Efficient Radial-Shell Model for 3D Tumor Spheroid Dynamics with Radiotherapy

Area of Science:

• Biomedical modeling
• Cancer research
• Mathematical oncology

Background:

• Three-dimensional (3D) tumor spheroids are vital in vitro models for studying radio(chemo)therapy, mimicking tumor microregions.
• Tumor spheroids present oxygen gradients affecting treatment sensitivity, but experiments are laborious and difficult to analyze long-term.
• Existing mathematical models are either computationally inexpensive but lack spatial resolution or are computationally expensive and heavily parameterized.

Purpose of the Study:

• To develop an efficient and accurate mathematical model for 3D tumor spheroid dynamics and radio(chemo)therapy response.
• To overcome the limitations of existing non-spatial and spatial models in predicting oxygen-dependent responses.
• To enhance the informative value of experimental data and support study design for combinatorial radio(chemo)therapy.

Main Methods:

• Development of a novel, effectively one-dimensional radial-shell (RS) mathematical model based on cellular dynamics within radial spheres.
• Exploitation of approximate rotational symmetry to incorporate 3D spheroid dynamics efficiently.
• Calibration and validation of the RS model against experimental spheroid growth curves for multiple cell lines with and without radiotherapy.

Main Results:

• The RS model accurately reproduces experimental spheroid growth curves, performing comparably to or better than 3D agent-based models.
• The model's computational efficiency allows for multi-parametric optimization within physiologically reasonable ranges.
• Analysis revealed that the spatial scale of cell interactions drives observed dynamic changes at small spheroid volumes.

Conclusions:

• The radial-shell model provides an efficient and accurate method for simulating 3D tumor spheroid growth and response to radio(chemo)therapy.
• The model facilitates the analysis of experimental data and aids in designing more effective therapeutic strategies.
• The RS model's parameterization allows for direct transfer to more complex 3D agent-based models, bridging computational gaps.