Computational Simulation of Laser Hair Removal

Laser hair removal (LHR) sessions are administered once in four to six weeks. This is based on the fact that the duration of catagen is about 4 weeks irrespective of body part and the hairs just entering catagen during LHR and hence resistant to laser, will be vulnerable 4 weeks later.

However we do not have reliable clinical evidence to prove this argument. This is mostly due to the fact that LHR is a tedious and time consuming process which takes 8 - 12 months and accurate objective assessment of improvement during and after the procedure is next to impossible. The duration of catagen is not constant as previously thought and it can vary between 2 weeks and 6 months. Hence the theoretical explanation related to the duration of catagen is weak. This article is an attempt to see the problem in a different perspective.

What do we do when we cannot have a clinical proof for a hypothesis? There are similar circumstances in scientific world for which an experimental proof is extremely difficult to procure. For example India cannot conduct several atomic tests to achieve infallible nuclear technology. Neither can we send 100 trial missions before the much hyped 'Chandrayan' expedition to the moon. Once the most basic data is acquired, the rest is deduced cleverly by mathematical simulation. Can LHR be simulated?

Mathematical simulation for LHR is not a new concept. Several models already exist which are considered reliable. Most of them are based on a popular simulation technique called 'Monte Carlo' simulation. The basic concept of Monte Carlo simulation is simple. If you do not know the probability of getting a 'head' when you toss a coin, toss the coin 1000 times (iterations) and count the number of heads. Definitely we do not need to perform simulations to understand the probability is 50%? Now try this.

Each hair has got 70% chance of being in anagen.

Anagen hairs have a mean life span of 171 days with a standard deviation of 20

Telogen hairs have a mean life span of 91 with a standard deviation of 15.

Anagen hairs grow at 0.24 mm per day. Telogen hairs do not grow.

The hairs can be at a depth of 1.5 to 2.4 mm below the surface.

The hair density over the face is 600 per cm2 with a SD of 40.

How much hair can you expect when you see your face in the mirror in the morning after the previous days shave?

Simulation can answer such questions by performing several iterations. However the answer may not be 100% accurate but a fairly good approximation. The above mentioned scenario is not complete as we have not introduced laser in the model. Hence the model ultimately is complex making it necessary to use a computer to simulate.

If we have the capability to simulate LHR, how do we measure response? What do patients call good response? Is it a reduction in the number of hairs or a reduction in the thickness or pigmentation? Some patients complain about abnormally long hair. So apparently hair length and growth rate is also important. So when we assess improvement we have to consider all these factors.

One Monte Carlo simulation of LHR (Kolinko, V. et al) suggested that an eight week gap between laser sessions may be more beneficial than a 4 week gap. This particular study however used only the reduction in number of hairs as the measure of improvement. Besides catagen stage was not included in the model because the number of hairs in catagen is small compared to other stages. Models like these are research tools and are beyond the grasp of physicians and patients. Hence it is difficult to use these models to test your own hypothesis. That motivated me to design a model which is internally complex and externally simple for everybody to use.

I used a modeling technique called 'agent based modeling' which in simple terms treats each hair as a separate entity and simulates LHR based on the known probability distribution. The simple description itself may be complicated enough. But the good thing about this model is that it has an intuitive visual interface and everybody can conduct simulations without knowing the intricacies of the model. The model was constructed using software called NetLogo developed by North-Western University (Chicago). The model is java based and can be directly run from your browser (like internet explorer). You can explore the model at this URL: http://www.gulfdoctor.net/model/lhr.htm The model may take a few minutes to load depending on your internet connection speed.

I conducted several simulations to see how the various factors including the gap between sessions affect the ultimate result. I was surprised to see that the observation of the previous model (8 weeks gap being more effective than 4 weeks gap) was corroborated by my model too. It becomes all the more significant since both studies use different modeling techniques. Besides I used a different and probably more reliable index to measure response. The model details are available from my article here: http://www.ijdvl.com/text.asp?2009/75/4/383/53135

The optimum gap between laser sessions could depend on various factors including anagen telogen ratio, the mean life span of hairs, hair density and the time gap between laser and assessment of improvement. The recommendation of 4 week gap based on the duration of catagen may be a gross generalization.

References:

• Casey, A.S. and Goldberg, D. (2008) Guidelines for laser hair removal, J Cosmet Laser Ther, 10, 24-33.

• Kolinko, V. and Littler, C.M. (2000) Mathematical modeling for the prediction and optimization of laser hair removal, Lasers Surg Med, 26, 164-176.

• Roersma, M.E. and Veldhuis, G.J. (2001) Proposal and evaluation of a Monte Carlo model for hair regrowth following plucking, Skin Res Technol, 7, 176-183.

• Sklar, E. (2007) NetLogo, a multi-agent simulation environment, Artif Life, 13, 303-311.

• Kolinko, V.G., Littler, C.M. and Cole, A. (2000) Influence of the anagen:telogen ratio on Q-switched Nd:YAG laser hair removal efficacy, Lasers Surg Med, 26, 33-40

• Eapen BR. Agent-based model of laser hair removal: A treatment optimization and patient education tool. Indian J Dermatol Venereol Leprol. 2009 July-Aug;75(4):383-87.