Revealing the uterine blood vessel network via virtual pathology

Introduction

Blood vessels (BVs) are generated, grow and die regularly within organisms as part of their perpetual change: growth process, injury, occurrences of pathological conditions, apoptosis, necrosis and more.

The distribution of the BV network at any point in time may provide valuable information with regard to the tissue condition,for example (i) whether it is in a growth or declining stage, (ii) it is in a recovery phase from injury (iii) its angiogenesis functionality and the like. Furthermore, differential comparison of the BV distribution at successive intervals may provide information about the pace and format by which these processes evolve (Burbank 2009, Tahergorabi & Khazaei 2012).

The skin, eye, intestine and uterine endometrium represent specific examples where examination and monitoring of BV distribution could be of value. The case of the endometrium is unique in that sense. In the endometrial tissue, BV distribution and its subsequent evolution play a distinctive role in tissue characterization. During the normal endometrial menstrual cycle, the BV three-dimensional network changes within a relatively short period of time. Most of the endometrial tissue is generated and washed out during the cycle within the time period of 4 weeks on average. It is well accepted that angiogenesis within the endometrium is closely related to the success or failure of the implantation of the embryo (Smith 2001).

In humans, the blood supply to and within the endometrium is maintained by a cascade of BVs of varying diameters. The uterine artery, arising from the internal iliac (Hypogastric) artery, supplies blood to the arcuate arteries from which the radial arteries run radially toward the uterus lumen and divide into the basal and spiral arteries (arterioles) that reside within the endometrium. The smallest diameter vessels in the endometrium undergo vascularization (Demir et al. 2010) and form capillaries. Here, we refer to both processes as ‘angiogenesis’. Table 1 provides a rough scale range of these BVs diameter. The complementary vein network leads the blood back from the tissue to the heart to excrete unnecessary substances and resupply the endometrium with oxygen and nutrients. The entire network promotes and controls tissue growth, nourishes the tissue and maintains its structure.

The process of endometrial angiogenesis is not yet fully understood, neither are the mechanisms by which endometrial BVs evolve during the menstrual cycle. There is evidence that these processes are unique to the endometrium (Rogers 1996, Hickey & Fraser, 2000, Gargett & Rogers 2001, Smith 2001), but authors also refer to them together with other angiogenesis phenomena (Carmeliet 2003). There are contradictory claims in the literature about BV evolution during the menstrual cycle, even with regard to the basic quantity of BV density (see, e.g. (Rogers 1996) vs (Maas et al. 2001)).

Measurement of the BVs attributes (e.g. diameter, direction, tortuosity, spectrum, average color) is feasible by imaging BVs at various wavelengths and modalities. These methods are preferred as they are non-destructive and minimally invasive. To fully utilize BV measurement, the following pre-conditions are necessary: (i) Two-dimensional spatial resolution of ~10–100 μm (cf. Table 1), (ii) some estimate of their z-coordinate (the depth within the tissue in which they reside), (iii) relative or absolute timestamp of the imaging, (iv) objective parametrization of the aforementioned attributes and (v) statistical approach to characterize the entire tissue angioarchitecture.

The current paper presents a method by which these preconditions for BV attributes within the endometrium are fulfilled. We demonstrate the method’s applicability through the data analysis of our clinical and pre-clinical trials, using endometrial biopsies.

Materials and methods

Analysis method

We statistically analyzed the BV network within the endometrial surface images, using all of the sample's acquired images (2× and 4× separately), by treating the BV population as a statistical ensemble. An exemplifying image is shown in Fig. 1, where BV computerized identification is overlaid (partially on the left and fully on the right). As such, we derived probability distribution functions (PDFs) and cumulative PDFs to describe the BV population.

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Image of fresh ex vivo endometrial tissue (swine), overlaid with the computerized identification of blood vessels. Right: all identified vessels. Left: identified vessels on the upper left corner only to allow assessment of the identification accuracy. Each image’s long side equals about 4.9 mm of tissue slab (common scale is shown on the left image).

