Beyond bilateral symmetry: geometric morphometric methods for any type of symmetry

Abstract Background Studies of symmetric structures have made important contributions to evolutionary biology, for example, by using fluctuating asymmetry as a measure of developmental instability or for investigating the mechanisms of morphological integration. Most analyses of symmetry and asymmetry have focused on organisms or parts with bilateral symmetry. This is not the only type of symmetry in biological shapes, however, because a multitude of other types of symmetry exists in plants and animals. For instance, some organisms have two axes of reflection symmetry (biradial symmetry; e.g. many algae, corals and flowers) or rotational symmetry (e.g. sea urchins and many flowers). So far, there is no general method for the shape analysis of these types of symmetry. Results We generalize the morphometric methods currently used for the shape analysis of bilaterally symmetric objects so that they can be used for analyzing any type of symmetry. Our framework uses a mathematical definition of symmetry based on the theory of symmetry groups. This approach can be used to divide shape variation into a component of symmetric variation among individuals and one or more components of asymmetry. We illustrate this approach with data from a colonial coral that has ambiguous symmetry and thus can be analyzed in multiple ways. Our results demonstrate that asymmetric variation predominates in this dataset and that its amount depends on the type of symmetry considered in the analysis. Conclusions The framework for analyzing symmetry and asymmetry is suitable for studying structures with any type of symmetry in two or three dimensions. Studies of complex symmetries are promising for many contexts in evolutionary biology, such as fluctuating asymmetry, because these structures can potentially provide more information than structures with bilateral symmetry.</p

The symmetry spectrum in a hybridising, tropical group of rhododendrons

Many diverse plant clades possess bilaterally symmetrical flowers and specialised pollination syndromes, suggesting that these traits may promote diversification. We examined the evolution of diverse floral morphologies in a species‐rich tropical radiation of Rhododendron. We used restriction‐site associated DNA sequencing on 114 taxa from Rhododendron sect. Schistanthe to reconstruct phylogenetic relationships and examine hybridisation. We then captured and quantified floral variation using geometric morphometric analyses, which we interpreted in a phylogenetic context. We uncovered phylogenetic conflict and uncertainty caused by introgression within and between clades. Morphometric analyses revealed flower symmetry to be a morphological continuum without clear transitions between radial and bilateral symmetry. Tropical Rhododendron species that began diversifying into New Guinea c. 6 million years ago expanded into novel floral morphological space. Our results showed that the evolution of tropical Rhododendron is characterised by recent speciation, recurrent hybridisation and the origin of floral novelty. Floral variation evolved via changes to multiple components of the corolla that are only recognised in geometric morphometrics with both front and side views of flowers

Mammary Glands Possess Intrinsic Molecular Laterality and Respond Left-Right Differently to Genetic and Pharmacological Manipulation

Mammary Glands Possess Intrinsic Molecular Laterality and Respond Left-Right Differently to Genetic and Pharmacological Manipulation. (Under the direction of Ann Ramsdell) More tumors form in the left (L) breast and tumors in the right (R) breast may be more aggressive. These epidemiological findings suggest L-R differences in overall tumor biology depending on the side of tumor origin, leading to the hypothesis that mammary glands are L-R different and have discordant responses to neoplastic risk factors. Here we show that normal mammary glands are molecularly L-R different, and have more mammary stem cells (MaSCs) in the L thoracic mammary gland (TMG). In addition, MaSCs from the L and R TMGs are molecularly and functionally different in vitro and in vivo. MaSCs respond to ErbB2 and EGFR inhibition via Lapatinib treatment asymmetrically. L-side MaSCs are inhibited by Lapatinib whereas R-side MaSCs increase in self-renewal with Lapatinib treatment. MMTV-NeuTg/Tg mice overexpress the oncogene Neu also known as ErbB2 or HER2 and model HER2+ breast cancer. MMTVNeuTg/Tg mouse TMGs respond L-R discordantly to oncogene overexpression resulting in asymmetric ductal network formation and discordant gene regulation. Furthermore, MaSCs are increased asymmetrically enhancing L-side enrichment of MaSCs, and MaSC in vitro function was asynchronously effected. Additionally, when gene expression is inverted in the MMTV-NeuTg/Tg model, MaSC in vitro growth, self-renewal, and response to Lapatinib is also inverted. Inguinal mammary glands (IMGs) of the MMTV-NeuTg/Tg model show delayed molecular laterality and are less sensitive to oncogene over-expression. When WT mice are exposed to estrogen (E2) neonatally, E2 induces asymmetric ductal morphogenesis, asymmetrically reduces luminal cell differentiation, and induces an asymmetric increase in MaSCs in TMGs. IMGs of E2 treated mice have no detectable L-R differences in morphology, suggesting IMGs are not as sensitive to early E2 exposure. Lastly, L-R differences in TMG development are shown to have an embryonic origin. RXRα+/- mice with altered embryonic development have asymmetric TMG development but not IMG development. Taken together these data show that L-R differences in TMGs originate embryonically, TMGs are lateralized organs that respond to stimulus L-R differently, and TMGs are more sensitive to perturbation than IMGs. These L-R differences in MaSC populations during normal development allow for L-R different responses to neoplasia, as well as correlate with L-R differences in patient outcome and response to therapy

