An New Energetic Approach to the Modeling of Human Joint Kinematics: Application to the Ankle

The objective of this dissertation is to develop and test a predictive model for the passive kinematics of human joints based on the energy minimization principle. To pursue this goal, the tibio-talar joint is chosen as a reference joint, for the reduced number of bones involved and its simplicity, if compared with other sinovial joints such as the knee or the wrist. Starting from the knowledge of the articular surface shapes, the spatial trajectory of passive motion is obtained as the envelop of joint configurations that maximize the surfaces congruence. An increase in joint congruence corresponds to an improved capability of distributing an applied load, allowing the joint to attain a better strength with less material. Thus, joint congruence maximization is a simple geometric way to capture the idea of joint energy minimization. The results obtained are validated against in vitro measured trajectories. Preliminary comparison provide strong support for the predictions of the theoretical model.

Technical innovations for the diagnosis and the rehabilitation of motor and perceptive impairments of the child with Cerebral Palsy

The treatment of the Cerebral Palsy (CP) is considered as the “core problem” for the whole field of the pediatric rehabilitation. The reason why this pathology has such a primary role, can be ascribed to two main aspects. First of all CP is the form of disability most frequent in childhood (one new case per 500 birth alive, (1)), secondarily the functional recovery of the “spastic” child is, historically, the clinical field in which the majority of the therapeutic methods and techniques (physiotherapy, orthotic, pharmacologic, orthopedic-surgical, neurosurgical) were first applied and tested. The currently accepted definition of CP – Group of disorders of the development of movement and posture causing activity limitation (2) – is the result of a recent update by the World Health Organization to the language of the International Classification of Functioning Disability and Health, from the original proposal of Ingram – A persistent but not unchangeable disorder of posture and movement – dated 1955 (3). This definition considers CP as a permanent ailment, i.e. a “fixed” condition, that however can be modified both functionally and structurally by means of child spontaneous evolution and treatments carried out during childhood. The lesion that causes the palsy, happens in a structurally immature brain in the pre-, peri- or post-birth period (but only during the firsts months of life). The most frequent causes of CP are: prematurity, insufficient cerebral perfusion, arterial haemorrhage, venous infarction, hypoxia caused by various origin (for example from the ingestion of amniotic liquid), malnutrition, infection and maternal or fetal poisoning. In addition to these causes, traumas and malformations have to be included. The lesion, whether focused or spread over the nervous system, impairs the whole functioning of the Central Nervous System (CNS). As a consequence, they affect the construction of the adaptive functions (4), first of all posture control, locomotion and manipulation. The palsy itself does not vary over time, however it assumes an unavoidable “evolutionary” feature when during growth the child is requested to meet new and different needs through the construction of new and different functions. It is essential to consider that clinically CP is not only a direct expression of structural impairment, that is of etiology, pathogenesis and lesion timing, but it is mainly the manifestation of the path followed by the CNS to “re”-construct the adaptive functions “despite” the presence of the damage. “Palsy” is “the form of the function that is implemented by an individual whose CNS has been damaged in order to satisfy the demands coming from the environment” (4). Therefore it is only possible to establish general relations between lesion site, nature and size, and palsy and recovery processes. It is quite common to observe that children with very similar neuroimaging can have very different clinical manifestations of CP and, on the other hand, children with very similar motor behaviors can have completely different lesion histories. A very clear example of this is represented by hemiplegic forms, which show bilateral hemispheric lesions in a high percentage of cases. The first section of this thesis is aimed at guiding the interpretation of CP. First of all the issue of the detection of the palsy is treated from historical viewpoint. Consequently, an extended analysis of the current definition of CP, as internationally accepted, is provided. The definition is