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Quantification of Breast Cancer Cell Invasiveness Using a Three-dimensional (3D) Model

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Three-dimensional multispecies nonlinear tumor growth--I Model and numerical method.

S M Wise¹, J S Lowengrub, H B Frieboes

¹Mathematics Department, University of Tennessee, Knoxville, TN 37996-1300, USA.

Journal of Theoretical Biology

|May 20, 2008

Summary

This study introduces a diffuse interface model for multispecies tumor growth, enabling detailed simulations of complex tumor morphologies. The model accurately captures avascular tumor growth and is computationally efficient for large-scale 3D analyses.

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Longitudinal Morphological and Physiological Monitoring of Three-dimensional Tumor Spheroids Using Optical Coherence Tomography

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Area of Science:

Computational biology
Mathematical modeling
Biophysics

Background:

Tumor growth and angiogenesis are complex processes.
Existing models often lack detailed descriptions of cell-cell interactions and morphology.
Previous simulations of tumor growth did not fully detail the underlying diffuse interface model.

Purpose of the Study:

To develop and analyze a diffuse interface continuum model for multispecies tumor growth and angiogenesis.
To describe the model's thermodynamic consistency and relation to mixture models.
To present a new numerical method for efficient simulation of tumor growth.

Main Methods:

Developed a diffuse interface continuum model replacing sharp interfaces with transition layers based on differential adhesion.
Introduced a continuum model of adhesion, thermodynamically consistent with mixture models.
Employed a fully adaptive, nonlinear multigrid/finite difference method for efficient simulations.

Main Results:

Demonstrated that the diffuse interface model reduces to a sharp interface model as interface thickness approaches zero.
Presented simulations of unstable avascular tumor growth in 2D and 3D.
Showcased the computational feasibility of large-scale 3D simulations for complex tumor morphologies.

Conclusions:

The diffuse interface model provides a thermodynamically consistent and detailed description of tumor progression.
The developed numerical techniques enable efficient, large-scale 3D simulations of tumor growth.
This work lays the foundation for investigating tumor invasion and angiogenesis in subsequent studies.