Continuum versus discrete model: a comparison for multicellular tumour spheroids.

Area of Science:

• Mathematical Biology
• Computational Biology
• Tumor Microenvironment Modeling

Background:

• Multicellular tumor spheroids exhibit complex growth dynamics influenced by nutrient availability and cell density.
• Understanding these dynamics is crucial for developing effective cancer therapies.

Purpose of the Study:

• To develop and validate a continuum model based on partial differential equations (PDEs) for simulating multicellular tumor spheroid growth.
• To compare the predictive power of the PDE model against an agent-based model and experimental data.

Main Methods:

• A PDE-based continuum model incorporating viable/necrotic cell densities and nutrient concentrations (oxygen, glucose).
• Model parameters were fitted to experimental tumor growth curves under varying nutrient conditions.
• Spherical symmetry assumption was applied for model simplification.
• Comparison with an off-lattice agent-based model (ABM).

Main Results:

• The PDE model accurately explains macroscopic tumor growth data, demonstrating its efficiency compared to the ABM.
• A necrotic core formation is necessary to reproduce experimental growth curves, consistent with ABM findings.
• Discrepancies were observed between the PDE model, ABM, and experimental data when evaluating morphometric properties.

Conclusions:

• Continuum PDE models are sufficient for explaining macroscopic tumor spheroid growth, offering a computationally efficient alternative to ABMs.
• Necrotic core development is a key factor in tumor growth dynamics.
• Further refinement of models is needed to capture detailed morphometric characteristics of tumors.