Associations Between Genetic Data and Quantitative Assessment of Normal Facial Asymmetry

Human facial asymmetry is due to a complex interaction of genetic and environmental factors. To identify genetic influences on facial asymmetry, we developed a method for automated scoring that summarizes local morphology features and their spatial distribution. A genome-wide association study using asymmetry scores from two local symmetry features was conducted and significant genetic associations were identified for one asymmetry feature, including genes thought to play a role in craniofacial disorders and development: NFATC1, SOX5, NBAS, and TCF7L1. These results provide evidence that normal variation in facial asymmetry may be impacted by common genetic variants and further motivate the development of automated summaries of complex phenotypes

Estimating Symmetry/Asymmetry in the Human Torso: A Novel Computational Method

Asymmetry in human body has largely been based on bilateral traits and/or subjective estimates, with potential usage in fields such as medicine, rehabilitation and apparel product design. In case of apparel, asymmetry in human body has been measured primarily by estimating differential linear measurement of bilateral traits. However, the characteristics of asymmetry can be better understood and be useful for clinicians and designers if it is quantified by considering the whole 3D surface. To address the prevailing issues in measuring asymmetry objectively, this research attempts to develop a novel method to quantify asymmetry that is robust, effective and non-invasive in operation. The method discussed here uses 3D scans of human torso to estimate asymmetry as a numerical index. Furthermore, using skeletal landmarks, twist and tilt measurements of the torsos are computed numerically. Together, these three measures can characterize the asymmetric/symmetric nature of a human torso. The approach taken in this research uses cross sections of torso to estimate local plane of symmetry that equi-divides a given cross section on the basis of its area, and connecting those planes to form a global surface that divides the torso volumetrically. The computational approach in estimating the area of cross section is based on the Green's theorem. The developed method was validated by both testing it on a known geometric model and by comparing the estimated index with subjective ratings by experts. This method has potential applications in various fields requiring characterizing asymmetry i.e., in case of scoliosis patients as diagnostic tool or an evaluation metric for rehabilitation efficiency, for body builders, and fashion models as an evaluation tool.Design, Housing and Merchandisin

Analysis of skull asymmetry in different historical periods using radiological examinations

Background: Asymmetry is a very common phenomenon in nature. Occurrence of asymmetry and knowledge of correct structure, especially a range of variability which is not a pathology but only an individual variation, are the basis for interpretation of results of radiological examination of the skulls both in research work and in diagnostic examinations, which are widely performed in modern medicine. There are many methods of estimation of the asymmetry. The aim of this study was to estimate the symmetry of skulls from selected historic populations. Material/Methods: The studied material consisted of two skull populations - contemporary consisting of 82 skulls and medieval - 77 skulls from Gródek. X-rays in P-A and skull-base projections were performed. The images were scanned and calibrated by means of MicroStation 95 Academic Edition software. Using tools for measurement of vector elements, distances between selected bilateral points of the skull were taken. All data were analyzed statistically. Results: Asymmetry was observed in the skulls of both populations. Some diameters were higher on the left side, some on the right side. High levels of asymmetry index in the superior facial part and in the posterior part of the skull base were observed. The levels of the asymmetry indexes in both groups were similar. Conclusions: Radiological pictures in two projections should be taken for correct analysis of the skull asymmetry. The examination of the asymmetry of the landmarks should be based on the analysis of diameters from two different points of reference. The human skull does not demonstrate a clear domination of one side. The largest variations were observed in the shape and localization of the foramina of the skull. It is associated with the differences of the position of the neurovascular elements which pass through these foramina

