A mathematical model of interleukin-6 dynamics during exercise

Physical exercise is known to reduce the chronic inflammatory status that leads to Type 2 Diabetes. Its beneficial effects seem to be exerted trough a primary production of the cytokine Interleukin-6 (IL-6) which triggers a cascade of anti-inflammatory cytokines. Consequently, IL-6 has a central role in the description of the metabolic effects of exercise. The aim of this study was to develop a model of IL-6 dynamics during exercise. A model constituted by two non-linear differential equations is proposed. Since IL-6 production seems to be dependent not only on exercise duration but also on exercise intensity, input to the model is represented by heart rate, which is known to correlate well with exercise intensity. Model implementation in a Matlab-based parametric identification procedure allowed optimization of adjustable characteristic coefficients of IL-6 dynamics during exercise. From the reported results, it can be concluded that this model is a suitable tool to reproduce IL-6 time course during the execution of a physical exercise. This model was the first step of a project aimed at describing the complete immune system response to exercise and at giving a comprehensive sight of the effects that exercise has on the metabolic system

Foot kinematics in patients with two patterns of pathological plantar hyperkeratosis

Background: The Root paradigm of foot function continues to underpin the majority of clinical foot biomechanics practice and foot orthotic therapy. There are great number of assumptions in this popular paradigm, most of which have not been thoroughly tested. One component supposes that patterns of plantar pressure and associated hyperkeratosis lesions should be associated with distinct rearfoot, mid foot, first metatarsal and hallux kinematic patterns. Our aim was to investigate the extent to which this was true. Methods: Twenty-seven subjects with planter pathological hyperkeratosis were recruited into one of two groups. Group 1 displayed pathological plantar hyperkeratosis only under metatarsal heads 2, 3 and 4 (n = 14). Group 2 displayed pathological plantar hyperkeratosis only under the 1st and 5th metatarsal heads (n = 13). Foot kinematics were measured using reflective markers on the leg, heel, midfoot, first metatarsal and hallux. Results: The kinematic data failed to identify distinct differences between these two groups of subjects, however there were several subtle (generally <3°) differences in kinematic data between these groups. Group 1 displayed a less everted heel, a less abducted heel and a more plantarflexed heel compared to group 2, which is contrary to the Root paradigm. Conclusions: There was some evidence of small differences between planter pathological hyperkeratosis groups. Nevertheless, there was too much similarity between the kinematic data displayed in each group to classify them as distinct foot types as the current clinical paradigm proposes

Knee Kinematics Estimation Using Multi-Body Optimisation Embedding a Knee Joint Stiffness Matrix: A Feasibility Study

The use of multi-body optimisation (MBO) to estimate joint kinematics from stereophotogrammetric data while compensating for soft tissue artefact is still open to debate. Presently used joint models embedded in MBO, such as mechanical linkages, constitute a considerable simplification of joint function, preventing a detailed understanding of it. The present study proposes a knee joint model where femur and tibia are represented as rigid bodies connected through an elastic element the behaviour of which is described by a single stiffness matrix. The deformation energy, computed from the stiffness matrix and joint angles and displacements, is minimised within the MBO. Implemented as a “soft” constraint using a penalty-based method, this elastic joint description challenges the strictness of “hard” constraints. In this study, estimates of knee kinematics obtained using MBO embedding four different knee joint models (i.e., no constraints, spherical joint, parallel mechanism, and elastic joint) were compared against reference kinematics measured using bi-planar fluoroscopy on two healthy subjects ascending stairs. Bland-Altman analysis and sensitivity analysis investigating the influence of variations in the stiffness matrix terms on the estimated kinematics substantiate the conclusions. The difference between the reference knee joint angles and displacements and the corresponding estimates obtained using MBO embedding the stiffness matrix showed an average bias and standard deviation for kinematics of 0.9±3.2° and 1.6±2.3 mm. These values were lower than when no joint constraints (1.1±3.8°, 2.4±4.1 mm) or a parallel mechanism (7.7±3.6°, 1.6±1.7 mm) were used and were comparable to the values obtained with a spherical joint (1.0±3.2°, 1.3±1.9 mm). The study demonstrated the feasibility of substituting an elastic joint for more classic joint constraints in MBO

Analysis of finger movement coordination during the Variable Dexterity Test and comparative activities of daily living

Background/Aims: This study aimed to analyse and compare finger coordination patterns during the performance of the Variable Dexterity Test (VDT) and comparative daily tasks. Methods: An optoelectronic system was used to record the joint angles of 10 healthy participants performing the VDT and daily tasks. Joint angles from digits 1 to 5 were cross-correlated across the tasks, providing a measure of the degree of finger movement coordination. Results: Correlation coefficients showed identifiable coordination patterns among the finger movements under analysis. Low correlation coefficients suggested the presence of independent finger movements during the performance of the selected tasks. Conclusions: Finger movement coordination patterns observed during activities of daily living are comparable with the patterns observed during performance of the Variable Dexterity Test for the three grasping patterns analysed in the stud

Modeling the human tibio-femoral joint using ex vivo determined compliance matrices.

