Statistical analyses in trials for the comprehensive understanding of organogenesis and histogenesis in humans and mice

Abstract

Statistical analyses based on the quantitative data from real multicellular organisms are useful as inductive-type studies to analyse complex morphogenetic events in addition to deductive-type analyses using mathematical models. Here, we introduce several of our trials for the statistical analysis of organogenesis and histogenesis of human and mouse embryos and foetuses. Multidimensional scaling has been applied to prove the existence and examine the mode of interkinetic nuclear migration, a regulatory mechanism of stem cell proliferation/differentiation in epithelial tubular tissues. Several statistical methods were used on morphometric data from human foetuses to establish the multidimensional standard growth curve and to describe the relation among the developing organs and body parts. Although the results are still limited, we show that these analyses are not only useful to understand the normal and abnormal morphogenesis in humans and mice but also to provide clues that could correlate aspects of prenatal developmental events with postnatal diseases.

For the analysis of complex morphogenetic events in multicellular organisms, various mathematical methods have been introduced. A reaction-diffusion model for biological pattern formation (1), models of lung branching morphogenesis (2), and vertex cell models for multicellular morphogenesis of successive self-construction of cells such as that in the formation of mammalian blastocysts (3) are among successful examples. These model-based studies are categorized as deductive-type mathematical analyses for understanding the developmental events in multicellular organism. While these models are used to explain natural morphogenetic events, they are theoretically generated and must be further modified before they can be matched with events in real organisms. Statistical analyses are another oppositely directed inductive-type of mathematical analyses based on the detailed quantitative data from real organisms. There are numerous studies on the simple correlation between two variables, such as those regarding the standard body and organ growth curves, and studies in developmental neurology such as those dealing with regional neuron numbers. However, fewer statistical studies have examined the complex morphogenesis in the developmental biology of humans, mice or other animals. This appears to be mainly due to a paucity of accurate and detailed quantitative morphogenetic data from the real multicellular organisms, such as the total and regional numbers, shape and three-dimensional (3D) arrangement of cells in the organs, or measurement of diameters of different organs or body parts, on which statistics can be performed.

We have been studying the development of human and mouse embryos and foetuses from the ultrastructure to macroscopic levels using various methods, including mathematical analyses. In the mathematical analyses, we have mainly used statistical methods based on the quantitative data obtained from human and mouse embryos and foetuses. In this review, we will first introduce the application of multidimensional scaling (MDS), a statistical analysis method, at the cellular level in a trial to prove the existence of and analyse the detailed modes of interkinetic nuclear migration (INM), a regulatory mechanism of stem cell proliferation and differentiation originally found in the neural epithelium, in the other epithelial tubular structures throughout the body. Then, we will extend our introduction of the trial to the application of mathematical analyses to studies on the macroscopic-level development of organs and body parts in human and mouse embryos and foetuses.

MDS for the Analysis of INM in the Epithelial Tubular Tissues in the Body

INM is an oscillatory nuclear movement linked with regulation of the cell cycle, proliferation and differentiation of stem cells in the epithelia. In INM, cell nuclei migrate along the apicobasal axis (AB axis) in synchrony with the cell cycle, forming a characteristic pseudostratified morphology (for review, see 4, 5). In the ventricular zone of the neuroepithelium, mitosis occurs at the apical surface, and then the nuclei migrate towards the basal side during G1 phase. After DNA synthesis there, the cell nuclei migrate back to the apical surface during G2 phase for the next cell cycle. Although INM was initially recognized in the developing neuroepithelium, later studies have reported INM or INM-like nuclear movement in various epithelia, not only those of ectoderm origin such as the lens and retinal epithelia (6), but also those of endoderm origin such as the liver bud (7) and intestinal (8, 9) epithelia, as well as the ureter, which is of mesoderm origin (9, 10).

INM in the neuroepithelium has been extensively analysed, initially using H³-thymidine autoradiography, then later by using immunohistochemistry for bromodeoxy-uridine (BrdU) and other nucleoside-analogues that are incorporated into the S phase nuclei (11), and more recently by advanced direct time-lapse video imaging of cultured epithelia (12). However, INM in the epithelia of endoderm origin or those of mesoderm origin had only been suggested based on the apical localization of mitotic figures and the roughly analysed changes in nuclear position (7, 8, 13). We therefore applied MDS, a statistical tool, to analyse in detail INM in the mouse embryonic endoderm-derived midgut epithelium as well as the mesoderm-derived ureteric epithelium, and described precise cyclic changes in the nuclear distribution using BrdU immunostaining data (for midgut, 9; for ureter, 9, 10).

