Mathematical modeling for the prediction and optimization of laser hair removal

The study of hair removal is a slow, tedious process. Efficacy evaluations require test-site observation for at least one complete hair cycle, a minimum of 6-8 months. In addition, tracking and counting individual hairs is extremely labor intensive. The objective of this study was to develop and evaluate a mathematical model for hair removal that could significantly speed the entire process.

Generally accepted kinetic and statistical modeling methods were used to develop a mathematical description of hair growth. The anagen and telogen percentages and decay times were the variables used to predict the kinetics of untreated hair. In the case that the follicles were treated, it was necessary to additionally consider the possible outcomes after treatment, making the calculations much too complicated for simple mathematical formulations. Therefore, a computerized statistical model was developed that considered the probabilities of no, partial, or complete follicular damage in addition to the untreated model variables. These models were then evaluated by comparing them to data derived from the literature and a study center.

Values derived from the mathematical model were capable of closely approximating the experimental results of untreated (shaving) and treated (plucking, electrolysis, ruby laser, Q-switched Nd:YAG laser) hair growth kinetics. The model was also shown to be useful for optimizing the number and interval of Q-switched Nd:YAG laser treatments.

A mathematical model can be used to reliably predict results from a variety of hair removal techniques. It also appears to be useful for optimizing a particular treatment protocol. In addition, the development of new hair removal products may be aided by using this method.