Load during prosthetic gait : is direct measurement better than inverse dynamics?

The knee forces and moments estimated by inverse dynamics and directly measured by a multiaxial transducer were compared during the gait of a transfemoral amputee. The estimated and directly measured forces and moments were relatively close. However, 3D inverse dynamics estimated only partially the forces and moments associated with the deformation of the prosthetic foot and locking of knee mechanism.

Loading applied on prosthetic knee of transfemoral amputee: comparison of inverse dynamics and direct measurements

Inverse dynamics is the most comprehensive method that gives access to the net joint forces and moments during walking. However it is based on assumptions (i.e., rigid segments linked by ideal joints) and it is known to be sensitive to the input data (e.g., kinematic derivatives, positions of joint centres and centre of pressure, inertial parameters). Alternatively, transducers can be used to measure directly the load applied on the residuum of transfemoral amputees. So, the purpose of this study was to compare the forces and moments applied on a prosthetic knee measured directly with the ones calculated by three inverse dynamics computations - corresponding to 3 and 2 segments, and « ground reaction vector technique » - during the gait of one patient. The maximum RMSEs between the estimated and directly measured forces (i.e., 56 N) and moment (i.e., 5 N.m) were relatively small. However the dynamic outcomes of the prosthetic components (i.e., absorption of the foot, friction and limit stop of the knee) were only partially assessed with inverse dynamic methods.

Direct measurement as a tool for assessing the accuracy of inverse dynamics

The understanding of the loads generated within the prosthetic leg can aid engineers in the design of components and clinicians in the process of rehabilitation. Traditional methods to assess these loads have relied on inverse dynamics. This indirect method estimates the applied load using video recordings and force-plates located at a distance from the region of interest, such as the base of the residuum. The well-known limitations of this method are related to the accuracy of this recursive model and the experimental conditions required (Frossard et al., 2003). Recent developments in sensors (Frossard et al., 2003) and prosthetic fixation (Brånemark et al., 2000) permit the direct measurement of the loads applied on the residuum of transfemoral amputees. In principle, direct measurement should be an appropriate tool for assessing the accuracy of inverse dynamics. The purpose of this paper is to determine the validity of this assumption. The comparative variable used in this study is the velocity of the relative body center of mass (VCOM(t)). The relativity is used to align the static (w.r.t. position) force plate measurement with the dynamic load cell measurement.

A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator

This paper presents an inverse dynamic formulation by the Newton–Euler approach for the Stewart platform manipulator of the most general architecture and models all the dynamic and gravity effects as well as the viscous friction at the joints. It is shown that a proper elimination procedure results in a remarkably economical and fast algorithm for the solution of actuator forces, which makes the method quite suitable for on-line control purposes. In addition, the parallelism inherent in the manipulator and in the modelling makes the algorithm quite efficient in a parallel computing environment, where it can be made as fast as the corresponding formulation for the 6-dof serial manipulator. The formulation has been implemented in a program and has been used for a few trajectories planned for a test manipulator. Results of simulation presented in the paper reveal the nature of the variation of actuator forces in the Stewart platform and justify the dynamic modelling for control.

Adaptation to stable and unstable dynamics achieved by combined impedance control and inverse dynamics model.

This study compared adaptation in novel force fields where trajectories were initially either stable or unstable to elucidate the processes of learning novel skills and adapting to new environments. Subjects learned to move in a null force field (NF), which was unexpectedly changed either to a velocity-dependent force field (VF), which resulted in perturbed but stable hand trajectories, or a position-dependent divergent force field (DF), which resulted in unstable trajectories. With practice, subjects learned to compensate for the perturbations produced by both force fields. Adaptation was characterized by an initial increase in the activation of all muscles followed by a gradual reduction. The time course of the increase in activation was correlated with a reduction in hand-path error for the DF but not for the VF. Adaptation to the VF could have been achieved solely by formation of an inverse dynamics model and adaptation to the DF solely by impedance control. However, indices of learning, such as hand-path error, joint torque, and electromyographic activation and deactivation suggest that the CNS combined these processes during adaptation to both force fields. Our results suggest that during the early phase of learning there is an increase in endpoint stiffness that serves to reduce hand-path error and provides additional stability, regardless of whether the dynamics are stable or unstable. We suggest that the motor control system utilizes an inverse dynamics model to learn the mean dynamics and an impedance controller to assist in the formation of the inverse dynamics model and to generate needed stability.

