Placental Growth and Development Analyzed through 2D and 3D Fractals

Abstract

Fractal geometry has many applications in physiology and anatomy, providing novel insights into the structure and function of biological systems and organs, including the placenta. The placenta is a vital fetal organ that is the means by which essential nutrients and oxygen are extracted from maternal blood and transferred to the developing fetus. Anatomically, the placenta is a highly intricate structure exhibiting self-similarity at different scales. The complex relationship between placental function in nutrient transfer and fetal growth follows the allometric metabolic scaling law. The variety of shapes of the placental chorionic plate, a 2D plane that contains the major chorionic arteries and veins, has been linked to measures of child health and neurodevelopmental outcomes. The microscopic arrangement of chorionic villi has also been demonstrated to have fractal properties that vary by gestational age and in different pathological conditions. Geographical Information Systems theory could be used to analyze the placental topography in the context of its surface vasculature. Measures of spatial autocorrelation can model placental growth and development over gestation. An ideal model would mark the timing, nature, and severity of gestational pathology modifying placental growth and, by extension, fetal development that leads to poor pregnancy outcomes.

1. Introduction

“Fractal” refers to a particular type of complex geometric shape that is distinct from the simple figures of classical or Euclidean geometry—the square, the circle, the sphere, and so on. A fractal can be used to quantify an irregularly shaped object or natural phenomena like coastlines and mountain ranges. Mandelbrot was the first to suggest that fractals could be an ideal tool in applied mathematics to model diverse phenomena—from physical objects to stock market behavior. Since its inception, the fractal concept has spawned a new system of geometry that has had significant implications for fields as diverse as physical chemistry, physiology, and fluid mechanics [1, 2, 3].

Fractals are “self-similar” at all scales, at least approximately, if not precisely. The similarities between levels are not necessarily obvious but they are present—providing order to chaos; for this reason, fractal analysis is used to generate quantitative measures of the complexity and self-similarity of biological structures and processes. This quantitative measure is termed a “fractal dimension,” which is an index for characterizing fractal patterns or sets by quantifying as a ratio of the change in complexity to the change in scale [4]. Fractal dimensions have been used to characterize physiological signals such as heart rate variability [5, 6] or respiratory rate [7, 8]. Comparing fractal dimensions can provide insight into the complexity and adaptability of these signals and has been applied to other conditions as diverse as sleep apnea, cardiovascular disease, and aging [9, 10].

Fractal analysis has also been applied to biological structures, such as the dichotomous hierarchical branching network structure of blood vessels [11, 12] and the morphology of (individual) neurons [13]. By quantifying the fractal properties of these structures, researchers can better understand their function and also developmental processes across time.

Fractal analysis has been used to study topics as diverse as the distribution of plant species in ecosystems [14] and the spatial distribution of neurons in the brain [15]. The mathematical analysis of large-scale spatial distributions and patterning of ecosystems and even social networks have all provided evidence that shared governing principles link rules that underlie the organization and self-organization of diverse systems.

The placenta is a disc-shaped organ primarily composed of blood vessels, connective tissue, and a thin trophoblast epithelium; weighs about a pound at full term; and is approximately an inch thick and 9 inches in diameter. The placenta comprises a fetal part and a maternal part (Figure 1). The fetal part consists of two membranes—the amnion and the chorion, the umbilical cord, the chorionic plate vasculature, and the villous tree. The maternal part consists of the decidua and the intervillous space filled with maternal blood.

Figure 1.

Schematic diagram of a human placenta. The fetal side comprises chorionic plate, chorionic surface arteries, and veins connected to the umbilical arteries and vein. The maternal side consists of the maternal decidua and basal plate with maternal vessels. The middle portion comprises placental villi in maternal blood.

The placenta is the anatomic and physiologic interface between the fetal and maternal environments during pregnancy. The newborn is entirely composed of nutrients transferred from the maternal to the fetal circulation across the placenta. By extension, birth weight (BW) depends on placental function. It has been demonstrated that the placental and fetal masses are related by an allometric exponent. Deviations from this range can illuminate physiological aberrations during the pregnancy and can be indicators of deviations from normal fetal-placental development.