then outlined in terms of a space dimension and then of a time dimension, hence it is highlighted where this definition is unacceptably lacking. The last part of the first section further stresses the importance of shifting from the traditional concept of CP as a palsy of development (defect analysis) towards the notion of development of palsy, i.e., as the product of the relationship that the individual however tries to dynamically build with the surrounding environment (resource semeiotics) starting and growing from a different availability of resources, needs, dreams, rights and duties (4). In the scientific and clinic community no common classification system of CP has so far been universally accepted. Besides, no standard operative method or technique have been acknowledged to effectively assess the different disabilities and impairments exhibited by children with CP. CP is still “an artificial concept, comprising several causes and clinical syndromes that have been grouped together for a convenience of management” (5). The lack of standard and common protocols able to effectively diagnose the palsy, and as a consequence to establish specific treatments and prognosis, is mainly because of the difficulty to elevate this field to a level based on scientific evidence. A solution aimed at overcoming the current incomplete treatment of CP children is represented by the clinical systematic adoption of objective tools able to measure motor defects and movement impairments. A widespread application of reliable instruments and techniques able to objectively evaluate both the form of the palsy (diagnosis) and the efficacy of the treatments provided (prognosis), constitutes a valuable method able to validate care protocols, establish the efficacy of classification systems and assess the validity of definitions. Since the ‘80s, instruments specifically oriented to the analysis of the human movement have been advantageously designed and applied in the context of CP with the aim of measuring motor deficits and, especially, gait deviations. The gait analysis (GA) technique has been increasingly used over the years to assess, analyze, classify, and support the process of clinical decisions making, allowing for a complete investigation of gait with an increased temporal and spatial resolution. GA has provided a basis for improving the outcome of surgical and nonsurgical treatments and for introducing a new modus operandi in the identification of defects and functional adaptations to the musculoskeletal disorders. Historically, the first laboratories set up for gait analysis developed their own protocol (set of procedures for data collection and for data reduction) independently, according to performances of the technologies available at that time. In particular, the stereophotogrammetric systems mainly based on optoelectronic technology, soon became a gold-standard for motion analysis. They have been successfully applied especially for scientific purposes. Nowadays the optoelectronic systems have significantly improved their performances in term of spatial and temporal resolution, however many laboratories continue to use the protocols designed on the technology available in the ‘70s and now out-of-date. Furthermore, these protocols are not coherent both for the biomechanical models and for the adopted collection procedures. In spite of these differences, GA data are shared, exchanged and interpreted irrespectively to the adopted protocol without a full awareness to what extent these protocols are compatible and comparable with each other. Following the extraordinary advances in computer science and electronics, new systems for GA no longer based on optoelectronic technology, are now becoming available. They are the Inertial and Magnetic Measurement Systems (IMMSs), based on miniature MEMS (Microelectromechanical systems) inertial sensor technology. These systems are cost effective, wearable and fully portable motion analysis systems, these features gives IMMSs the potential to be used both outside specialized laboratories and to consecutive collect series of tens of gait cycles. The recognition and selection of the most representative gait cycle is then easier and more reliable especially in CP children, considering their relevant gait cycle variability. The second section of this thesis is focused on GA. In particular, it is firstly aimed at examining the differences among five most representative GA protocols in order to assess the state of the art with respect to the inter-protocol variability. The design of a new protocol is then proposed and presented with the aim of achieving gait analysis on CP children by means of IMMS. The protocol, named ‘Outwalk’, contains original and innovative