Effect of hamstring injuries on kicking in soccer using inverse dynamics

Las lesiones musculares del muslo tienen una gran incidencia en el fútbol. El objetivo del estudio ha sido desarrollar un nuevo procedimiento para evaluar el efecto de las lesiones de isquiotibiales en los golpeos con el pie s en el fútbol utilizando los principios de la dinámica inversa. El trabajo se ha centrado en la evaluación de la diferencia entre sujetos que habían sufrido la lesión en los últimos 5 años y los que no. Se analizaron 17 jugadores de fútbol profesionales realizando cinco tiros con el empeine y cinco con el interior del pie. Los movimientos se registraron mediante una plataforma de fuerza y un sistema de captura de movimiento Vicon funcionando a 500Hz. Los participantes también tomaron parte en una prueba de isocinético en la que se midió el torque isocinético en 60 º/s y 120 º/s. Se observaron diferencias significativas en los parámetros cinemáticos y cinéticos entre los dos grupos (lesionados y no lesionados) en la fase posterior del golpeo y en el instante de máxima flexión de cadera. No se encontraron diferencias significativas entre los dos grupos en la prueba isocinética tradicional. Estos resultados indican que el procedimiento empleado probablemente podría ser muy útil en la evaluación del efecto de las lesiones de isquiotibiales en el fútbol.

Different mechanisms involved in adaptation to stable and unstable dynamics.

Recently, we demonstrated that humans can learn to make accurate movements in an unstable environment by controlling magnitude, shape, and orientation of the endpoint impedance. Although previous studies of human motor learning suggest that the brain acquires an inverse dynamics model of the novel environment, it is not known whether this control mechanism is operative in unstable environments. We compared learning of multijoint arm movements in a "velocity-dependent force field" (VF), which interacted with the arm in a stable manner, and learning in a "divergent force field" (DF), where the interaction was unstable. The characteristics of error evolution were markedly different in the 2 fields. The direction of trajectory error in the DF alternated to the left and right during the early stage of learning; that is, signed error was inconsistent from movement to movement and could not have guided learning of an inverse dynamics model. This contrasted sharply with trajectory error in the VF, which was initially biased and decayed in a manner that was consistent with rapid feedback error learning. EMG recorded before and after learning in the DF and VF are also consistent with different learning and control mechanisms for adapting to stable and unstable dynamics, that is, inverse dynamics model formation and impedance control. We also investigated adaptation to a rotated DF to examine the interplay between inverse dynamics model formation and impedance control. Our results suggest that an inverse dynamics model can function in parallel with an impedance controller to compensate for consistent perturbing force in unstable environments.

Parallelism in Manipulator Dynamics

This paper addresses the problem of efficiently computing the motor torques required to drive a lower-pair kinematic chain (e.g., a typical manipulator arm in free motion, or a mechanical leg in the swing phase) given the desired trajectory; i.e., the Inverse Dynamics problem. It investigates the high degree of parallelism inherent in the computations, and presents two "mathematically exact" formulations especially suited to high-speed, highly parallel implementations using special-purpose hardware or VLSI devices. In principle, the formulations should permit the calculations to run at a speed bounded only by I/O. The first presented is a parallel version of the recent linear Newton-Euler recursive algorithm. The time cost is also linear in the number of joints, but the real-time coefficients are reduced by almost two orders of magnitude. The second formulation reports a new parallel algorithm which shows that it is possible to improve upon the linear time dependency. The real time required to perform the calculations increases only as the [log2] of the number of joints. Either formulation is susceptible to a systolic pipelined architecture in which complete sets of joint torques emerge at successive intervals of four floating-point operations. Hardware requirements necessary to support the algorithm are considered and found not to be excessive, and a VLSI implementation architecture is suggested. We indicate possible applications to incorporating dynamical considerations into trajectory planning, e.g. it may be possible to build an on-line trajectory optimizer.

