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					          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

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

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
       1. Grow: an inflow ( a “rate” in VenSim notation). The
          grow inflow depends on 3 auxiliary variables:
            a. Growth rate is set to an initial value of .44
            b. Telogen the resting period is set to an initial
               value of 80.
            c. 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”.

       2. fall out: an outflow               depends on 2 auxiliary
          variables anagen and               telogen, and the value in hair
       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


Mustaches (beards or whiskers)

 Armpit hairs

 Pubic hairs

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