Mathematical modeling of microtube-driven regrowth of gliomas after local resection

Alexandra Shyntar; Thomas Hillen; Alexandra Shyntar; Thomas Hillen

doi:10.3934/mbe.2025003

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 1: 52-72. doi: 10.3934/mbe.2025003

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Mathematical modeling of microtube-driven regrowth of gliomas after local resection

Alexandra Shyntar ,
Thomas Hillen ^,

Department of Mathematical and Statistical Science, University of Alberta, Edmonton, AB T6G 2G1, Canada

Received: 02 August 2024 Revised: 14 November 2024 Accepted: 12 December 2024 Published: 24 December 2024

Recently, glioblastoma tumors were shown to form tumor microtubes, which are thin, long protrusions that help the tumor grow and spread. Follow-up experiments were conducted on mice in order to test what impact the tumor microtubes have on tumor regrowth after the partial removal of a tumor region. The surgery was performed in isolation and along with growth-inhibiting treatments such as a tumor microtube-inhibiting treatment and an anti-inflammatory treatment. Here, we have proposed a partial differential equation model applicable to describe the microtube-driven regrowth of the cancer in the lesion. We found that the model is able to replicate the main trends seen in the experiments such as fast regrowth, larger cancer density in the lesion, and further spread into healthy tissue. The model indicates that the dominant mechanisms of re-growth are growth-inducing wound-healing mechanisms and the proliferative advantage from the tumor microtubes. In addition, tumor microtubes provide orientational guidance from the untreated tissue into the lesion.
- tumor microtubes,
- glioblastoma modeling,
- anisotropic diffusion
Citation: Alexandra Shyntar, Thomas Hillen. Mathematical modeling of microtube-driven regrowth of gliomas after local resection[J]. Mathematical Biosciences and Engineering, 2025, 22(1): 52-72. doi: 10.3934/mbe.2025003

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Abstract

Recently, glioblastoma tumors were shown to form tumor microtubes, which are thin, long protrusions that help the tumor grow and spread. Follow-up experiments were conducted on mice in order to test what impact the tumor microtubes have on tumor regrowth after the partial removal of a tumor region. The surgery was performed in isolation and along with growth-inhibiting treatments such as a tumor microtube-inhibiting treatment and an anti-inflammatory treatment. Here, we have proposed a partial differential equation model applicable to describe the microtube-driven regrowth of the cancer in the lesion. We found that the model is able to replicate the main trends seen in the experiments such as fast regrowth, larger cancer density in the lesion, and further spread into healthy tissue. The model indicates that the dominant mechanisms of re-growth are growth-inducing wound-healing mechanisms and the proliferative advantage from the tumor microtubes. In addition, tumor microtubes provide orientational guidance from the untreated tissue into the lesion.

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