1 Section of Child Life and Health, Department of Reproductive and Developmental Sciences, University of Edinburgh and 2 School of Computer Science, University of St Andrews, UK 3 To whom correspondence should be addressed at: Department of Haematology/Oncology, Royal Hospital for Sick Children, 17 Millerfield Place, Edinburgh EH9 1LW, UK. e-mail: hamish.wallace{at}luht.scot.nhs.uk
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Abstract |
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Key words: fertility/human oocyte/ovarian failure/radiotherapy
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Introduction |
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The human ovary is endowed with a fixed pool of primordial follicles, maximal at 5 months of gestational age, which steadily declines throughout life, culminating in the menopause at an average age of 51 years. Follicle depletion, as a result of atresia and recruitment towards ovulation, leads to premature exhaustion of the follicle pool and menopause long before death, in contrast to other mammals. A number of mathematical models have been proposed in humans to describe the rate of follicle decline based on a series of data describing the number of follicles present at different ages in humans (Block, 1952, 1953; Richardson et al., 1987
).
For any given age, the size of the follicle pool can be estimated based upon a mathematical model of decline. The rate of oocyte decline represents an instantaneous rate of temporal change, based upon the remaining population pool. Therefore, reduction of the follicle pool as a consequence of cytotoxic therapy will result in premature exhaustion of the pool, and advance the onset of the menopause. In order to predict the age of menopause in patients who have experienced radiotherapy to a field that includes the ovaries, the extent of the radiation-induced damage to the follicle pool must be determined.
We have previously estimated the dose of radiation required to destroy 50% of primordial follicles (LD50) to be <4 Gy (Wallace et al., 1989a). For a given dose of radiotherapy, the surviving fraction can be determined and the age of menopause predicted by applying a mathematical model for decay. In this way, patients can be counselled appropriately with regard to their reproductive life span and their window of opportunity for fertility (Wallace et al., 2001
).
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Methods |
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It is estimated that during embryo development, approximately seven million germ cells are formed in the ovarian rudiment, but only two million are present at birth and 300 000 by menarche (Block, 1952; Baker, 1963
). The precise number of oocytes remaining at menopause is unclear. Ovarian follicles have been counted in the ovaries of 43 females aged 644 years, following accidental death, and the number of follicles present at menopause was predicted, using linear extrapolation, to be 2200 (Block, 1952
). This is likely to be an overestimate, as further studies of follicle numbers present in the ovaries of pre-, peri- and post-menopausal women have demonstrated that <1000 ovarian follicles remain in peri-menopausal women, indicating that follicle decline accelerates in the decade preceding menopause (Richardson et al., 1987
). With only an estimated 400 ovulations occurring during the reproductive period, this progressive reduction is attributable to follicle death by apoptosis.
Evidence for temporal decline has been well characterized in rodents, and early mathematical models were constructed based on a model of negative exponential rate of decay: y = A exp(bx), where A is the number of follicles present at birth; or, following a logarithmic transformation to give a model for linear decay: log(y) = log(A)bx, where x refers to age, y to the number of follicles and b(>0) is the rate of exponential decay (Faddy et al., 1983).
The rate of decline (b) was then determined by applying simple regression analyses of logged number of follicles against age. Each model can be described as y(x) = f(x) for x between zero (birth) and the estimated age of menopause, where y(x) is the estimated number of follicles present at age x, and f(x) is a function used to obtain y(x). The proposed mathematical models vary depending upon the chosen subset of data describing follicle numbers at different ages. Richardson et al. provided the mathematical model (Richardson et al., 1987):
log10(y) = 6.13 ± 0.33 0.06 ± 0.01x based on one source of data (Block, 1952), and:
log10(y) = 5.94 ± 0.37 0.04 ± 0.01x based on another source of data (Gougeon et al., 1984).
We previously described the function log10(y) = 6.3 0.06x, based on two sources of data (Block, 1952; Baker, 1963
).
The above models are constructed using data describing a population aged 644 years. Therefore, it is with some reservation that these models have a wider application from birth to menopause. Furthermore, none of the above models make use of more than two data sources, and a larger data set is likely to produce a more accurate model.