Measuring mechanical properties of tendon in vivo

Introduction: Understanding the mechanical properties of tendon is an important step to guiding the process of improving athletic performance, predicting injury and treating tendinopathies. The speed of sound in a medium is governed by the bulk modulus and density for fluids and isotropic materials. However, for tendon,which is a structural composite of fluid and collagen, there is some anisotropy requiring an adjustment for Poisson’s ratio. In this paper, these relationships are explored and modelled using data collected, in vivo, on human Achilles tendon. Estimates for elastic modulus and hysteresis based on speed of sound data are then compared against published values from in vitro mechanical tests. Methods: Measurements using clinical ultrasound imaging, inverse dynamics and acoustic transmission techniques were used to determine dimensions, loading conditions and longitudinal speed of sound for the Achilles tendon during a series of isometric plantar flexion exercises against body weight. Upper and lower bounds for speed of sound versus tensile stress in the tendon were then modelled and estimates derived for elastic modulus and hysteresis. Results: Axial speed of sound varied between 1850 to 2090 m.s−1 with a non-linear, asymptotic dependency on the level of tensile stress in the tendon 5–35 MPa. Estimates derived for the elastic modulus ranged between 1–2 GPa. Hysteresis derived from models of the stress-strain relationship, ranged from 3–11%. These values agree closely with those previously reported from direct measurements obtained via in vitro mechanical tensile tests on major weight bearing tendons. Discussion: There is sufficiently good agreement between these indirect (speed of sound derived) and direct (mechanical tensile test derived) measures of tendon mechanical properties to validate the use of this non-invasive acoustic transmission technique. This non-invasive method is suitable for monitoring changes in tendon properties as predictors of athletic performance, injury or therapeutic progression.

Non-invasive clinical measurement of the viscoelastic properties of tendon using acoustic wave transmission

Background. In isotropic materials, the speed of acoustic wave propagation is governed by the bulk modulus and density. For tendon, which is a structural composite of fluid and collagen, however, there is some anisotropy requiring an adjustment for Poisson's ratio. This paper explores these relationships using data collected, in vivo, on human Achilles tendon and then compares estimates of elastic modulus and hysteresis against published values from in vitro mechanical tests. Methods. Measurements using conventional B-model ultrasound imaging, inverse dynamics and acoustic transmission techniques were used to determine dimensions, loading conditions and longitudinal speed of sound in the Achilles tendon during a series of isometric plantar flexion exercises against body weight. Upper and lower bounds for speed of sound versus tensile stress in the tendon were then modelled and estimates of the elastic modulus and hysteresis of the Achilles tendon derived. Results. Axial speed of sound varied between 1850 and 2090 ms-1 with a non-linear, asymptotic dependency on the level of tensile stress (5-35 MPa) in the tendon. Estimates derived for the elastic modulus of the Achilles tendon ranged between 1-2 GPa. Hysteresis derived from models of the stress-strain relationship, ranged from 3-11%. Discussion. Estimates of elastic modulus agree closely with those previously reported from direct measurements obtained via mechanical tensile tests on major weight bearing tendons in vitro [1,2]. Hysteresis derived from models of the stress-strain relationship is consistent with direct measures from various mamalian tendon (7-10%) but is lower than previous estimates in human tendon (17-26%) [3]. This non-invasive method would appear suitable for monitoring changes in tendon properties during dynamic sporting activities.

Static load bearing exercises during rehabilitation of individuals with transfemoral amputation fitted with osseointegrated implant: Kinetic analysis

The desire to solve problems caused by socket prostheses in transfemoral amputees and the acquired success of osseointegration in the dental application has led to the introduction of osseointegration in the orthopedic surgery. Since its first introduction in 1990 in Gothenburg Sweden the osseointegrated (OI) orthopedic fixation has proven several benefits[1]. The surgery consists of two surgical procedures followed by a lengthy rehabilitation program. The rehabilitation program after an OI implant includes a specific training period with a short training prosthesis. Since mechanical loading is considered to be one of the key factors that influence bone mass and the osseointegration of bone-anchored implants, the rehabilitation program will also need to include some form of load bearing exercises (LBE). To date there are two frequently used commercially available human implants. We can find proof in the literature that load bearing exercises are performed by patients with both types of OI implants. We refer to two articles, a first one written by Dr. Aschoff and all and published in 2010 in the Journal of Bone and Joint Surgery.[2] The second one presented by Hagberg et al in 2009 gives a very thorough description of the rehabilitation program of TFA fitted with an OPRA implant. The progression of the load however is determined individually according to the residual skeleton’s quality, pain level and body weight of the participant.[1] Patients are using a classical bathroom weighing scale to control the load on the implant during the course of their rehabilitation. The bathroom scale is an affordable and easy-to-use device but it has some important shortcomings. The scale provides instantaneous feedback to the patient only on the magnitude of the vertical component of the applied force. The forces and moments applied along and around the three axes of the implant are unknown. Although there are different ways to assess the load on the implant for instance through inverse dynamics in a motion analysis laboratory [3-6] this assessment is challenging. A recent proof- of-concept study by Frossard et al (2009) showed that the shortcomings of the weighing scale can be overcome by a portable kinetic system based on a commercial transducer[7].

