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Review
. 2015 May;77(5):846-56.
doi: 10.1007/s11538-015-0067-7. Epub 2015 Mar 21.

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

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Free PMC article
Review

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

Pamela R Jackson et al. Bull Math Biol. .
Free PMC article

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 [Formula: see text] 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 [Formula: see text] 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.

Figures

Fig. 1
Fig. 1
a Example “diffuse” tumor annotated with GTR margin (red) and model predicted margin (green) needed to remove 99 % of tumor cells and b example “nodular” tumor annotated with GTR margin (red) and model predicted margin (green) needed to remove 99 % of tumor cells. The closer the GTR and model predicted 99 % margins are, the better the survival outcomes for patients receiving a GTR. Adapted from (Baldock et al. 2014a)
Fig. 2
Fig. 2
Pre-treatment MRI’s (yellow boxes) used to calculate alpha parameter from the linear-quadratic model. Top patient has an alpha parameter of 0.340 /Gy which the model predicts is radio-sensitive. Bottom patient (0.016 /Gy) is predicted to be radio-resistant. Tumor growth curves show top patient post-treatment MRI tumor radius (blue dot on blue line) is highly deflected from the UVC simulation (red line). Bottom patient post-treatment MRI tumor radius is hardly deflected from the UVC. Post-treatment MRI’s (blue boxes) show that the model-predicted radio-sensitive patient’s tumor is much more responsive to treatment than the model-predicted radio-resistant patient
Fig. 3
Fig. 3
Calculation of the Days Gained score. Blue line is the UVC simulated based on the pretreatment patient MRI data (pink dots on blue line). The one-dimensional straight-line distance from UVC to the post-treatment MRI point is the Days Gained score. The four-dimensional anatomical brain tumor is shown in its native position within the patient’s brain. Color indicates density of tumor cells where red is high density. Adapted from (Neal et al. 2013a)
Fig. 4
Fig. 4
a The range of ρ/D values for IDH1 wild-type and mutant tumors. The mean value of ρ/D is significantly different between wild-type (n = 42) and mutant (n = 11) tumors (p = 0.0057, t test). b Example IDH1 wild-type and mutant tumors with model-predicted tumor cell density overlay where blue is low tumor cell density and red is high tumor cell density. Adapted from (Baldock et al. 2014b)

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