MDS is a statistical tool used in information visualization to find similarities or dissimilarities among data sets in a large matrix. It has been applied to compare multivariate data sets such as genomic data sets, growth patterns in individual organs from foetuses, and large data sets obtained from functional magnetic resonance (MR) imaging (14, 15). Briefly, a set of data from each item is first computed as a distance matrix and then assigned to a location in n-dimensional space, in which the first dimension is the most important for representing the differences (16). In a previous study (9), pregnant mouse dams at embryonic day (E)11.5, E12.5 and E13.5 were injected with BrdU and sacrificed 1, 2, 4, 6, 8, 10 and 12 h later to collect embryos. Serial sections of the midgut epithelium were immunostained against BrdU. The positions of the BrdU (+) nuclei in the six layers (positions 1–6) along the AB axis were measured, and represented as a nuclear population (%) histogram at each time point. We assigned the nuclear distribution (histogram) data set, which contained six variables (portions 1–6) obtained from each time point, to a location in 2D space to compare the similarities of the histograms (Fig. 1). In the resultant 2D configuration, closer proximity between any two items in a graph is interpreted as greater similarity between them. We can thus interpret changes in the BrdU (+) nuclei distribution represented in the 2D graph during the time course as reflecting the chronological nuclear movement. A cyclic change in the distribution pattern of BrdU (+) nuclei is observed and is consistent with the existence of INM in the midgut (9). Although the pattern of nuclear distribution change in the ureter is different from that of the midgut and is not a closed circle (Fig. 1), we further confirmed in the following analyses that a cyclic change in the nuclear distribution pattern consistent with INM does exist not only in the ureteric epithelium, but also along the entire length of the intestine, oesophagus and trachea (10, Nitta, T. and Kaneda, R., unpublished observations).

Fig. 1.

Measurement of nuclear position in the epithelium and the MDS analysis, modified from Figs. 2, 4 in (9). (Upper left panel) The position of the nucleus corresponds to the relative distance between the nucleus and the basement membrane (BM). It is expressed as the ratio of the absolute distance of the center of the nucleus from the BM minus half-nuclear length (x) to its maximal value (y). (Upper right panel) Histograms of the labelled-nuclei population (%) at each time point (1–12 h post-injection, respectively) of E11.5/E12.5 midgut and E11.5 ureter. (Lower panel) 2D representation of nuclear distribution pattern of seven time points in E11.5/E12.5 midgut and E11.5 ureter analysed by MDS.

MDS analysis of the changes in the distribution pattern of labelled nuclei, when compared with direct time-lapse video imaging of the living tissue, is a laborious and indirect approach relying on fixed histological samples, but it nonetheless has some clear complementary merits over video imaging. First, the results from the MDS method reflect the genuine in vivo situation, even if they do so indirectly, whereas the current video-imaging only observes cultured tissue and cannot observe the genuine in vivo conditions. Second, while the data from current video imaging only represent the behaviour of individual, randomly selected nuclei, and thus cannot provide a global perspective of the entire epithelium, the MDS method can statistically analyse a large number of nuclei from the entire epithelium within the tissue. This makes it possible to detect, under genuine in vivo conditions, differences in the INM mode between different tissues, parts of organs, or developmental stages, as discussed below, as well as between normal and abnormal conditions such as gene-knockout or after drug treatment. In fact, in the midgut epithelium, modes of circular change in the nuclear distribution pattern were different between E11.5 and E12.5. The cell cycle was estimated to be 12 h at E11.5 and 10 h at E12.5 from the histogram patterns and the result of MDS study, and the basal-to-apical migration during the S/G2/M phase spanned up to 6 h on both dates, while the apical-to-basal migration during the G1 phase became shorter at E12.5. In addition, in the ureter, whole intestine, oesophagus and trachea, MDS studies revealed that the S/G2/M phase is constantly 6 h, while the G1 phase varies depending on the organ or gestational date (10, Nitta, T. and Kaneda R., unpublished observations).

