Predicting extraction and uptake of arterial energy metabolites by the mammary glands of lactating cows when blood flow is perturbed

Abstract

Previous work shows that mammary uptake of milk precursors from blood can be affected by the rate of blood flow (F) to the glands. The purpose of the current work was to test the ability of compartmental and cylindrical capillary models to account for the variation in mammary extraction and net uptake of plasma metabolites produced by perturbation of mammary F. The data for model fitting were obtained from a previous experiment in which mammary arteriovenous differences of acetate + β-hydroxybutyrate (2C), glucose, triacylglycerol (TAG), and long-chain fatty acids (LCFA) were measured in 4 cows before, during, and after intraarterial infusion of inhibitors of endothelial nitric oxide synthase and cyclooxygenase, which are 2 major systems of F control in the mammary glands. The 4 models tested were (1) constant extraction within each cow, (2) clearance from an extracellular compartment is a linear function of F with an intercept, (3) total capillary volume in a cylindrical representation is a linear function of F with an intercept, and (4) uptake from an extracellular compartment obeys Henri-Michaelis-Menten kinetics, where maximum velocity (Vmax) is a linear function of F with an intercept. According to prediction errors, model 4 fitted 2C extraction data best, accounting for 82% of the observed variation. The estimated Km (Henri-Michaelis-Menten constant) for venous 2C was 0.4 mM. For glucose clearance, a variant of model 2 with a positive effect of 2C uptake on clearance was identified as best, producing a coefficient of determination (R(2)) of 0.31. For TAG, model 2 with a positive effect of arterial TAG concentration on TAG clearance was best, with an R(2) of 0.22. For LCFA, model 2 with a positive effect of arterial LCFA on LCFA clearance was best, with an R(2) of 0.29. Models 2 and 3 fitted the extraction data with the same R(2)-values and prediction errors, so both compartmental and cylindrical approaches to describing the vascular bed were equally capable of describing the effect of F on mammary uptakes. A combined fit of all best-fit models to extraction data for all 4 metabolites at once explained 52, 42, 73, and 77% of variation in net uptakes of 2C, glucose, TAG, and LCFA, respectively. According to the fitted model, each 1 L/min increase in F increased the mammary volumes of distribution of 2C, glucose, TAG, and LCFA by 13, 14, 18, and 7%, respectively.

Keywords: dairy cow; mammary blood flow; mammary uptake; modeling.