Analytical morphometry of sagittal fronto-facial profiles of 2nd-6th month human foetus

A prominent problem in the morphological study of developing biological structures is shape parametrization with the aim to evaluate transformations in a non subjective way. We carried out an analytical morphometrical study on a series of human embryos, by means of the S.A.M. (Shape Analytical Morphometry) software package. After standardization and normalization of the fronto-facial sagittal profiles, the analytical procedures applied were: 1) Fourier analysis: each profile was considered as an irregular but periodic function obtained by the sum of sinusoids of increasing order. 2) Shape Asymmetry Evaluation: couples of profiles are compared by means of "Janus" procedure; by a parabolic fitting we obtained parameters able to evaluate allometric and isometric differences between the two profiles. The preliminary results of the applied procedures indicated that rate and direction of allometric and isometric growth are not constant during the time.     

Nuclear morphometry and estrogen receptors in infiltrating ductal carcinoma of the breast

In this study ten cases of breast infiltrating ductal carcinoma have been considered. In all of them the content of ER has been evaluated by using monoclonal antibodies. Five of them were ER positive and five were ER negative. For the morphometric study ten nuclei of each case have been considered. By using the S.A.M. (Shape Analytical Morphometry) work-station an analytical study of the nuclear shape was performed. The first step was the extraction of fundamental shape which describes the basic shape of original contour without its irregularities. It was obtained by using two parametric equations. The second step was the evaluation of shape asymmetry by S.A.E. (Shape Asymmetry Evaluator). Finally the contour irregularities were evaluated by Fourier analysis. Along with analytical parameters, dimensions (area, perimeter and maximum diameter) were considered too. All obtained data were submitted to univariate statistical analysis (Student's T test) to compare the two groups (ER positive and ER negative tumors). Area, perimeter and maximum diameter were significatively greater in ER negative cases while analytical parameters were not discriminant between the two groups.     

Spreading of cells on various substrates evaluated by fourier analysis of shape

Summary In order to evaluate in mathematical terms the morphological changes occurring in the course of cell spreading, Fourier analysis of shape was applied. Human urothelial Hu 961 b cells plated on type IV collagen, fibronectin, laminin, glass and bovine serum albumine (BSA) were studied. Fourier parameters describing cell shape as well as surface areas covered by the cells on the substrate were subjected to statistical analysis. Using analysis of variance and discriminant analysis it was found that parameters describing cell shape (both gross shape of cells and their fine scale contour foldings) possessed a higher power of discrinunation between the cells spread on various substrates than the differences in cell surface areas. In the course of observation (75 and 150 min) the highest number of attached cells and highest degree of spreading were found when cells were plated on type IV collagen. Moderate alterations in cell shape and moderate increase of surface area were seen in the group of cells seeded on fibronectin, whereas the cells plated on laminin, glass and BSA revealed a moderate increase of surface area, but no changes in their shape were observed. The differences in attachment of cells and in the degree of their spreading might be due to the variation in expression of plasma membrane receptors for various substrates. The Fourier analysis of cell shape coupled with measurement of surface area is a good tool for quantitative evaluation of cell spreading and can be used for discrimination between cells spread on different substrates.Supported in part by a grant (MZ-XIV) from the Polish Ministry of Health and Welfare     

Spreading of cells on various substrates evaluated by Fourier analysis of shape

In order to evaluate in mathematical terms the morphological changes occurring in the course of cell spreading, Fourier analysis of shape was applied. Human urothelial Hu 961 b cells plated on type IV collagen, fibronectin, laminin, glass and bovine serum albumin (BSA) were studied. Fourier parameters describing cell shape as well as surface areas covered by the cells on the substrate were subjected to statistical analysis. Using analysis of variance and discriminant analysis it was found that parameters describing cell shape (both gross shape of cells and their fine scale contour foldings) possessed a higher power of discrimination between the cells spread on various substrates than the differences in cell surface areas. In the course of observation (75 and 150 min) the highest number of attached cells and highest degree of spreading were found when cells were plated on type IV collagen. Moderate alterations in cell shape and moderate increase of surface area were seen in the group of cells seeded on fibronectin, whereas the cells plated on laminin, glass and BSA revealed a moderate increase of surface area, but no changes in their shape were observed. The differences in attachment of cells and in the degree of their spreading might be due to the variation in expression of plasma membrane receptors for various substrates. The Fourier analysis of cell shape coupled with measurement of surface area is a good tool for quantitative evaluation of cell spreading and can be used for discrimination between cells spread on different substrates.     

