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Patient-specific parameter estimates of glioblastoma multiforme growth dynamics from a model with explicit birth and death rates

1 School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
2 Department of Neurosurgery, Barrow Neurological Institute, St. Josephs Hospital and Medical Center, Phoenix, AZ 85013, USA

Special Issues: Practical Insights from Cancer Models

Glioblastoma multiforme (GBM) is an aggressive primary brain cancer with a grim prog-nosis. Its morphology is heterogeneous, but prototypically consists of an inner, largely necrotic core surrounded by an outer, contrast-enhancing rim, and often extensive tumor-associated edema beyond. This structure is usually demonstrated by magnetic resonance imaging (MRI). To help relate the three highly idealized components of GBMs (i.e., necrotic core, enhancing rim, and maximum edema ex-tent) to the underlying growth “laws,” a mathematical model of GBM growth with explicit motility, birth, and death processes is proposed. This model generates a traveling-wave solution that mimics tumor progression. We develop several novel methods to approximate key characteristics of the wave profile, which can be compared with MRI data. Several simplified forms of growth and death terms and their parameter identifiability are studied. We use several test cases of MRI data of GBM patients to yield personalized parameterizations of the model, and the biological and clinical implications are discussed.
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Keywords glioblastoma multiforme; parameter estimation; reaction-diffusion models; patient-specific models

Citation: Lifeng Han, Steffen Eikenberry, Changhan He, Lauren Johnson, Mark C. Preul, Eric J. Kostelich, Yang Kuang. Patient-specific parameter estimates of glioblastoma multiforme growth dynamics from a model with explicit birth and death rates. Mathematical Biosciences and Engineering, 2019, 16(5): 5307-5323. doi: 10.3934/mbe.2019265


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