title: Environmental factors in breast cancer invasion: a mathematical modelling review.
abstract: This review presents a brief overview of breast cancer, focussing on its heterogeneity and the role of mathematical modelling and simulation in teasing apart the underlying biophysical processes. Following a brief overview of the main known pathophysiological features of ductal carcinoma, attention is paid to differential equation-based models (both deterministic and stochastic), agent-based modelling, multi-scale modelling, lattice-based models and image-driven modelling. A number of vignettes are presented where these modelling approaches have elucidated novel aspects of breast cancer dynamics, and we conclude by offering some perspectives on the role mathematical modelling can play in understanding breast cancer development, invasion and treatment therapies.
authors.affiliation: School of Mathematical Sciences, and ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Gardens Point, Brisbane, Qld, Australia.
authors.forename: Alex
authors.initials: A
authors.lastname: Simmons
authors.affiliation: School of Mathematical Sciences, and ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Gardens Point, Brisbane, Qld, Australia.
authors.forename: Pamela M
authors.initials: PM
authors.lastname: Burrage
authors.affiliation: School of Mathematical Sciences, and ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Gardens Point, Brisbane, Qld, Australia; Mathematical Institute, University of Oxford, Oxford, United Kingdom; Molecular Sense Ltd, Oxford, United Kingdom.
authors.forename: Dan V
authors.initials: DV
authors.lastname: Nicolau
authors.affiliation: The University of Queensland, Centre for Clinical Research and School of Medicine and Pathology Queensland, The Royal Brisbane and Women's Hospital, Brisbane, Qld, Australia.
authors.forename: Sunil R
authors.initials: SR
authors.lastname: Lakhani
authors.affiliation: School of Mathematical Sciences, and ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Gardens Point, Brisbane, Qld, Australia; Department of Computer Science, University of Oxford, United Kingdom. Electronic address: kevin.burrage@qut.edu.au.
authors.forename: Kevin
authors.initials: K
authors.lastname: Burrage
mesh_terms: D001943:Breast Neoplasms / Q000175:diagnosis / Q000473:pathology / Q000628:therapy*; D002454:Cell Differentiation / Q000502:physiology*; D002465:Cell Movement / Q000502:physiology*; D049109:Cell Proliferation / Q000502:physiology*; D005260:Female; D006801:Humans; D008962:Models, Theoretical; D009361:Neoplasm Invasiveness
keywords: Breast cancer; ductal carcinoma in situ; mathematical modelling; mathematical oncology