The role of interhemispheric cortico-cortical connections in bimanual coordination in the rat

Bimanual coordination – in which both hands work together to achieve a goal – is crucial for basic needs of life, such as gathering and feeding. The mammalian body has a left and right side which is often symmetrically shaped, but raises the question of how does the brain organize two sides of our body in a coordinated manner. The overall aim of this thesis is to better-understand neural mechanism of bimanual coordination. Bimanual coordination is highly developed in primates, where it has been most extensively studied. Rodents also exhibit remarkable dexterity and coordination of forelimbs during food handling and consumption. However, rodents have been less commonly used in the study of bimanual coordination because of limited quantitative measuring techniques. To study the neural mechanism of bimanual coordination using rodents, therefore, first requires a method to measure and classify bimanual movements. In this thesis, I propose a high-resolution tracking system that enables kinematic analysis of rat forelimb movements. The system quantifies forelimb movements bilaterally in head-fixed rats during food handling and consumption. Forelimb movements occurring naturally during feeding were encoded as continuous 3-D trajectories. The trajectories were then automatically segmented and analyzed, using a novel algorithm, according to the laterality of movement speed or the asymmetry of movement direction across the forelimbs. Bilateral forelimb movements were frequently observed during spontaneous food handling. Both symmetry and asymmetry in movement direction were observed, with symmetric bilateral movements quantitatively more common. Using the proposed method, I further investigated a key hypothesis that the corpus callosum, the thickest commissure connecting two cerebral cortices, mediates bimanual movements. I performed pharmacological blockade of the anterior corpus callosum (aCC) in which commissures from cortical forelimb motor areas are reciprocally connected. The kinematic analysis of bimanual coordination during food handling revealed that the frequency of occurrence of symmetric bimanual movements was reduced by aCC inhibition. In counterpart, asymmetric bimanual movements were increased. Other global scales of motor skills, such as mean food drop rate, and mean consumption time remained unchanged. Bilateral multiunit recordings from corresponding cortical areas showed positively correlated activity patterns in the large majority of interacting pairs. The present study also found that the putative excitatory neurons were also positively correlated with putative inhibitory neurons in the opposite hemisphere, suggesting interhemispheric inhibition via inhibitory neurons. Collectively, these results suggest that the symmetric bimanual movements in rodents are modulated by the anterior corpus callosum via both excitatory and inhibitory connections of two motor cortices.Okinawa Institute of Science and Technology Graduate Universit

Quantitative Multimodal Mapping Of Seizure Networks In Drug-Resistant Epilepsy

Over 15 million people worldwide suffer from localization-related drug-resistant epilepsy. These patients are candidates for targeted surgical therapies such as surgical resection, laser thermal ablation, and neurostimulation. While seizure localization is needed prior to surgical intervention, this process is challenging, invasive, and often inconclusive. In this work, I aim to exploit the power of multimodal high-resolution imaging and intracranial electroencephalography (iEEG) data to map seizure networks in drug-resistant epilepsy patients, with a focus on minimizing invasiveness. Given compelling evidence that epilepsy is a disease of distorted brain networks as opposed to well-defined focal lesions, I employ a graph-theoretical approach to map structural and functional brain networks and identify putative targets for removal. The first section focuses on mesial temporal lobe epilepsy (TLE), the most common type of localization-related epilepsy. Using high-resolution structural and functional 7T MRI, I demonstrate that noninvasive neuroimaging-based network properties within the medial temporal lobe can serve as useful biomarkers for TLE cases in which conventional imaging and volumetric analysis are insufficient. The second section expands to all forms of localization-related epilepsy. Using iEEG recordings, I provide a framework for the utility of interictal network synchrony in identifying candidate resection zones, with the goal of reducing the need for prolonged invasive implants. In the third section, I generate a pipeline for integrated analysis of iEEG and MRI networks, paving the way for future large-scale studies that can effectively harness synergy between different modalities. This multimodal approach has the potential to provide fundamental insights into the pathology of an epileptic brain, robustly identify areas of seizure onset and spread, and ultimately inform clinical decision making

Developing advanced mathematical models for detecting abnormalities in 2D/3D medical structures.