solutions oriented at obtaining joint kinematic with calibration procedures extremely comfortable for the patients. The results of a first in-vivo validation of Outwalk on healthy subjects are then provided. In particular, this study was carried out by comparing Outwalk used in combination with an IMMS with respect to a reference protocol and an optoelectronic system. In order to set a more accurate and precise comparison of the systems and the protocols, ad hoc methods were designed and an original formulation of the statistical parameter coefficient of multiple correlation was developed and effectively applied. On the basis of the experimental design proposed for the validation on healthy subjects, a first assessment of Outwalk, together with an IMMS, was also carried out on CP children. The third section of this thesis is dedicated to the treatment of walking in CP children. Commonly prescribed treatments in addressing gait abnormalities in CP children include physical therapy, surgery (orthopedic and rhizotomy), and orthoses. The orthotic approach is conservative, being reversible, and widespread in many therapeutic regimes. Orthoses are used to improve the gait of children with CP, by preventing deformities, controlling joint position, and offering an effective lever for the ankle joint. Orthoses are prescribed for the additional aims of increasing walking speed, improving stability, preventing stumbling, and decreasing muscular fatigue. The ankle-foot orthosis (AFO), with a rigid ankle, are primarily designed to prevent equinus and other foot deformities with a positive effect also on more proximal joints. However, AFOs prevent the natural excursion of the tibio-tarsic joint during the second rocker, hence hampering the natural leaning progression of the whole body under the effect of the inertia (6). A new modular (submalleolar) astragalus-calcanear orthosis, named OMAC, has recently been proposed with the intention of substituting the prescription of AFOs in those CP children exhibiting a flat and valgus-pronated foot. The aim of this section is thus to present the mechanical and technical features of the OMAC by means of an accurate description of the device. In particular, the integral document of the deposited Italian patent, is provided. A preliminary validation of OMAC with respect to AFO is also reported as resulted from an experimental campaign on diplegic CP children, during a three month period, aimed at quantitatively assessing the benefit provided by the two orthoses on walking and at qualitatively evaluating the changes in the quality of life and motor abilities. As already stated, CP is universally considered as a persistent but not unchangeable disorder of posture and movement. Conversely to this definition, some clinicians (4) have recently pointed out that movement disorders may be primarily caused by the presence of perceptive disorders, where perception is not merely the acquisition of sensory information, but an active process aimed at guiding the execution of movements through the integration of sensory information properly representing the state of one’s body and of the environment. Children with perceptive impairments show an overall fear of moving and the onset of strongly unnatural walking schemes directly caused by the presence of perceptive system disorders. The fourth section of the thesis thus deals with accurately defining the perceptive impairment exhibited by diplegic CP children. A detailed description of the clinical signs revealing the presence of the perceptive impairment, and a classification scheme of the clinical aspects of perceptual disorders is provided. In the end, a functional reaching test is proposed as an instrumental test able to disclosure the perceptive impairment. References 1. Prevalence and characteristics of children with cerebral palsy in Europe. Dev Med Child Neurol. 2002 Set;44(9):633-640. 2. Bax M, Goldstein M, Rosenbaum P, Leviton A, Paneth N, Dan B, et al. Proposed definition and classification of cerebral palsy, April 2005. Dev Med Child Neurol. 2005 Ago;47(8):571-576. 3. Ingram TT. A study of cerebral palsy in the childhood population of Edinburgh. Arch. Dis. Child. 1955 Apr;30(150):85-98. 4. Ferrari A, Cioni G. The spastic forms of cerebral palsy : a guide to the assessment of adaptive functions. Milan: Springer; 2009. 5. Olney SJ, Wright MJ. Cerebral Palsy. Campbell S et al. Physical Therapy for Children. 2nd Ed. Philadelphia: Saunders. 2000;:533-570. 6. Desloovere K, Molenaers G, Van Gestel L, Huenaerts C, Van Campenhout A, Callewaert B, et al. How can push-off be preserved during use of an ankle foot orthosis in children with hemiplegia? A prospective controlled study. Gait Posture. 2006 Ott;24(2):142-151.

