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The authors have declared that no competing interests exist.

Conceived and designed the experiments: AS GM. Performed the experiments: AS GM. Analyzed the data: AS GM. Contributed reagents/materials/analysis tools: AS GM. Wrote the paper: AS GM.

Precise estimation of the number of follicles in ovaries is of key importance in the field of reproductive biology, both from a developmental point of view, where follicle numbers are determined at specific time points, as well as from a therapeutic perspective, determining the adverse effects of environmental toxins and cancer chemotherapeutics on the reproductive system. The two main factors affecting follicle number estimates are the sampling method and the variation in follicle numbers within animals of the same strain, due to biological variability. This study aims at assessing the effect of these two factors, when estimating ovarian follicle numbers of neonatal mice. We developed computer algorithms, which generate models of neonatal mouse ovaries (simulated ovaries), with characteristics derived from experimental measurements already available in the published literature. The simulated ovaries are used to reproduce

Accurate estimation of ovarian follicle numbers is the foundation of reproductive biology [

Mean follicle numbers in mice are known to vary considerably between animals of the same strain [

We have developed computer algorithms to computationally generate mouse ovaries, based on spatial and morphological characteristics derived from measurements performed on actual ovarian sections of neonatal mice. Herein, we report how the deviation of the follicle-number estimates from their actual mean is affected by the number of ovaries and sampling frequency used.

In this work we use the term ‘simulated’ ovary to indicate a computer model made of spheres in a 3-dimensional space, the size and the spatial distribution of which closely resemble those of follicles within a real ovary. More specifically, the sizes of these spherical structures are based on the average sizes of actual follicles measured on ovarian sections of C57Bl/6 mice, for different developmental stages [

The raw data for the modelling were collected from published data of the neonatal mouse ovaries. Actual follicle number estimates were obtained from the data published by Kerr's group [

Age in days | Total primordial follicles (± |
Total primary follicles (± |
Total secondary follicles (± |
---|---|---|---|

7 | 1987 ± 203 | 569 ± 35 | 5 ± 4 |

12 | 2317 ± 289 | 362 ± 34 | 328 ± 34 |

Average follicle numbers in whole neonatal mouse ovaries (mean ± standard error of the mean): data reported by Kerr

Follicle Stage | Day 8 | Day 12 | |||
---|---|---|---|---|---|

Diameter (μm)± |
Distance (μm)± |
Diameter (μm) ± |
Distance (μm) ± |
||

Primordial | 20 ± 5 | 30 ± 25 | 18 ± 5 | 24 ± 17 | |

Primary | 48 ± 5 | 69 ± 29 | 51 ± 10 | 70 ± 29 | |

Secondary | – | – | 79 ± 7 | 174 ± 77 |

Average follicle

We need to emphasise here two important issues. Firstly, we are using the follicle-number of day 7 mice (_{f}, were measured only on those follicles showing a clear sharp nucleus on the section, disregarding any follicles that had a fuzzy or imperceptible nuclear profile. The diameter is determined as the average between two perpendicular segments taken on the follicle profile (see methods in [_{o}, were additionally measured on ovarian sections from randomly selected follicles, which present an oocyte in their cross-sectional profile. The following diameter ratios were then calculated: _{o-f} = _{o}/_{f}, where _{o} and _{f} are the average oocyte and follicle diameters, respectively; these ratios are developmental-stage dependent, as reported in

Follicle Stage | _{o-f} = _{o} /_{f} |
---|---|

Primordial | 0.78 |

Primary | 0.64 |

Secondary | 0.54 |

The following subsections will illustrate how simulated ovaries are generated; the relative computer algorithms were implemented in Fortran 77, unless otherwise stated.

In order to generate a simulated ovary of specific age we randomly select the number of follicles for each developmental stage. We assume that follicle numbers follow a Gaussian distribution, with mean and standard deviation reported in _{stage}) of follicles is obtained for the given developmental stage. We then generate each follicle by randomly assigning to it a diameter. We assume that follicle diameters follow a Gaussian distribution, with mean and standard deviation reported in _{stage} follicles are generated.

