Vascular endothelial growth factorVascular endothelial growth factor (VEGF, vɛdʒ'ɛf), originally known as vascular permeability factor (VPF), is a signal protein produced by many cells that stimulates the formation of blood vessels. To be specific, VEGF is a sub-family of growth factors, the platelet-derived growth factor family of cystine-knot growth factors. They are important signaling proteins involved in both vasculogenesis (the de novo formation of the embryonic circulatory system) and angiogenesis (the growth of blood vessels from pre-existing vasculature).
CoagulationCoagulation, also known as clotting, is the process by which blood changes from a liquid to a gel, forming a blood clot. It potentially results in hemostasis, the cessation of blood loss from a damaged vessel, followed by repair. The mechanism of coagulation involves activation, adhesion and aggregation of platelets, as well as deposition and maturation of fibrin. Coagulation begins almost instantly after an injury to the endothelium lining a blood vessel.
Diagonal matrixIn linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is , while an example of a 3×3 diagonal matrix is. An identity matrix of any size, or any multiple of it (a scalar matrix), is a diagonal matrix. A diagonal matrix is sometimes called a scaling matrix, since matrix multiplication with it results in changing scale (size).
Tissue engineeringTissue engineering is a biomedical engineering discipline that uses a combination of cells, engineering, materials methods, and suitable biochemical and physicochemical factors to restore, maintain, improve, or replace different types of biological tissues. Tissue engineering often involves the use of cells placed on tissue scaffolds in the formation of new viable tissue for a medical purpose but is not limited to applications involving cells and tissue scaffolds.
AngiogenesisAngiogenesis is the physiological process through which new blood vessels form from pre-existing vessels, formed in the earlier stage of vasculogenesis. Angiogenesis continues the growth of the vasculature mainly by processes of sprouting and splitting, but processes such as coalescent angiogenesis, vessel elongation and vessel cooption also play a role. Vasculogenesis is the embryonic formation of endothelial cells from mesoderm cell precursors, and from neovascularization, although discussions are not always precise (especially in older texts).
EndotheliumThe endothelium (: endothelia) is a single layer of squamous endothelial cells that line the interior surface of blood vessels and lymphatic vessels. The endothelium forms an interface between circulating blood or lymph in the lumen and the rest of the vessel wall. Endothelial cells form the barrier between vessels and tissue and control the flow of substances and fluid into and out of a tissue. Endothelial cells in direct contact with blood are called vascular endothelial cells whereas those in direct contact with lymph are known as lymphatic endothelial cells.
Matrix decompositionIn the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems. In numerical analysis, different decompositions are used to implement efficient matrix algorithms. For instance, when solving a system of linear equations , the matrix A can be decomposed via the LU decomposition.
Endothelial progenitor cellEndothelial progenitor cell (or EPC) is a term that has been applied to multiple different cell types that play roles in the regeneration of the endothelial lining of blood vessels. Outgrowth endothelial cells are an EPC subtype committed to endothelial cell formation. Despite the history and controversy, the EPC in all its forms remains a promising target of regenerative medicine research. Developmentally, the endothelium arises in close contact with the hematopoietic system.
Transformation matrixIn linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation matrix of . Note that has rows and columns, whereas the transformation is from to . There are alternative expressions of transformation matrices involving row vectors that are preferred by some authors. Matrices allow arbitrary linear transformations to be displayed in a consistent format, suitable for computation.
Function compositionIn mathematics, function composition is an operation ∘ that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g is applied to the result of applying the function f to x. That is, the functions f : X → Y and g : Y → Z are composed to yield a function that maps x in domain X to g(f(x)) in codomain Z. Intuitively, if z is a function of y, and y is a function of x, then z is a function of x.
