## Abstract #2

**Section:**Workshops

**Session:**Workshop: NANP Nutrition Models

**Format:**Oral

**Day/Time:**Sunday 9:30 AM–10:45 AM

**Location:**Room 300 CD

# 2

Mark D. Hanigan

**Introduction and model construction: Part II (exercises).**Mark D. Hanigan

^{*1}, Veridiana L. Daley^{2}, Timothy J. Hackmann^{3},^{1}Virginia Tech, Blacksburg, VA,^{2}National Animal Nutrition Program, University of Kentucky, Lexington, KY,^{3}University of Florida, Gainesville, FL.The principles of mathematical modeling in agricultural sciences are well described by France and Thornley (1984). They categorized models as static or dynamic, empirical or mechanistic, and deterministic or stochastic, although, in practice, these categories are a continuum. This talk and exercise will focus on the mechanics of building and solving a compartmental model of intestinal N metabolism. A simple regression equation is often used to represent static processes; for example, dCP = CP_In × 0.65. This approach only considers fractional digestion of CP in the gut, and ignores any effects of other factors such as passage rate or microbial activity. In this simple model, a fast rate of passage would have the same digestibility as a slow rate. If one wants to represent residence time effects on CP digestion, then consideration of the pool size is needed. Mechanisms controlling CP digestion in the rumen can be incorporated into the model to yield better estimates. A dynamic model with a rumen pool of CP and a representation of rates of passage and degradation driven by microbial activity can be constructed and fitted to data to derive information on those mechanisms An intestinal model can be linked to the rumen model to further predict intestinal digestions and amino acid absorption. If rates of passage and degradation are known, it can also be used to predict outcomes when system inputs are manipulated. A representation of this system will be built by participants using R and fit to example data. The model can easily be extended, as there is no mathematical limit to the complexity that can be incorporated. Pool size, and thus the fluxes driven by pool size, can be solved numerically using a computer and numerical integration algorithms. As demonstrated with the example problem, compartmental modeling is very useful for modeling nutrient metabolism and animal performance as nutrient flow through a series of compartments and into product or excreta can be represented.

**Key Words:**mathematical model, type, review