Blood interaction mathematical model

The mathematical model of our vascular-coupled nephron tree thus consists of (i) 12 sets of coupled ODEs describing individual nephrons, (ii) a set of linear algebraic equations that determines the blood pressure drop from one branching point to another, and (iii) algebraic relations for the vascular interaction. 

Ashford JR, Cobby JM Drug interactions. The effects of alcohol and meprobamate applied sii y and jointly in human subjects. III. The concentrations of alcohol ai meprobamate in the blood and their effects cn perfmnance aiiplicaticm of mathematical models. J StudAlcc ol (1975) (Siqjpl 7), 140-61. 

The effects of blood flow on heat transfer in living tissue have been examined for more than a century, dating back to the experimental studies of Bernard in 1876. Since then, mathematical modeling of the complex thermal interaction between the vasculature and tissue has been a topic of interest for numerous physiologists, physicians, and engineers. A major problem for theoretical prediction of temperature distribution in tissue is the assessment of the effect of blood circulation, which is the dominant mode of heat removal and an important cause of tissue temperature inhomogeneity. 

The simplest methodology is two-dimensional (2D) quantitative structure-activity relationships (QSAR), in which calculated descriptors of molecules are related to an end point of interest via a mathematical relationship to estimate a numerical or categorical value for that end point. The mathematical relationship is fitted to a training set of compounds for which data for the end point has been measured experimentally. New molecules can then be described with the descriptors used in the model and their end point values predicted. 2D QSAR methods can be used to predict the interaction of compoimds with protein targets or antitargets and are widely used for prediction of physicochemical and ADME properties, such as hpophilicity, solubility, hiunan intestinal absorption, and blood-brain barrier penetration [18]. An excellent review of the strategies and pitfalls of 2D QSAR has been published by Lewis and Wood [19]. 

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