Morphological variations of an invasive cyprinid fish (Carassius gibelio) in lentic and lotic environments inferred from the body,otolith, and scale shapes

This study investigated the morphological variation of gibel carp Carassius gibelio collected from various water bodies in Türkiye. The fish samples were obtained from three dams (Karacaören-1, Karakaya, and Keban), two natural lakes (Beyşehir and Suğla), and a river (the Tigris River). The dimorphism in body shape was examined with geometric morphometrics, while elliptic Fourier analysis and shape indices were used to describe the variation in lapilli otoliths (hereafter “otoliths”) and scale shapes. The body of C. gibelio revealed higher variations, particularly in the body depth, snout length, caudal fin, and caudal peduncle, among different stations. Geometric morphometric analysis determined a streamlined body shape of C. gibelio in the Tigris River compared to other stations, while C. gibelio from the natural lakes had a deeper body shape. The body of C. gibelio exhibited a significant homogenous shape between the Beyşehir and Suğla lakes, providing the lowest Procrustes distance. The elliptic Fourier analysis revealed that the otolith shape varied significantly between all stations. However, the scale shape was remarkably similar among nearby areas such as Karacaören dam, Suğla, and Beyşehir lakes. These results evinced high degree of intra-population morphological variation in C. gibelio in response to prevailing environmental conditions that probably facilitate their successful establishment in a novel environment.     

Patterning of geographic variation in Middle Pleistocene Homo frontal bone morphology

A quantitative assessment of the frontal bone morphology of a sample of Middle Pleistocene hominins was undertaken in order to address questions regarding their population structure and evolutionary history. Outline tracings of the frontal bones of forty-seven fossil crania were obtained, and size-standardized measurements were then computed using an Elliptical Fourier analysis of these tracings. Principal component scores of the Fourier harmonic amplitudes were derived and served as a quantitative representation of the morphology of the frontal bone. Morphological, geographical, and temporal distance matrices were then constructed between each pair of fossils. A partial Mantel matrix correlation test was performed between morphological and geographical distance matrices, controlling for temporal distance, in order to determine if the pattern of geographical differentiation in features of the frontal bone of mid-Pleistocene Homo followed that of an isolation-by-distance model of population structure. The results of the partial Mantel tests indicate that the overall patterning of differentiation in the features of the frontal bone cannot best be explained by a population structure shaped by isolation-by-distance. Additionally, various aspects of the frontal bone quantified here follow different patterns of geographical differentiation, suggesting that a mosaic pattern of evolution holds true for characters within one cranial region and not just for those between regions.     

Numerical evaluation of changes in the cytoplasmic microtubule complex of C3H mouse cells by optical diffractometry and of changes in cell shape by Fourier analysis

MO mouse cells in culture on glass were treated with taxol, or nocodazole, or incubated at 4 degrees C to alter their cytoplasmic microtubule complex (CMTC). From each treated group and from an untreated group, 30 cells stained with an antiserum against tubulin, were photographed under the photomicroscope, and negatives were analysed by optical diffractometry. Differences between groups of cells were tested by variance analysis. Phase-contrast micrographs of the same cells were used for Fourier analysis of cell shape. Both types of analyses provided numerical objective data about changes in the CMTC and in cell shape that were typical for the kind of treatment. We conclude that optical diffractometry of immunostained cells and Fourier analysis of cell shape are complementary to photomicroscopy for the study of the CMTC in cell populations cultured on an artificial substrate.     