Several approaches have been used to devise a model of the human tibio-femoral joint for embedment in lower limb musculoskeletal models. However, no study has considered the use of cadaveric 6x6 compliance (or stiffness) matrices to model the tibio-femoral joint under normal or pathological conditions. The aim of this paper is to present a method to determine the compliance matrix of an ex vivo tibio-femoral joint for any given equilibrium pose. Experiments were carried out on a single ex vivo knee, first intact and, then, with the anterior cruciate ligament (ACL) transected. Controlled linear and angular displacements were imposed in single degree-of-freedom (DoF) tests to the specimen and resulting forces and moments measured using an instrumented robotic arm. This was done starting from seven equilibrium poses characterized by the following flexion angles: 0°, 15°, 30°, 45°, 60°, 75°and 90°. A compliance matrix for each of the selected equilibrium poses and for both the intact and ACL deficient specimen was calculated. The matrix, embedding the experimental load-displacement relationship of the examined DoFs, was calculated using a linear least squares inversion based on a QR decomposition, assuming symmetric and positive-defined matrices. Single compliance matrix terms were in agreement with the literature. Results showed an overall increase of the compliance matrix terms due to the ACL transection (2.6 ratio for rotational terms at full extension) confirming its role in the joint stabilization. Validation experiments were carried out by performing a Lachman test (the tibia is pulled forward) under load control on both the intact and ACL-deficient knee and assessing the difference (error) between measured linear and angular displacements and those estimated using the appropriate compliance matrix. This error increased non-linearly with respect to the values of the load. In particular, when an incremental posterior-anterior force up to 6 N was applied to the tibia of the intact specimen, the errors on the estimated linear and angular displacements were up to 0.6 mm and 1.5°, while for a force up to 18 N the errors were 1.5 mm and 10.5°, respectively. In conclusion, the method used in this study may be a viable alternative to characterize the tibio-femoral load-dependent behavior in several applications

Integration of Human Walking Gyroscopic Data Using Empirical Mode Decomposition

The present study was aimed at evaluating the Empirical Mode Decomposition (EMD) method to estimate the 3D orientation of the lower trunk during walking using the angular velocity signals generated by a wearable inertial measurement unit (IMU) and notably flawed by drift. The IMU was mounted on the lower trunk (L4-L5) with its active axes aligned with the relevant anatomical axes. The proposed method performs an offline analysis, but has the advantage of not requiring any parameter tuning. The method was validated in two groups of 15 subjects, one during overground walking, with 180° turns, and the other during treadmill walking, both for steady-state and transient speeds, using stereophotogrammetric data. Comparative analysis of the results showed that the IMU/EMD method is able to successfully detrend the integrated angular velocities and estimate lateral bending, flexion-extension as well as axial rotations of the lower trunk during walking with RMS errors of 1 deg for straight walking and lower than 2.5 deg for walking with turns

Monitoring tools for robust estimation of cluster weighted models

In a robust approach to model fitting for the cluster weighted model, many choices are to be made by the statistician: specifying the shape of the clusters in the explanatory variables, assuming (or not) equal variance for the errors in the re- gression lines, and setting hyper-parameter values for the robust estimation to be protected from outliers and contamination. The most delicate hyper-parameter to specify is perhaps the percentage of trimming, or the amount of data to be excluded from the estimate, to ensure reliable inference. In this work we introduce diagnos- tic tools to help the professional, or the scientist who needs to group the data, to make an educated choice about this hyper-parameter, after a first exploration of the resulting model space

Monitoring tools for robust estimation of cluster weighted models = Strumenti di monitoring per la stima robusta del modello Cluster Weighted

Nella stima robusta di un cluster weighted model, lo statistico deve fare molte scelte: specificare la forma dei cluster nelle variabili esplicative, assumere (o meno) varianza uguale per gli errori nelle linee di regressione e impostare i va- lori degli iper-parametri per la stima robusta, per evitare la distorsione generata da valori anomali e contaminazione. L’iper-parametro pi`u delicato da specificare `e la percentuale di trimming, ovvero la quantit`a di dati da escludere nella stima per garantirne l’affidabilit`a. In questo lavoro introduciamo specifici strumenti dia- gnostici per aiutare il professionista, o lo scienziato che ha bisogno di classificare i dati, a compiere una scelta ragionata a riguardo di tale iper-parametro, anche in base ad una prima esplorazione dello spazio delle soluzioni.In a robust approach to model fitting for the cluster weighted model, many choices are to be made by the statistician: specifying the shape of the clusters in the explanatory variables, assuming (or not) equal variance for the errors in the re- gression lines, and setting hyper-parameter values for the robust estimation to be protected from outliers and contamination. The most delicate hyper-parameter to specify is perhaps the percentage of trimming, or the amount of data to be excluded from the estimate, to ensure reliable inference. In this work we introduce diagnos- tic tools to help the professional, or the scientist who needs to group the data, to make an educated choice about this hyper-parameter, after a first exploration of the resulting model space

Group-wise penalized estimation schemes in model-based clustering

Gaussian mixture models provide a probabilistically sound clustering approach. However, their tendency to be over-parameterized endangers their utility in high dimensions. To induce sparsity, penalized model-based clustering strategies have been explored. Some of these approaches, exploiting the link between Gaussian graphical models and mixtures, allow to handle large precision matrices, encoding variables relationships. By assuming similar components sparsity levels, these methods fall short when the dependence structures are group-dependent. Our proposal, by penalizing group-specific transformations of the precision matrices, automatically handles situations where under or over-connectivity between variables is witnessed. The performances of the method are shown via a real data experimen

Penalized Model-Based Clustering with Group-Dependent Shrinkage Estimation

Gaussian mixture models (GMM) are the most-widely employed approach to perform model-based clustering of continuous features. Grievously, with the increasing availability of high-dimensional datasets, their direct applicability is put at stake: GMMs suffer from the curse of dimensionality issue, as the number of parameters grows quadratically with the number of variables. To this extent, a methodological link between Gaussian mixtures and Gaussian graphical models has recently been established in order to provide a framework for performing penalized model-based clustering in presence of large precision matrices. Notwithstanding, current methodologies do not account for the fact that groups may be under or over-connected, thus implicitly assuming similar levels of sparsity across clusters. We overcome this limitation by defining data-driven and component specific penalty factors, automatically accounting for different degrees of connections within groups. A real data experiment on handwritten digits recognition showcases the validity of our proposal