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An EM algorithm for shape classification based on level sets.

In this paper, we propose an expectation-maximization (EM) approach to separate a shape database into different shape classes, while simultaneously estimating the shape contours that best exemplify each of the different shape classes. We begin our formulation by employing the level set function as the shape descriptor. Next, for each shape class we assume that there exists an unknown underlying level set function whose zero level set describes the contour that best represents the shapes within that shape class. The level set function for each example shape in the database is modeled as a noisy measurement of the appropriate shape class's unknown underlying level set function. Based on this measurement model and the judicious introduction of the class labels as the hidden data, our EM formulation calculates the labels for shape classification and estimates the shape contours that best typify the different shape classes. This resulting iterative algorithm is computationally efficient, simple, and accurate. We demonstrate the utility and performance of this algorithm by applying it to two medical applications.

Algorithms↗

Echocardiographic analysis of regional and global left ventricular shape in Chagas' cardiomyopathy.

Chagas' heart disease is a common form of cardiomyopathy in Latin America and an important cause of cardiac morbidity and mortality there. Left ventricular (LV) apical aneurysm and LV dysfunction are frequent findings in Chagas' cardiomyopathy. Because cardiac shape has important implications for LV function, we sought to characterize regional and global changes in LV geometry in Chagas' heart disease. Quantitative shape analysis was performed on 2-dimensional echocardiograms from 43 patients with Chagas' cardiomyopathy. Regional shape was quantitated by measuring endocardial curvature and global shape was evaluated by Fourier shape analysis of the endocardial contour. Data from 22 age- and sex-matched normal test subjects were used for comparison. Regional shape analysis demonstrated decreased apical curvature (consistent with blunting of normal apical shape) in the group with Chagas' disease compared with controls (apical 2-chamber view: 19 +/- 1 vs 24 +/- 1 [p = 0.0039] at end-diastole and 20 +/- 2 vs 29 +/- 3 [p = 0.0019] at end-systole). Fourier shape power index was decreased in the Chagas' group, consistent with a more spherical ventricle (apical 2-chamber view: 9 +/- 1 vs 17 +/- 2 [p <0.0001] at end-diastole and 12 +/- 1 vs 35 +/- 3 [p <0.0001] at end-systole). Shape changes among the population with Chagas' disease were further evaluated in those with end-diastolic volumes equal to or greater than the median for the group (104 ml) and those < 104 ml. Global shape did not differ between patients with dilated ventricles and those with relatively nondilated ventricles. Diastolic Fourier shape power index = 8 +/- 2 in dilated ventricles compared with 9 +/- 5 in nondilated ventricles (p = 0.53); systolic Fourier shape power index = 10 +/- 2 in dilated versus 14 +/- 2 in nondilated ventricles (p = 0.15) (apical 2-chamber view). In Chagas' cardiomyopathy, LV apical deformation results in disruption of the optimal global prolate-ellipsoid shape, even in patients with relatively preserved LV volumes.

Adult↗

Preparation and crystallization kinetics of new structurally well-defined star-shaped biodegradable poly(L-lactide)s initiated with diverse natural sugar alcohols.