Citation: Reproduction and Fertility 4, 1; 10.1530/RAF-22-0135

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We focused on two BV features: (i) w – the BV average width (along its length), which is equivalent to its diameter and (ii) the BV average color ratio, as calculated from its image red–green–blue (RGB) colors. We used the color ratio:

This ratio, is considered to represent z – the BV average depth beneath the tissue surface that faces the lumen of the uterus. Such representation is based on differential absorption and scattering models for different light wavebands (Bashkatov et al. 2011, Jacques 2013).

The PDFs of the BV's diameter and color ratio may be functions of the cycle dating, t, or conditional probability such as the diameter distribution given a certain tissue depth (color ratio). These functions may or may not eliminate the normalization factor of the probability of finding a BV (of any diameter) within the unit volume of tissue surface unit area .

We modeled the BV PDF at a specific time and depth (t and z) with a log-normal distribution with the mean (log) of its diameter and its standard deviation .

Results

Human samples

Figure 2 depicts the BV diameter distribution function, as calculated from a sample of 344 2× magnification images. All images of all patients, regardless of their cycle day, were collated together to yield the general behavior or BV diameter distribution differences as a function of tissue depth. The deepest tissue layer (smallest color ratio, value) is shown on the upper panel and more superficial layers, by the order of their bin values, are shown on the lower panels. The most superficial tissue layer which abuts the uterine cavity is shown on the bottom panel. The raw histograms of the BV diameter distribution, as drawn from the total number of identified BVs in the layer's depth (N_BV), are also shown. The solid curve line is the overlaid log-normal function model of and its corresponding fitting parameters (ω,σ), as well as the average layer's value ( bin average value).

Supplementary Figure 1 (see section on supplementary materials given at the end of this article) shows the results of the identical analysis as obtained from 625 images taken under 4X magnification, where the bin limits and average values within each depth bin (layer) are identical to those in the 2X figure (Fig. 2).

In both figures (Fig. 2 and Supplementary Fig. 1) a very clear trend of increased ("average diameter") as function of layer's depth exists, whereas the change in the distribution "width" (σ) as function of depth is less evident due to the image resolution, i.e., the narrowest identifiable BV.

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Human endometrial tissues: normalized probability distribution functions of blood vessel diameters within depth measure ((B + G)/R). The upper panel shows the PDF for the deepest endometrial layer, whereas the one before lower shows the same function for the most superficial credible layer. The relative number density of the vessels can be read from the total number (N_bv), and the log-normal function model parameters are written on the right of each panel. Calculated from 48 samples collected from adult women. Processed from 344 images of 2× magnification, each covers a few square millimeters.

Citation: Reproduction and Fertility 4, 1; 10.1530/RAF-22-0135

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Figure 3 shows the change in the ω fitting parameter of the PDF for the BV diameter distribution as a function of the tissue layer's depth, namely, by interpretation, its distance from the lumen of the uterine cavity. The independent results from the 2× magnification sample (X symbol) and 4× (square symbols) are also shown. The ω parameter is in the log and hence the small values on the y-axis. The difference in the narrowest identifiable BV, due to the higher spatial resolution under the 4× magnification causes the sharper descent of the ω values as we go up the layers under the 4×X magnification. Following our realization of a distinct global trend for BV diameter distribution as a function of the endometrial layer, we turned to time-evolution of the BV diameter–color relationship. When assessed individually, each one of the two features (diameter, color) ensemble distribution did not show clear evidence for an evolution track along the cycle time course. However, the combination of the two characteristics, namely the conditional probability does clearly display an evolution line. We split the color space into two bins only, as opposed to the six color bins in Fig. 2 and Supplementary Fig. 1. This was done in order to reduce sampling errors due to the smaller number of captured images for each cycle day.

