Mathematical modeling of multicellular tumor spheroids quantifies inter-patient and intra-tumor heterogeneity.

in NPJ systems biology and applications by Adam A Malik, Kyle C Nguyen, John T Nardini, Cecilia C Krona, Kevin B Flores, Sven Nelander

TLDR

  • A novel model that combines proliferation and migration terms accurately describes the growth of patient-derived spheroids, with implications for brain tumor research.

Abstract

In the study of brain tumors, patient-derived three-dimensional sphere cultures provide an important tool for studying emerging treatments. The growth of such spheroids depends on the combined effects of proliferation and migration of cells, but it is challenging to make accurate distinctions between increase in cell number versus the radial movement of cells. To address this, we formulate a novel model in the form of a system of two partial differential equations (PDEs) incorporating both migration and growth terms, and show that it more accurately fits our data compared to simpler PDE models. We show that traveling-wave speeds are strongly associated with population heterogeneity. Having fitted the model to our dataset we show that a subset of the cell lines are best described by a "Go-or-Grow"-type model, which constitutes a special case of our model. Finally, we investigate whether our fitted model parameters are correlated with patient age and survival.

Overview

  • The study aims to develop a novel model to accurately describe the growth of patient-derived three-dimensional sphere cultures, a crucial tool in brain tumor research.
  • The model combines terms for proliferation and migration of cells to distinguish between cell number increase and radial movement.
  • The study uses a system of partial differential equations (PDEs) to describe the growth of spheroids and compares its accuracy to simpler PDE models.

Comparative Analysis & Findings

  • The novel model was shown to fit the data more accurately than simpler PDE models.
  • Traveling-wave speeds were found to be strongly associated with population heterogeneity.
  • A subset of cell lines was best described by a 'Go-or-Grow'-type model, a special case of the novel model.

Implications and Future Directions

  • The study highlights the importance of accurately modeling spheroid growth in brain tumor research.
  • Future research could investigate the correlation between fitted model parameters and patient-specific characteristics, such as age and survival.
  • Exploration of the 'Go-or-Grow' model could lead to better understanding of cell line behavior and implications for treatment development.
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