Construction of the above models is based on the assumption that ovarian follicle decline follows simple exponential decay; however, it is now recognized that the loss of ovarian follicles is more complex. A graphical representation of ovarian follicle number, expressed logarithmically against age, suggested that ovarian follicle decline is bi-exponential with broken-stick regression (Faddy et al., 1992). An increase in the rate of exponential decline appeared to occur at age 38 years, corresponding to a follicle pool of 25 000. Following these observations, Faddy et al. proposed a more comprehensive model of piecewise exponential decay (Faddy et al., 1992
) based on a least squares fit to data from three other authors (Block, 1952
, 1953; Gougeon, 1984
; Richardson et al., 1987
):
loge(y) = 952 000 0.097x for 0 < x < 37.5 and:
loge(y) = e19.02 0.237x for 37.5 < x < 51
Although data from Baker were not used (Baker, 1963), the value at birth of 952 000 is in line with his results, and assumes a population of 1000 follicles at a menopause occurring at age 51 years. However, this model fails to concord with the distribution of menopausal ages described by Trelour (Trelour, 1981
). Furthermore, biologically, this abrupt change when the oocyte population falls to 25 000 is unlikely; more plausibly, the change is likely to represent an instantaneous rate of temporal change based on the remaining population pool, which is expressed mathematically as a differential equation. Faddy and Gosden provided a revised model (Faddy and Gosden, 1996
) obtained by incorporating Trelours data into a least squares analysis of the four quantitative studies in terms of the differential equation:
dy/dx = y[0.0595 + 3716/(11 780 + y)] (1) with initial value y(0) = 701 200.
We consider this to be the best model currently available, and have solved it to revise our estimate of the radiosensitivity of the human oocyte based upon additional data from young women who developed ovarian failure following treatment with TBI.
Patients
We studied two cohorts of women with ovarian failure secondary to radiotherapy treatment for childhood cancer. The first cohort comprised of eight post-pubertal women, median age 17.1 years (range 15.421.5), recruited from paediatric oncology late effects clinics throughout Scotland (Bath et al., 1999) (Table I). The patients had been treated with TBI, 14.4 Gy in eight fractions over 3 days, during first or second remission for leukaemia at age 11.5 years (range 4.915.1). No shielding to the ovary was applied. All patients received chemotherapy with standard Medical Research Council (MRC) trials for acute lymphoblastic leukaemia or acute myeloid leukaemia.
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From the first cohort, ovarian failure developed in six of the eight subjects at a median age of 13.2 years (range 12.516.0) and all six had received sex steroid replacement therapy (Table I). The remaining two patients had progressed spontaneously through puberty without sex steroid replacement therapy, although they had irregular menstrual cycles and intermittently elevated gonadotrophins. In the second cohort, premature ovarian failure occurred in 18 of the 19 women, at a median age of 12.7 years (range 9.715.9; Table II).
We have obtained a solution to the differential equation described by Faddy and Gosden above (Faddy and Gosden, 1996) using a seventh-eighth order continuous RungeKutta numerical method. Application of the FaddyGosden model for healthy untreated women aged 051 years enables the oocyte population to be determined for any given age (Figure 1).
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Results |
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Solving g(z) = 50 gives an LD50 of 1.99 Gy
Figure 2 demonstrates the estimation of LD50 for the human oocyte. The dose required to completely destroy the follicle pool, D0 (LD100), is an infinite number of Gy, since we are assuming a logarithmic model.
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Discussion |
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The aetiology of ovarian failure in both our cohorts of patients is likely to be irradiation induced. The patients in the first cohort who had received TBI were treated with standard MRC chemotherapy protocols that include alkylating agents and cytosine. Ovarian function appeared to be preserved after standard treatment for acute lymphoblastic leukaemia (Wallace et al., 1993). We have described decreased LH secretion and short luteal phases in young women whose treatment included low dose cranial irradiation (Bath et al., 2001
), but premature ovarian failure is not described, although these women may go on to have an early menopause.
