ArticleMathematical biosciences and engineering : MBE2019
Patient-specific parameter estimates of glioblastoma multiforme growth dynamics from a model with explicit birth and death rates.
Article in Mathematical biosciences and engineering : MBE, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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Who cites it
3 citing papers in PubMed.
- Mathematical modeling of multicellular tumor spheroids quantifies inter-patient and intra-tumor heterogeneity.NPJ systems biology and applications · 2025Article
- Practical Understanding of Cancer Model Identifiability in Clinical Applications.Life (Basel, Switzerland) · 2023Article
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7 authors.
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Abstract
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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