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Avascular tumour growth models based on anomalous diffusion.

Sounak Sadhukhan1, S K Basu2

  • 1Department of Computer Science, Institute of Science, Banaras Hindu University, Varanasi, 221005, India. sounaks.cse@gmail.com.

Journal of Biological Physics
|March 19, 2020
PubMed
Summary
This summary is machine-generated.

This study models avascular tumor growth using fractional diffusion equations, offering a more accurate description of biological systems than simple diffusion models. Anomalous diffusion models provide better insights into tumor microenvironments and clinical facts.

Keywords:
Anomalous diffusionAvascular tumour growthDiffusion with memoryFractional derivativeFractional diffusion equation

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Area of Science:

  • Mathematical modeling of biological systems
  • Tumor microenvironment dynamics
  • Anomalous diffusion processes

Background:

  • Avascular tumor growth is complex, involving heterogeneous diffusion through porous cellular membranes.
  • Previous models often used simple diffusion, not fully capturing biological system complexities.
  • Fractional diffusion equations are better suited for modeling heterogeneous biological systems.

Purpose of the Study:

  • To develop and investigate fractional diffusion models for avascular tumor growth.
  • To compare fixed-order and variable-order fractional models with memory formalism.
  • To understand tumor-microenvironment interactions before angiogenesis.

Main Methods:

  • Developed a spherical model initially based on simple diffusion.
  • Upgraded the model using fractional diffusion equations (fixed and variable order).
  • Incorporated memory formalism into anomalous diffusion models.

Main Results:

  • Anomalous diffusion models provide a closer description to clinical facts than simple models.
  • All models offer macroscopic insights into the tumor microenvironment.
  • Anomalous diffusion models showed moderate sensitivity to parameter changes.

Conclusions:

  • Fractional diffusion models, particularly anomalous ones, are valuable for studying avascular tumor growth.
  • These models enhance understanding of tumor-microenvironment interactions and physical changes.
  • The findings support improved diagnostics, therapies, and prognostics for tumors.