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Change of the log-normal fitting parameter ω in units of log (μm) for BV diameter PDF as a function of tissue depth within depth (color) bins. The average (B + G)/R values represent the endometrial layer depth, whereas smaller values (x-axis) represent layers more distant from the lumen of the uterine cavity (’deeper’). Distributions calculated from 2× (X symbols) and 4× (square symbols) image samples. Vertical error bars are of the order of the symbol size.

Citation: Reproduction and Fertility 4, 1; 10.1530/RAF-22-0135

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All patient images of the same cycle day (as determined by histology) were collated together to obtain the BV diameter PDFs within the two-color bins. Each PDF was then modeled by the log-normal distribution, and fitting parameters were derived along with their confidence level. For each one of the two fitting parameters (ω,σ), we plotted the ratio of the parameter as calculated by the deep half of the tissue (at that cycle day) vs the superficial half. Figure 4 depicts the results of these ratios as a function of the cycle day. The ratio of the distribution ‘average’ (ω in the log space), as depicted on the left-hand side of the figure, shows a clearcut evolution line. The global regression line (long line) does not adequately describe the ratio evolution in time, but the two regression lines, one for each cycle phase, seem to provide good modeling of the parameter ratio evolution. Interestingly, the slope change of the ratio evolution shows a pivotal point at or near day 14 (‘ovulation’), which separated the two cycle phases. The same slope change appears on the right-hand side of the figure, where the ratio of the ‘width’ (σ, in log) fitting parameter evolution is depicted. It is important to note that the parameter ratio within the two-color bins, is rather constant throughout day 14, and thereafter, it changes its slope. In general, as the endometrium progresses through the secretory phase, the BV diameter distribution of the superficial layer is narrower (‘tighter’) than that of the deep layer.

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Log-normal fitting parameter ratios of the BV diameter PDFs as a function of the cycle day. Two symmetrial (in color) populations of deep and superficial BVs PDFs were fitted for each cycle day cluster of patients. For each cycle day, the ratio of the result and log-normal variance and standard deviation were calculated. Long lines are regression lines for the entire cycle duration. Short lines are regression lines for the proliferative and secretory phases separately. Cycle days are inferred by histology. The bins central values are (B + G)/R = 0.5 and 1.5 (deep and superficial, respectively).

Citation: Reproduction and Fertility 4, 1; 10.1530/RAF-22-0135

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Swine samples

All samples were taken together, regardless of the cycle day yielded the color (depth)–diameter distribution as depicted in Fig. 5.

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Swine: normalized probability distribution functions of blood vessel diameters within depth measure ((B + G)/R). The upper panel shows the PDF for the deepest endometrial layer, whereas the one before the lowest shows the same function for the most superficial credible layer. The bottom panel also involves artifacts of misinterpreted fresh blood flow. The relative number density of the vessels can be read from the total number (N_bv, on the left), and the log-normal function model parameters are written on the right of each panel. Images of four adult sow endometria, proven fertile, 2× magnification, 73 images altogether, each of a few square millimeters.

Citation: Reproduction and Fertility 4, 1; 10.1530/RAF-22-0135

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The diameter distribution (log-normal) average, ω, exhibits a very clear trend as a function of depth and as summarized in Fig. 6.

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ω fitting parameter in units of log (μm) of the log-normal distribution model for the BV diameter of swine as a function of the tissue depth (deep is smaller x-axis value). Y-errors are of the order of the symbol size.

