Mathematical modeling of tumor-induced angiogenesis

NV Mantzaris, S Webb, HG Othmer - Journal of mathematical biology, 2004 - Springer
Cancer is a collection of diseases with the common feature of uncontrolled cellular growth.
Most tissues in the body can give rise to cancer, some even yield several types, and each …

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 …

Modelling and mathematical problems related to tumor evolution and its interaction with the immune system

N Bellomo, L Preziosi - Mathematical and Computer Modelling, 2000 - Elsevier
This paper provides a survey of mathematical models and methods dealing with the analysis
and simulation of tumor dynamics in competition with the immune system. The characteristic …

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 …

Dynamics of colorectal cancer

F Michor, Y Iwasa, C Lengauer, MA Nowak - Seminars in cancer biology, 2005 - Elsevier
Colorectal cancer results from an accumulation of mutations in tumor suppressor genes and
oncogenes. An additional defining characteristic of colorectal cancer is its genetic instability …

The design and development of DaunoXome® for solid tumor targeting in vivo

EA Forssen - Advanced drug delivery reviews, 1997 - Elsevier
This article reviews the formulation development and characterization of the tumor-targeting
daunorubicin liposome preparation, DaunoXome®. The identification of liposome …

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 …

Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies

ME Orme, MAJ Chaplain - … Medicine and Biology: A Journal of …, 1997 - ieeexplore.ieee.org
There is a very strong link between the vascularization of a tumour and the spread of the
disease, both locally and to distant sites (Gimbrone et al., 1974, J. Natl. Cancer Inst. 52, 413 …

Lattice and non-lattice models of tumour angiogenesis

MJ Plank, BD Sleeman - Bulletin of mathematical biology, 2004 - Springer
In order to progress from the relatively harmless avascular state to the potentially lethal
vascular state, solid tumours must induce the growth of new blood vessels from existing …

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 …