This study presents syntheses, structural characterization, and crystallization kinetic investigation of new structurally well-defined star-shaped poly(l-lactide)s (PLLAs). First, a series of new 3- to 6-arm star-shaped PLLAs were synthesized through SnOct(2) catalyzed ring-opening polymerization of (l)-lactide with natural sugar alcohols of glycerol, erythritol, xylitol, and sorbitol as the favorable initiators. Subsequently, their chemical structures were characterized by means of GPC, NMR, and viscometer with respect to the star-shaped structures, demonstrating the well-defined arm structures as evidenced on the g(1/2)/g' values, where g and g' denote the ratios of mean-square radius of gyration and intrinsic viscosity of a star-shaped polymer to those of a linear structural reference with similar absolute molecular weight. Furthermore, spherulite morphologies and growth rates were studied by a polarized microscopy (POM) for the synthesized star-shaped PLLAs with different molecular weights, and it was found that the more arms of a star-shaped PLLA finally resulted in a lower spherulite growth rate. With regard to the crystallization kinetics of these star-shaped PLLAs, isothermal and nonisothermal crystallization were examined by differential scanning calorimeter (DSC). It was found that Avrami exponent n values of isothermal crystallization were almost independent of the isothermal crystallization temperature T(c) for different series of star-shaped PLLAs. In contrast, the values of Avrami exponent n were observed to strongly depend on the star-shaped structures with different arms, implying their distinct nucleation mechanisms, and the more arms of a star-shaped PLLA led to a slower isothermal crystallization rate. On the basis of a modified Avrami equation, new light was shed on the nonisothermal crystallization kinetics for the star-shaped PLLAs, and the activation energies were found to vary from 146.86 kJ/mol for the linear PLLA EG-3 to 221.23 kJ/mol of the star-shaped S-3, demonstrating much decreased crystallizabilities of star-shaped PLLAs with more arms.

Biodegradation, Environmental↗

Additivity and interaction between size ratio and response category in the comparison of size-discrepant shapes.

In Experiment 1, subjects made same-different judgments to pairs of shapes that could differ (irrelevantly) in size and in which different pairs combined distinct shapes. Size discrepancy had an effect both on same and different responses. However, the effect on different responses was not monotonic across size discrepancies. It is argued that this nonmonotonicity was produced by a form of bias acting to slow different responses for same-sized pairs. Consistent with the proposed bias account, the nonmonotonic size-discrepancy effect on different trials was eliminated in Experiment 2, in which trials were blocked by size ratio. In Experiment 3, subjects performed a task similar to that in Experiments 1 and 2. However, additional visual information was added inside the bounding contour of the shapes, and this information was either the same or different across shapes. The match between within-contour information across shapes (whether same or different) was varied orthogonally with whether the bounding contours of the shapes were the same or different. In this experiment subjects decided whether the bounding contours of the shapes were the same or different, while ignoring the added information within the contours. When the added information matched across the two shapes, same responses were facilitated relative to when the added information mismatched. The converse occurred for different responses. This effect was more pronounced when the shapes were shown at the same size than when the shapes were at different sizes. In general, the results suggest that (a) size discrepancy affects some perceptual operations that are preliminary to shape matching, and (b) bias mechanisms can play an important role in shape-matching experiments in which the shapes can be shown in different sizes. The interaction of two processes--size scaling and bias--can account for these and hitherto contradictory results in the literature.

Form Perception↗

Simple triangular approximations of auditory filter shapes.

At present, the most popular auditory filter shape model is one with a rounded peak and exponentially decaying filter skirts (Patterson & Moore, 1986). Unfortunately, the complex nature of this "roex" filter model may, in some instances, have hindered the application of the auditory filter shape in clinical measurements of frequency selectivity. Moreover, some of the assumptions of the roex filter model may be violated at high sound-pressure levels (SPLs) and this limitation has also been a factor when considering the roex auditory filter shape in the clinic. Our purpose is to introduce a simplified method that is adequate for obtaining clinically useful estimates of triangular-shaped auditory filters. Although the triangular-shaped filter model faces the same problems as the roex model at high SPLs, the calculations and assumptions underlying the former are far less complicated. The triangular filter model also retains many of the qualitative properties and advantages afforded by roex-fitted auditory filter shapes. In this report, we review the basic concepts underlying auditory filter shape estimates and describe our methods for measuring and fitting the triangular-shaped filter model. We then present normative triangular filter shapes and compare these estimates with auditory filter shapes fitted by other means. Finally, we present selected examples of triangular filter shapes fitted to the masked thresholds of hearing-impaired patients. For the most part, the triangular-shaped filter model offers the clinician a satisfactory compromise for obtaining estimates of auditory filter shape and frequency selectivity at moderately intense and high SPLs.

Adult↗

Shape representation in area V4: position-specific tuning for boundary conformation.

