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

• Published in: NPJ systems biology and applications Vol. 11; no. 1; pp. 20 - 14
• Main Authors: Malik, Adam A., Nguyen, Kyle C., Nardini, John T., Krona, Cecilia C., Flores, Kevin B., Nelander, Sven
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 15.02.2025; Nature Publishing Group; Nature Portfolio
• Subjects: 631/114; 631/67; 639/705/1041; Bioinformatics; Biology; Biomedical and Life Sciences; Brain cancer; Brain Neoplasms; Brain tumors; Cell culture; Cell migration; Cell Movement; Cell number; Cell Proliferation; Computational Biology/Bioinformatics; Computer Appl. in Life Sciences; Data processing; Glioblastoma; Humans; Hypotheses; Life Sciences; Mathematical models; Multicellular tumor spheroids; Parameter estimation; Partial differential equations; Patient-Specific Modeling; Patients; Population density; Radiation therapy; Spheroids; Spheroids, Cellular - physiology; Systems Biology; Tumor Cells, Cultured - physiology; Tumors
• ISSN: 2056-7189; 2056-7189
• DOI: 10.1038/s41540-025-00492-3

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.