A review of mathematical models for the formation of vascular networks

M Scianna, CG Bell, L Preziosi - Journal of theoretical biology, 2013 - Elsevier
Two major mechanisms are involved in the formation of blood vasculature: vasculogenesis
and angiogenesis. The former term describes the formation of a capillary-like network from …

Computational models for mechanics of morphogenesis

MA Wyczalkowski, Z Chen, BA Filas… - … defects research part …, 2012 - Wiley Online Library
In the developing embryo, tissues differentiate, deform, and move in an orchestrated manner
to generate various biological shapes driven by the complex interplay between genetic …

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 …

Contact-inhibited chemotaxis in de novo and sprouting blood-vessel growth

RMH Merks, ED Perryn, A Shirinifard… - PLoS computational …, 2008 - journals.plos.org
Blood vessels form either when dispersed endothelial cells (the cells lining the inner walls of
fully formed blood vessels) organize into a vessel network (vasculogenesis), or by sprouting …

Biophysical models of tumour growth

P Tracqui - Reports on Progress in Physics, 2009 - iopscience.iop.org
Tumour growth is a multifactorial process, which has stimulated in recent decades the
development of numerous models trying to figure out the mechanisms controlling solid …

Fractal analysis of vascular networks: insights from morphogenesis

S Lorthois, F Cassot - Journal of theoretical biology, 2010 - Elsevier
Considering their extremely complicated and hierarchical structure, a long standing question
in vascular physio-pathology is how to characterize blood vessels patterns, including which …

Characteristics of Pattern Formation and Evolution in Approximations of Physarum Transport Networks

J Jones - Artificial life, 2010 - direct.mit.edu
Most studies of pattern formation place particular emphasis on its role in the development of
complex multicellular body plans. In simpler organisms, however, pattern formation is …

Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist

RM Crossley, S Johnson, E Tsingos, Z Bell… - Frontiers in cell and …, 2024 - frontiersin.org
The extracellular matrix (ECM) is a highly complex structure through which biochemical and
mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a …

On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process

JA Flegg, SN Menon, PK Maini… - Frontiers in physiology, 2015 - frontiersin.org
Over the last 30 years, numerous research groups have attempted to provide mathematical
descriptions of the skin wound healing process. The development of theoretical models of …

A pharmacologically based multiscale mathematical model of angiogenesis and its use in investigating the efficacy of a new cancer treatment strategy

F Billy, B Ribba, O Saut, H Morre-Trouilhet… - Journal of theoretical …, 2009 - Elsevier
Tumor angiogenesis is the process by which new blood vessels are formed and enhance
the oxygenation and growth of tumors. As angiogenesis is recognized as being a critical …