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.Ministerio de Economía y Competitividad DPI2013-44371-PMinisterio de Economía y Competitividad DPI2014-58233-

About kinematic consistency in the inverse dynamics problem in biomechanics

No se encuentra entidad editora.The inverse dynamic analysis is used in the study of the human gait to evaluate the reaction forces transmitted between anatomical segments and to calculate the net joint moments resulting from the muscle activity in each joint. There are two approaches well defined. In the clinical field reconstruction techniques are often applied. The errors caused, mainly, by the relative movement of the skin over the bones make that the joint centres localized in two adjacent segments do not place the same position in the space. Velocities and accelerations are obtained through numerical derivation of the position. Finally, joint moment are calculated to balance the equilibrium equations. On the other hand, the engineers employ multibody models. They apply techniques to reduce the measurement errors and to obtain kinematically consistent data up to the acceleration level and calculate reaction and driving actions by means of the Lagrange multipliers. There is no agreement about which approach provides better results. The first procedure presents errors due to the skin motion which are avoid in the second method introducing errors inherent to the model. In this work, the two approaches were compared. Dynamic residuals defined to balance the Newton's equations were used as a measure of the model goodness. A discussion about the effect of the kinematically inconsistent data on the second approach was carried out. Results highlighted that the addition to the recorded motion of kinematic constrains according to a multibody model could lead to worse results in the inverse dynamic problem

Influence of musculotendon geometry variability in muscle forces and hip bone-on-bone forces during walking

Inverse dynamics problems are usually solved in the analysis of human gait to obtain reaction forces and moments at the joints. However, these actions are not the actual forces and moments supported by the joint structure, because they do not consider the forces of the muscles acting across the joint. Therefore, to analyse bone-on bone forces it is necessary to estimate those muscle forces. Usually, this problem is addressed by means of optimization algorithms. One of the parameters required to solve this problem is the musculotendon geometry. These data are usually taken from cadavers or MRI data from several subjects, different from the analysed subject. Then, the model is scaled to the subject morphology. This procedure constitutes a source of error. The goals of this work were two. First, to perform a sensitivity analysis of the influence of muscle insertion locations on the muscle forces acting on the hip joint and on the hip joint bone-on-bone forces. Second, to compare the hip joint bone-on-bone forces during gait cycle obtained through muscle insertion locations taken from a musculoskeletal model template and a scaling procedure to those obtained from a subject-specific model using an MRI of the subject. The problem was solved using OpenSim. Results showed that anatomical variability should be analysed from two perspectives. One the one hand, throughout the gait cycle, in a global way. On the other hand, at a characteristic instant of the gait cycle. Variations of ±1 cm in the position of the attachment points of certain muscles caused variations of up to 14.21% in averaged deviation of the muscle forces and 58.96% in the peak force in the modified muscle and variations up to 57.23% in the averaged deviation of the muscle force and up to 117.23% in the peak force in the rest of muscles. Then, the influence of that variability on muscle activity patterns and hip bone-on-bone forces could be described more precisely. A biomechanical analysis of a subject-specific musculoskeletal model was carried out. Using MRI data, variations up to 5 cm in the location of the insertion points were introduced. These modifications showed significant differences between the baseline model and the customized model: within the range [-12%, 10%] for muscle forces and around 35% of body weight for hip bone-on-bone forces.Ministerio de Economía, Industria y Competitividad DPI2016-80796-P

Influence of the Temporomandibular Joint in the Estimation of Bone Density in the Mandible through a Bone Remodelling Model

Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly citedThe temporomandibular joint (TMJ) plays a key role in the distribution of stresses in the mandible during mastication and consequently in the distribution of bone density, due to the interconnection between both variables through bone remodelling. Two finite element models of the mandible were compared to study the influence of the redistribution of stresses produced by the joint: (1) a model without TMJ, but with simplified boundary conditions to replace the joint, as done in previous models; (2) a more realistic model including the articular disc and some ligaments present in the TMJ. The stresses and strains in both models were compared through the strain energy density, used in many bone remodelling models as a measure of the mechanical stimulus. An anisotropic bone remodelling model was used to simulate the behaviour of mandible bone and to estimate its density distribution. The results showed that the TMJ strongly affects the stress distribution, the mechanical stimulus, and eventually the bone density, and not only locally in the condyle, but also in the whole mandible. It is concluded that it is utterly important to include a detailed model of the TMJ to estimate more correctly the stresses in the mandible during mastication and, from them, the bone density and anisotropy distribution

Reliability and Validity Study of the Chamorro Assisted Gait Scale for People with Sprained Ankles, Walking with Forearm Crutches

Objective The aim of this study was to design and validate a functional assessment scale for assisted gait with forearm crutches (Chamorro Assisted Gait Scale—CHAGS) and to assess its reliability in people with sprained ankles. Design Thirty subjects who suffered from sprained ankle (anterior talofibular ligament first and second degree) were included in the study. A modified Delphi technique was used to obtain the content validity. The selected items were: pelvic and scapular girdle dissociation(1), deviation of Center of Gravity(2), crutch inclination(3), steps rhythm(4), symmetry of step length(5), cross support(6), simultaneous support of foot and crutch(7), forearm off(8), facing forward(9) and fluency(10). Two raters twice visualized the gait of the sample subjects which were recorded. The criterion-related validity was determined by correlation between CHAGS and Coding of eight criteria of qualitative gait analysis (Viel Coding). Internal consistency and inter and intra-rater reliability were also tested. Results CHAGS obtained a high and negative correlation with Viel Coding. We obtained a good internal consistency and the intra-class correlation coefficients oscillated between 0.97 and 0.99, while the minimal detectable changes were acceptable. Conclusion CHAGS scale is a valid and reliable tool for assessing assisted gait with crutches in people with sprained ankles to perform partial relief of lower limbs.Telefonica Chair “Intelligence in Networks” of the University of Seville, Spai

