Biomaterial Database

Lattice and non-lattice models of tumour angiogenesis. 2004

M J Plank, and B D Sleeman

School of Mathematics, University of Leeds, Leeds LS2 9JT, UK. m.plank@math.canterbury.ac.nz

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 ones, a process called angiogenesis. The capillary growth centres around endothelial cells: there are several cell-based models of this process in the literature and these have reproduced some of the key microscopic features of capillary growth. The most common approach is to simulate the movement of leading endothelial cells on a regular lattice. Here, we apply a circular random walk model to the process of angiogenesis, and thus allow the cells to move independently of a lattice; the results display good agreement with empirical observations. We also run simulations of two lattice-based models in order to make a critical comparison of the different modelling approaches. Finally, non-lattice simulations are carried out in the context of a realistic model of tumour angiogenesis, and potential anti-angiogenic strategies are evaluated.

UI	MeSH Term	Description	Entries
D008954	Models, Biological	Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.	Biological Model,Biological Models,Model, Biological,Models, Biologic,Biologic Model,Biologic Models,Model, Biologic
D008955	Models, Cardiovascular	Theoretical representations that simulate the behavior or activity of the cardiovascular system, processes, or phenomena; includes the use of mathematical equations, computers and other electronic equipment.	Cardiovascular Model,Cardiovascular Models,Model, Cardiovascular
D009369	Neoplasms	New abnormal growth of tissue. Malignant neoplasms show a greater degree of anaplasia and have the properties of invasion and metastasis, compared to benign neoplasms.	Benign Neoplasm,Cancer,Malignant Neoplasm,Tumor,Tumors,Benign Neoplasms,Malignancy,Malignant Neoplasms,Neoplasia,Neoplasm,Neoplasms, Benign,Cancers,Malignancies,Neoplasias,Neoplasm, Benign,Neoplasm, Malignant,Neoplasms, Malignant
D009389	Neovascularization, Pathologic	A pathologic process consisting of the proliferation of blood vessels in abnormal tissues or in abnormal positions.	Angiogenesis, Pathologic,Angiogenesis, Pathological,Neovascularization, Pathological,Pathologic Angiogenesis,Pathologic Neovascularization,Pathological Angiogenesis,Pathological Neovascularization
D002196	Capillaries	The minute vessels that connect arterioles and venules.	Capillary Beds,Sinusoidal Beds,Sinusoids,Bed, Sinusoidal,Beds, Sinusoidal,Capillary,Capillary Bed,Sinusoid,Sinusoidal Bed
D003198	Computer Simulation	Computer-based representation of physical systems and phenomena such as chemical processes.	Computational Modeling,Computational Modelling,Computer Models,In silico Modeling,In silico Models,In silico Simulation,Models, Computer,Computerized Models,Computer Model,Computer Simulations,Computerized Model,In silico Model,Model, Computer,Model, Computerized,Model, In silico,Modeling, Computational,Modeling, In silico,Modelling, Computational,Simulation, Computer,Simulation, In silico,Simulations, Computer
D004730	Endothelium, Vascular	Single pavement layer of cells which line the luminal surface of the entire vascular system and regulate the transport of macromolecules and blood components.	Capillary Endothelium,Vascular Endothelium,Capillary Endotheliums,Endothelium, Capillary,Endotheliums, Capillary,Endotheliums, Vascular,Vascular Endotheliums
D006801	Humans	Members of the species Homo sapiens.	Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D000818	Animals	Unicellular or multicellular, heterotrophic organisms, that have sensation and the power of voluntary movement. Under the older five kingdom paradigm, Animalia was one of the kingdoms. Under the modern three domain model, Animalia represents one of the many groups in the domain EUKARYOTA.	Animal,Metazoa,Animalia
D013269	Stochastic Processes	Processes that incorporate some element of randomness, used particularly to refer to a time series of random variables.	Process, Stochastic,Stochastic Process,Processes, Stochastic