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
Drive shaft and transmission
Speedo-meter
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
Drive shaft and transmission
Speedo-meter
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
Glucose diffusion in bloodstream
a b cells measure glucose
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
Glucose diffusion in bloodstream
a b cells measure glucose
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
Glucose diffusion in bloodstream
a b cells measure glucose
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