Janeiro , Rio de Janeiro, Brazil .

Journal of Computational Biology : a Journal of Computational Molecular Cell Biology
|May 15, 2015
PubMed
Summary

This study introduces a mathematical model to estimate tumor size evolution during cancer treatment. The model accounts for cell populations and drug dynamics, aiding in understanding chemotherapy effectiveness.

Keywords:
cancer modelinginverse problemparticle filterstate estimation problemtumor size

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Area of Science:

  • Oncology
  • Mathematical Biology
  • Computational Science

Background:

  • Cancer involves uncontrolled cell growth and metastasis.
  • Mathematical models are crucial for understanding tumor dynamics and drug interactions.
  • Accurate state estimation is vital for effective cancer therapy.

Purpose of the Study:

  • To solve a state estimation problem for tumor size evolution.
  • To develop a model incorporating tumor, normal, and angiogenic cells, plus drug masses.
  • To analyze the impact of chemotherapy and anti-angiogenic drugs on tumor progression.

Main Methods:

  • Utilized a nonlinear ordinary differential equation system for state evolution.
  • Incorporated measurements of tumor and normal cell counts for inverse analysis.
  • Employed an auxiliary sampling importance resampling particle filter algorithm.
  • Treated model parameters as Gaussian random variables to account for uncertainties.

Main Results:

  • Successfully estimated tumor size evolution using the developed model.
  • Demonstrated the model's capability in handling uncertainties in parameters.
  • Validated the approach with test cases involving a pancreatic cancer chemotherapy protocol.

Conclusions:

  • The proposed state estimation method provides a robust framework for modeling tumor growth dynamics.
  • The particle filter approach effectively integrates cell population data and drug effects.
  • This modeling strategy offers potential for optimizing cancer treatment strategies, particularly for pancreatic cancer.