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.
journal_name
Sci Repjournal_title
Scientific reportsauthors
Ma Z,Niu B,Phan TA,Stensjøen AL,Ene C,Woodiwiss T,Wang T,Maini PK,Holland EC,Tian JPdoi
10.1038/s41598-020-63394-wsubject
Has Abstractpub_date
2020-04-20 00:00:00pages
6642issue
1issn
2045-2322pii
10.1038/s41598-020-63394-wjournal_volume
10pub_type
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