Visual shape recognition in primates depends on a multi-stage pathway running from primary visual cortex (V1) to inferotemporal cortex (IT). The mechanisms by which local shape signals from V1 are transformed into selectivity for abstract object categories in IT are unknown. One approach to this issue is to investigate shape representation at intermediate stages in the pathway, such as area V4. We studied 109 V4 cells that appeared sensitive to complex shape in preliminary tests. To achieve a more complete picture of shape representation in V4, we tested each cell with a set of 366 stimuli, constructed by systematically combining convex and concave boundary elements into closed shapes. Using this large, diverse stimulus set, we found that all the cells in our sample responded to a wide variety of shapes and did not appear to encode any single type of global shape. However, for most cells the shapes evoking strongest responses were characterized by a consistent type of boundary conformation at a specific position within the stimulus. For example, a given cell might be tuned for shapes containing concave curvature at the right, with other parts of the shape having little or no effect on responses. Many cells were tuned for more complex boundary configurations (e.g., a convex angle adjacent to a concave curve). We quantified this kind of shape tuning with Gaussian functions on a curvature x position domain. These tuning functions fit the neural responses much better than tuning functions based on edge or axis orientation. Thus individual V4 cells appear to encode moderately complex boundary information at specific locations within larger shapes. This finding suggests that, at intermediate stages in the V1-IT transformation, complex objects are represented at least partly in terms of the configurations and positions of their contour components.

Animals↗

MR imaging of hepatic masses: diagnostic significance of wedge-shaped areas of increased signal intensity surrounding the lesion.

OBJECTIVE: Wedge-shaped areas of increased signal intensity surrounding focal hepatic lesions on T2-weighted images have been described as an occasional finding in patients with hepatic metastases. We reviewed MR images of patients with benign and malignant focal hepatic lesions to determine the prevalence and diagnostic significance of this finding, and in particular to determine if these wedge-shaped areas are characteristic of cancer. MATERIALS AND METHODS: One hundred twenty-one patients with focal hepatic lesions (65 patients with metastases, 14 patients with hepatocellular carcinoma, and 42 patients with benign conditions) underwent MR imaging of the liver at 1.0 T. Axial spin-echo T1-weighted and spin-echo and turbo spin-echo T2-weighted MR images were obtained. The MR images were retrospectively evaluated: the number and size of the lesions and the presence of wedge-shaped areas surrounding the lesions were recorded; in patients with cancer, follow-up MR images and a clinical course were used to study the evolution of the lesions and the adjacent wedge-shaped areas. The final diagnosis in patients with cancer was proved by clinical course (54 patients) or fine-needle aspiration biopsy (25 patients); in patients with benign lesions, the findings on various other imaging techniques were accepted as conclusive. RESULTS: The wedge-shaped areas were noted on T2-weighted images in 16 (25%) of 65 patients with metastases, in 3 (21%) of 14 patients with hepatocellular carcinoma, and in 5 (12%) of 42 patients with benign lesions. In 11 of the 16 patients with metastases and wedge-shaped areas of increased signal intensity, a metastatic lesion within the wedge-shaped area was detectable; in the remaining five patients, a metastatic lesion appeared during the subsequent clinical course. In some instances, the wedge-shaped area obscured the lesion. In patients with benign conditions, the wedge-shaped area was frequently seen in association with hemangiomas (4 of 13, 31%). CONCLUSION: Our results show that wedge-shaped areas of increased signal intensity surrounding lesions on T2-weighted MR images are a common finding in patients with focal hepatic lesions. The wedge-shaped areas cannot be considered pathognomonic of malignant lesions because they are also seen in patients with benign conditions (hemangioma, abscess). However, the appearance of these wedge-shaped areas in a patient with cancer should suggest a metastasis. The possibility that hepatic lesions could be obscured by these wedge-shaped areas also should be considered when response to treatment is being evaluated.

Adult↗

Quantitative genetics of plastron shape in slider turtles (Trachemys scripta).

