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Title: Stochastic growth pattern of untreated human glioblastomas predicts the survival time for patients
Abstract

Glioblastomas are highly malignant brain tumors. Knowledge of growth rates and growth patterns is useful for understanding tumor biology and planning treatment logistics. Based on untreated human glioblastoma data collected in Trondheim, Norway, we first fit the average growth to a Gompertz curve, then find a best fitted white noise term for the growth rate variance. Combining these two fits, we obtain a new type of Gompertz diffusion dynamics, which is a stochastic differential equation (SDE). Newly collected untreated human glioblastoma data in Seattle, US, re-verify our model. Instead of growth curves predicted by deterministic models, our SDE model predicts a band with a center curve as the tumor size average and its width as the tumor size variance over time. Given the glioblastoma size in a patient, our model can predict the patient survival time with a prescribed probability. The survival time is approximately a normal random variable with simple formulas for its mean and variance in terms of tumor sizes. Our model can be applied to studies of tumor treatments. As a demonstration, we numerically investigate different protocols of surgical resection using our model and provide possible theoretical strategies.

 
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NSF-PAR ID:
10154454
Author(s) / Creator(s):
; ; ; ; ; ; ; ; ;
Publisher / Repository:
Nature Publishing Group
Date Published:
Journal Name:
Scientific Reports
Volume:
10
Issue:
1
ISSN:
2045-2322
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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