Menopause is triggered by the number of ovarian follicles falling below a threshold number and is irreversible because oogonial stem cells disappear after birth. Since it is the result of programmed disappearance of a limited store of follicles, menopause can be predicted using mathematical models based on total follicle counts at different ages. Our model shows follicle numbers decline bi-exponentially rather than as a simple exponential function of age, as had been assumed, with a first exponential rate parameter of -0.097 and a second of -0.237. The change occurred when numbers had fallen to the critical figure of 25,000 at age 37.5 years. The unexpectedly faster rate of ovarian ageing afterwards lowers the follicle population to 1000 at approximately 51 years, and was adopted as the menopausal threshold because it corresponds to the median age of menopause in the general population. Had the earlier rate persisted menopause would not be expected until 71 years. The impact of step reductions of follicle numbers on the prospective span of menstrual life was predicted by the model. A reduction by 50% before age 30 years resulted in the threshold being reached at 44 years and 0.6 year later for every subsequent year until age 37.5 years after which it is reached at 48 years. A reduction of 90% in childhood before age 14 years could result in menopause as early as 27 years, with increments of 0.6 year per year afterwards until after 37.5 years when it is expected at age 41 years.(ABSTRACT TRUNCATED AT 250 WORDS)

Aim: To compare the effectiveness of two anti-infective protocols for the treatment of peri-implant

The store of primordial follicles in the ovary is fixed before birth and dwindles with age until it is unable to provide enough Graafian stages to sustain menstrual cyclicity. According to a simple bi-exponential model of ageing, the rate of follicle disappearance increases at age 37.5 years (or when 25 000 follicles remain) so that the numbers fall to approximately 1000 at 51 years, the median age of menopause in the population. This study attempts to produce a biologically more realistic model of follicle disappearance and harmonizes follicle dynamics with the distribution of menopausal ages from an American survey. The step-change in the rate of follicle attrition was replaced by a model which assumed that this rate changes more gradually with the size of the follicle store. This produced a distribution of predicted menopausal ages (based on an assumed threshold of 1000 follicles) which was closer to observed data. The fit further improved when the model was modified by having a threshold that varied across the population. Using such a stochastic threshold model for menopause, the number of fertile years remaining could be forecast with an acceptable margin of uncertainty if it ever becomes possible to estimate the size of the follicle store in vivo.

A tractable skew t -distribution on the real line is proposed. This includes as a special case the symmetric t -distribution, and otherwise provides skew extensions thereof.The distribution is potentially useful both for modelling data and in robustness studies. Properties of the new distribution are presented. Likelihood inference for the parameters of this skew t -distribution is developed. Application is made to two data modelling examples.

Aim: The aim of this prospective cohort study was to evaluate an anti-infective surgical protocol

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These results highlight the importance of treating early periodontitis along with smoking cessation, in those under 30 years of age. They further show that calculus removal, plaque control, and the control of gingivitis are essential in preventing disease progression, further loss of attachment and ultimately tooth loss.