Development of a new galaxy classification technique and its application to the zCOSMOS survey

The purpose of this Thesis is to develop a robust and powerful method to classify galaxies from large surveys, in order to establish and confirm the connections between the principal observational parameters of the galaxies (spectral features, colours, morphological indices), and help unveil the evolution of these parameters from $z \sim 1$ to the local Universe. Within the framework of zCOSMOS-bright survey, and making use of its large database of objects ($\sim 10\,000$ galaxies in the redshift range $0 < z \lesssim 1.2$) and its great reliability in redshift and spectral properties determinations, first we adopt and extend the \emph{classification cube method}, as developed by Mignoli et al. (2009), to exploit the bimodal properties of galaxies (spectral, photometric and morphologic) separately, and then combining together these three subclassifications. We use this classification method as a test for a newly devised statistical classification, based on Principal Component Analysis and Unsupervised Fuzzy Partition clustering method (PCA+UFP), which is able to define the galaxy population exploiting their natural global bimodality, considering simultaneously up to 8 different properties. The PCA+UFP analysis is a very powerful and robust tool to probe the nature and the evolution of galaxies in a survey. It allows to define with less uncertainties the classification of galaxies, adding the flexibility to be adapted to different parameters: being a fuzzy classification it avoids the problems due to a hard classification, such as the classification cube presented in the first part of the article. The PCA+UFP method can be easily applied to different datasets: it does not rely on the nature of the data and for this reason it can be successfully employed with others observables (magnitudes, colours) or derived properties (masses, luminosities, SFRs, etc.). The agreement between the two classification cluster definitions is very high. ``Early'' and ``late'' type galaxies are well defined by the spectral, photometric and morphological properties, both considering them in a separate way and then combining the classifications (classification cube) and treating them as a whole (PCA+UFP cluster analysis). Differences arise in the definition of outliers: the classification cube is much more sensitive to single measurement errors or misclassifications in one property than the PCA+UFP cluster analysis, in which errors are ``averaged out'' during the process. This method allowed us to behold the \emph{downsizing} effect taking place in the PC spaces: the migration between the blue cloud towards the red clump happens at higher redshifts for galaxies of larger mass. The determination of $M_{\mathrm{cross}}$ the transition mass is in significant agreement with others values in literature.

Lesion detection and classification in breast cancer: evaluation of approaches based on morphological features, tracer kinetic modelling and semi-quantitative parameters in MR functional imaging (DCE-MRI)

The diagnosis, grading and classification of tumours has benefited considerably from the development of DCE-MRI which is now essential to the adequate clinical management of many tumour types due to its capability in detecting active angiogenesis. Several strategies have been proposed for DCE-MRI evaluation. Visual inspection of contrast agent concentration curves vs time is a very simple yet operator dependent procedure, therefore more objective approaches have been developed in order to facilitate comparison between studies. In so called model free approaches, descriptive or heuristic information extracted from time series raw data have been used for tissue classification. The main issue concerning these schemes is that they have not a direct interpretation in terms of physiological properties of the tissues. On the other hand, model based investigations typically involve compartmental tracer kinetic modelling and pixel-by-pixel estimation of kinetic parameters via non-linear regression applied on region of interests opportunely selected by the physician. This approach has the advantage to provide parameters directly related to the pathophysiological properties of the tissue such as vessel permeability, local regional blood flow, extraction fraction, concentration gradient between plasma and extravascular-extracellular space. Anyway, nonlinear modelling is computational demanding and the accuracy of the estimates can be affected by the signal-to-noise ratio and by the initial solutions. The principal aim of this thesis is investigate the use of semi-quantitative and quantitative parameters for segmentation and classification of breast lesion. The objectives can be subdivided as follow: describe the principal techniques to evaluate time intensity curve in DCE-MRI with focus on kinetic model proposed in literature; to evaluate the influence in parametrization choice for a classic bi-compartmental kinetic models; to evaluate the performance of a method for simultaneous tracer kinetic modelling and pixel classification; to evaluate performance of machine learning techniques training for segmentation and classification of breast lesion.

In vivo evaluation of the translations of the gleno-humeral joint using Magnetic resonance imaging

