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- Title
Stochastic growth pattern of untreated human glioblastomas predicts the survival time for patients.
- Authors
Ma, Ziwei; Niu, Ben; Phan, Tuan Anh; Stensjøen, Anne Line; Ene, Chibawanye; Woodiwiss, Timothy; Wang, Tonghui; Maini, Philip K.; Holland, Eric C.; Tian, Jianjun Paul
- 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.
- Subjects
GLIOBLASTOMA multiforme; BRAIN tumors; STOCHASTIC differential equations; SURGICAL excision; TUMOR treatment
- Publication
Scientific Reports, 2020, Vol 10, Issue 1, p1
- ISSN
2045-2322
- Publication type
Article
- DOI
10.1038/s41598-020-63394-w