Detecting abnormalities in two-dimensional (2D) and three-dimensional (3D) medical structures is among the most interesting and challenging research areas in the medical imaging field. Obtaining the desired accurate automated quantification of abnormalities in medical structures is still very challenging. This is due to a large and constantly growing number of different objects of interest and associated abnormalities, large variations of their appearances and shapes in images, different medical imaging modalities, and associated changes of signal homogeneity and noise for each object. The main objective of this dissertation is to address these problems and to provide proper mathematical models and techniques that are capable of analyzing low and high resolution medical data and providing an accurate, automated analysis of the abnormalities in medical structures in terms of their area/volume, shape, and associated abnormal functionality. This dissertation presents different preliminary mathematical models and techniques that are applied in three case studies: (i) detecting abnormal tissue in the left ventricle (LV) wall of the heart from delayed contrast-enhanced cardiac magnetic resonance images (MRI), (ii) detecting local cardiac diseases based on estimating the functional strain metric from cardiac cine MRI, and (iii) identifying the abnormalities in the corpus callosum (CC) brain structure—the largest fiber bundle that connects the two hemispheres in the brain—for subjects that suffer from developmental brain disorders. For detecting the abnormal tissue in the heart, a graph-cut mathematical optimization model with a cost function that accounts for the object’s visual appearance and shape is used to segment the the inner cavity. The model is further integrated with a geometric model (i.e., a fast marching level set model) to segment the outer border of the myocardial wall (the LV). Then the abnormal tissue in the myocardium wall (also called dead tissue, pathological tissue, or infarct area) is identified based on a joint Markov-Gibbs random field (MGRF) model of the image and its region (segmentation) map that accounts for the pixel intensities and the spatial interactions between the pixels. Experiments with real in-vivo data and comparative results with ground truth (identified by a radiologist) and other approaches showed that the proposed framework can accurately detect the pathological tissue and can provide useful metrics for radiologists and clinicians. To estimate the strain from cardiac cine MRI, a novel method based on tracking the LV wall geometry is proposed. To achieve this goal, a partial differential equation (PDE) method is applied to track the LV wall points by solving the Laplace equation between the LV contours of each two successive image frames over the cardiac cycle. The main advantage of the proposed tracking method over traditional texture-based methods is its ability to track the movement and rotation of the LV wall based on tracking the geometric features of the inner, mid-, and outer walls of the LV. This overcomes noise sources that come from scanner and heart motion. To identify the abnormalities in the CC from brain MRI, the CCs are aligned using a rigid registration model and are segmented using a shape-appearance model. Then, they are mapped to a simple unified space for analysis. This work introduces a novel cylindrical mapping model, which is conformal (i.e., one to one transformation and bijective), that enables accurate 3D shape analysis of the CC in the cylindrical domain. The framework can detect abnormalities in all divisions of the CC (i.e., splenium, rostrum, genu and body). In addition, it offers a whole 3D analysis of the CC abnormalities instead of only area-based analysis as done by previous groups. The initial classification results based on the centerline length and CC thickness suggest that the proposed CC shape analysis is a promising supplement to the current techniques for diagnosing dyslexia. The proposed techniques in this dissertation have been successfully tested on complex synthetic and MR images and can be used to advantage in many of today’s clinical applications of computer-assisted medical diagnostics and intervention

Stags of the Sea or Hedgehogs of the Harbor? Inferring the Point of Sculpin Cranial Weaponry