In the pseudostratified ventricular epithelium of the mouse embryonic brain as deduced by detailed BrdU-labelling analyses (11), the cell cycle length increases from 8.1 to 18.4 h between E11 and E16. Although the S/G2/M/ phase remained constant for around 6 h, the G1 phase progressively increased from 3.2 h at E11 to 12.4 h at E16. These findings from different organs suggest both a similarity in S/G2/M phase length among these organs and a dissimilarity in the G1 phase, and further suggest a corresponding similarity and dissimilarity in the molecular mechanisms involved. Several different models of the molecular mechanisms of INM have been proposed based on data mainly from studies of the developing vertebrate brain or retina (for review, see 17). Microtubule-dynein motor and/or actomyosin systems have been suggested to operate in the basal-to-apical linear migration during the G2 phase. On the other hand, not only active autonomous models based on kinesin or actomyosin systems but also a passive stochastic or displacement mechanism by apically migrating G2 phase nuclei has been proposed for apical-to-basal G1 phase movement. In the epithelia of endoderm or mesoderm origin, the molecular mechanisms of INM remain almost totally unproved. MDS studies on the midgut as well as other epithelial tubular organs so far examined revealed that the INM modes and duration of the apical movement during G2/M phase are similar among these organs, suggesting that a similar basic mechanism is operative in each. On the other hand, in the case of basal movement during the G1 phase, differences were noted depending on the date and organs, suggesting that the molecular mechanisms were also different. This discrepancy between constant S/G2/M mode and variable G1 mode appeared against a simple passive displacement model of basally oriented nuclei by apically moving nuclei. Moreover, although in mice the apical nuclear movement is quicker than the basal movement, in ferrets the basal movement is quicker than the apical movement (18). Therefore, the molecular mechanisms of INM may differ or be modified depending on many conditions. These fine regulations of INM may make it possible to regulate precisely stem/progenitor cell generation, which in turn would regulate the number of daughter cells and the resultant regional size and shape of organs (for review, see 17, 19, 20). MDS analyses may thus be useful to detect differences in the mode and phase duration of INM and to use the corresponding differences as clues to verify the molecular mechanisms in operation.

Human Organogenesis and Histogenesis

We will next describe our trial to introduce mathematical methods into the analyses of human prenatal development at the macroscopic level, which is not only useful for understanding normal and abnormal human development, but also may suggest underlying molecular mechanisms. In humans, after implantation, three germ layers as well as body axes are formed in 3 weeks, and from ∼3 to 8 weeks after fertilization, dramatic morphogenesis of the overall shape of organs and external body structures occurs and tissue stem cells differentiate in each organ or body part of the embryo (organogenesis). Thereafter till some point either before birth or in early postnatal life depending on the organ, multiple types of organ-specific cells differentiate and are organized into elaborated tissues in the organs (Fig. 2), which eventually become functional (histogenesis). Embryonic development is characterized by dynamic and gross changes in the external appearance in accord with internal organogenesis, whereas foetal growth includes nearly parallel development of body parts. Therefore, embryonic development can be expressed by a qualitative description of external features to a better extent than foetal growth. However, quantitative information on body parts together with that on the whole body is indispensable for studying growth rates, developmental delays due to pathological causes, and comparisons with other mammalian species. While previous research has predominantly focused on normal versus abnormal organogenesis of organs, i.e. congenital malformation, histogenesis is directly connected with the function of organs, which continues till the end of life and therefore deserves much more attention (21).

Fig. 3.

Mathematical analyses at the macroscopic level. (A) Scatter plot of 3D data (x, y, z) = (spleen length, pancreas length, liver length) and 1D standard curve (solid line) in 3D space for the growth process of (x, y, z) in 3D space. (B) Conformal transformation of the upper limb image. A left image of the upper limb was transformed into a right image by Möbius transformation, which is described as follows:

$$M_{(z)}=\frac{az+b}{cz+d}$$

where z is a complex variable, and a, b, c, d are complex constants. Here, a, b, c, d are 10 + i, 17, 4 + i and 5i, respectively. Cross-ratio is invariant between two images. p, p′: Acromiale, q, q′: Lateral epcondyle, r, r′: Stylion, s, s′: Dactylion.

Fig. 2.