With no biochemical markers available to predict those patients for whom premature ovarian failure is likely, information to determine the extent of radiotherapy-induced damage and prediction of the likely fertile window will be helpful for reproductive counselling. Oocyte radiosensitivity differs tremendously between species, with the mouse oocyte (LD50 0.15 Gy) being about 350 times more radiosensitive than that of the monkey (LD50 50 Gy). The radiosensitivity of the human oocyte has been reported in a number of studies, although the majority of these have focused on radiotherapy treatment in adult patients. Bianchi estimated the LD50 for human oocytes to be 618 Gy (Bianchi, 1983). In these patients, radiotherapy was administered for the treatment of benign gynaecological disorders to induce an artificial menopause. Permanent ovarian failure was induced in a group of 72 patients, most of whom were >40 years old at time of treatment, following administration of 625 roentgens (
6 Gy) (Bianchi, 1983
). In a study of 2000 females treated with radiotherapy for menorrhagia, permanent ovarian failure was induced in 97% of patients following irradiation with 510.5 Gy. In this study, our revised estimate of the LD50 for the human oocyte is significantly less than previously reported.
We have based our calculations on the assumption that the rate of decline of the surviving fraction of oocytes is not greater than that for a non-irradiated ovary. This is based upon the observation that oocytes die in interphase within a few hours of irradiation, becoming pyknotic and then removed by phagocytosis within a few days (Lindop, 1969). Furthermore, in irradiated fetal rat ovaries, severely damaged germ cells degenerate rapidly and are eliminated from the ovary within a few days of exposure. It is reported that the subsequent rate of oocyte depletion is lower in irradiated animals than in controls (Beaumont, 1964
). If this were true, then the surviving fraction for each patient would be lower than we have estimated, indicative of increased radiosensitivity of the human oocyte and, consequently, a lower LD50.
Radiotherapy treatment before puberty may result in significant ovarian follicle depletion. However, the earliest clinical manifestation of ovarian follicle exhaustion is failure of pubertal development in association with elevated gonadotrophins. Delay in the diagnosis of ovarian failure would result in an overestimation of the LD50. Estimation of the LD50 (<2 Gy) for the cohort of patients treated with 14.4 Gy TBI was lower than our previous estimate of that (4 Gy) for our original cohort of 19 patients who received 30 Gy abdominal irradiation. The LD50 of 4 Gy is likely to be an overestimation, largely attributable to the long lag period between treatment and the earliest detection of clinical ovarian failure. It is now clear that the oocyte pool of these females would have been exhausted at an earlier age than that at which clinical manifestations could be detected. Using the solution to the FaddyGosden model has enabled us to recalculate the LD50 for the original cohort and, to our surprise, the estimate (5.15 Gy) is higher than we previously reported. The reason for the overestimate remains the higher radiation dose received by the first cohort, who were treated at a younger age, with a resulting longer lag period between treatment and the detection of ovarian failure. We therefore maintain that the most accurate estimate (LD50 <2 Gy) is calculated from applying the FaddyGosden solution to the second cohort, who were treated at an older age [median 11.5 (range 4.915.1) versus 4 (113) years] and with a lower total radiation dose.
A further consideration when applying our construct clinically is the uncertainty of the impact of fractionated doses of radiotherapy. Our estimation of the LD50 may be considered as an upper limit, because it does not take into consideration the fractionated schedule of radiotherapy.
Solving the FaddyGosden mathematical model for ovarian follicle decline using a seventh-eighth order continuous RungeKutta numerical method, and applying the solution to new clinical data on age at development of ovarian failure after TBI (14.4 Gy), has enabled a more accurate estimate of the radiosensitivity of the human oocyte. Calculation of the dose of radiation received by each ovary, combined with a more accurate estimate of the radiosensitivity of the human oocyte, will facilitate our ability to provide more scientific fertility counselling to young women at risk of a premature menopause following the successful treatment of cancer.
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References |
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Submitted on June 19, 2002; accepted on September 5, 2002