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A compartmental capillary, convolution integration model to investigate nutrient transport and metabolism in vivo from paired indicator/nutrient dilution curves

Departments of ¹Animal and Poultry Science and ²Clinical Studies, University of Guelph, Guelph, Ontario, Canada

Submitted 13 April 2004 ; accepted in final form 17 December 2004

Thirty-three paired indicator/nutrient dilution curves across the mammary glands of four cows were obtained after rapid injection of para-aminohippuric acid (PAH) plus glucose into the external iliac artery. For the measurement of extracellular volume and kinetics of nutrient uptake from indicator dilution curves, several models of solute dispersion and disappearance have been proposed. The Crone-Renkin models of exchange in a single capillary assume negligible washout of solutes from the extracellular space and do not describe entire dilution curves. The Goresky models include a distribution of capillary transit times to generate whole system outflow profiles but require two indicators to parametize extracellular behavior. A compartmental capillary, convolution integration model is proposed that uses one indicator to account for the extracellular behavior of the nutrient after a paired indicator/nutrient injection. With the use of an iterative approach to least squares, unique solutions for nonexchanging vessel transit time _µ and its variance were obtained from all 33 PAH curves. The average of heterogeneous vascular transit times was approximated as 2 = 8.5 s. The remainder of indicator dispersion was considered to be due to washout from a well-mixed compartment representing extracellular space that had an estimated volume of 5.5 liters or 24% of mammary gland weight. More than 99% of the variation in the time course of venous PAH concentration after rapid injection into the arterial supply of the mammary glands was explained in an unbiased manner by partitioning the organ into a heterogeneous nonexchanging vessel subsystem and a well-mixed compartmental capillary subsystem.

indicator dilution; mathematical models; arteriovenous differences

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				T. G. Madsen, D. R. Trout, S. R. L. Cieslar, N. G. Purdie, M. O. Nielsen, and J. P. Cant The Histamine H1 Receptor Is Not Involved in Local Control of Mammary Blood Flow in Dairy Cows J Dairy Sci, June 1, 2008; 91(6): 2461 - 2468. [Abstract] [Full Text] [PDF]

				F. Qiao, D. R. Trout, C. Xiao, and J. P. Cant Kinetics of glucose transport and sequestration in lactating bovine mammary glands measured in vivo with a paired indicator/nutrient dilution technique J Appl Physiol, September 1, 2005; 99(3): 799 - 806. [Abstract] [Full Text] [PDF]