Histogenesis of the human kidney (A) and pancreas (B), and large individual variations in the size of the human foetal pancreas (C and D) (21). (A) At 3 months of gestation, newly formed glomeruli are observed, and at 5 through 7 months, the number of layers of the glomeruli increases in the cortex, while the medulla, which consists of renal tubules, elongates. In the magnified view of the cortex at 7 months (right-most panel), the glomeruli in deeper layers that were formed earlier became larger than those in the layers closer to the surface that were more newly formed. (B) At 3 months, only branching pancreatic ducts are observed, while at 5 through 7 months the exocrine acini as well as islet anlages start to develop. (C) Scatter plot of the weight of the pancreas versus CRL. Note that there are wide variations in the pancreas weight in the similarly sized foetuses. (D) Two pancreases from the two foetuses with CRL 165 mm (upper) and 167 mm (lower) are shown. The pancreas weights are 0.165 g (upper) and 0.322 g (lower), and the total volumes of islets are 0.25 mm³ (upper) and 1.29 mm³ (lower), as deduced by stereology of serial sections. CRL: crown-rump length. Ms: months of gestation. Scale bars: 200 µm (A), 50 µm (B); Arrows: glomerulus (A), islet (B).

There have been numerous morphometric studies on human foetal growth, and these have tended to employ large numbers of specimens to obtain not only direct post-partum measurements from an embryological or anthropological standpoint, but also in utero real-time measurements using ultrasonography from an obstetric standpoint for diagnostic purposes (22; for earlier references, see 23). However, most of these studies have dealt with whole-body dimensions such as crown-rump length (CRL) or body weight in addition to a limited number of organ diameters (22, 24). Compared to studies on foetuses, those on human embryonic development have been fewer in number, have used smaller numbers of embryos—not infrequently from mothers with pathological conditions—and in almost all cases examined only whole-body dimensions (for review, see 23). It has thus been impossible to perform statistical analysis on human embryonic development except in relation to systemic growth.

We have been studying human prenatal development using a large number of embryos and foetuses obtained through legal and ethical procedures from artificial abortions undergone by mainly healthy Japanese mothers (Kyoto Collection) (23, 25–27). Therefore, these embryos and foetuses can be considered to be representative of the normal Japanese population during the prenatal period. We obtained morphometric data on many measurements of the external features and organs of the human foetuses by either direct observation or dissection, as well as by using three-dimensionally reconstructed MR images (21, 26). As for the embryos, using a large number of fixed externally normal human embryos, we determined the axes, measuring landmarks, and measurements of various parts of the embryo as well as the whole body, and established a standard value for each measurement during the embryonic period (23). Based on these morphometric data, we have been performing mathematical analysis of the development of human embryos and foetuses, trying to establish multidimensional standards of development of organs and to elucidate the ‘rules’, if any, that control or harmonize the organogenesis and histogenesis of multiple organs.

Harmonized Development of Organs and Body Parts in Human Development

Various statistical and mathematical methods have been used to draw a precise standard growth curve for the whole body and organs during human development, because reliable standard growth curves can be applied to both clinical diagnosis and early intervention in diseases. In addition, numerous single or multiple regression models have been proposed to reveal the correlation between pairs of variables, such as CRL and lung volume (28), or to predict an unknown dependent variable using known variables, e.g. ultrasonographic estimation of foetal body weight from the biparietal diameter, or estimation of femur length and abdominal circumference using a polynomial function (29). However, because of the complexity in the multidimensional analysis, the relationship among multiple organs in development has not been examined in detail, although organs may affect the development of other organs in a manner mediated through humoral or neural factors, or physically through contact in the limited space.

MDS for the Analysis of Synchronous Growth of Human Organs

We therefore examined similarities in growth patterns among foetal organs using multivariate analysis and tried to detect and analyse harmonized development among multiple organs (14). As described above, the MDS method visualizes the similarities between different datasets in a large matrix into a 2D or 3D scatter diagram, and therefore MDS is one of appropriate methods for analysing the harmonic development of multiple organs by analysing the synchrony of their growth. Using this technique, we showed the harmonized development of lungs and spleen in the human foetus, and predicted that an interaction or common growth factors related to both organ developments may exist (15). Recently, Li et al. (30) suggested that the Jumonji domain containing-3 (Jmjd3) gene, which is a histone demethylase, plays an important role in the prenatal development of both the lung and spleen, based on their observation of a smaller lung and spleen in Jmjd3-knockout mice compared to wild-type mice.

We thus utilized MDS at both cell/tissue level for the analysis of INM and at macroscopic level for the analysis of possible harmonized development of organs. We next introduce our trial to use other mathematical methods to analyse organ development in humans and animals at macroscopic level.

