扩展血管生成PDEs模型的分析和数值特性

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...

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...

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...

Physiological pharmacokinetic models, often called flow-limited or perfusion models, typically assume a swift drug distribution between tissue and venous blood, creating a rapid drug equilibrium. This premise is based on the idea that drug diffusion is extremely fast, and the cell membrane presents no barrier to drug permeation. In this scenario, where no drug binding occurs, the drug concentration in the tissue equals that of the venous blood leaving the tissue. This greatly simplifies the...