Methodology to Analyse Three-Dimensional Asymmetries in the Forces Applied to the Pedals in Cycling.

The asymmetries study between both legs of the forces applied to the pedals in cycling is important because they may affect the performance of the cyclist or prevent the occurrence of injuries. Studies focused on analysing asymmetries in forces tend to consider only the effective force, disregarding the three-dimensional nature of the force. Furthermore, these studies do not analyse the possible physical or neurological causes that may have led to the appearance of the asymmetries. This paper presents a methodology to carry out three-dimensional analysis of the asymmetries of the forces applied in both pedals and discriminate the possible sources of these asymmetries. Seven participants, amateurs and without pathologies, were analysed. Two commercial pedals were instrumented to measure the three components of the force applied to each pedal. The Normalized Symmetry Index (NSI) and the Cross Correlation Coefficient (CCC) were used for the asymmetries analysis. Results showed that both indexes need to be used in conjunction to analyse the causes of asymmetry in the pedal forces from a 3D perspective along the pedal cycle. The NSI is an index that makes it possible to evaluate asymmetry by considering only the value of the force applied by each leg at each instant. The CCC makes it possible to evaluate whether the temporal evolutions of the forces applied by each leg are similar. Preliminary results suggest that the proposed methodology is effective for analysing asymmetries in the forces in a pedalling cycle from a three-dimensional point of view. Forces in the sagittal plane showed a high level of symmetry. The lateral-medial force presented the highest level of asymmetry due to the difference in the magnitudes of the applied forces by both legs and the existing time shift between the two force patterns. The results of this work will allow for more complete and accurate three-dimensional dynamic analyses of the lower body during pedalling.

Design and Validation of a Device Attached to a Conventional Bicycle to Measure the Three-Dimensional Forces Applied to a Pedal.

Knowledge of the forces applied to the pedals during cycling is of great importance both from the point of view of improving sporting performance and medical analysis of injuries. The most common equipment for measuring pedal forces is usually limited to the study of forces in the sagittal plane. Equipment that measures three-dimensional forces tends to be bulky and to be incorporated into bicycles that are modified to accommodate it, which can cause the measurements taken to differ from those obtained in real pedalling conditions. This work presents a device for measuring the 3D forces applied to the pedal, attachable to a conventional bicycle and pedals, which does not alter the natural pedalling of cyclists. The equipment consists of four gauges located on the pedal axis and two on the crank, controlled by a microcontroller. Pedal forces measurements were made for six cyclists, with results similar to those shown in the literature. The correct estimation of the lateral-medial direction force is of great interest when evaluating a possible overload at the joints; it will also allow a comparison of the effectiveness index during pedalling, showing the role of this component in this index from a mechanical standpoint.

A procedure to estimate normal and friction contact parameters in the stance phase of the human gait.

A new approach to estimate normal and tangential contact parameters in the foot-ground contact during human gait was proposed. A correct estimation of the contact parameters would be very important in the resolution of predictive forward dynamic problems. The normal contact forces have been well estimated in the literature. But accurate estimation of tangential forces has not been reached yet. This work proposed a new procedure to accurately estimate friction forces. The approach has been based on the consideration of the modulus of the tangential force instead of its components. This modulus was introduced together with the modulus of the normal contact force and its two associated moments in an optimization algorithm to fit the contact forces provided by the model to the experimental data obtained with a force plate. An inverse dynamics problem was solved as a step previous to the optimization algorithm. The results showed that both the normal and tangential forces and the moments in the horizontal plane were in agreement with the experimental measurements. This work also analyzed the influence on the results of the friction law. The results obtained with the general friction law, which considered dry (static and dynamic) and viscous friction, were compared with results provided by simpler laws. The analysis of the components of the friction forces pointed out the importance of the Stribeck component in the resultant force instead of the viscous friction which played a minimal role. But for modelling the stick-slip transition, the implementation of a general friction law is necessary.

On the Use of Bone Remodelling Models to Estimate the Density Distribution of Bones. Uniqueness of the Solution.

Bone remodelling models are widely used in a phenomenological manner to estimate numerically the distribution of apparent density in bones from the loads they are daily subjected to. These simulations start from an arbitrary initial distribution, usually homogeneous, and the density changes locally until a bone remodelling equilibrium is achieved. The bone response to mechanical stimulus is traditionally formulated with a mathematical relation that considers the existence of a range of stimulus, called dead or lazy zone, for which no net bone mass change occurs. Implementing a relation like that leads to different solutions depending on the starting density. The non-uniqueness of the solution has been shown in this paper using two different bone remodelling models: one isotropic and another anisotropic. It has also been shown that the problem of non-uniqueness is only mitigated by removing the dead zone, but it is not completely solved unless the bone formation and bone resorption rates are limited to certain maximum values.