Gleno-humeral joint (GHJ) is the most mobile joint of the human body. This is related to theincongr uence between the large humeral head articulating with the much smaller glenoid (ratio 3:1). The GHJ laxity is the ability of the humeral head to be passively translated on the glenoid fossa and, when physiological, it guarantees the normal range of motion of the joint. Three-dimensional GHJ linear displacements have been measured, both in vivo and in vitro by means of different instrumental techniques. In vivo gleno-humeral displacements have been assessed by means of stereophotogrammetry, electromagnetic tracking sensors, and bio-imaging techniques. Both stereophotogrammetric systems and electromagnetic tracking devices, due to the deformation of the soft tissues surrounding the bones, are not capable to accurately assess small displacements, such as gleno-humeral joint translations. The bio-imaging techniques can ensure for an accurate joint kinematic (linear and angular displacement) description, but, due to the radiation exposure, most of these techniques, such as computer tomography or fluoroscopy, are invasive for patients. Among the bioimaging techniques, an alternative which could provide an acceptable level of accuracy and that is innocuous for patients is represented by magnetic resonance imaging (MRI). Unfortunately, only few studies have been conducted for three-dimensional analysis and very limited data is available in situations where preset loads are being applied. The general aim of this doctoral thesis is to develop a non-invasive methodology based on open-MRI for in-vivo evaluation of the gleno-humeral translation components in healthy subjects under the application of external loads.

Three-dimensional joint kinematics of swimming using body-worn inertial and magnetic sensors

Wearable inertial and magnetic measurements units (IMMU) are an important tool for underwater motion analysis because they are swimmer-centric, they require only simple measurement set-up and they provide the performance results very quickly. In order to estimate 3D joint kinematics during motion, protocols were developed to transpose the IMMU orientation estimation to a biomechanical model. The aim of the thesis was to validate a protocol originally propositioned to estimate the joint angles of the upper limbs during one-degree-of-freedom movements in dry settings and herein modified to perform 3D kinematics analysis of shoulders, elbows and wrists during swimming. Eight high-level swimmers were assessed in the laboratory by means of an IMMU while simulating the front crawl and breaststroke movements. A stereo-photogrammetric system (SPS) was used as reference. The joint angles (in degrees) of the shoulders (flexion-extension, abduction-adduction and internal-external rotation), the elbows (flexion-extension and pronation-supination), and the wrists (flexion-extension and radial-ulnar deviation) were estimated with the two systems and compared by means of root mean square errors (RMSE), relative RMSE, Pearson’s product-moment coefficient correlation (R) and coefficient of multiple correlation (CMC). Subsequently, the athletes were assessed during pool swimming trials through the IMMU. Considering both swim styles and all joint degrees of freedom modeled, the comparison between the IMMU and the SPS showed median values of RMSE lower than 8°, representing 10% of overall joint range of motion, high median values of CMC (0.97) and R (0.96). These findings suggest that the protocol accurately estimated the 3D orientation of the shoulders, elbows and wrists joint during swimming with accuracy adequate for the purposes of research. In conclusion, the proposed method to evaluate the 3D joint kinematics through IMMU was revealed to be a useful tool for both sport and clinical contexts.

A New Test Rig for In-Vitro Evaluation of the Knee Joint Behaviour

The evaluation of the knee joint behavior is fundamental in many applications, such as joint modeling, prosthesis and orthosis design. In-vitro tests are important in order to analyse knee behavior when simulating various loading conditions and studying physiology of the joint. A new test rig for in-vitro evaluation of the knee joint behavior is presented in this paper. It represents the evolution of a previously proposed rig, designed to overcome its principal limitations and to improve its performances. The design procedure and the adopted solution in order to satisfy the specifications are presented here. Thanks to its 6-6 Gough-Stewart parallel manipulator loading system, the rig replicates general loading conditions, like daily actions or clinical tests, on the specimen in a wide range of flexion angles. The restraining actions of knee muscles can be simulated when active actions are simulated. The joint motion in response to the applied loads, guided by passive articular structures and muscles, is permitted by the characteristics of the loading system which is force controlled. The new test rig guarantees visibility so that motion can be measured by an optoelectronic system. Furthermore, the control system of the new test rig allows the estimation of the contribution of the principal leg muscles in guaranteeing the equilibrium of the joint by the system for muscle simulation. Accuracy in positioning is guaranteed by the designed tibia and femur fixation systems,which allow unmounting and remounting the specimen in the same pose. The test rig presented in this paper permits the analysis of the behavior of the knee joint and comparative analysis on the same specimen before and after surgery, in a way to assess the goodness of prostheses or surgical treatments.