The mathematics of cancer: integrating quantitative models

PM Altrock, LL Liu, F Michor - Nature Reviews Cancer, 2015 - nature.com
Mathematical modelling approaches have become increasingly abundant in cancer
research. The complexity of cancer is well suited to quantitative approaches as it provides …

A review of mathematical models for tumor dynamics and treatment resistance evolution of solid tumors

A Yin, DJAR Moes, JGC van Hasselt… - CPT …, 2019 - Wiley Online Library
Increasing knowledge of intertumor heterogeneity, intratumor heterogeneity, and cancer
evolution has improved the understanding of anticancer treatment resistance. A better …

Sex differences in GBM revealed by analysis of patient imaging, transcriptome, and survival data

W Yang, NM Warrington, SJ Taylor… - Science translational …, 2019 - science.org
Sex differences in the incidence and outcome of human disease are broadly recognized but,
in most cases, not sufficiently understood to enable sex-specific approaches to treatment …

Classical mathematical models for description and prediction of experimental tumor growth

S Benzekry, C Lamont, A Beheshti… - PLoS computational …, 2014 - journals.plos.org
Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be
expressed as mathematical models. To explore this further, quantitative analysis of the most …

Integrating mechanism-based modeling with biomedical imaging to build practical digital twins for clinical oncology

C Wu, G Lorenzo, DA Hormuth, EABF Lima… - Biophysics …, 2022 - pubs.aip.org
Digital twins employ mathematical and computational models to virtually represent a
physical object (eg, planes and human organs), predict the behavior of the object, and …

Imaging of intratumoral heterogeneity in high-grade glioma

LS Hu, A Hawkins-Daarud, L Wang, J Li, KR Swanson - Cancer letters, 2020 - Elsevier
Abstract High-grade glioma (HGG), and particularly Glioblastoma (GBM), can exhibit
pronounced intratumoral heterogeneity that confounds clinical diagnosis and management …

Clustering functional magnetic resonance imaging time series in glioblastoma characterization: A review of the evolution, applications, and potentials

M De Simone, G Iaconetta, G Palermo, A Fiorindi… - Brain Sciences, 2024 - mdpi.com
In this paper, we discuss how the clustering analysis technique can be applied to analyze
functional magnetic resonance imaging (fMRI) time-series data in the context of …

Mathematical modeling of tumor growth and treatment

H Enderling, M AJ Chaplain - Current pharmaceutical design, 2014 - benthamdirect.com
Using mathematical models to simulate dynamic biological processes has a long history.
Over the past couple of decades or so, quantitative approaches have also made their way …

Predictive digital twin for optimizing patient-specific radiotherapy regimens under uncertainty in high-grade gliomas

A Chaudhuri, G Pash, DA Hormuth… - Frontiers in Artificial …, 2023 - frontiersin.org
We develop a methodology to create data-driven predictive digital twins for optimal risk-
aware clinical decision-making. We illustrate the methodology as an enabler for an …

Growth dynamics of untreated glioblastomas in vivo

AL Stensjøen, O Solheim, KA Kvistad… - Neuro …, 2015 - academic.oup.com
Background Glioblastomas are primary malignant brain tumors with a dismal prognosis.
Knowledge of growth rates and underlying growth dynamics is useful for understanding …