System Dynamics (VenSim) Challenge: Apprenticeship Level 1
Simulating Hair Growth
Background Reading
As mammals we have hair on our bodies. Our hair grows to different lengths. Our eyebrows are short and the hair on the scalp can be a meter long. We will explore the mechanisms that determine how long your hairs grow.
When you brush your hair a few hairs come out. We lose between 50 and 100 hairs each day from our scalp. After the hair falls out the root rests a few days or weeks and then starts to grow again.
The growing phase is called anogen. The anogen phase is different lengths of time for different types of hair. Short hairs like eye brows only grow a few weeks. Your scalp hair can grow for years. 85% of your hairs are in anogen.
After the anogen phase the hair enters Catagen. Catagen is only lasts a week or 2. This is a transition period. The living cells of the hairs root slow down and change their structure. Only 1% of your hairs are in catagen.
Telogen is the final phase. Telogen is a resting phase. During telogen the hair doesn't grow. Telogen lasts a few months. 14% of hairs are in telogen. Some hairs fall out during Telogen. A few hairs don't fall out until the new hair starts to grow in the next anogen phase.
Scientists have observed hairs on different parts of the body. They find these ranges of growth for different kinds of hair.
Scalp hair
* Anagen , grows 4 to 8 years
* Telogen, rests 2 to 4 months
Average growth rate (mm/day)
* Scalp 0.44(mm/day)
* Temple 0.39(mm/day)
Eyelashes. trunk, and extremities
* Anagen, grows 1 to 6 months
* Telogen, rests 2 to 4 months
* Average growth rate
* Coarse body hairs 0.27(mm/day)
* Eyebrows 0.15(mm/day)
* Mustaches (beards or whiskers) 0.4(mm/day)
* Armpit hairs 0.3(mm/day)
* Pubic hairs 0.2(mm/day
Certification Challenge
Your task is to construct a VenSim model to answer the questions below.
We are interested in the value held in the reservoir called “hair length”.
Hair length has 2 rates, one coming in and one coming out.
- Grow: an inflow ( a “rate” in VenSim notation). The grow inflow depends on 3 auxiliary variables:
- Growth rate is set to an initial value of .44
- Telogen the resting period is set to an initial value of 80.
- Anagen the growing period is set to an initial value of 1500.
The formula in grow is= PULSE TRAIN( 10 , anagen , 1=+anagen+telogen , 10000 )*growth rate
The function PULSE TRAIN( {start},{duration}, {repeat}, {end}) gives a pulse of 1 starting at time step “start”, continuing each time step for “duration” more steps. This is repeated after “repeat” time steps. The process is stopped when the time step reaches “end”.
- fall out: an outflow depends on 2 auxiliary variables anagen and telogen, and the value in hair length.
The formula in fall out is= PULSE TRAIN(10+anagen+telogen , 1 , 10+anagen+telogen , 10000 )*hair length
The time unit for this model is days.
We want to run it from 0 to 10,000 days or just over 25 years. Your time step should be set to .25. Your model should have:
1 box variable
3 auxiliary variables
6 connectors
If you assume that telogen lasts for 3 months or 90 days, what is the length of anogen for each of these hair types?
Coarse body hairs
Eyebrows
Mustaches (beards or whiskers)
Armpit hairs
Pubic hairs