Citation: Reproduction and Fertility 4, 1; 10.1530/RAF-22-0135

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The premise behind the aforementioned results for the human endometrium is that they are not the only possible configuration for the BV network as a function of depth, nor of the progression in time thereof. In order to corroborate these observations, we repeated the calculation for the four swine we had data for. By histological assessment, the swine were on their cycle days 2, 8, 14 and 16 (in a 21-day cycle). Seventy-three ex vivo endometrial surface images of the four swine under 2× magnification were used for the following analysis. Figure 5 shows the BV diameter PDF of all the swine regardless of their cycle day. The uppermost layer (the lowermost panel) was somewhat contaminated by fresh surface blood. In contrast to the human data, the ‘average’ of the log distribution (ω) becomes smaller as the layer deepens. Figure 6 shows this trend of the log-average (ω) dependence on tissue depth with the positive slope as the layer becomes more superficial. Figure 6 shows the equivalent figure to the one in humans (Fig. 3), depicting the change of the distribution ‘width’ ω as function of tissue depth. Deeper layers (smaller (B + G)/R values have a smaller average width with respect to more superficial layers.

This observation proves the robustness of the method since the BV distribution of other mammals is known to be different to that of humans (see further in the discussion).

Discussion

The statistical method presented here may help to resolve some of the uncertainty in the endometrial angiogenesis process and establish clarity in the face of competing hypotheses. We have demonstrated that by treating the BV population as a statistical ensemble, one can differentiate between different depths of BVs, using their color attribute as obtained in visual light images. This approach differentiates between evolution paths when BV diameter distribution is taken into account. The use of visible-light, non-destructive imaging also allows monitoring of the BV population evolution over a period of time within the very same tissue. The identification of a BV depth with its generation time (’age’) may or may not be justified according to the angiogenesis processes that have led to its creation.

In order to maximize the differentiating power of the method, we split the PDFs of the BVs (all together or within tissue layers) into a multiplication of their normalization factor, namely their total density, and their diameter distribution. These functions can then be determined with various mathematical models (Chappell et al. 2011) (Logsdon et al. 2014) that attempt to describe angiogenesis. For instance, their shape teaches whether new endometrial BVs are generated through sprouting, intussusception (a.k.a. splitting angiogenesis) or elongation. We showed elsewhere (Y Or, Y Shufaro, S Mashiach, B Czernobilsky, S Aviel-Ronen, L Apel-Sarid, M Dahan, T S Kolat, personal communication) that two-dimensional blood vessel density (BVD) alone (without splitting into depth layers) does not sufficiently characterize the endometrial evolution track.

There is a close relationship between the extracted PDFs and the underlying processes leading to their construction. For instance, a new endometrial layer has more sprouting or splitting potential locations than an older (deeper) endometrial layer and one may therefore expect a diameter distribution for the new endometrial layer to have a bigger normalization factor (’more vessels’) in addition to its shape to be heavily inclined toward smaller diameter values.

Alternatively, one may argue that older endometrial layer by virtue of its age had a longer time to generate its BVs and therefore should be denser, with a higher normalization factor, but in keeping with the previous scenario – more inclined toward bigger diameter values.

An alternative scenario may argue that the endometrial tissue growth rate is much faster than the BV diameter growth rate and therefore the diameter distribution should be similar and narrow (with small diameters) throughout the depth of the endometrium.

A good example of the different statistical expressions of processes can be demonstrated if we compare (1) elongation (Gambino et al. 2002) and (2) intussusception, where each one represents a single mechanism of angiogenesis.

In the case of elongation, the BV diameter distribution should stay relatively constant, and if elongation occurs at all endometrial layers, deeper layers should have a different normalization factor (namely BVD) yet a consistent normalized distribution (’shape’). On the contrary, if intussusception rules, a deeper layer that has already undergone splitting and the diameter distribution would lean toward smaller diameter values in comparison to the newly generated upper layer with thicker BVs.

In reality, probably all four possible processes described in the introduction contribute to the BV plexus, but there may well be different weightings for different processes throughout the various phases of the menstrual cycle. The method we presented here may be used to identify and track intussusceptive angiogenesis, which has so far been beyond reach in human studies and mostly observed in animal data (Du Cheyne et al. 2021). The current statistical, time-evolution approach can now be combined with other methods to quantify its contribution to the overall angiogenesis process. The differential weightings may be the reason for the contrasting behavior of the swine BV PDF as a function of depth vs the human data as shown in this paper. This differential PDF behavior adds to the body of knowledge regarding differences between different mammalian species (mice, rhesus macaques, ewes) when it comes to angiogenesis (see e.g. Girling et al. (2007), Chappell et al. (2012) and references therein).

