*Review of Publication:* Coan, P.M., Ferguson-Smith, A.C., and G.J. Burton (2004) Developmental Dynamics of the Definitive Mouse Placenta Assessed by Stereology, Biology of Reproduction, 70, 1806 -1813

The authors used unbiased stereology to study the morphometric development of the mouse placenta for the purposes of “quantifying the subsequent growth of the different components and estimating the theoretical diffusional properties of the definitive chorioallantoic placenta” and “analyzing physical details of the developing chorioallantoic mouse placenta that are of direct physiological importance” (Coan et al., 2004, paragraph four and six). In the labyrinth the blood in the maternal blood space is separated from the fetal blood by only a thin barrier of trophoblast cells called the interhemal membrane (Coan et al., fig. 1). A significant increase in the surface and decrease of the thickness of the interhemal membrane were shown between embryonic day twelve and one-half and embryonic day eighteen and one-half. Both the surface increase and the thickness decrease of this fetal/maternal barrier would contribute to an increase in the theoretical diffusion capacity of oxygen.

Resin embedding was used for high magnification estimates of volume, volume-fraction, surface, length, and thickness in the placental labyrinth, but systematic random sampling was not used. Resin will shrink a lot less than paraffin but exhaustive sampling and systematic random sampling can’t be done using resin-embedded sections. Paraffin sections were used for the Cavalieri estimator for low-magnification volume estimates, and systematic random sampling was used. Ideally, however, systematic random sampling should be used throughout the whole of the placenta for all probes.

Vertical sections were obtained: the chorionic plate was used as the horizontal direction making the direction perpendicular to the chorionic plate the vertical direction. Placentas were cut in half and those halves weighed and fixed.

**PARAFFIN SECTIONS FOR ESTIMATES OF PLACENTA VOLUME AND VOLUME FRACTION OF PLACENTAL COMPONENTS**

Placental halves were embedded in paraffin and exhaustively sectioned at seven microns. Systematic random sampling was used to pick sections and those were stained with hematoxylin and eosin. Shrinkage correction factors for the XY dimensions were applied.

**Volume**

The Cavalieri/point-counting probe and a 1.25x objective were used to estimate volume (Coan, et al., equation 1) on systematically selected paraffin sections.

**Fractional Volumes**

The area-fraction-fractionator probe and a 10x objective were used to estimate the percent by volume (Coan, et al., equation 2) of the Decidua basalis, the junctional zone, and the labyrinth zone using systematically selected paraffin sections. Systematic random sampling was used on the intra-section level also. The volumes of the components were calculated by multiplying these estimates of percent by volume by the estimate of the total volume (see ‘Volume’ above).

**RESIN SECTIONS FOR ESTIMATES OF VOLUME, SURFACE AND LENGTH DENSITIES AND INTERHEMAL MEMBRANE THICKNESS IN THE LABYRINTH ZONE**

The other half of a given placenta was embedded in epoxy resin and sections close to the middle were taken at one micron and stained with Methylene blue. This means systematic random sampling was not used on the inter-section level. Shrinkage was negligible in the XY plane. For intra-section sampling, two fields of view were picked systematically and randomly per section.

**Volumes**

The fraction by volume of the maternal-blood-space, the fetal capillaries, and the trophoblasts that make up the bulk of the interhemal membrane was estimated using the area fraction fractionator probe and a 100x objective. The total volume of a given component was calculated by multiplying the percent volume by the total estimated volume of the labyrinth zone (see ‘Fractional Volumes’ above).

**Surface Areas**

The cycloids for Sv probe and a 100x objective were used to estimate the surface per volume of the border between the maternal-blood-space (mbs) and the fetal capillaries (fc) (Coan et al., equation 3). This border is called the interhemal membrane. The vertical direction had to be indicated before the cycloids were superimposed on the image of the section. Intersections of the cycloids with the mbs and fc barrier were counted, and points that fall on the labyrinth zone were also counted, to arrive at estimates of the surface of the border between the mbs and fc per the volume of the labyrinth zone. These surface densities were multiplied by the estimates of the volume of the labyrinth zone (see ‘Fractional Volumes’, above) to arrive at estimates of the surface of the mbs/fc border-barrier (interhemal membrane).

**Mean Capillary Length and Diameter**

The image plane was used as a probe with a 60X objective to estimate the mean length per volume of fetal capillaries in the labyrinth (Coan et al., equation 4). The product of these length densities and the labyrinth volume (see ‘Fractional Volumes’, above) yielded an estimate of the length of capillaries in the labyrinth. To ensure isotropy of interaction between the probes and the capillary lengths, isotropic sections should be used, but they were not. If the capillaries themselves were isotropic in three-dimensional orientation, then any orientation of the tissue could be used.

Since the capillaries are close to cylinders, a model-based assumption, the cross sectional area was calculated by dividing the estimated volume of the fetal capillaries by their estimated length (Coan et al., equation 4).

**Interhemal Membrane Thickness**

The orthogonal intercepts probe was used to estimate the thickness of the barrier between the maternal blood space and the closest fetal capillaries in the labyrinth. Specifically, the reciprocal of each thickness estimate was calculated and summed. The reciprocal of that times the number of estimates is the harmonic mean thickness; but it must be multiplied by 8/3π to correct for overestimation due to orthogonal sections.

**Oxygen Diffusing Capacity**

The mean surface area estimate of the maternal blood space/fetal capillary border (interhemal membrane; see ‘Surface Areas’ above) divided by its harmonic mean thickness (see ‘Interhemal Membrane Thickness’ above) is used to determine the diffusing capacity. That product is multiplied by the Krogh diffusion coefficient for oxygen to calculate the diffusing capacity (Coan, et al., equation 7).

Coan, P.M., Ferguson-Smith, A.C., and G.J. Burton (2004) Developmental Dynamics of the Definitive Mouse Placenta Assessed by Stereology, Biology of Reproduction, 70, 1806 -1813

**COMMENTS**

In this study of the placenta, isotropic probes for length and surface could not be used because the sections were too thin. Since an isotropic probe could not be fit into the section, one must either prove that the objects being sampled are themselves isotropic, or manipulate the tissue to ensure isotropy. No attempt was made to prove the former, although the assumption that the fetal capillaries are oriented randomly in three dimensions (isotropic) may have been made to justify the use of the image plane as the probe to estimate their length (see ‘Mean Capillary Length and Diameter’ above). To manipulate the tissue to ensure isotropy, either isotropic or vertical sections must be used. In this study vertical sections were used. To avoid the technical difficulty of using vertical sections and to be able to use preferential sections, thick sections could have been used. If thick sections were used there would have been room for the spaceballs probe to estimate length and the isotropic fakir probe to estimate surface, obviating the need for vertical sections. If thin sections must be used, perhaps to achieve good histology, then the probes used in this paper are good choices.

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