Shape variation is widespread in nature and embodies both a response to and a source for evolution and natural selection. To detect patterns of shape evolution, one must assess the quantitative genetic underpinnings of shape variation as well as the selective environment that the organisms have experienced. Here we used geometric morphometrics to assess variation in plastron shell shape in 1314 neonatal slider turtles (Trachemys scripta) from 162 clutches of laboratory-incubated eggs from two nesting areas. Multivariate analysis of variance indicated that nesting area has a limited role in describing plastron shape variation among clutches, whereas differences between individual clutches were highly significant, suggesting a prominent clutch effect. The covariation between plastron shape and several possible maternal effect variables (yolk hormone levels and egg dimensions) was assessed for a subset of clutches and found to be negligible. We subsequently employed several recently proposed methods for estimating heritability from shape variables, and generalized a univariate approach to accommodate unequal sample sizes. Univariate estimates of shape heritability based on Procrustes distances yielded large values for both nesting populations (h2 approximately 0.86), and multivariate estimates of maximal additive heritability were also large for both nesting populations (h2max approximately 0.57). We also estimated the dominant trend in heritable shape change for each nesting population and found that the direction of shape evolution was not the same for the two sites. Therefore, although the magnitude of shape evolution was similar between nesting populations, the manner in which plastron shape is evolving is not. We conclude that the univariate approach for assessing quantitative genetic parameters from geometric morphometric data has limited utility, because it is unable to accurately describe how shape is evolving.

Animals↗

Elliptical fourier analysis of symphyseal shape in great ape mandibles.

The midsagittal profile of the mandibular symphysis has served as both a taxonomic marker and a phylogenetically salient character in debates over hominoid evolution. Nevertheless, the utility of symphyseal shape as an informative attribute for paleobiological reconstructions is suspect. Quantification of shape variation has proven to be particularly problematic; it has long been recognized that conventional linear measurements (and the indices derived from them), while replicable, summarize aspects of shape very poorly because of the vast amount of contour information that is lost in the process. In this study, a type of Fourier analysis is applied to cross-sectional contours of ape mandibles in order to provide a mathematical accounting of shape variation in a "global" sense; that is, by applying the "totality" of contour information in a comparative analysis. Shape variation in the mandibular symphysis is explored through the decomposition of coordinate data into elliptical Fourier coefficients. These coefficients are used to compute average taxonomic distances (ATD) among individuals of chimpanzees, gorillas, and orang-utans. The resulting shape-based distances are summarized via clustering (UPGMA) and ordination (principal coordinates analysis-PCO). Principal coordinate scores are subjected to analysis of variance in univariate and multivariate designs; these data are also applied to discriminant function analyses. Species and sex effects on morphology are statistically significant; however, no significant interaction of these factors is indicated. This would seem to imply that patterns of sexual dimorphism are not distinct among great apes; to the contrary, within-species sex comparisons reveal that significant size and shape dimorphism is present only in Gorilla. Despite significant size dimorphism in Pan and Pongo, significant shape differences between males and females are not apparent in these taxa. These results suggest that it is theoretically possible to sort taxa by a symphyseal shape criterion, but the discriminant function results suggest that there still exists a large potential for error in assigning particular shapes to a given species or sex. Thus, despite real shape differences among these species, the use of symphyseal shape as a character in species identification or in systematic arguments remains limited and problematic.

Analysis of Variance↗

Genetic control of fruit shape acts prior to anthesis in melon ( Cucumis melo L.).

Genetic control of fruit shape in Cucumis melo was studied using QTL analysis in two Recombinant Inbred (RI) populations consisting of 163 and 63 individuals, respectively, obtained by crossing the same round-fruited parent with two different elongated-fruit lines. Fruit shape is mainly explained by fruit length in these two populations. Most QTLs for fruit shape and ovary shape detected were found to co-segregate, thus demonstrating early control of fruit shape during ovary development. A high level of correlation between fruit shape and ovary shape was also found in 14 unrelated genetic lines, a finding which suggests that control of fruit shape by gene(s) active early in the ovary is a general feature in C. melo. Two major flower genes, a ( monoecious) and p ( pentamerous), were shown to have major effects on fruit shape. Major tightly linked QTLs for fruit and ovary shape were found close to the a and p genes, probably reflecting their pleiotropic effect on fruit shape. Moreover, one of the two QTLs detected in the Védrantais x PI 414723 population was also found in the Védrantais x PI 161375 population. Variation of fruit shape in melon could be due to variations having quantitative effects on a large set of genes that are probably involved in ovary development.

