Simultaneous inference for misaligned multivariate functional data

We consider inference for misaligned multivariate functional data that represents the same underlying curve, but where the functional samples have systematic differences in shape. In this paper we introduce a new class of generally applicable models where warping effects are modeled through nonlinear transformation of latent Gaussian variables and systematic shape differences are modeled by Gaussian processes. To model cross-covariance between sample coordinates we introduce a class of low-dimensional cross-covariance structures suitable for modeling multivariate functional data. We present a method for doing maximum-likelihood estimation in the models and apply the method to three data sets. The first data set is from a motion tracking system where the spatial positions of a large number of body-markers are tracked in three-dimensions over time. The second data set consists of height and weight measurements for Danish boys. The third data set consists of three-dimensional spatial hand paths from a controlled obstacle-avoidance experiment. We use the developed method to estimate the cross-covariance structure, and use a classification setup to demonstrate that the method outperforms state-of-the-art methods for handling misaligned curve data.Comment: 44 pages in total including tables and figures. Additional 9 pages of supplementary material and reference

A method for measuring human foot shape during running stance

Knowledge of the three dimensional shape of the human foot is important in the design of shoes to facilitate correct fit. Currently only the static shape of the foot is considered despite the fact that the foot undergoes changes in its shape, particularly in athletic pursuits, due to associated movements and loadings. Attempts, presented in research, have been made to measure dynamic foot shape. However, to date, measurements have been limited in detail as well as restricted to walking gait, as a result of the method. The work of this thesis aimed to develop a methodology that would be capable of measuring the three dimensional shape of the human foot during the stance phase of gait, in locomotion speeds associated with running. [Continues.

Mechanisms underlying muscle recruitment in response to postural perturbations

The neural and sensory mechanisms underlying appropriate muscle recruitment in response to balance challenges remains elusive. We asked whether the decerebrate cat preparation might be employed for further investigation of postural mechanisms. First, we evaluated the muscular activation patterns and three-dimensional whole limb forces generated by a modified premammillary decerebrated cat. We hypothesized that directionally appropriate muscle activation does not require the cerebral cortices. Furthermore, we hypothesized that the muscle responses would generate functionally appropriate and constrained force responses similar to those reported in the intact animal. Data confirmed both of our hypotheses and suggested important roles for the brainstem and spinal cord in mediating directionally appropriate muscular activation. Second, we investigated how individual muscle activation is translated to functional ground reaction forces. We hypothesized that muscles are selectively activated based upon their potential counteractive endpoint force. Data demonstrated that the endpoint force generated by each muscle through stimulation was directed oppositely to the principal direction of each muscle's EMG tuning curve. Further, muscles that have variable tuning curves were found to have variable endpoint forces in the XY plane. We further hypothesized that the biomechanical constraints of individual muscle actions generate the constrained ground reaction forces created in response to support surface perturbations. We found that there was a lack of muscles with strong medial-lateral actions in the XY plane. This was further exaggerated at long stance conditions, which corresponds to the increased force constraint present in the intact animal under the same conditions. Third, we investigated how loss of cutaneous feedback from the footpads affects the muscle recruitment in response to support surface perturbations. We utilized our decerebrate cat model as it allows 1) isolation of the proprioceptive system (cutaneous and muscle receptor) and 2) observation of the cutaneous loss before significant compensation by the animal. We hypothesized that muscle spindles drive directionally sensitive muscle activation during postural disturbances. Therefore, we expected that loss of cutaneous feedback from the foot soles would not alter the directional properties of muscle activation. While background activity was significantly diminished, the directionally sensitive muscular activation remained intact. Due to fixation of the head, the decerebrate cat additionally does not have access to vestibular or visual inputs. Therefore, this result strongly implicates muscle receptors as the primary source of directional feedback. Finally to confirm that muscle receptors, specifically muscle spindles, are capable of generating feedback to drive the directionally tuning, we investigated the response properties of muscle spindles to horizontal support surface perturbations in the anesthetized cat. As previously stated, we hypothesized that muscle spindles provide the feedback necessary for properly directed muscular responses. We further hypothesized that muscle spindles can relay feedback about the perturbation parameters such as velocity and the initial stance condtion. Results confirmed that muscle spindle generate activation patterns remarkably similar to muscular activation patterns generated in the intact cat. This information, along the knowledge that cutaneous feedback does not substantially eliminate directional tuning, strongly suggests that muscle spindles contribute the critical directional feedback to drive muscular activation in response to support surface perturbations.Ph.D.Committee Chair: T. Richard Nichols; Committee Member: Lena Ting; Committee Member: Shawn Hochman; Committee Member: Thomas Burkholder; Committee Member: Timothy Cop

