Nonlinear modelling of cancer: bridging the gap between cells and tumours

JS Lowengrub, HB Frieboes, F Jin, YL Chuang, X Li… - …, 2009 - iopscience.iop.org
Despite major scientific, medical and technological advances over the last few decades, a
cure for cancer remains elusive. The disease initiation is complex, and including initiation …

Biomechanical modelling of tumor growth with chemotherapeutic treatment: a review

J Xu, Y Wang, H Gomez, X Feng - Smart Materials and Structures, 2023 - iopscience.iop.org
The efficiency of chemotherapy in the treatment of cancer depends on the administration
schedule, such as dosage, timing and frequency, and the release control if self-assembled …

Mathematical models of cancer cell plasticity

HN Weerasinghe, PM Burrage, K Burrage… - Journal of …, 2019 - Wiley Online Library
Quantitative modelling is increasingly important in cancer research, helping to integrate
myriad diverse experimental data into coherent pictures of the disease and able to …

BIO-LGCA: a cellular automaton modelling class for analysing collective cell migration

A Deutsch, JM Nava-Sedeño, S Syga… - PLoS computational …, 2021 - journals.plos.org
Collective dynamics in multicellular systems such as biological organs and tissues plays a
key role in biological development, regeneration, and pathological conditions. Collective …

Identification of intrinsic in vitro cellular mechanisms for glioma invasion

M Tektonidis, H Hatzikirou, A Chauvière… - Journal of theoretical …, 2011 - Elsevier
Invasion of malignant glioma is a highly complex phenomenon involving molecular and
cellular processes at various spatio-temporal scales, whose precise interplay is still not fully …

Control of tumor growth distributions through kinetic methods

L Preziosi, G Toscani, M Zanella - Journal of theoretical biology, 2021 - Elsevier
The mathematical modeling of tumor growth has a long history, and has been
mathematically formulated in several different ways. Here we tackle the problem in the case …

[HTML][HTML] A high-performance cellular automaton model of tumor growth with dynamically growing domains

J Poleszczuk, H Enderling - Applied mathematics, 2014 - ncbi.nlm.nih.gov
Tumor growth from a single transformed cancer cell up to a clinically apparent mass spans
many spatial and temporal orders of magnitude. Implementation of cellular automata …

Cancer stem cells: a minor cancer subpopulation that redefines global cancer features

H Enderling, L Hlatky, P Hahnfeldt - Frontiers in oncology, 2013 - frontiersin.org
In recent years cancer stem cells (CSCs) have been hypothesized to comprise only a minor
subpopulation in solid tumors that drives tumor initiation, progression, and metastasis; the so …

A hybrid multiscale model for cancer invasion of the extracellular matrix

N Sfakianakis, A Madzvamuse, MAJ Chaplain - Multiscale Modeling & …, 2020 - SIAM
The ability to locally degrade the extracellular matrix (ECM) and interact with the tumor
microenvironment is a key process distinguishing cancer cells from normal cells, and is a …

Investigation of the migration/proliferation dichotomy and its impact on avascular glioma invasion

K Böttger, H Hatzikirou, A Chauviere… - … Modelling of Natural …, 2012 - cambridge.org
Gliomas are highly invasive brain tumors that exhibit high and spatially heterogeneous cell
proliferation and motility rates. The interplay of proliferation and migration dynamics plays an …