Influence of oxidative stress on women’s fertility: A model with a generational age Caputo’s fractional derivative

Cellular aging associated with telomeric shortening plays an important role in female fertility. In addition to natural decline, due to the loss of telomeric repeats during cell division, other factors such oxidative stress (OS), accelerate telomere shortening by causing a dramatic loss of telomeric repeats. Thus, mathematical models to better understand the accelerated aging leading to infertility are lacking in the literature. An initial and boundary value problem (IBVP) with a diffusion-advection equation was considered to describe the evolution of a cell population undergoing a gradual decrease of the proliferation potential due to the end-replication problem (Olovnikov, 1973). In this paper we propose a continuum model that attempts to capture the random telomere shortening caused by OS, replacing the advection term with a Caputo’s fractional derivative of order $\beta$, $0<\beta <1$, with respect to the generational age. The distance between the order of the Caputo derivative and 1 was considered the oxidation parameter. The mathematical model was applied to the human follicular growth from preantral to pre-ovulatory follicle, in young and older women to study the influence of oxidation and low telomerase activity on the aging rate of the pre-ovulatory follicle. We observed that as OS increases, the generational age of granulosa cells (GCs) increases as well, suggesting that telomeres of these GCs will be aged. Although middle-aged women treated with antioxidants could reduce the negative effects of OS on telomeres, antioxidants in combination with good levels of telomerase activity yield the best results regarding the reduction of generational aging of GCs.