The process described in the previous subsection generates _{tot_fol} = ∑ _{stage} spheres of different sizes, which need to be inserted in a virtual spherical volume (the simulated ovary) without overlapping, and with a spatial arrangement typical of follicles in an actual ovary [_{ovary}, has to be selected. For this purpose, the total volume occupied by the follicles, _{tot_fol}, is calculated as the sum of the volumes of each follicle, _{ovary}. The value to be assigned to _{ovary} is calculated as in

In order to insert a follicle into the simulated ovary volume, a radial-direction of the ovary is randomly chosen (see page 111 of [

Once all the _{tot_fol} follicles are inserted in the virtual spherical volume, the follicle profile density, ρ_{profile}, is calculated on the equatorial section of the simulated ovary:
_{section} is the area of the equatorial ovarian section, ^{i}_{profile} is the area occupied by follicle-profile _{p} is the number of follicle profiles on an equatorial section (see also

3-D renderings of day 8 and day 12 simulated ovaries, created using the Perspective of Vision Ray tracer (

Ovary age | Actual ρ_{profile} ( |
---|---|

Day 8 | 0.47 |

Day 12 | 0.64 |

350 simulated ovaries of day 8 and 12 were generated to perform the analyses herein; this number of ovaries allows sampling adequately all the relevant Gaussian distributions mentioned above, and ensures realistic follicle numbers, diameters and spatial arrangement.

The primary objective of this work is to assess the error when estimating follicle numbers in neonatal C57Bl/6 mouse ovaries. For this purpose, the simulated ovaries are computationally analysed in order to reproduce follicle counting experiments. The ovaries are virtually sectioned and their follicle-number is estimated by applying the unbiased stereological technique, more specifically the disector and the fractionator ([

The unique advantage of the simulated ovaries is that the total number of follicles is ^{N,f} for the number of follicles, when using a sample of ^{N,f} is effectively an estimate of the error of follicle numbers when performing a real counting experiment with

In order to estimate the ^{N,f} with sufficient statistical power, we generated

In ^{N,f} would depend on the chosen set of simulated ovaries; to eliminate this dependence, we use ^{N,f} ~ ^{N,f}. This is repeated for each of the 20 groups made of 10,000 samples of

Part of a day 8 simulated ovary, a) and its corresponding cross section, b). Primordial (red) and primary (green) follicles numbered respectively in both a) and b) are virtually sectioned. Yellow arrows point at follicles in the immediate vicinity of the numbered ones, albeit not appearing in the 2D section. Oocyte, nucleus and nucleolus have been added to the model for illustrative purposes, c). These structures can also be simulated based on real measurements, in order to be used in the stereological counting. d) shows an example of a secondary, a primary and two primordials (blue arrows) with all internal profiles visible (day 12 ovary).

The ^{N,f}, is estimated according to

As expected, a similar trend is obtained when counting primary follicles in day 8 ovaries, (

The

The accurate estimation of follicle numbers in mammalian ovaries is a crucial and still challenging task in the field of reproductive biology [

We have presented quantitatively how the accuracy in estimating the mean follicle number is affected by varying the number of ovaries and choosing different counting frequency—Figs.

It is interesting to compare the

Sometimes, a caveat for a sufficient number of animals is the challenge to harvest them; mice need to be bred, which can be expensive and time-consuming. Furthermore, if the study involves a mutation that affects the health of the mouse, as well as fertility, it may be difficult to collect a large number of ovaries. In those cases in which the number of ovaries cannot be chosen arbitrary, the simulated ovary can provide insight on how a higher a number of sections can improve the counting accuracy. This applies particularly to experiments performed using human ovaries, which are extremely rare and challenging to obtain (e.g. the data set in [

Finally, the simulated ovary approach can be adapted for and applied to other organs characterised by a large number of individual functional units (e.g. neuronal and glial cells in the brain). In fact, the study of the development of these organs, or the effects of toxins, radiation exposure, environment or genes on their function, directly relates to the accurate counting of their functional units.

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Schematic representation of the bootstrapping approach for generating random samples of simulated ovaries.

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