Patient-Specific Mathematical Neuro-Oncology: Using a Simple Proliferation and Invasion Tumor Model to Inform Clinical Practice

Abstract

Glioblastoma multiforme (GBM) is the most common malignant primary brain tumor associated with a poor median survival of 15–18 months, yet there is wide heterogeneity across and within patients. This heterogeneity has been the source of significant clinical challenges facing patients with GBM and has hampered the drive toward more precision or personalized medicine approaches to treating these challenging tumors. Over the last two decades, the field of Mathematical Neuro-oncology has grown out of desire to use (often patient-specific) mathematical modeling to better treat GBMs. Here, we will focus on a series of clinically relevant results using patient-specific mathematical modeling. The core model at the center of these results incorporates two hallmark features of GBM, proliferation and invasion (D), as key parameters. Based on routinely obtained magnetic resonance images, each patient’s tumor can be characterized using these two parameters. The Proliferation-Invasion (PI) model uses and D to create patient-specific growth predictions. The PI model, its predictions, and parameters have been used in a number of ways to derive biological insight. Beyond predicting growth, the PI model has been utilized to identify patients who benefit from different surgery strategies, to prognosticate response to radiation therapy, to develop a treatment response metric, and to connect clinical imaging features and genetic information. Demonstration of the PI model’s clinical relevance supports the growing role for it and other mathematical models in routine clinical practice.

CNS Anticancer Drug Discovery and Development: 2016 conference insights

“…This included phenotypic cell models driven by MRI imaging scale metrics. This approach has led to a proliferation-invasion (PI) model that utilizes patient MRI data to uniquely estimate glioma cell density using proliferation and diffusion (invasion) rate parameters [29,30]. The PI model has been extended to a proliferation-invasion-hypoxia-necrosisangiogenesis model specifically used to analyze anti-angiogenic therapy and the need for gross total resection.…”

Simulating the growth of hepatic metastases from carcinoma of the pancreas using LabVIEW

“…The model was used to simulate surgical resection for 70 patients with glioblastoma and predicted the survival in this group [7]. In addition to predicting tumor growth the PI model has been used to identify patients who might respond to various surgical strategies, predict response to radiation therapy and to connect clinical imaging features and genetic information [11]. While the clinical behavior of glioblastoma is not the same as adenocarcinoma of the pancreas, computational oncology may offer insights into various therapeutic approaches for patients with adenocarcinoma of the pancreas [8].…”

3D Mathematical modeling of glioblastoma suggests that transdifferentiated vascular endothelial cells promote resistance to current standard-of-care therapy.

“…Mathematical models of GBM range from discrete agent-based models, which track the behaviors of individual cells, to cellular automaton models, which describe the motion of discrete cells on a lattice and enable simulations at super-cell scales, to continuum models that track the dynamics of cell densities or volume fractions at tissue-level scales. See recent review articles for further details and references (26)(27)(28). Because of their simplicity, continuum reaction-diffusion equations have been widely used to describe the infiltration of GBM cells in the brain (29)(30)(31) and to develop patient-specific therapeutic approaches (32,33).…”