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Model of ovarian reserve from conception to the menopause

The Wallace-Kelsey model, is a model of the establishment and decline in human ovarian reserve from conception to the menopause. The model is named after Hamish Wallace MD, a Pediatric Oncologist at the Royal Hospital for Sick Children, Edinburgh, and Tom Kelsey PhD, a Senior Research fellow at the University of St Andrews. The model is a peak function obtained by fitting candidate models to histological estimates of ovarian reserve.

Formula

The model is an asymmetric double-Gaussian cumulative (ADC) curve of the form

${log_{10}(y)={\frac {a}{4}}\left[1 {\mbox{Erf}}\left({\frac {x b {\frac {c}{2}}}{d{\sqrt {2}}}}\right)\right]\left[1-{\mbox{Erf}}\left({\frac {x b-{\frac {c}{2}}}{e{\sqrt {2}}}}\right)\right]}\!$

where y = non-growing follicle (NGF) population, x = age, a, b & c define the scale and amplitude of the curve, and d & e define the rates of population establishmnet and decline.

In the Wallace-Kelsey model the paramataters a, b, c, d & e are given values that provide the best fit to a combined histological dataset:

${log_{10}(NGF)={\frac {5.56}{4}}\left[1 {\mbox{Erf}}\left({\frac {age 25.6 {\frac {52.7}{2}}}{0.074{\sqrt {2}}}}\right)\right]\left[1-{\mbox{Erf}}\left({\frac {age 25.6-{\frac {52.7}{2}}}{24.5{\sqrt {2}}}}\right)\right]}\!$

See also

• Population
• Mathematical models
• Logistic function

External links

• Malthusian Growth Model from Steve McKelvey, Department of Mathematics, Saint Olaf College, Northfield, Minnesota
• Logistic Model from Steve McKelvey, Department of Mathematics, Saint Olaf College, Northfield, Minnesota

Template:Population Template:Modelling ecosystems

Category:Empirical laws Category:Mathematical modeling Category:Population