Multidimensional Standard Curve for Human Foetal Organs

In another paper, we proposed an efficient method by which to find a multidimensional standard curve for the development process of human foetal organs (Fig. 3A). The proposed method also identifies an approximate prediction region, which can be efficiently applied to diagnose foetal malformation (31). While the 2D standard curve only shows the relation between one organ and the whole body, the multidimensional standard curve is useful to examine the mutual relationship among the growth patterns of multiple organs. We applied the following logistic function to draw a 1D growth curve in multidimensional space because of its simplicity of the estimation of parameters:

$$f\left(t\text{|}\mu ,\beta ,\gamma \right)=\frac{\gamma }{1+\text{exp}\left(-\left(\mu +\beta t\right)\right)},\hspace{0.5em}0\le t<\infty ,$$

where the parameter µ denotes the location of the curve, β is the parameter that controls how rapidly the curve increases, and γ > 0 is the parameter of the upper bound that the curve approaches as t increases. If CRL is used as a time variable, t, instead of foetal age, and the organ size or weight is denoted as a p-dimensional variable, z, the following nonlinear regression model can be considered:

$$z_i=f_i+{\epsilon }_i,\hspace{0.5em}i=1,\hspace{0.5em}\dots ,\hspace{0.5em}N,$$

where $z_i={\left[z_{i1}\dots z_{ip}\right]}^T,\hspace{0.5em}{f}_i={\left[f_1(t_i)\dots f_p(t_i)\right]}^T$, $f_j\left(t\right)=f\left(t\text{|}{\mu }_j,{\beta }_j,{\gamma }_j\right)\left(j=1,\dots ,\hspace{0.5em}p\right)$, and ${\epsilon }_1,\dots ,\hspace{0.5em}{\epsilon }_n$ are i.i.d. p-dimensional random vectors with zero mean and finite covariance.

The following estimated regression function is constructed as a 1D curve for foetal organ development in p-dimensional space:

$$f\left(t\text{|}\widehat{\theta }\right)={\left[f_1\left(t\text{|}{\widehat{\theta }}_1\right)\dots f_p\left(t\text{|}{\widehat{\theta }}_p\right)\right]}^T$$

where $\widehat{\theta }$ is maximum likelihood estimators of $\theta =\left[{\theta }_1^T\dots {\theta }_p^T\right]$ when the parameter vector is denoted as ${\theta }_j={\left[{\mu }_j{\beta }_j{\gamma }_j\right]}^T$ (j = 1,2,…, p). We call this $f\left(t\text{|}\widehat{\theta }\right)$ the multidimensional standard curve for development of the foetal organ expressed by the variable z.

The confidence and prediction ellipsoids can be obtained in p-dimensional space regarding the standard growth curve instead of the confidence interval in n-dimensional space to examine whether or not a new data is within normal range. When we have a new data $[(t,\text{z})=\left(t,z_1,z_2\right)=\left(\text{CRL, Chest circumference, Arm length}\right)]$ for p = 2, which is inside the prediction interval in the univariate plot, it may be outside of the prediction ellipsoid made from $f\left(t\text{|}\widehat{\theta }\right)$ (31). This result suggests that a multidimensional standard curve is more sensitive to disturbances in development than a conventional univariate standard curve. The multidimensional standard curve may detect the disturbance of the growth balance of multiple organs, which leads to the predisposition of postnatal diseases, and the early intervention could be undertaken during pregnancy to prevent those diseases.

Conformal and Quasiconformal Mapping for Analyses of the Growth Balance Among the Body Parts

Petukhov reported on the cross-ratio invariance among body parts, such as the phalanges, during human development (32). For four arbitrary landmarks (p, q, r, s), the cross-ratio for (p, q, r, s) is defined as follows:

$$CR\left(p,\hspace{0.5em}q,\hspace{0.5em}r,\hspace{0.5em}s\right)=\frac{|p-r|·|q-s|}{|q-r|·|p-s|}$$

When (p, q, r, s) are (Acromiale, Radiale, Stylion, Dactylion), this equation is described as follows:

$$\frac{|\text{upper arm plus forearm length}|·|\text{forearm plus hand length}|}{|\text{forearm length}|·|\text{total length of upper limb}|}.$$

The cross-ratio is invariant if a Möbius transformation, which is one of the conformal transformations, maps (p, q, r, s) into (p′, q′, r′, s′), while there exists a Möbius transformation which maps (p, q, r, s) into (p′, q′, r′, s′) if the cross-ratio is invariant (Fig. 3B). Hence, if the cross-ratio using landmarks p, q, r, s is invariant between the foetus and adult, the growth of the upper limb can be described by Möbius mapping.