Development of an Innovative Biomechanical Model for Clinical Gait Analysis

Work contained in this thesis describes a new biomechanical model for clinical gait analysis. Identified problems with current models are related to the subjective reasonableness of their underlying modelling assumptions and used to guide development of a new model. Gait scores were developed to evaluate alternative modelling solutions in terms of cycle average position, range, inter-cycle variability and movement pattern. An overly simple pro-forma model was developed to facilitate evaluation of the effects of complexity from alternative modelling approaches, both existing and newly developed. A clinical interpretation of Euler angles, widely used to describe joint orientations and movements, is presented. Leading directly from this interpretation, simple, joint-specific rules are derived that ensure calculated angles match clinical terminology. Other identified concerns are tackled on a per body-segment basis, with each segment presenting a different challenge. Identified problems with current trunk models were related to difficulties of orientating and tracking movement of the whole based on a selected sub-region. This was solved via the development of a more holistic solution, which additionally reduces the need for patient upper body exposure. For the pelvis and thigh segments, excessive soft tissue cover was identified as the major issue and resolved by the amalgamation of published methods with the novel introduction of fixed length thigh segments and a bespoke axial alignment calibration procedure. Foot model accuracy was improved by the application of bespoke calibration(s) that relates a defining flat foot posture to the position of surface markers, thus reducing the requirement for accurate placement over bony landmarks. Existing multi-segment foot models were grouped by a novel complexity index. Analysis of each group revealed an optimal balance with hind, medial forefoot, and lateral forefoot divisions. A model with this configuration was developed and outputs related to existing clinical terminology describing the foot shape

Biomechanics of Sport Rehabilitation

It is well known that athletes are frequently injured due to the large stress present in most sport performances as well as accidents of different nature. In most cases such lesions involve muscles, ligaments, joint, bones and in several cases also peripheral nerves. In all these cases clinical treatments for restoring the athlete's capabilities are applied: casting, immobilisation, surgical intervention, traditional and specific rehabilitation procedures. A question of great relevance concerns how and when the complete motor recovery of the athlete has been reached, In fact the parameters which are normally used to assess the complete recovery of a normal subject are not sufficient to assess the recovery of a high level athlete, considering the complex mechanical demand which the musculo-skeletal apparatus must satisfy to reach the required performance. In other words, after an accident, the motor recovery accepted for a normal subject can be absolutely inadequate for an athlete. It is therefore necessary to identify new techniques to assess the efficiency of the rehabilitation procedures in the sport domain. Recent technological developments make it possible simultaneous measurements and processing of a set of biomechanical variables related to kinematics, kinetics. and EMG activity during high level performance, so that the deviation from normality can be assessed, where normality is considered the reference pattern of the athlete when expressing a good performance and in the best shape. Such a quantitative evaluation of motor efficiency in .athletes is also important considering that in many cases of accident is difficult to differentiate the role of pure physiological deficiencies from the psychological ones which are often consistent in limiting the possibility of reaching results previously obtained. In order to reach this goal, it IS important to define suitable protocols to monitor the motor apparatus behaviour when performing selected exercises. In this presentation, the methodological approach used to set up the aforementioned protocols will be discussed. Examples of application for the evaluation of basic motor actions (vertical jumping, running) and of specific sport actions (cycling, sprint start, tennis) be illustrated with particular reference to performance assessment and rehabilitative applications

Precursor films in wetting phenomena

The spontaneous spreading of non-volatile liquid droplets on solid substrates poses a classic problem in the context of wetting phenomena. It is well known that the spreading of a macroscopic droplet is in many cases accompanied by a thin film of macroscopic lateral extent, the so-called precursor film, which emanates from the three-phase contact line region and spreads ahead of the latter with a much higher speed. Such films have been usually associated with liquid-on-solid systems, but in the last decade similar films have been reported to occur in solid-on-solid systems. While the situations in which the thickness of such films is of mesoscopic size are rather well understood, an intriguing and yet to be fully understood aspect is the spreading of microscopic, i.e., molecularly thin films. Here we review the available experimental observations of such films in various liquid-on-solid and solid-on-solid systems, as well as the corresponding theoretical models and studies aimed at understanding their formation and spreading dynamics. Recent developments and perspectives for future research are discussed.Comment: 51 pages, 10 figures; small typos correcte

The utility of gait as a biological characteristic in forensic investigations – An empirical examination of movement pattern variation using biomechanical and anthropological principles

Forensic gait analysis is generally defined as the analysis of gait features from video footage to assist in criminal investigations. Although an attractive means to detect suspects since data can be collected from a distance without their knowledge, forensic gait analysis presently lacks method validation and quality standards, not only due to insufficient research, but also because certain scientific foundations, such as the assumption of gait uniqueness, have not been adequately addressed. To test the scientific basis of this premise, a suitable dataset replicating an ideal forensic gait analysis scenario was compiled from the Karlsruhe Institute of Technology (Germany) database. Biomechanical analysis of sagittal plane human motion in the bilateral shoulder, elbow, hip, knee, and ankle joints was conducted across complete gait cycles of twenty participants, to investigate the degree to which intraindividual variation impacts interindividual variation, according to the following aims: (1) to better understand the relationship between form (anatomy) and function (physiology) of human gait, (2) to investigate the basis of gait uniqueness by examining similarities and differences in joint angles, and (3) to build upon current theoretical foundations of gait-based human identification. The findings indicate different degrees of movement asymmetry given body region and gait sub-phase, thereby challenging previous methods employing interchangeable use of bilateral motion data, and the use of ‘average’ gait cycles to represent the gait of an individual irrespective of body side. Furthermore, interindividual variability in all five joints is influenced by body side to different extents depending on gait sub-phase and body region, thereby challenging the claim of holistic uniqueness of gait features across all body regions and gait events. Given the findings of this thesis and paucity regarding empirical basis to support expertise, exerting caution when evaluating gait-based evidence admissibility is highly recommended, since the utility of gait in identification is currently limited