Metric and non-metric randomization methods, geographic variation, and the single-species hypothesis for Asian and African Homo erectus

This paper proposes a statistical test of the single-species hypothesis using non-metric characters as a complement to statistical tests using more traditional metric characters. The sample examined is that of Asian and African Homo erectus. The paleoanthropological community is divided on the taxonomic distinction of these fossils, with workers arguing both for and against the species-level distinction between Asian and African populations. Previous arguments have focused on patterns of apparent morphological differentiation between the African and Asian cranial samples. To assess this question, three tests were performed that compared the range of variation in the fossil sample to a single-species group with a similar geographic distribution; this comparative sample was composed of 221 modern humans from Africa and Asia. For the first test, 23 metric characters were analyzed on the fossil and comparative samples. Using resampling procedures, the variation for these characters was examined, recreating 1000 samples from the human analogs and comparing the CV distributions of these samples to the CVs of the fossil group. The second test used the metric data to calculate a Euclidean distance between the African and Asian fossil samples. This distance was compared to a distribution of Euclidean distances calculated between 1000 randomly selected samples of African and Asian modern humans. For the third test, a grading scale was created for ten non-metric characters that encompassed the total morphological variation found in the fossil and modern human samples. The Manhattan distance between the Asian and African fossil samples was calculated and compared to a distribution of distances calculated between 1000 randomly selected samples of African and Asian moderns. The first two tests, using the metric data, failed to falsify the null hypothesis. However, in the third test, using non-metric data, the total Manhattan distance for the fossil sample approached the 100th percentile of the resampled distances calculated from the moderns. The implications of the contrasting results are discussed.     

Comparative evaluation of techniques for the harmonic analysis of human motion data

Four mathematical techniques for the estimation of the Fourier coefficients of pseudoperiodic non-exact discrete functions were submitted to comparative evaluation. These techniques were devised within the following basic procedures: (1) numerical harmonic analysis applied either directly or after redistribution of the data points through some interpolation procedure, so that they be evenly spaced in time and exactly fit on cycle period; (2) fitting of the empirical data with an analytical model followed by the calculation of the Fourier integrals of this model. The evaluation was carried out with special reference to the use of these techniques for processing human motion photogrammetric data. The following criteria were used: (1) accuracy of the Fourier coefficient estimates, (2) capability of yielding information about this accuracy, (3) a priori information needed regarding the statistical properties of the experimental error, (4) factors concerning implementation in digital computers. Practical information was obtained for the non-specialist user with regard to the choice of one technique among the several possible in particular circumstances.     

Ultrasonic model and system for measurement of corneal biomechanical properties and validation on phantoms

Non-invasive measurement of biomechanical properties of corneas may provide important information for ocular disease management and therapeutic procedures. An ultrasonic non-destructive evaluation method with a wave propagation model was developed to determine corneal biomechanical properties in vivo. In this study, we tested the feasibility of the approach in differentiating the mechanical properties of soft contact lenses as corneal phantoms. Three material types of soft contact lenses (six samples in each group) were measured using a broadband ultrasound transducer. The ultrasonic reflections from the contact lenses were recorded by a 500MHz/8-bit digitizer, and displayed and processed by a PC. A reference signal was recorded to compute the normalized power spectra using Fast Fourier Transformation. An inverse algorithm based on least-squares minimization was used to reconstruct three parameters of the contact lenses: density, thickness, and elastic constants lambda+2micro. The thickness of each sample was verified using an electronic thickness gauge, and the averaged density for each type of lenses was verified using Archimedes' principle and manufacturer's report. Our results demonstrated that the ultrasonic system was able to differentiate the elastic properties of the three types of the soft contact lenses with statistical significance (P-value<0.001). The reconstructed thicknesses and densities agreed well with the independent measurements. Our studies on corneal phantoms indicated that the ultrasonic system was sensitive and accurate in measuring the material properties of cornea-like structures. It is important to optimize the system for in vivo measurements.