Angiogenesis - understanding the mathematical challenge

Pamela F Jones1, Brian D Sleeman

  • 1Leeds Institute of Molecular Medicine, University of Leeds, JIF Building, St. James's University Hospital, Leeds LS9 7TF, UK. p.jones@leeds.ac.uk

Angiogenesis
|October 20, 2006
PubMed

Related Concept Videos

Mechanism of Angiogenesis01:10

Mechanism of Angiogenesis

Blood vessel formation starts early during embryonic development, around day 7. In the extraembryonic yolk sac, mesodermal precursor cells called hemangioblast proliferate and differentiate into angioblast. Angioblasts express vascular endothelial growth factor receptor 2 or VEGFR2, which binds VEGF-A, a proangiogenic factor, guiding blood vessel formation. VEGF signaling promotes angioblasts to form a blood island in the developing embryo. Angioblasts further differentiate, giving rise to...
Regulation of Angiogenesis and Blood Supply01:24

Regulation of Angiogenesis and Blood Supply

Rapidly dividing tumors, embryos, and wounded tissues require more oxygen than usual, lowering the oxygen concentration in the blood. At low oxygen or hypoxic conditions, an oxygen-sensitive transcription factor called the hypoxia-inducible factor 1 or HIF1 is activated. HIF1 is a dimeric protein of alpha (ɑ) and beta (β) subunits.  Under optimal oxygen conditions, HIF1β is present in the nucleus while HIF1ɑ remains in the cytosol. HIF1ɑ is hydroxylated by prolyl hydroxylase and factor...
Applications of Integration to Find Blood Flow01:27

Applications of Integration to Find Blood Flow

Blood flow through a cylindrical blood vessel can be mathematically described using the principles of laminar flow, a regime in which fluid moves smoothly in parallel layers. In this model, the velocity of the blood is not uniform across the cross-section of the vessel; rather, it varies with the radial distance from the center. The maximum velocity occurs along the central axis, decreasing progressively toward the vessel walls, where it reaches zero due to viscous drag.Approximating Blood...
Overview of Cell-Matrix Interactions01:24

Overview of Cell-Matrix Interactions

The extracellular matrix or ECM holds cells together to form a tissue and allows the cells within the tissue to communicate. ECM comprises proteins such as fibronectin, collagen, laminin, etc. The most abundant protein in this space is collagen. Collagen fibers are interwoven with carbohydrate-containing protein molecules called proteoglycans. ECM allows cell migration and provides a structural scaffold at cell adhesion that anchors the cell when the extracellular matrix proteins interact with...
Fundamental Mathematical Principles in Pharmacokinetics: Calculus and Graphs01:21

Fundamental Mathematical Principles in Pharmacokinetics: Calculus and Graphs

The fundamental mathematical principles, such as calculus and graphs, play crucial roles in analyzing drug movement and determining pharmacokinetic parameters. Differential calculus examines rates of change and helps to determine the dissolution rate of drugs in biofluids, as well as how drug concentrations change over time. For instance, it can help calculate the rate of elimination of a drug from the body based on its concentration-time profile.
On the other hand, integral calculus focuses on...
Bernoulli's Equation: Problem Solving01:16

Bernoulli's Equation: Problem Solving

A Venturi meter is essential for measuring fluid flow rates in pipelines. It utilizes the relationship between fluid velocity and pressure described by Bernoulli's equation. When installed in a sewage system, the Venturi meter accurately determines the wastewater flow rate by measuring pressure differences.
The first step is to compute the cross-sectional areas of the pipe and the Venturi throat to analyze the pressure difference indicated by the pressure gauge. Next, the continuity equation is...