Chromosome Mapping↗

Mutual information in coupled multi-shape model for medical image segmentation.

This paper presents extensions which improve the performance of the shape-based deformable active contour model presented earlier in [IEEE Conf. Comput. Vision Pattern Recog. 1 (2001) 463] for medical image segmentation. In contrast to that previous work, the segmentation framework that we present in this paper allows multiple shapes to be segmented simultaneously in a seamless fashion. To achieve this, multiple signed distance functions are employed as the implicit representations of the multiple shape classes within the image. A parametric model for this new representation is derived by applying principal component analysis to the collection of these multiple signed distance functions. By deriving a parametric model in this manner, we obtain a coupling between the multiple shapes within the image and hence effectively capture the co-variations among the different shapes. The parameters of the multi-shape model are then calculated to minimize a single mutual information-based cost criterion for image segmentation. The use of a single cost criterion further enhances the coupling between the multiple shapes as the deformation of any given shape depends, at all times, upon every other shape, regardless of their proximity. We found that this resulting algorithm is able to effectively utilize the co-dependencies among the different shapes to aid in the segmentation process. It is able to capture a wide range of shape variability despite being a parametric shape-model. And finally, the algorithm is robust to large amounts of additive noise. We demonstrate the utility of this segmentation framework by applying it to a medical application: the segmentation of the prostate gland, the rectum, and the internal obturator muscles for MR-guided prostate brachytherapy.

Algorithms↗

A statistical method for biological shape comparisons.

Biological shape data combine two sorts of information: genometric location and biological homology. The link between these two is the landmark, a set of biologically corresponding points located in all the forms of a series. Analysis of shapes as configurations of landmarks proceeds most effectively by D' Arcy Thompson's (1917, 1942) method of transformations. In this tradition, shape change is not the arithmetical difference of distances, angles, and ratios measured on shapes separately; rather, it is a mensurand in its own right, the geometrical deformation taking the Cartesian coordinate space of one form onto that of another in accord with biological homology. Such a deformation may be displayed, continuously or discretely, as a symmetric tensor field of principal crosses, pairs of directions which start and finish at 90 degrees. At any point, along one of these directions the dilatation, or dimensionless rate of change of length, is largest; along the other, smallest. These are the principal dilatations. All conventional scalar descriptions of the shape change may be deduced from the tensor presentation. This article reviews the statistical description of mean biological form-changes viewed in this way, and introduces linearized significance tests for mean shape change and mean size change. The tests, which make no reference to any set of size or shape variables, are based in a convenient parametric distribution for shape changes in triangles of landmarks. On a suitable null hypothesis, the ratio of the difference of the principal dilatations of the mean deformation to the sum of their standard errors goes as square root of pi/2 approximately 0.88 times an approximate t-ratio for shape change; the sum of the deviations of those dilatations from unity, divided by the sum of their standard errors, goes as square root of 2/2 approximately 0.71 times an approximate t-ratio for size change. The difference between these two constants reflects the divergent selection bias of the pair of principal dilatations. In matched studies, the difference of the principal dilatations of the mean change, divided by the mean difference of the principal dilatations case by case, is square root of 2/pi N times an approximate X2 for shape difference. Examples are presented that test cephalometric data in three scientific contexts: comparison of groups of biological shapes observed once each; characterization of mean difference in a matched design (namely, mean growth in one group observed twice); and description of mean differences in growth between groups of shapes each observed twice.

Adolescent↗

Induction of L-form-like cell shape change of Bacillus subtilis under microculture conditions.