In contrast to most permanent viscera that have more fixed shapes, the placenta is amoeboid and responds to intrauterine exposures by modifying its gross and microscopic structure and vascularization [16, 17, 18, 19, 20, 21, 22, 23, 24, 25]. Shape variations that mark altered placental vascularization include irregularities of chorionic surface area, shape, thickness, and vascular patterning and cord insertion [26]. As compared to the traditional crude measures of length, breadth, and average thickness, a comprehensive measurement of placental shape and surface vessels has been shown to provide a powerful reflection of the intrauterine environment that can inform on postnatal risks [12, 27]. Fractal geometry has already helped to characterize and differentiate the branching patterns of placental chorionic surface vasculature and villous distribution at different gestational stages and for different pathological conditions [12, 28, 29]. Altered proportions of the chorionic plate (a very small chorionic plate area or a very large and expansive chorionic plate) or placental disk thickness (a thin or thick disk) has been correlated with changes in BW. Moreover, the changes in chorionic surface vascular resistance and extent of villous arborization would, in theory, represent very different fetal-placental relationships resulting from exposures to the intrauterine environment at different gestational time points and resulting in different lifelong health risks.

This chapter focuses on the anatomic and physiologic fractality of the placenta.

2. The fractal placenta

2.1 Placental weight

Allometric scaling, which describes how the size, shape, or physiology of an organ changes in relation to metabolism, had its first major proponent in Max Kleiber. Kleiber’s law postulated that the metabolic rate of an organism scales as a power function of its body mass [30]. While he hypothesized that the value of the exponent should be 2/3, experimental data showed that 3/4 was a better fit. The 3/4 exponent was later justified using hydrodynamic optimality [31]. This scaling has proved remarkably constant for a wide range of organisms from the smallest microbes to the largest vertebrates and plants [32].

Ahern in 1966 (as cited in [33]) suggested that the complex relationship between placental function in nutrient transfer and fetal growth could also be analyzed allometrically by substituting placental weight (PW) for basal metabolic rate and fetal BW for body mass, as seen below.

$$PlacentalWeight=\alpha \times BirthWeigh{t}^{\text{β}}$$

Ahern posited a 2/3 scaling for his relationship, as postulated by Kleiber. We tested this scaling relation in a sample of 24,601 term singleton pregnancies from the National Collaborative Perinatal Project [34]. The allometric metabolic equation was solved for α and β by rewriting PW = α(BW)^β as ln(PW) = ln(α) + β[ln(BW)]. The results obtained were in remarkable agreement with Kleiber’s law: β = 0.78 ± 0.02, α = 1.03 ± 0.17. Rearranging the terms in the equation, and since ln(1) = 0, β = [ln(PW)/ln(BW)]. We interpret β as a non-linear measure of placental efficiency; when β increases, PW is greater relative to BW, implying reduced placental functional efficiency, and when β decreases, BW is relatively larger for a given PW (implying greater placental efficiency). While the fetoplacental weight ratio is more universal in clinical practice, it is a linear version of β, which contrasts with the logarithmic growth of the fetus and placenta approaching term. Thus, understanding the allometric scaling relationship between the placenta and fetus is important for clarifying the impact of environmental stressors on placental structure/function and the effects of that stressor on the fetus.

Another example of how broadly applicable this 3/4 scaling relationship was found for twin pregnancies. We computed β for viable monochorionic (MC) and dichorionic (DC) twin pregnancies [35]. In DC twins, each sibling has its “own” placenta, while MC twins share a single placenta. β was found to be 0.76 ± 0.02 for both MC and DC twins. This range is very close to what was found for term singleton pregnancies. Finally, while the wild-type mouse placenta is structurally very different from the human, the same scaling exponent relates mouse fetal and placental weights but only after the time when the branched labyrinth has developed [36].