Cross-ratios were examined in the upper limb, lower limb, and trunk during development, but the cross-ratios in many parts were variable with growth, suggesting that the developmental course of the growth balance among the body parts cannot be described by a Möbius transformation in most cases (33). However, this course could be successfully approximated by means of a simple linear or trigonometric function when the cross-ratio was used as a variable (33). We used five variables to develop a ‘triple-ratio’ that was invariant by a Möbius transformation, and indicated that it is possible to extend this ratio into more dimensions than five (33). A series of cross- and triple-ratios can be useful for the multivariate analysis of morphological growth.

As a related research, the harmonized development of foetuses can be evaluated using ‘dilatation’ which is a measure of the discrepancy from a conformal map (34). Using dilatation, a harmonious development could be extracted in the relation between the cerebrum and liver, and between the spleen and kidney.

Quantification of the Change in the Morphological Structures

Thin-plate spline and Procrustes distance

The thin-plate spline function is applied to examine morphological changes. In this method, multiple landmarks on one object are specified and the minimum bending energy (BE) is calculated when this object is transformed into another object so that the landmarks are overlaid. BE is calculated at a coordinate (x, y) on the plate by the following equation (35):

$$\text{BE}\left(x,y\right)=\left(\frac{{\text{d}}^{2}U}{\text{d}{x}^2}\right)+2\left(\frac{{\text{d}}^{2}U}{\text{d}x\text{d}y}\right)+\left(\frac{{\text{d}}^{2}U}{\text{d}{y}^2}\right).$$

The function U is the fundamental solution to the biharmonic equation which is described as $U\left(\text{r}\right)=-r^2\ln r^2$, where r is the distance between a pair of landmarks in the reference configuration.

Then, the total BE is given by

$$\mathrm{Total}\mathrm{BE}={\displaystyle \int }\left(\mathrm{BE}\left(x,y\right)\text{d}x\text{d}y\right)$$

To examine the deformation of 2D morphology in biological structures, the minimized total BE can be used as an index because the minimized BE represents the minimized curvature of the plate (35), therefore, the thin-plate spline can be useful to compare the morphological difference during organ development between two developmental stages or two individuals. A difference in mandible shape could be detected between Ror2-knockout and heterozygous or wild-type mice at E18.5 using BE, while BE revealed no difference between the Ror2 heterozygous and wild-type mice, which have similar morphology (36). The thin-plate spline is also used for registration between the medical images by selection of the landmarks, i.e. cross-modality registration of breast MRI and mammography (37), or histological and MR images of brain (37) or prostate (39).

Similarly, the Procrustes distance is the sum of the squared distances between corresponding landmarks on the images, and can be used to examine the shape difference by comparing the configurations of the landmarks between two structures (35, 36).

Discussion

Just as statistics are used in epidemiological studies to explore unknown relationships within large data sets on the body and diseases and to identify risk and preventive factors, we can use statistics in the analysis of complex morphogenetic events in multicellular organisms based on the quantitative data from real organisms in order to clarify the relationship or to induce the rule and principle among events. In this way, we show that MDS can be applied to prove the existence of INM and to detect, under genuine in vivo conditions, differences in the INM mode among multiple organs, between gestational dates, or between control and experimental conditions such as in wild-type versus genetically modified animals. Obtaining data on the nuclear distribution for MDS analysis is indeed laborious, which is one of the reasons why this type of statistical study has been less popular, especially since the development of time-lapse video imaging. However, whether at the level of the cell, organ, or individual organism, accurate quantitative data including total and regional cell numbers from real organisms are essential not only for inductive-type statistical analyses but also for deductive-type model-based analyses of morphogenesis, since without detailed accurate information of the target structure, neither a solid base for induction nor a clear goal for deduction can be set.

