Creating models of physical systems

1. Creating models of physical systems BIOE 4200

2. Creating models • Describe how system works in words • Draw schematic or block diagram • Identify variables/quantities in system • Recast block diagram based on variables of interest • Derive mathematical equations for components within block diagrams • Lecture limited to first three steps • Remaining steps will be discussed later

3. Cruise control example • Set desired speed • System depresses accelerator if measured speed is below desired speed • System releases accelerator if measured speed exceeds desired speed • Engine revs or idles in response to accelerator • Drive shaft & transmission translate engine rpm into wheel rpm • Speedometer measures actual speed • System compares measured & desired speed

4. Cruise control schematic Set desired speed Depress or release accelerator Engine revs or idles Speedo-meter Drive shaft and transmission

5. Cruise control variables Desired speed Accelerator depth Set desired speed Depress or release accelerator Engine revs or idles Measured speed Engine rpm Actual speed Speedo-meter Drive shaft and transmission

6. Blood glucose regulation • Body sets desired blood glucose levels • Pancreatic a cells release glucagon if measured blood glucose falls below desired blood glucose • Pancreatic b cells release insulin if measured blood glucose exceeds desired blood glucose • Various organs release glucose in response to glucagon or uptake glucose in response to insulin • Release or uptake of glucose changes glucose levels • a and b cells measure blood glucose levels • a and b cells compare measured & desired blood glucose levels

7. Blood glucose schematic Set desired blood glucose a & b cells release hormones Release or uptake glucose a & b cells measure glucose Glucose diffusion in bloodstream

8. Blood glucose variables Desired glucose Glucagon Set desired blood glucose a & b cells release hormones Release or uptake glucose Insulin Measured glucose Glucose release Actual glucose a & b cells measure glucose Glucose diffusion in bloodstream

9. What to include & ignore • No model exactly reproduces the physical system! • Therefore different models could be used • Factors to consider: • Level of detail needed • Time scale under consideration • External factors not under control of the system • Example: add glucose intake (eating) and metabolism (exercise, etc.) to blood glucose regulation model

10. Adding external factors Desired glucose Glucagon Set desired blood glucose a & b cells release hormones Release or uptake glucose Insulin Measured glucose Glucose release Actual glucose a & b cells measure glucose Glucose diffusion in bloodstream Eating Exercise

11. One small step ... • Created simplistic diagrams of two systems • Next we need to identify what physical quantities we need to look at • Blood glucose change after eating a candy bar • Activity of a specific insulin receptor after eating a candy bar • Then we will discuss the process of replacing the various blocks in these schematics with mathematical equations