The consistency of the scaling factor values in relatively well populations of singletons, twins, and mice makes β, the ubiquitous exponent of Kleiber’s law, a useful proxy for understanding pathologic placental structure, and by extension, function in singleton and twin human pregnancies.

2.2 Chorionic plate vasculature

From the umbilical cord insertion on the chorionic plate extends a highly variable network of arterial and venous high capacitance/low resistance vessels. The chorionic surface arteries branch repeatedly, finally exiting the chorionic plate from the network of fetal stem vessels and terminal villi filled with capillaries that carry fetal blood into proximity to the maternal blood in the intervillous space. The capillaries then unite to form venules and join the chorionic surface veins that carry the oxygenated blood and nutrients to the fetus. Unlike other regions in the human body, the chorionic arterial and venous networks do not run in parallel. The basis(es) of these variations is unknown but is hypothesized to be local adaptations to intrauterine variations in the decidua, vasculature, and/or local inflammation.

A search for fractal relationships in the whole placenta has been done using MRI and X-ray angiograms of casted placenta fact [37, 38]. However, using MRI and casting the placenta for X-ray angiograms are not trivial and cannot be routinely performed. Therefore, we elected to study placental fractals with hand-traced placental chorionic surface vessel networks from digital 2D images of post-delivery placentas (Figure 2) [39]. From such images of chorionic vessels, their length and branching characteristics—the number of branch points, branching diameters, vessel paths, branching angles, tortuosity, and branching generations—can be extracted [27]. The mean fractal dimension of the chorionic surface arterial network computed from binary images of the tracings of normal term pregnancies was similar to that of term pregnancies with diabetes and preeclampsia but differed from that of preterm pregnancies [12]. The number of arterial branch points per unit of chorionic plate area of placentas of uncomplicated pregnancies differed from those of pregnancies with diabetes or preeclampsia [12]. The fact that the fractal dimension of normal pregnancies differed from that of preterm pregnancies raises the question of whether preterm birth could be a consequence of sub-optimal placental function.

Figure 2.

a) 2D image of the fetal surface of placenta, b) placental surface vascular tracing based on protocol described in [39]. Source: Adapted from [27].

Another study compared the fractal dimension of placental chorionic surface arterial networks from 197 normal singleton pregnancies and 60 monochorionic twins (twins sharing the same placenta). The twins’ group was subdivided into two groups: one with significant BW discordance (BW of one twin is greater than the other one by >20%) and the other without BW discordance. BW discordance in twins has been associated with neonatal mortality risk. It was found that the fractal dimension of singleton pregnancies was significantly lower from twins, both with and without BW discordance [40]. On the other hand, the branch points per unit area between the term singleton and the twin placentas remained the same. These findings suggest that despite having different intrinsic branching characteristics of placental chorionic surface vasculature, the singleton and twin pregnancies may have a similar “angiogenic potential,” which can regulate and/or limit their overall growth.

Placental chorionic surface vessel features have also shown differences between the term “well” general population pregnancies and high autism-risk pregnancies (subsequent pregnancies of mothers that already have children with autism diagnosis). The chorionic surface vessels of 89 pregnancies from the high autism-risk Early Autism Risk Longitudinal Investigation (EARLI) cohort, in general, had fewer branch points, thicker and less tortuous arteries, better extension to the surface boundary, and smaller branch angles as compared to 201 pregnancies from the general population-based National Children’s Study.

Another approach to evaluate the spatial distribution and development across the gestation of placental surface vasculature is to employ Voronoi diagrams. A Voronoi diagram is a partition of a plane into regions close to each of a given set of objects [41]. In the simplest case, these objects are just finitely multiple points in the plane (called seeds, sites, or generators). For each seed, there is a corresponding region, called a Voronoi cell, consisting of all points of the plane closer to that seed than to any other. Voronoi diagrams have practical and theoretical applications in various fields, primarily science and technology [42, 43]. We compared the surface vascular spatial distribution of the high autism-risk EARLI cohort and the general population-based National Children’s Study cohort by dividing the chorionic plate area into Voronoi cells. The Voronoi cells were computed by choosing the midpoints of placental surface vascular branches as Voronoi seeds. The histograms of Voronoi cell areas were plotted, and it was found that the scaled distributions of Voronoi cell areas in the two cohorts collapsed into a single distribution, but the EARLI cohort showed a lower branching density [44]. The fact that both the cohorts showed similar spatial distribution of the surface vessels could indicate that the overall mechanism for the formation and development of the vasculature is the same in normal and high autism-risk pregnancies, but is less active in the high autism-risk pregnancies, yielding a lower branching density.