Finite element analysis of the human mastication cycle.

The aim of this paper is to propose a biomechanical model that could serve as a tool to overcome some difficulties encountered in experimental studies of the mandible. One of these difficulties is the inaccessibility of the temporomandibular joint (TMJ) and the lateral pterygoid muscle. The focus of this model is to study the stresses in the joint and the influence of the lateral pterygoid muscle on the mandible movement. A finite element model of the mandible, including the TMJ, was built to simulate the process of unilateral mastication. Different activation patterns of the left and right pterygoid muscles were tried. The maximum stresses in the articular disc and in the whole mandible during a complete mastication cycle were reached during the instant of centric occlusion. The simulations show a great influence of the coordination of the right and left lateral pterygoid muscles on the movement of the jaw during mastication. An asynchronous activation of the lateral pterygoid muscles is needed to achieve a normal movement of the jaw during mastication.

A study of the temporomandibular joint during bruxism.

A finite element model of the temporomandibular joint (TMJ) and the human mandible was fabricated to study the effect of abnormal loading, such as awake and asleep bruxism, on the articular disc. A quasilinear viscoelastic model was used to simulate the behaviour of the disc. The viscoelastic nature of this tissue is shown to be an important factor when sustained (awake bruxism) or cyclic loading (sleep bruxism) is simulated. From the comparison of the two types of bruxism, it was seen that sustained clenching is the most detrimental activity for the TMJ disc, producing an overload that could lead to severe damage of this tissue.

Effect of non-uniform thickness of samples in stress relaxation tests under unconfined compression of samples of articular discs.

A precise information of the biomechanical properties of soft tissues is required to develop a suitable simulation model, with which the distribution of stress and strain in the complex structures can be estimated. Many soft tissues have been mechanically characterized by stress relaxation tests under unconfined or confined compression. In general, full-thickness samples are extracted to reduce the damage in the tissue as much as possible. However, it is not guaranteed that these samples have a uniform thickness or, in other words, planar parallel faces. In particular, in the articular disc of the temporomandibular joint, many studies can be found testing full-thickness samples for which that thickness is known to be non-uniform, while making the assumption of uniaxial stress state to extract the mechanical properties from those tests. That inaccuracy may have a strong influence in some cases and needs a profound revision. The main goal of this work is to quantify the error committed in that assumption and the influence of the variation of thickness on that error in a particular test: stress relaxation tests under unconfined compression. Based on this error and defining an allowable tolerance, a criterion is established to reject samples depending on their aspect ratio.

Numerical simulation of a relaxation test designed to fit a quasi-linear viscoelastic model for temporomandibular joint discs.

The main objectives of this work are: (a) to introduce an algorithm for adjusting the quasi-linear viscoelastic model to fit a material using a stress relaxation test and (b) to validate a protocol for performing such tests in temporomandibular joint discs. This algorithm is intended for fitting the Prony series coefficients and the hyperelastic constants of the quasi-linear viscoelastic model by considering that the relaxation test is performed with an initial ramp loading at a certain rate. This algorithm was validated before being applied to achieve the second objective. Generally, the complete three-dimensional formulation of the quasi-linear viscoelastic model is very complex. Therefore, it is necessary to design an experimental test to ensure a simple stress state, such as uniaxial compression to facilitate obtaining the viscoelastic properties. This work provides some recommendations about the experimental setup, which are important to follow, as an inadequate setup could produce a stress state far from uniaxial, thus, distorting the material constants determined from the experiment. The test considered is a stress relaxation test using unconfined compression performed in cylindrical specimens extracted from temporomandibular joint discs. To validate the experimental protocol, the test was numerically simulated using finite-element modelling. The disc was arbitrarily assigned a set of quasi-linear viscoelastic constants (c1) in the finite-element model. Another set of constants (c2) was obtained by fitting the results of the simulated test with the proposed algorithm. The deviation of constants c2 from constants c1 measures how far the stresses are from the uniaxial state. The effects of the following features of the experimental setup on this deviation have been analysed: (a) the friction coefficient between the compression plates and the specimen (which should be as low as possible); (b) the portion of the specimen glued to the compression plates (smaller areas glued are better); and (c) the variation in the thickness of the specimen. The specimen's faces should be parallel to ensure a uniaxial stress state. However, this is not possible in real specimens, and a criterion must be defined to accept the specimen in terms of the specimen's thickness variation and the deviation of the fitted constants arising from such a variation.