A remarkable cell shape change was observed in Bacillus subtilis strain 168 under microculture conditions on CI agar medium (Spizizen's minimal medium supplemented with a trace amount of yeast extract and Casamino acids). Cells cultured under a cover glass changed in form from rod-shaped to spherical, large and irregular shapes that closely resembled L-form cells. The cell shape change was observed only with CI medium, not with Spizizen's minimum medium alone or other rich media. The whole-cell protein profile of cells grown under cover glass and cells grown on CI agar plates differed in several respects. Tandem mass analysis of nine gel bands which differed in protein expression between the two conditions showed that proteins related to nitrate respiration and fermentation were expressed in the shape-changed cells grown under cover glass. The cell shape change of CI cultures was repressed when excess KNO3 was added to the medium. Whole-cell protein analysis of the normal rod-shaped cells grown with 0.1% KNO3 and the shape-changed cells grown without KNO3 revealed that the expression of the branched-chain alpha-keto acid dehydrogenase complex (coded by the bfmB gene locus) was elevated in the shape-changed cells. Inactivation of the bfmB locus resulted in the repression of cell shape change, and cells in which bfmB expression was induced by IPTG did show changes in shape. Transmission electron microscopy of ultrathin sections demonstrated that the shape-changed cells had thin walls, and plasmolysis of cells fixed with a solution including 0.1 M sucrose was observed. Clarifying the mechanism of thinning of the cell wall may lead to the development of a new type of cell wall biosynthetic inhibitor.

Bacillus subtilis↗

Processing of shape defined by disparity in monkey inferior temporal cortex.

Neurons in the monkey inferior temporal cortex (IT) have been shown to respond to shapes defined by luminance, texture, or motion. In the present study, we determined whether IT neurons respond to shapes defined solely by binocular disparity, and if so, whether signals of disparity and other visual cues to define shape converge on single IT neurons. We recorded extracellular activity from IT neurons while monkeys performed a fixation task. Among the neurons that responded to at least one of eight random-dot stereograms (RDSs) containing different disparity-defined shapes, 21% varied their responses to different RDSs. Responses of most of the neurons were positively correlated between two sets of RDSs, which consisted of different dot patterns but defined the same set of eight shapes, whereas responses to RDSs and their monocular images were not correlated. This indicates that the response modulation for the eight RDSs reflects selectivity for shapes (or their component contours) defined by disparity, although responses were also affected by dot patterns per se. Among the neurons that showed selectivity for shapes defined by luminance or disparity, 44% were activated by both cues. Responses of these neurons to luminance-defined shapes and those to disparity-defined shapes were often positively correlated to each other. Furthermore the stimulus rank, which was determined by the magnitude of responses to shapes, generally matched between these cues. The same held true between disparity and texture cues. The results suggest that the signals of disparity, luminance, and texture cues to define the shapes converge on a population of single IT neurons to produce the selectivity for shapes.

Animals↗

Geometric estimates of heritability in biological shape.

The recently developed geometric morphometrics methods represent an important contribution of statistics and geometry to the study of biological shapes. We propose simple protocols using shape distances that incorporate geometric techniques into linear quantitative genetic models that should provide insights into the contribution of genetics to shape variation in organisms. The geometric approaches use Procrustes distances in a curved shape space and distances in tangent spaces within and among families to estimate shape heritability. We illustrate the protocols with an example of wing shape variation in the honeybee, Apis mellifera. The heritability of overall shape variation was small, but some localized components depicting shape changes on distal wing regions showed medium to large heritabilities. The genetic variance-covariance matrix of the geometric shape variables was significantly correlated with the phenotypic shape variance-covariance matrix. A comparison of the results of geometric methods with the traditional multivariate analysis of interlandmark distances indicated that even with a larger dimensionality, the interlandmark distances were not as rich in shape information as the landmark coordinates. Quantitative genetics studies of shape should greatly benefit from the application of geometric methods.

Animals↗

Conventional root canal therapy of C-shaped mandibular second molar. A case report.

