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

Florian Franke1,2, Soňa Michlíková3,4, Sebastian Aland2,5,6

  • 1DataMedAssist Group, HTW Dresden-University of Applied Sciences, 01069 Dresden, Germany.

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Summary

A new radial-shell mathematical model accurately simulates 3D tumor spheroid growth and radio(chemo)therapy response, offering an efficient alternative to complex experiments and computational models.

Keywords:
3D growthcellular automatongrowth curveminimal modelradial shell modelradiation therapysimulationspatio-temporal mathematical modellingspheroidssystems biologytumor relapse

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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.