MATHEMATICAL-ANALYSIS OF THE RELATIONSHIP BETWEEN BLOOD-FLOW AND UPTAKE OF NUTRIENTS IN THE MAMMARY-GLANDS OF A LACTATING COW

A dynamic mathematical model of blood flow regulation in the mammary glands of a lactating cow was constructed from a principle of local vasodilator release in response to changes in intracellular adenylate charge. An equation was derived to predict uptake of the milk precursors acetate, glucose, amino acids and fatty acids, as affected by mammary blood flow rate. Metabolism of the precursors to milk components and CO2 was simulated with a set of empirically derived equations. Relative rates of ATP production and utilization regulated both the number of perfused capillaries and the conductance of arteriolar segments in the mammary glands. The model simulated local control phenomena of functional and reactive hyperaemia, and simulation of autoregulation under changing arterial pressure suggested a predominance of precapillary sphincter regulation. It was predicted that an increase in blood flow without the mammary capacity to utilize blood metabolites efficiently would be detrimental to milk synthesis. Conversely, increased blood flow through changes in mammary activity resulted in predictions of higher milk production. It was proposed that the equation for uptake, v(i) = [i](A)(1-exp(-k(i) Vol(cap)N(cap)/BFtot))BFtot, be used in analysis of mammary arteriovenous differences.