An EMG-driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo

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Abstract

This paper examined if an electromyography (EMG) driven musculoskeletal model of the human knee could be used to predict knee moments, calculated using inverse dynamics, across a varied range of dynamic contractile conditions. Muscle–tendon lengths and moment arms of 13 muscles crossing the knee joint were determined from joint kinematics using a three-dimensional anatomical model of the lower limb. Muscle activation was determined using a second-order discrete non-linear model using rectified and low-pass filtered EMG as input. A modified Hill-type muscle model was used to calculate individual muscle forces using activation and muscle tendon lengths as inputs. The model was calibrated to six individuals by altering a set of physiologically based parameters using mathematical optimisation to match the net flexion/extension (FE) muscle moment with those measured by inverse dynamics. The model was calibrated for each subject using 5 different tasks, including passive and active FE in an isokinetic dynamometer, running, and cutting manoeuvres recorded using three-dimensional motion analysis. Once calibrated, the model was used to predict the FE moments, estimated via inverse dynamics, from over 200 isokinetic dynamometer, running and sidestepping tasks. The inverse dynamics joint moments were predicted with an average R2 of 0.91 and mean residual error of ∼12 Nm. A re-calibration of only the EMG-to-activation parameters revealed FE moments prediction across weeks of similar accuracy. Changing the muscle model to one that is more physiologically correct produced better predictions. The modelling method presented represents a good way to estimate in vivo muscle forces during movement tasks.

Introduction

Measuring the forces applied to a joint and estimating how these forces are partitioned to surrounding muscles, ligaments, and articular surfaces is fundamental to understanding joint function, injury, and disease. Inverse dynamics can be used to estimate the external load applied to a joint, however, the contribution from muscles to support or generate this load is far more difficult to determine given the indeterminate nature of the joint. One solution to this problem is to estimate muscle forces based on an objective function within an optimisation routine, for example, minimising muscle stress. By default, the use of an objective function cannot account individual muscle activation patterns. Another solution uses electromyography (EMG) in conjunction with an appropriate anatomical and muscle model to estimate the forces produced in each muscle (e.g. Lloyd and Buchanan, 1996; McGill, 1992). Since ‘EMG-driven’ models rely on measured muscle activity to estimate muscle force, these models implicitly account for a subject's individual activation patterns without the need to satisfy any constraints imposed by an objective function. This is important if we wish to investigate tissue loading throughout a wide range of tasks and contractile conditions, as the activation of muscle depends on the control task and can be quite different for the same joint angle and joint torque (Tax et al., 1990; Buchanan and Lloyd, 1995). Indeed, in isometric tasks Lloyd and Buchanan (2001) showed quite different activation patterns between subjects to generate the same relative knee moments in flexion/extension and varus/valgus directions, resulting in quite different amounts of support provided by the muscles and ligaments.

EMG-driven models have been developed to estimate muscle forces for the lower back (McGill and Norman, 1986; McGill, 1992; Granata and Marras, 1993; Thelen et al., 1994; Nussbaum and Chaffin, 1998), elbow (Soechting and Flanders, 1997; Buchanan et al., 1998), shoulder (Laursen et al., 1998), knee (White and Winter, 1993; Lloyd and Buchanan, 1996; Piazza and Delp, 1996), and ankle (Hof and van den Berg (1981a), Hof and van den Berg (1981b)). As direct measures of muscle force in vivo are difficult, EMG-driven models are typically validated to external joint moments measured using an inverse dynamics approach. The ability of EMG-driven models to predict joint moments during a wide range of activities has proven difficult in the past, and several methods have been devised to satisfy this moment constraint. One such method involves using an error term or ‘gain’ to ensure the predicted moments from a model match the externally measured moments for each task (e.g. McGill, 1992). An alternate method involves using a non-linear least squares optimisation procedure to alter specific parameters within the model to ensure that the moment constraints are closely met (Hatze, 1981; Lloyd and Buchanan, 1996). However, all previous EMG-driven models have been tested on either static/isometric tasks (e.g. Hatze, 1981; Thelen et al., 1994; Lloyd and Buchanan, 1996; Laursen et al., 1998) or a limited set of dynamic tasks (e.g. Nussbaum and Chaffin, 1998).

If EMG-driven modelling is to become a useful tool in estimating in vivo tissue loading, then we need to have confidence that models are indeed reflecting the actual activated muscles. This confidence can be attained if the model is capable of predicting joint moments over a varied range of dynamic contractile conditions, which is obviously a stringent requirement.

It can be argued that to predict joint moments across a wide range of tasks, the model must mathematically represent the underlying anatomy and physiology of the system. Thus, to allow predictions across a number of different subjects, it is important to calibrate the model to an individual by adjusting subject-specific model parameters (e.g. Hatze, 1981; Lloyd and Buchanan, 1996; Nussbaum and Chaffin, 1998). This adjustment is necessary as people are inherently different. For example, people have different strengths and variation in relative strength of the knee flexor and extensor muscles (e.g. Aagaard et al., 1997; Hayes and Falconer, 1992; Read and Bellamy, 1990). Additionally, quite different knee torque–angle relationships have been shown between runners and cyclists (Herzog et al., 1991) and that the peak of hamstring torque–angle relationships can be moved to longer muscle lengths from eccentric training of these muscles (Brockett et al., 2001). Thus, the models need to account for these differences, but as Nussbaum and Chaffin (1998) point out, earlier EMG-driven models that have used parameters or ‘gains’ with no physiological basis compromise construct validity and perhaps limit the ability to predict across tasks and subjects. Model constructs and parameters should therefore have an anatomical and physiological basis that is constrained within a calibration process specific to an individual.

The aim of this paper was to determine if an EMG-driven model could predict joint moments across a wide range of tasks and contractile conditions, using the knee as an example. The model was based on anatomical and physiological characteristics of muscle and EMG, and calibrated to an individual using appropriate physiologically based parameters across a selection of varied tasks. An additional aim was to examine the ability of the model to predict knee joint moments across weeks using muscle model parameters obtained from an initial calibration. Finally, we tested if making the model less physiologically correct affected model predictions.

Section snippets

Model development

The model uses raw EMG and joint kinematics, recorded during a range of static and dynamic trials, as input to estimate individual muscle forces and, subsequently, joint moments. The model is generic in that it can be adapted to any joint, given appropriate anatomical and physiological data. For the purpose of this study, we have modelled the human knee joint. There are four main parts to this overall model: (1) Anatomical model, (2) EMG-to-activation model, (3) Hill-type muscle model, and (4)

Results

Following calibration, the model predicted FE knee moments with a mean (S.D.) R2 of 0.91±0.04 across 204 running, sidestepping, and dynamometer trials (Table 1). Mean residual error for these predictions was ∼12 Nm (Table 1) and when normalised to body weight was less than 0.2 Nm/kg. Table 2, Table 3 summarise the global parameters for each subject following calibration. The dynamic knee model was capable of predicting FE moments across a wide range of tasks from running, to crossover cutting and

Discussion

Many studies have shown the promise of EMG-driven musculoskeletal models to estimate muscle forces and predict human joint moments over a limited set of test data. The current model, following subject-specific calibration, predicted the inverse dynamic FE knee joint moments determined from a wide range of tasks and different contractile conditions, thus supporting the hypothesis of this study. The same muscle model parameters were also used to give close predictions of knee joint moments across

Acknowledgements

The authors wish to acknowledge the support of the National Health and Medical Research Council of Australia (Grant #991134) and Musculographics Inc.

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