The fractal nature of the chorionic plate vessels is thought to be important for multiple reasons. Not only does it help to increase the surface area of the vessel, allowing for a more efficient gas exchange between the fetus and the mother, but it also helps distribute the blood optimally and protects the vessels from injury. Deviations of placental vasculature from their standard fractal nature can help to identify potential pathological outcomes and also understand the underlying mechanisms across the gestation that potentially influence the child health outcome.

2.3 Placental shape: 2D fractal models

An average delivered human placenta is more or less round, with a centrally inserted umbilical cord and has a relatively uniform thickness. However, a fair number of placentas are irregularly shaped [45] and can be classified into several well-defined geometrical patterns (Figure 3). This is not true for our “permanent” organs (heart, lungs, etc.), which have standard shapes, and any deviations result in obvious dysfunction. In the National Collaborative Perinatal Project data, irregular placental shapes were associated with lower BW for placental weight, suggesting variably shaped placentas have altered function. The traditional measurements of placental shape in terms of major and minor axes and average placental thickness are highly subjective. Technological advances have made it exceedingly easy to capture a simple photograph of the placenta with a unit distance marker such as a ruler (Figure 3). Such photographs have allowed precise measurements of placental shape (deviation from roundness), cord eccentricity (how central or noncentral the umbilical cord insertion is), area, perimeter, and so on. [16]. Placental efficiency has been suggested to be affected by patterns of placental growth, specifically, the relationship between chorionic plate area and disk thickness [16, 34, 46, 47].

Figure 3.

Multiple shapes of the human placenta. The left column shows round/oval-shaped placentas, the middle column shows star-shaped placentas, and the right column shows multilobed placentas. Adapted from [46].

Empirical models based on diffusion-limited aggregation have suggested specific shape variations to have their origins at distinct periods in gestation (Figure 4) [46, 49]. These models have also accounted for multilobed and star-shaped placentas (two of the most common patterns of abnormally shaped placentas). Also, they have provided empirical evidence that the shape of the placenta does reflect the underlying vascular fractal; deviations from the umbilical cord insertion are associated with reduced placental functional efficiency. These deviations are contemplated to reflect placental compensations responding to stressors or variability in the intrauterine environment. Studies have also shown that chorionic plate measures by ultrasound at 11–14 weeks are significantly correlated with similar features observed at term [49]. Thus, these shape measures can provide insights into the impacts of intrauterine environmental influences at different gestational points that lead up to the “final” placenta at delivery and help study their temporal and collective impacts on the child’s health.

Figure 4.

Varieties of placental shape abnormalities and time of origin, based on empirical modeling of fractal growth. Source: [48].

Digital photographs of the fetal placenta surface and the sliced placental disk from 129 high autism-risk newborns in the EARLI cohort and 267 newborns in the National Children’s Study Vanguard pilot were analyzed to extract comparable measures of placental chorionic surface shape, umbilical cord displacement, and disk thickness [50]. Placental thickness measures were moderately higher in high autism-risk cases. The placentas of high autism-risk pregnancies were also rounder and more regular in perimeter than general population placentas. This data were in line with the evidence presented from a small nested case-control comparison of 52 autism cases and 161 controls from the Avon Longitudinal Study of Parents and Children general population pregnancy cohort study, which showed that children who would receive an autism diagnosis had reduced cord insertion eccentricity and reduced villous branching growth as compared to their sex and gestational age-matched peers [51]. Reduced placental shape variability observed in high ASD-risk siblings compared to low-risk controls may indicate a restricted ability to compensate for intrauterine changes. In other words, the placentas of children with a high autism risk prefer a uniform intrauterine environment and do not respond effectively to any stressors, which could lead to a sub-optimal placenta and, by extension, a poor neurodevelopmental outcome.