Dynamic input to determine hip joint moments, power and work on the prosthetic limb of transfemoral amputees: ground reactions vs knee reactions

Study Design: Comparative analysis Background: Calculations of lower limbs kinetics are limited by floor-mounted force-plates. Objectives: Comparison of hip joint moments, power and mechanical work on the prosthetic limb of a transfemoral amputee calculated by inverse dynamics using either the ground reactions (force-plates) or knee reactions (transducer). Methods: Kinematics, ground reactions and knee reactions were collected using a motion analysis system, two force-plates and a multi-axial transducer mounted below the socket, respectively. Results: The inverse dynamics using ground reactions under-estimated the peaks of hip energy generation and absorption occurring at 63 % and 76 % of the gait cycle (GC) by 28 % and 54 %, respectively. This method over-estimated a phase of negative work at the hip (from 37 %GC to 56 %GC) by 24%. It under-estimated the phases of positive (from 57 %GC to 72 %GC) and negative (from 73 %GC to 98 %GC) work at the hip by 11 % and 58%, respectively. Conclusions: A transducer mounted within the prosthesis has the capacity to provide more realistic kinetics of the prosthetic limb because it enables assessment of multiple consecutive steps and a wide range of activities without issues of foot placement on force-plates. CLINICAL RELEVANCE The hip is the only joint that an amputee controls directly to set in motion the prosthesis. Hip joint kinetics are associated with joint degeneration, low back pain, risks of fall, etc. Therefore, realistic assessment of hip kinetics over multiple gait cycles and a wide range of activities is essential.

Review of direct measurement of inner prosthesis loading in transfemoral amputation: Potential benefits for evidence-based practice

The understanding of the load applied on the residuum through the prosthesis of individuals with transfemoral amputation (TFA) is essential to address a number of concerns that could strongly reduce their quality of life (e.g., residuum skin lesion, prosthesis fitting, alignment). This inner prosthesis loading could be estimated using a typical gait laboratory relying on inverse dynamics equations. Alternative, technological advances proposed over the last decade enabled direct measurement of this kinetic information in a broad variety of situations that could potentially be more relevant in clinical settings. The purposes of this presentation are (A) to review the literature about recent developments in measure and analyses of inner prosthesis loading of TFA, and (B) to extract information that could potentially contribute to a better evidence-based practice.

Direct measurement of prosthetic loading for evidence-based practice

The demand for an evidence-based clinical practice involving lower limb amputees is increasing. Some of the critical care decisions are related to the loading applied on the residuum partially responsible for comfort and functional outcome. This loading can be assessed using inverse dynamics equations. Typically, this method requires a gait laboratory (e.g., 3D motion analysis system, force-plates). It is mainly suited for the analysis only few steps of walking while being expensive and labour intensive. However, recent scientific and industrial developments demonstrated that discrete and light portable sensors can be placed within the prosthesis to measure accurately the loading during an unlimited number of steps and activities of daily living. Several studies indicated that method based on direct measurements might provide more realistic results. Furthermore, it is a user-friendly method more accessible to clinicians, such as prosthetists. The purpose of this symposium will be to give an overview of these additional opportunities for clinicians to obtain relevant data for evidence-based practice. The three main aims will be: • To present some of the equipment used for direct measurements, • To propose ways to analyse some key data sets, • To give some practical example of data sets for transtibial and transfemoral amputees.