Tracking glioblastoma progression after initial resection with minimal reaction-diffusion models

Authors

• Duane C. Harris, School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ 85281, USA.
• Giancarlo Mignucci-Jiménez, Department of Neurosurgery, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ 85013, USA.
• Yuan Xu, Department of Neurosurgery, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ 85013, USA.
• Steffen E. Eikenberry, School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ 85281, USA.
• C Chad Quarles, Department of Neurosurgery, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ 85013, USA.
• Mark C. Preul, Department of Neurosurgery, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ 85013, USA.
• Yang Kuang, School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ 85281, USA.
• Eric J. Kostelich, School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ 85281, USA.

Document Type

Article

Abstract

We describe a preliminary effort to model the growth and progression of glioblastoma multiforme, an aggressive form of primary brain cancer, in patients undergoing treatment for recurrence of tumor following initial surgery and chemoradiation. Two reaction-diffusion models are used: the Fisher-Kolmogorov equation and a 2-population model, developed by the authors, that divides the tumor into actively proliferating and quiescent (or necrotic) cells. The models are simulated on 3-dimensional brain geometries derived from magnetic resonance imaging (MRI) scans provided by the Barrow Neurological Institute. The study consists of 17 clinical time intervals across 10 patients that have been followed in detail, each of whom shows significant progression of tumor over a period of 1 to 3 months on sequential follow up scans. A Taguchi sampling design is implemented to estimate the variability of the predicted tumors to using 144 different choices of model parameters. In 9 cases, model parameters can be identified such that the simulated tumor, using both models, contains at least 40 percent of the volume of the observed tumor. We discuss some potential improvements that can be made to the parameterizations of the models and their initialization.

Medical Subject Headings

Brain Neoplasms (diagnostic imaging, pathology, surgery); Chemoradiotherapy (methods); Diffusion; Glioblastoma (diagnostic imaging, pathology, surgery); Humans; Magnetic Resonance Imaging

Publication Date

3-28-2022

Publication Title

Mathematical biosciences and engineering : MBE

E-ISSN

1551-0018

Volume

19

Issue

6

First Page

5446

Last Page

5481

PubMed ID

35603364

Digital Object Identifier (DOI)

10.3934/mbe.2022256

Recommended Citation

Harris, Duane C.; Mignucci-Jiménez, Giancarlo; Xu, Yuan; Eikenberry, Steffen E.; Quarles, C Chad; Preul, Mark C.; Kuang, Yang; and Kostelich, Eric J., "Tracking glioblastoma progression after initial resection with minimal reaction-diffusion models" (2022). Neurosurgery. 2343.
https://scholar.barrowneuro.org/neurosurgery/2343