2.4 Placental shape: 3D

While placental shape defined by the chorionic plate aspect ratio and placental thickness from slices of placenta have provided invaluable insights into the relations between placental shape and function, the placenta is a three-dimensional organ, and a 3D digital image may be more useful to understand the timing and cause of variations in placental shape. The 3D image can provide the overall placental volume and also help in visualizing and analyzing the spatial distribution of placental thickness—the primary dimension of placental growth in the third trimester [52]. Additionally, we can proxy time order in the placenta by assigning x, and y coordinates referencing the umbilical cord as the site of origin (0,0), with time order inferred from increasing distance from the umbilical cord (Figure 5).

Figure 5.

Fetal side of a placental 3D scan (left); thickness map of the placental 3D scan with thicker portions shown in red and thinner portions shown in green and blue (middle); polar map conversion of thickness map where the insertion point is along the x-axis and the y-axis demonstrates the radial growth in different directions over gestation (right).

Our group used a 3D surface scanner to scan 264 placentas from the National Children’s Study and 105 placentas from the high-autism EARLI cohort [53]. They computed placental volume and the maximum radius from the umbilical insertion point and volumes encompassed within each of the ten concentric circles with radii at each decile % of the maximum radius (Figure 6). Two slopes were then computed for placental volume distribution during two time periods: early placental growth (1–6 deciles) and late growth (7–10 deciles). The placental volume and its growth trajectory differed between normal and high autism-risk pregnancies. Early growth trajectory of high autism-risk placentas showed sex-dimorphism, indicating an underlying mechanism of placental growth that differentiates boys and girls, which may lead to a differential rate of autism diagnosis between them.

Figure 6.

Fetal side of a placental 3D scan (left); deciles drawn over thickness map of the placenta based on the maximum radius to determine volume growth over the gestation (right). Source: [53].

2.4.1 Spatial analysis of the placenta using geographical information system (GIS) theory

What the stand-alone 2D and 3D approaches lack is a true cohesive method to quantify the observed patterns/deviations in the placental structure at different scales and, by extension, explore the processes that may have generated the patterns/deviations. Spatial analysis helps define attributes in the context of their location and neighborhood and helps explore spatial patterns and relationships of data points, features, or regions in a given area. Geographical information system (GIS) provides the tools to capture, store, manipulate, analyze, and visualize spatial data. Apart from geographical applications such as studying land cover patterns and river trajectories [54, 55], spatial analysis has found biological applications such as identifying spatial patterns of neuronal activity, muscle fibers, and gene expression [56, 57, 58]. The fractal nature of GIS arises from the fact that spatial phenomena often exhibit self-similarity across multiple scales, and GIS is designed to represent and analyze such phenomena at different scales of analysis. One way to understand the fractal nature of GIS is to consider how it can be used to analyze land cover patterns. Land cover patterns, such as forests, grasslands, and urban areas, often exhibit fractal structures, with similar patterns appearing at different scales of analysis. GIS can be used to capture and analyze these patterns at different scales, from the individual tree or building to the landscape or region as a whole.

GIS theory can be applied to study the placental topography from the placental 2D images and 3D scans. The placental topography can be compared to a country or state’s landscape, while the placental vasculature compares to river networks. In typical GIS mapping, exposures such as air pollution are assigned to geographic sites (a county or region); site, exposure, and even change over time can be considered jointly in analysis. We can similarly map the placental chorionic plate as sets of x and y coordinates, with assigned local attributes such as disk thickness, and distance to the nearest surface vessel or branch points. This approach promises to greatly improve our ability to model the placenta in fetal origins research.