Animal weapons are thought to have evolved to compete for reproductive opportunities within a species. Across the diverse weapon-bearing taxa, several evolutionary trends have emerged: (1) increasing complexity and relative size across ontogeny, (2) sexual dimorphism, and (3) higher levels of random deviations from symmetry (i.e., fluctuating asymmetry) than non-weaponized structures in the same individual. While the evolution of weapons in charismatic animals such as cervids and ceratopsian dinosaurs have received extensive attention, weapon evolution in fishes has received relatively little. In this dissertation, I explore the evolution of cranial weapons in a group of fishes known as sculpins (superfamily Cottoidea), specifically, the subfamily Oligocottinae. I use digital models of evolution built from computed tomography (CT) scans to quantitatively describe the shape of the weaponized preopercle bone and multivariate statistics to compare the shape across species. I examine the assumptions of common macroevolutionary techniques and make recommendations for how to accommodate natural variation in morphology. In the second chapter, coauthors and I contrast 2D vs. 3D landmark-based geometric morphometrics in the fish subfamily Oligocottinae by using 3D landmarks from CT-generated models and comparing the morphospace of the 3D landmarks to one based on 2D landmarks from images. The 2D and 3D shape variables capture common patterns across taxa, such that the pairwise Procrustes distances among taxa correspond and the trends captured by principal component analysis are similar in the xy plane. We use the two sets of landmarks to test several ecomorphological hypotheses from the literature. Both 2D and 3D data reject the hypothesis that head shape correlates significantly with the depth at which a species is commonly found. However, in taxa where shape variation in the z-axis is high, the 2D shape variables show sufficiently strong distortion to influence the outcome of the hypothesis tests regarding the relationship between mouth size and feeding ecology. In the third chapter, coauthors and I address the issue that, while virtually anyone can access the wealth of open access CT data that have been deposited onto repositories such as MorphoSource, relatively few have the training to easily derive a desirable product from them. This chapter fills the gap between the data and the researcher and provides a starting point for interested readers to begin their own analyses of CT data without requiring anything more than a reasonably up to date computer and access to the internet. We outline a set of practices in the production, visualization and analysis of CT data. We focus on those often-tedious nuances of data preparation, formatting, and navigating software that commonly hinder progress in CT-based studies of anatomy, functional morphology, and macroevolution. We also emphasize tools useful for creating pedagogical aides such as 3D prints and images of anatomical structures. In the fourth chapter, I infer the primary function of preopercular spines in oligocottine sculpins. From dissuading predators to gaining an edge on intraspecific rivals, weapons have evolved to meet various needs in both vertebrates and invertebrates. Animals with the most extreme weapons use them to battle conspecifics, but some weapons are used for defense against predation, and others serve as a signal. Many fishes have evolved armaments, but the function of these structures is rarely observed. How, for example, sculpins use the horn-like spines that project from their head remains mysterious. We used previously described trends in the morphology and development of weapons in terrestrial animals to deduce the function of the weaponized preopercle in all sixteen species of sculpins in the subfamily Oligocottinae, which display a diversity of spine shapes, reproductive habits, and degrees of territoriality. We investigated three hallmarks of offensive weapons: ontogenetic change, sexual dimorphism, and fluctuating asymmetry. Geometric morphometrics of microCT scans show no sexual dimorphism in preopercular spine shape, but there is phylogenetically widespread ontogenetic shape change. Fluctuating asymmetry is low to moderate across species. Taken together, these results suggest that despite a form that evokes comparisons to bovid horns, the spines of oligocottine sculpins have evolved primarily as a defense against predators. In the fifth chapter, coauthors and I describe the assumptions made both explicitly and implicitly in many studies of comparative anatomy and macroevolution and test whether these assumptions are robust in a case study of the preopercle shape in oligocottine sculpins. For example, many studies use only one side of one individual to represent the anatomy of a species. We test: (1) the degree to which the shape of the preopercle of one side of an individual matches the shape of the preopercle on its other side, (2) whether trends in ontogenetic shape change of the preopercle are identical on the left and right sides within a species, and (3) the degree to which intraspecific variation affects the outcomes of two common tests of comparative anatomy: allometric growth and morphological character evolution. We find that the left and right side of an individual are more similar in shape to each other than to the preopercle of a different individual only about 52% of the time and that, in fact, a small number of individuals (~2%) actually have a preopercle on one side of their head that is more similar in shape to the preopercle of a member of a different species than it is to the shape of the preopercle on the other side of their own head. We find that 4/17 species show statistically-significant allometric growth of the preopercle on one side of the head but not on the other. Finally, we find that intraspecific variation leads to highly unstable results of common macroevolutionary analyses when species are represented by low (n < 5 - 8) sample sizes. Taken together, these results suggest that trait estimates for species are robust only when based on modest to high sample sizes. They further show that systematic differences in shape and development thereof may be present in left vs. right sides of individuals within a species and careful consideration should be given to whether the left, right, or symmetric component of both is used to represent the shape of each individual