Abstract #7

# 7
Dynamic deterministic models.
T. Hackmann*1, 1University of Florida, Gainesville, FL.

This lesson will demonstrate how to construct dynamic deterministic models, which are popular for mechanistic modeling in nutrition research. This type of model represents a biological system as a set of state variables and simulates how these variables change over time. For example, it can represent the rumen system using state variables for fiber, protein, and starch; subsequently, it can simulate the size of these nutrient pools over a feeding cycle. The model is written formally using differential equations, but it can be drawn first as a compartmental model diagram. In this diagram, each state variable is represented by a rectangle (a pool). Arrows leading to and from a pool represents input and output of material. For the rumen, these arrows commonly represent nutrient intake, digestion, and passage. The diagram is then translated into a set of differential equations. These equations define the change of state variables (pools) over time as the difference between inputs and outputs [i.e., d(state variable)/dt = inputsoutputs]. These inputs and outputs, in turn, are functions of parameters (e.g., digestion and passage rates) and other state variables. After defining values of parameters, the model is solved and used to generate predictions. A simple model may have an analytical solution, but a more complex model must be solved numerically (e.g., with Euler’s method and difference equations). During a demonstration exercise, the speaker will show how to construct a simple (one-pool) model of rumen fermentation by coding difference equations into an Excel spreadsheet. During a hands-on exercise, participants will construct their own, multi-pool model.

Key Words: mathematical model, state variable, differential equation