Implementing GIS broadly involves three steps:

1. define the spatial entity: We first need to define the spatial unit on which the analysis is to be conducted. The placental topography can be divided into units (akin to counties on a state map). The placental 3D image can be divided based on a raster (i.e., divide a map into equal squares and check adjoining squares, or it can be divided in a biological context e.g., registering the 2D surface vessels on the 3D image and using chorionic surface arterial branch points as Voronoi seeds and dividing the placenta into Voronoi cells) (Figure 7)

2. define the neighborhood: Spatial analysis helps to explore patterns and relationships of attributes in the context of its location and neighborhood; for example, how does mean income compare in the tri-state area? Once the spatial entity is established, it is important to figure out the neighbors with whom the attribute value is to be compared (Figure 8). One option is to consider all the neighbors with adjoining Voronoi cell borders. Another option is to select all Voronoi cells within a particular radial band (e.g., 2 cm, 5 cm). A third option is to select a fixed neighbor of nearest neighbors (e.g., 2, 3 or 4 nearest neighbors).

3. using a spatial analysis statistic to compute the spatial distribution: Moran’s I is the most commonly used spatial autocorrelation measure [59]. Like other correlation coefficients, Moran’s I ranges between −1 and 1. Autocorrelation is high when neighboring physical sites share similar attributes and low when there is variability in those attributes. Moran’s I can therefore provide indices of placental structural simplicity or uniformity (reflected in positive Moran’s I and high autocorrelation) or their structural complexity or variability (represented variably by patterns of positive or negative Moran’s I, in either or both global and local autocorrelation) (Figure 9). Thus, a range of Moran’s I capture complex aspects of placental topography and thereby provide an important window into understanding the intrauterine environment across gestation.

Figure 7.

Dividing placental topography. a) 3D placental thickness map, b) 2D surface vessel tracing, c) registered output of 2D vessels overlaid on the 3D thickness map, d) division of placental surface into Voronoi cells by using the branch points as Voronoi seeds.

Figure 8.

Neighborhood selection for GIS-mapping of the placenta (blue cell is the Voronoi cell of interest). All adjacent neighbors that share a boundary, as shown by green cells (left), k-nearest neighbors (middle), neighbors determined by radial distance (right).

Figure 9.

Different patterns of placental thickness distribution. a) Uniform thickness distribution will have high Moran’s I for near and distant neighbors, b) clustered thickness distribution will have high Moran’s I for near neighbors and lower Moran’s I for distant neighbors, c) patches or starfish-like pattern will have lower Moran’s I for near neighbors and higher Moran’s I for distant neighbors, d) random thickness distribution will have lower Moran’s I for both near and distant neighbors.

Since the placenta grows outward from the umbilical insertion point across the gestation, GIS also allows for analysis of rates of change of placental features over time. Combining loci with attributes related to cord insertion, the placenta can be modeled in its full spatial and temporal context. Under the NIH’s Environmental influences on Child Health Outcomes (ECHO) program, we are currently developing GIS-based models of the placenta to study if prenatal stressors (maternal depression and stress) impact child well-being and neurodevelopment via the mediating effects of the placenta.

2.5 Villous spatial distribution

Terminal villi are the tips of the chorionic villi that have matured to have a thin trophoblast epithelium, which is in direct contact with the maternal intervillous blood and cores of villous stroma, including capillaries, fibroblasts, and Hofbauer cells, the placenta’s resident immune cell. These terminal villi are the surface area for the exchange of nutrients, oxygen, and waste products between the mother and fetus.

The marked variation in the appearance of the villi has been well appreciated irrespective of the placental size. The variation in villous distribution (measured as both packing density and lacunarity) has been demonstrated to impact the placental efficiency [60]. This histologic variation is likely associated with the high capacity of the placenta for genetic variation, in terms of chromosomal mosaicism and epigenetic variation (in terms of DNA methylation). PW depends on villous histology, including both villous structure and spatial distribution. Morphometric assessment of placental mature villi in healthy, smoking and non-smoking women demonstrated that the fractal dimension increased with the number of cigarettes smoked per day [28]. Another study computed the fractal dimension of villi from placental histology slides of different grades of distal villous hypoplasia (a correlate of fetal growth restriction) and compared them to the average grading of expert pathologists. The fractal dimension decreased as the grade of distal villus hypoplasia increased and showed a fair correlation with the experts’ grades [29]. Thus, the fractal dimension helps to capture the variation in the structural and spatial distribution of the placental villi that may be a result of exposures such as smoking during pregnancy or due to an underlying pathological condition.

