The LMSR method for providing a multidimensional understanding of growth standard in human fetuses.

A new nonlinear multivariate regression method called the LMSR method is proposed, by which a multidimensional understanding for the development process of human fetuses can be provided. Statistically important quantities such as median, skewness, coefficient of variation, and correlation of underlying structure can be described by corresponding smooth curves. Those curves can be obtained by a fine combination of a multivariate power transformation of data and penalized likelihood. It will be shown that the LMSR method and some associated tools are clearly efficient in analyzing development process of human fetuses.

Statistical analysis with dilatation for development process of human fetuses.

This paper is concerned with the development process of human fetuses. Though the development process of human fetuses still includes many unknown issues, it is known that a certain harmonious relationship between the organs can be observed. This knowledge is based on our intuition, but we have no theory which clarifies these harmonized developments. The paper aims to give a mathematical understanding of the notion of harmonized development through the use of dilatation, which is a measure of the departure from conformal mapping. The asymptotics for dilatation have been developed using certain efficient models of quasiconformal mapping. The proposed method of dilatation is effectively applied to the human fetus data.

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

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.

Analysis of the harmonized growth pattern of fetal organs by multidimensional scaling and hierarchical clustering.

The development of an organ may be affected by various growth and differentiation factors released from other organs. These factors are believed to have important effects on the development of multiple organs. To detect and analyze harmonized development among multiple organs, similarities in growth patterns among fetal organs were examined using multivariate analysis. Ninety human fetuses obtained from the Kyoto Collection of Human Embryos were dissected. Harmonized development of organs was evaluated by multidimensional scaling and cluster analysis using measurements (length, width, height, and weight) of the fetal organs. Similar growth patterns were observed between the brain, including cerebrum, diencephalon, and midbrain (cerebrum-to-midbrain [Cer-Mid]), and pituitary (crown-rump length [CRL] 95-155 mm). Further, similar growth patterns were observed between the liver and Cer-Mid and cerebellum (Cb; CRL 156-202 mm), and between Cer-Mid and Cb (CRL 203-253 mm). Similarities in growth patterns were also observed between right and left lungs (CRL 99-235 mm) and between the aorta and heart (CRL 139-187 mm), but not between the lung and pulmonary trunk. These findings revealed synchronized development among fetal organs and suggested a functional and structural relationship among different organs in the prenatal period. These relationships include the existence of common factors in organ development, such as cross-talk mediated by humoral factors, and the presence of an anatomical and functional relationship in the fetal circulatory system.

Dimension selection for feature selection and dimension reduction with principal and independent component analysis.

This letter is concerned with the problem of selecting the best or most informative dimension for dimension reduction and feature extraction in high-dimensional data. The dimension of the data is reduced by principal component analysis; subsequent application of independent component analysis to the principal component scores determines the most nongaussian directions in the lower-dimensional space. A criterion for choosing the optimal dimension based on bias-adjusted skewness and kurtosis is proposed. This new dimension selector is applied to real data sets and compared to existing methods. Simulation studies for a range of densities show that the proposed method performs well and is more appropriate for nongaussian data than existing methods.