Examination of Fig. 2 and 5 reveals a clear trend that an shouldn't necessarily exist a-priori. It is only due to the correct identification of the ‘color’ for the BV with the ‘depth’ coordinate that lends meaning to it.

In the swine case of Fig. 5, deeper layers (top panels) show a tail of relatively large diameter vessels. As we go to more superficial layers (downward on the plot) this ‘tail’ diminishes and thus, both the average size diameter goes to smaller values (plot maximum goes to the right) and the standard deviation becomes smaller (plots become narrower).

The human sample exhibits the same trend of a shortening distribution ‘tail’ as BVs closer to the tissue surface are considered. However, unlike the swine samples, the tail continues to much higher diameters. In view of the fact that the human cycle is longer (28 days) than the swine's (21 days), this makes logical sense. It may reflect, for instance, the difference between the human menstrual cycle and an animal estrous one.

From the measurement perspective, even if the tissue effective absorption coefficients are different for swine and humans, or the utilized light sources are different, the method is still self-referenced. The differences in absorption and illumination will globally affect the attenuation for each ‘color/depth’ layer but will not affect the trend.

The immediate practical use, therefore, of the proposed method could be the identification of abnormal evolution of the BV network that leads to various pathologies. Thus, as demonstrated here, even endometrial dating may be achieved through the identification of the relative BV population at different endometrial tissue depths. In combination with other digital, in vivo, imaging and calculations, such endometrial dating may be more accurate than the traditional histological methods (Noyes et al. 1950, Acosta et al. 2000, Dubowy et al. 2003, Murray et al. 2004).

Conclusions

Our study provides a time series of the superficial angiogenesis within the endometrium. However, the rapid growth of BVs in the endometrium may shed light on other mechanisms of angiogenesis in other human tissues. Thus, a solid statistical model of the former should advance a deeper understanding of the latter. In addition to being a practical tool for more accurate endometrial dating, BV statistical characterization and statistical description can also contribute to an enhanced understanding of endometrial pathologies in which BVs play a leading role. We propose that this method may even lead to more precise endometrial dating which may help in more accurate determination of, for example embryo transfer timing within IVF treatments.

Supplementary materials

This is linked to the online version of the paper at https://doi.org/10.1530/RAF-22-0135.

Declaration of interest

All with Fertigo Medical Ltd.: Tsafrir Kolatt and Shlomo Mashiach are shareholders and stock option holders, Tsafrir Kolatt is an employee, Yuval Or is a stock options holder, Mazal Dahan and Yuval Or obtain personal fees from Fertigo Medical Ltd.

Funding

This study was supported by Fertigo Medical Ltd., Zichron Yaakov, Israel and the Innovation Authority of the State of Israel, Israel (Grant 63107).

Ethical approval

The study was approved by Kaplan Medical center Ethics Committee (# 0193-17-KMC) and the Rabin Medical Center Ethics Committee (# 0399-19-RMC). Written consent has been obtained from each patient or subject after full explanation of the purpose and nature of all procedures used. It has been registered under the NIH clinical trials registry (ID NCT04288843).

Data availability

The data underlying this article were provided by Fertigo Medical Ltd. with permission. Data will be shared on request to the corresponding author with permission from Fertigo Medical Ltd.

Author contribution statement

All authors had substantial contributions to the conception or deign of the work; or the acquisition, analysis, or interpretation of data. YO, TsK & MD drafted the work YS, SM, BC, SAR & LAS revisited it critically for important intellectual content. All authors approved a version for publication and agreed to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.