The C-shaped root canal system and treatment implications were first described by Cooke and Cox in 1979. C-shaped canals are most frequently found in mandibular second molars, but they can occur in any mandibular molar, and they have been reported in maxillary molars as well. C-shaped mandibular molars are characterized by a C-shaped groove that connects one or more root canals. This groove can occur anywhere along the root canal system, making it difficult to diagnose and treat. A C-shaped root canal system may appear completely normal at the level of the pulp chamber but can begin to manifest itself in the middle or apical one-third. Furthermore, C-shaped canals are challenging if not impossible to predict radiographically. C-shaped canals in mandibular second molars are found most frequently in the Chinese population, with reports showing up to a 31.5% incidence, as compared to an approximate 7% incidence in the general population. This case report demonstrates an incidence of a C-shaped canal that was unable to be detected radiographically and which contained three separate root canals that communicated in the apical one-third of the root canal system. Canal orifices were located approximately 2 mm below the level of the CEJ, which is in agreement with a recent micro-computed tomography study of C-shaped mandibular molars that found 98% of all C-shaped molars studied had orifices located 1 mm to 3 mm below the CEJ. The CT study also found that all C-shaped canals contained fused roots and confirmed previous findings that the C-shape configuration varies greatly throughout the length of the canal.

Adult↗

Pelvic growth: ontogeny of size and shape sexual dimorphism in rat pelves.

The mammalian pelvis is sexually dimorphic with respect to both size and shape. Yet little is known about the differences in postnatal growth and bone remodeling that generate adult sexual dimorphism in pelvic bones. We used Sprague-Dawley laboratory rats (Rattus norvegicus), a species that exhibits gross pelvic size and shape dimorphism, as a model to quantify pelvic morphology throughout ontogeny. We employed landmark-based geometric morphometrics methodology on digitized landmarks from radiographs to test for sexual dimorphism in size and shape, and to examine differences in the rates, magnitudes, and directional patterns of shape change during growth. On the basis of statistical significance testing, the sexes became different with respect to pelvic shape by 36 days of age, earlier than the onset of size dimorphism (45 days), although visible shape differences were observed as early as at 22 days. Males achieved larger pelvic sizes by growing faster throughout ontogeny. However, the rates of shape change in the pelvis were greater in females for nearly all time intervals scrutinized. We found that trajectories of shape change were parallel in the two sexes until age of 45 days, suggesting that both sexes underwent similar bone remodeling until puberty. After 45 days, but before reproductive maturity, shape change trajectories diverged because of specific changes in the female pelvic shape, possibly due to the influence of estrogens. Pattern of male pelvic bone remodeling remained the same throughout ontogeny, suggesting that androgen effects on male pelvic morphology were constant and did not contribute to specific shape changes at puberty. These results could be used to direct additional research on the mechanisms that generate skeletal dimorphisms at different levels of biological organization.

Aging↗

Evaluation of variable line-shape models and prior information in automated 1H spectroscopic imaging analysis.

Analysis of in vivo short TE 1H spectra is complicated by broad baseline signal contributions and resonance line-shape distortions. Although the assumptions of ideal metabolite resonance line-shapes and slowly varying baseline signals can be used to separate these signals, the presence of broad or asymmetric line-shapes can invalidate this model. More complex line-shape models are computationally expensive or difficult to constrain, particularly for the low signal-to-noise commonly found for in vivo MR spectroscopic imaging applications. In this study, two time-domain models for fitting variable spectral line-shapes are examined, one using B-splines and another using summed sinusoids. The methods were verified using both phantom and human data, and Monte Carlo simulations were used to evaluate variations in calculated metabolite amplitudes due to interactions between the baseline and line-shape estimations. Additional studies investigated the use of prior line-shape information, obtained from either a water MRSI measurement or calculations from B(0) maps, to determine parameter starting values or optimization constraints. Both line-shape models showed the ability to fit the variety of line-shapes present in both the phantom and human MRSI data, with similar or improved accuracy over a Gaussian line-shape model; however, this improvement resulted in only minor improvement for the high-SNR phantom data and moderate improvements in regions with asymmetry for the fitted in vivo metabolite images. The use of prior line-shape information was of most benefit when applied toward setting optimization constraints but was of limited benefit when used to define initial starting values.

Aspartic Acid↗