Modeling the dynamics of human hair cycles by a follicular automaton

Abstract

The hair follicle cycle successively goes through the anagen, catagen, telogen, and latency phases, which correspond, respectively, to hair growth, arrest, shedding, and absence before a new anagen phase is initiated. Experimental observations collected over a period of 14 years in a group of 10 male volunteers, alopecic and nonalopecic, allowed us to determine the characteristics of scalp hair follicle cycles. On the basis of these observations, we propose a follicular automaton model to simulate the dynamics of human hair cycles. The automaton model is defined by a set of rules that govern the stochastic transitions of each follicle between the successive states anagen, telogen, and latency, and the subsequent return to anagen. The transitions occur independently for each follicle, after time intervals given stochastically by a distribution characterized by a mean and a variance. The follicular automaton model accounts both for the dynamical transitions observed in a single follicle and for the behavior of an ensemble of independently cycling follicles. Thus, the model successfully reproduces the evolution of the fractions of follicle populations in each of the three phases, which fluctuate around steady-state or slowly drifting values. We apply the follicular automaton model to the study of spatial patterns of follicular growth that result from a spatially heterogeneous distribution of parameters such as the mean duration of anagen phase. When considering that follicles die or miniaturize after going through a critical number of successive cycles, the model can reproduce the evolution to hair patterns similar to well known types of diffuse or androgenetic alopecia.human scalp hair ͉ hair follicle cycles ͉ automaton model ͉ alopecia H uman hair represents an ensemble of some 10 5 hair follicles that continually evolve over the course of time. At any moment, a follicle is either growing (anagen or A phase) or ceasing to grow and involuting (catagen or C phase) but still on the scalp (telogen or T phase) before shedding and entering a new cycle. These successive phases constitute a follicular cycle (1-4). The duration of such a cycle is variable but typically ranges from a few months to several years (5, 6). Each follicle can undergo repeated cycles until it eventually dies or miniaturizes to give rise to a vellus hair (7,8); the vellus hair shaft is not pigmented and has a cross-sectional diameter much shorter than normal (9). Whether miniaturization (M) occurs progressively or abruptly is still unclear. If a large proportion of follicles die or miniaturize, alopecia-balding-ensues, with a severity that depends on the location of lost follicles (10) and on the amount of total hair that is irreversibly shed.The most comprehensive data on the human hair cycle were provided by a study carried out over a period of 14 years in a group of 10 normal and alopecic male volunteers (5, 6, 11). The data were collected by using the phototrichogram technique, which allowed determining the duration of A and T phases of each f...

An automaton model for the cell cycle

“…Spatially coupled automata can account for the propagation of waves in excitable media. Here, as in a follicular automaton model for hair cycles [35,36], we consider spatially independent automata. Thus we assume that, within a population, the dynamics of a cycling cell will not be influenced by the state of neighbouring cells.…”

La vie révélée du follicule de cheveu humain

“…La technique du phototrichogramme a permis de montrer que le cheveu pousse à la vitesse de 0,3 mm/j) [20], que la durée des phases varie d'un individu à l'autre [17] et que la phase dont l'amplitude varie le plus au cours du temps est la phase anagène [17,19]. De plus, si l'on considère un follicule pris individuellement, la durée de ses différentes phases varie d'un cycle à l'autre de façon apparemment alétoire, ce qui suggère l'absence d'influence du cycle n sur le cycle n + 1, et l'absence d'influence de la durée de la phase i sur celle de la phase i + 1 [21]. Enfin, le pourcentage des cheveux en phase anagène et télogène fluctue au cours du temps, autour d'une valeur moyenne [21].…”

“…De plus, si l'on considère un follicule pris individuellement, la durée de ses différentes phases varie d'un cycle à l'autre de façon apparemment alétoire, ce qui suggère l'absence d'influence du cycle n sur le cycle n + 1, et l'absence d'influence de la durée de la phase i sur celle de la phase i + 1 [21]. Enfin, le pourcentage des cheveux en phase anagène et télogène fluctue au cours du temps, autour d'une valeur moyenne [21]. De l'analyse de ces fluctuations et du caractère apparemment aléatoire de la durée des phases, il ressort que les transitions d'une phase à l'autre se produisent indépendamment pour chaque follicule, de façon non déterministe, après des intervalles de temps donnés, de façon stochastique, à partir d'une loi log-normale de distribution caractérisée par une moyenne et une variance pour chacune des phases [21].…”

“…Enfin, le pourcentage des cheveux en phase anagène et télogène fluctue au cours du temps, autour d'une valeur moyenne [21]. De l'analyse de ces fluctuations et du caractère apparemment aléatoire de la durée des phases, il ressort que les transitions d'une phase à l'autre se produisent indépendamment pour chaque follicule, de façon non déterministe, après des intervalles de temps donnés, de façon stochastique, à partir d'une loi log-normale de distribution caractérisée par une moyenne et une variance pour chacune des phases [21]. Le comportement stochastique de chaque follicule assure la permanence de la chevelure, mais reflète aussi la multiplicité des acteurs susceptibles de moduler son activité : facteurs de croissance (IGF-1, HGF, FGF-2, KGF…), hormones (androgènes et oestrogènes, mais aussi vitamine D et tri-iodothyronine [22][23][24][25]), cytokines (comme l'IL-1α [26]).…”

The hair follicle enigma

“…way, [4] it moves from an active steady state to a dormant steady state and vice versa. Second, the structure of the active anagen follicle is by itself a treasure of complexity, with more than 15 different cell types distributed in two compartments of mesenchymal origin (the dermal papilla and the connective tissue sheath/CTS) and four of epithelial origin (matrix, outer root sheath/ORS, inner root sheath/IRS and shaft), not to mention the appended sebaceous and apocrine glands, and arrector pili muscle.…”