We have been using stereology not only in developmental neurology (40, 41) to elucidate the novel functions of humoral factors such as LIF and leptin in the histogenesis of the brain, but also to count total epithelial cell numbers along the whole intestinal length (Kuramoto, J., unpublished data) to examine the relation between the INM mode and resultant histological morphology at each site of the intestine. Stereology has been developed and applied to obtain accurate quantitative data with much less effort in biomedical research (42) including neurology (40, 41, 43) and developmental biology such as for the quantitative study of developing renal glomeluri (44). Stereology can be applied from the organ level to organelle level, because it estimates structural quantities by applying randomized geometrical probes to a specimen irrespective of the sample size (45). However, while stereology has been used to obtain quantitative data, there have been few statistical analyses exploring relations within the data stereology generates. Furthermore, real 3D morphology of the target structure per se may not have been accurately understood due to the limitations imposed on the observation methods. For example, the intestinal epithelium and other epithelial tubular structures in the embryo have long been considered as stratified based on light microscopic observation of the sections, although we reported the epithelia of stomach and intestine as single pseudostratified based on scanning and transmission electron microscopic combined with light microscopic observations (46, 47). Only recently, these embryonic tubular epithelia have been widely acknowledged to be pseudostratified single columnar (8), which is the basis of INM, an oscillatory nuclear movement along the AB axis of the single epithelium. Thus, both the correct observation and accurate quantitative data are indispensable to understand the real morphogenetic events.

We are also trying to establish a multidimensional standard and to analyse the ‘harmonized’ development of organs and body parts using statistical methods. The results should be useful not only for better understanding of the organogenesis and histogenesis but also for early and more accurate diagnosis of deviations from the standard. Furthermore, from morphometric analysis of the foetuses in the Kyoto Collection, we have detected large variation in the sizes of the organs in human foetuses of similar body sizes (21, 26). In the brain and sensory organs, various functional disorders occur as a result of localized defects during histogenesis, because their histological structures are highly specialized in a region-specific manner. On the other hand, in the case of other so-called solid organs such as the liver, kidney, pancreas and lung, which consist of a large number of structural-functional units of similar size and function, such as nephrons in the kidney, the organ size is basically proportional to the total number of units and thus to the total organ function, which comprises the regular function required for ordinary life and the reserve needed for extraordinary situations (21). Therefore, the size and total functional capacity of the organ may be related to the individual’s predisposition to organ-based diseases in later life (21, 48, 49). The Developmental Origins of Health and Disease (DOHaD) hypothesis posits that the incidence of certain adult diseases is linked to prenatal development under malnutrition; DOHaD was put forward based on retrospective cohort studies and extensive studies using animal models (50, 51). Epigenetic modifications to DNA and related proteins have been suggested to be involved in the mechanisms (52). However, diseases in adults are mostly due to functional disturbance in various individual combinations of organs, whereas the above-mentioned epigenetic and other metabolic/physiologic mechanisms are general and systemic and thus have not yet been successfully correlated with concrete and individual patterns of organ dysfunction (21, 53). Our working hypothesis is that individual variations in the sizes of multiple organs, which reflect the total functional capacity of each organ, are generated at the end of histogenesis and play a role as the individual predisposition in the life-long function of the organs, and thus an additional mechanism to the above-described metabolic ones to produce individually variable patterns in the developmental origins of postnatal health and disease (21). Congenital anomalies, structural and functional defects which exist at the time of birth, can be largely categorized into congenital malformations characterized by macroscopic abnormalities and those without apparent macroscopic abnormalities. The second group of congenital anomalies is characterized by abnormalities at the microscopic level and by disturbed organ-specific function. These first and second types of anomalies are caused by disturbed development during the organogenesis and histogenesis, respectively (21). While there has been extensive study of congenital defects in the central nervous system and sensory organ systems at the histological and/or functional levels because of their regional specificities and thus high sensitivity to deficits, much less attention has been paid to the histogenesis of other solid organs as causative factors of diseases or dysfunctions. What, then, is the multidimensional standard of foetal organ development, and how are the sizes of multiple organs related with each other, and is the ‘harmony’, if any, compatible with the rapid changes in our living environments? Our understanding of the molecular mechanisms at the localized area of histogenesis of each organ has been dramatically advanced in recent years. However, the possible relations among the different and remote organs and the genetic and environmental control mechanisms that determine the total number of functional units of organs remain mostly unknown, or more correctly, unaddressed so far as ‘unnoticed congenital anomalies’ (21). By applying statistics on morphometric data from large number of specimens of the Kyoto Collection, we are trying to answer or to collect clues to answer these questions. In addition to statistical analyses on the macroscopic and microscopic quantitative data, the possible relation between INM and the organogenesis and histogenesis of the organ needs to be explored by experimental studies, because INM is the mechanism of stem/progenitor cell proliferation/differentiation to produce and control the number and types of daughter cells that eventually determine the size, shape, and function of each organ.