The effect of kinematic constraints in the inverse dynamics problem in biomechanics

The inverse dynamics is a classic problem to be solved in gait analysis. The solution is the vector of joint reactions and driving actions which is essential to perform a kinetic analysis of the human gait. Multibody system techniques are widely used to solve this problem. However, it is not clear in the literature if mathematical constraints of the joints should be fulfilled nor what is the effect of these constraints on the kinetic results. The effect of using or not kinematic data consistent with the joint constraints on the kinetic results is not clear either. Different methods to solve the inverse kinematics and inverse kinetics problems were implemented in this work to satisfy the joint constraints, the procedure to fulfil them or the type of joint constraints imposed. The goodness of these methods has been evaluated by means of dynamic residuals, which are required due to all the errors arising from gait measurement that may unbalance the dynamic equation. Results show that the imposition of kinematic constraints can lead to worse results in the kinetic results if the multibody model is too simplistic. However, this kind of approach can be necessary if further studies are performed, as a force sharing problem, where the reaction and driving actions should be properly defined

Infuence of the load exerted over a forearm crutch in spatiotemporal step parameters during assisted gait: pilot study

Background: Assisted gait with forearm crutches is frequently performed during the recovery of musculoskeletal injuries of the lower limb. The amount of body weight applied to the crutch or crutches depends on the pathology and the treatment phase. The transition from assisted gait with two crutches to a single crutch is usually rec‑ ommended when the subject is able to load the 50% of the body weight upon the afected member. An altered assisted gait will cause biomechanic alterations and, therefore, longer treatments and relapses. The aim of this study was to analyze the infuence of 10, 25 and 50% of body weight applied to a forearm crutch during a uni‑ lateral assisted gait in the spatial and temporal step parameters to determine the load that produces alterations in gait biomechanics and the load that does not. Methods: Eleven healthy subjects performed normal gait (NG) and assisted gait with a forearm crutch, in which the applied loads were: comfortable (C), 25 and 50% of their body weight. Vicon System was employed for gait recording. GCH System 2.0 and GCH Control Software 1.0 controlled the loads. The variables were: step length, step period, velocity, step width and step angle. Friedman test compared all the gait modalities: NG and the diferent loads. Wilcoxon signed-rank test analyzed ipsilateral and contralateral step parameters to the crutch globally and for each subject. Results: Friedman test showed signifcant diferences between NG, C, 25 and 50%, especially for step period and velocity. Wilcoxon test had signifcant diferences only in 4 of the 20 general comparisons between ipsilateral and contralateral steps to the crutch. In the analysis by subjects, step length, step period and velocity showed 79/132, 110/132 and 58/66 signifcant diferences, respectively. Conclusions: The increase in the load exerted over a forearm crutch produced an increase in the step period, accompanied by a reduction of step length and gait veloc‑ ity. Step width and step angle were not modifed. The unloading of 25 and 50% of body weight on a single crutch is incorrect from the biomechanical point of view. Two crutches should be employed when the body weight to unload exceeds 10%

Infuence of the load exerted over a forearm crutch in spatiotemporal step parameters during assisted gait: pilot study

Background: Assisted gait with forearm crutches is frequently performed during the recovery of musculoskeletal injuries of the lower limb. The amount of body weight applied to the crutch or crutches depends on the pathology and the treatment phase. The transition from assisted gait with two crutches to a single crutch is usually rec‐ ommended when the subject is able to load the 50% of the body weight upon the afected member. An altered assisted gait will cause biomechanic alterations and, therefore, longer treatments and relapses. The aim of this study was to analyze the infuence of 10, 25 and 50% of body weight applied to a forearm crutch during a uni‐ lateral assisted gait in the spatial and temporal step parameters to determine the load that produces alterations in gait biomechanics and the load that does not. Methods: Eleven healthy subjects performed normal gait (NG) and assisted gait with a forearm crutch, in which the applied loads were: comfortable (C), 25 and 50% of their body weight. Vicon System was employed for gait recording. GCH System 2.0 and GCH Control Software 1.0 controlled the loads. The variables were: step length, step period, velocity, step width and step angle. Friedman test compared all the gait modalities: NG and the diferent loads. Wilcoxon signed-rank test analyzed ipsilateral and contralateral step parameters to the crutch globally and for each subject. Results: Friedman test showed signifcant diferences between NG, C, 25 and 50%, especially for step period and velocity. Wilcoxon test had signifcant diferences only in 4 of the 20 general comparisons between ipsilateral and contralateral steps to the crutch. In the analysis by subjects, step length, step period and velocity showed 79/132, 110/132 and 58/66 signifcant diferences, respectively. Conclusions: The increase in the load exerted over a forearm crutch produced an increase in the step period, accompanied by a reduction of step length and gait veloc‐ ity. Step width and step angle were not modifed. The unloading of 25 and 50% of body weight on a single crutch is incorrect from the biomechanical point of view. Two crutches should be employed when the body weight to unload exceeds 10%