The fractal nature of the placental villi is thought to be an adaptation that maximizes the exchange of materials between the mother and fetus, allowing for an efficient transfer of nutrients and oxygen to support fetal growth and development. A quantitative assessment of the spatial distribution of placental villi and their fractal properties can help distinguish sub-optimal systems that lead to poor pregnancy outcomes.

3. Discussion

The placenta has been shown to have a fractal nature at different scales. This has been observed in the allometric scaling of its weight and infant BW, its macroscopic shape and surface vasculature, and its microscopic villi shape and distribution. Fractal analysis of the placenta at these various scales can provide an improved understanding of the pregnancy and also help early identification of potential risk factors.

The allometric scaling relationship between the fetal and placental weights can help identify sub-optimal placentas. The fact that the allometric scaling holds true for both singleton and twin pregnancies demonstrates that all pregnancies could be governed by the same underlying capacity. The cord insertion and underlying vasculature influence the placental growth early in gestation and can determine the overall placental shape at delivery. The rate of placental growth and function varies across gestation and can be captured with the 3D placental volume trajectories going out from the umbilical cord insertion. The fractal nature of the plate and its vasculature is highly influenced by the intrauterine exposures and gives a glimpse into the placental growth and its effort in trying to reach the optimal morphology and function across the gestation. Deviations of this fractality could be used as early markers of potentially risky pregnancy outcomes. The sexual dimorphism of neurodevelopmental outcomes such as autism is also captured by the placental shape and vasculature fractality and could be used as early biomarkers to identify the risk of such outcomes and develop early intervention plans to help the child and family. The microscopic villi, which are the functional units of the placenta, are routinely captured by pathologists on a regular histology slide. The fractal dimensions of these villi have been observed to vary with poor pregnancy outcomes and could be an invaluable quantification tool to complement the histopathological evaluation of pathologists. Studying the spatial distribution and the growth trajectory of the placenta by combining the chorionic plate vasculature data with the 3D shape of the placenta can provide a great model for examining the placental growth in the context of the intrauterine environment across gestation.

Thus, investigating the fractal nature of the placenta at different scales can illuminate the mechanisms of its growth and function and also helps to identify early risks of poor pregnancy outcomes.

4. Conclusion

The placenta is a complex and highly organized structure that facilitates the exchange of nutrients and waste between the mother and fetus. By studying its fractal nature, we can gain a better understanding of its branching patterns and organization at different scales. This knowledge can help us identify potential abnormalities and develop new treatments for placental disorders. Research has shown that the fractal dimension of the placenta is related to fetal growth and BW. By analyzing the fractal properties of the placenta early in pregnancy, we may be able to predict the risk of adverse pregnancy outcomes, such as preterm birth or fetal growth restriction. Fractal analysis can be used to develop new imaging techniques that can provide detailed information about placental structure and function. For example, researchers can use fractal analysis to create three-dimensional models of the placenta that can be used for virtual reality simulations and surgical planning. The placenta is quintessential for fetal development. By understanding the fractal nature of the placenta, we may be able to gain a better understanding of how the placenta develops and functions over time, which could lead to new insights into fetal development.

Overall, studying the fractal nature of the placenta can provide valuable insights into its structure, function, and development and may ultimately lead to new treatments for placental disorders and better pregnancy outcomes.

Acknowledgments

The GIS-based method developed to study the placental topography that is reported in this chapter was supported by the Environmental influences on Child Health Outcomes (ECHO) Program, Opportunity and Infrastructure Fund Award Number U2COD023375.

Conflict of interest

The authors declare no conflict of interest.