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 …
and angiogenesis. The former term describes the formation of a capillary-like network from …
Mathematical modeling of the onset of capillary formation initiating angiogenesis
HA Levine, BD Sleeman, M Nilsen-Hamilton - Journal of Mathematical …, 2001 - Springer
It is well accepted that neo-vascular formation can be divided into three main stages (which
may be overlapping):(1) changes within the existing vessel,(2) formation of a new …
may be overlapping):(1) changes within the existing vessel,(2) formation of a new …
Mechanics and chemotaxis in the morphogenesis of vascular networks
The formation of vascular networks in vitro develops along two rather distinct stages: during
the early migration-dominated stage the main features of the pattern emerge, later the …
the early migration-dominated stage the main features of the pattern emerge, later the …
A mechanochemical model of angiogenesis and vasculogenesis
D Manoussaki - ESAIM: Mathematical Modelling and Numerical …, 2003 - cambridge.org
Vasculogenesis and angiogenesis are two different mechanisms for blood vessel formation.
Angiogenesis occurs when new vessels sprout from pre-existing vasculature in response to …
Angiogenesis occurs when new vessels sprout from pre-existing vasculature in response to …
Continuous and discrete mathematical models of tumor-induced angiogenesis
ARA Anderson, MAJ Chaplain - Bulletin of mathematical biology, 1998 - Elsevier
Angiogenesis, the formation of blood vessels from a pre-existing vasculature, is a process
whereby capillary sprouts are formed in response to externally supplied chemical stimuli …
whereby capillary sprouts are formed in response to externally supplied chemical stimuli …
Mesoscopic and continuum modelling of angiogenesis
Angiogenesis is the formation of new blood vessels from pre-existing ones in response to
chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a …
chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a …
Mathematical modelling of angiogenesis
MAJ Chaplain - Journal of neuro-oncology, 2000 - Springer
Angiogenesis, the formation of blood vessels from a pre-existing vasculature, is a process
whereby capillary sprouts are formed in response to externally supplied chemical stimuli …
whereby capillary sprouts are formed in response to externally supplied chemical stimuli …
A model of growing vascular structures
F Nekka, S Kyriacos, C Kerrigan, L Cartilier - Bulletin of mathematical …, 1996 - Springer
Increasing attention is being paid to the configuration and development of vascular
structures and their possible correlations with physiological events. The study of …
structures and their possible correlations with physiological events. The study of …
Mathematical modelling of tumour-induced angiogenesis: network growth and structure
M Chaplain, A Anderson - Angiogenesis in brain tumors, 2004 - Springer
Angiogenesis, the formation of blood vessels from a pre-existing vasculature, is a process
whereby capillary sprouts are formed in response to externally supplied chemical stimuli …
whereby capillary sprouts are formed in response to externally supplied chemical stimuli …
Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies
SR McDougall, ARA Anderson, MAJ Chaplain… - Bulletin of mathematical …, 2002 - Elsevier
Angiogenesis, the formation of blood vessels from a pre-existing vasculature, is a process
whereby capillary sprouts are formed in response to externally supplied chemical stimuli …
whereby capillary sprouts are formed in response to externally supplied chemical stimuli …