The effect of muscle weakness on the capability gap during gross motor function: a simulation study supporting design criteria for exoskeletons of the lower limb

Experimental data

Eight healthy subjects (61 +/− 8 kg, 23 +/− 3 years) provided written informed consent in accordance with the ethical committee of UZ Leuven to participate in this study. Each subject performed the selected ADL three times (Figure 1). The selected ADL are: sit-to-stand, stand-to-sit, gait, stair ascent, stair descent. The sit-to-stand movement is measured at self-selected speed in four conditions: a chair height of 100% knee height and 120% knee height, with and without hand support. A crutch of 75 cm height is used in the hand support condition. The gait data is measured overground at self-selected speed and on a split-belt treadmill at 3 and 5 km/h. The stair ascent and descent is measured using a staircase with 20 cm height and 40 cm width for each step. Motion data is collected with 10 Vicon cameras, sampled at 100 Hz. Ground reaction forces are measured using three force plates (Amti), sampled at 1000 Hz. The muscle activity of the rectus femoris, vastus lateralis, biceps femoris medialis, tibialis anterior, soleus and gastrocnemius lateralis are measured with surface electromyography (EMG, zero wire, Aurion, It), sampled at 1000 Hz. The SENIAM EMG placement protocol was used [8]. The EMG data were band-pass filtered (20–400 Hz), rectified and low pass filtered with a cutoff frequency of 10 Hz.

Modeling and simulation

Opensim 3.1 is used for the dynamic simulations of human movement [9]. A generic musculoskeletal model (MM) with 23 degrees of freedom (DOF) and 92 musculotendon actuators was scaled to match the anthropometry and weight of the subject (name MM: 3DGaitModel2392) [10]. The scaled model reproduced the measured motion of the markers by means of an inverse kinematics algorithm that minimizes the squared distances between the measured markers and the markers on the scaled model. The motion of the model and the external forces from the force plates were used to calculate the joint moments with inverse dynamics (Opensim 3.1). The joint moments were normalized to the body mass of the subject. Muscle forces were calculated using the dedicated static optimization in Opensim. The goal function of the optimization solves the muscle redundancy problem by minimizing the sum of muscle activation squared.

Simulation of muscle weakness

The simulations of muscle weakness were performed by a stepwise decrease of the maximal isometric force of the muscles in the MM ranging from 0 to 100% in steps of 10%. Decreasing the maximal isometric force of a muscle scales the force-length and force-velocity curves of the Hill-type muscle model. We assume an identical reduction in maximal isometric forces for all the muscles [11]. To compensate for muscle weakness, ideal moment actuators were added to the joints, which represent the motors of an exoskeleton in the simulation that would be available to deliver the assistance that is needed to successfully perform the task. The cost function of the static optimization, that minimizes the summed squared muscle activations, was supplemented with an additional term to account for the ideal moment actuators:

nMa: Number of ideal moment actuators

k: The selected specific DOF of the MM

a_t: Activation of the ideal moment actuator

N: Number of muscles in the MM

a_m: Activation of the muscle

F ⁰ _mv : Maximal isometric force of the muscle

l_m : Length of the muscle

V _m : Velocity of the muscle fiber

r_m,k : Moment arm of the muscle on the DOF k

We assigned an optimal moment of ${\tau }_{t,k}^0$ = 1 Nm to the ideal moment actuators, therefore making them costly to use (i.e. high activations are required to use this actuator). Hence, actuation by muscles is preferred over actuation by the ideal moment actuators.

Representation of the results

The analysis of the simulation results mainly focused on the sagittal plane joint moments, since for the tasks studied, these moments clearly exceed the joint moments required in other movement planes. For each subject the task requirements and capability gaps were calculated for the different ADL. The task requirements, i.e. the joint moments and joint powers imposed by the task to the joints, were calculated with inverse dynamics in Opensim. The maximal task requirement is identified as the maximal joint moment observed during the spectrum of ADL analyzed in this study. The capability gap is calculated by subtracting the joint moment generated by the muscle actuators in the MM (motor capability) from the joint moment imposed by the task (task requirements) and corresponds to the joint moment generated by the ideal moment generators. The capability gap for the different ADL was calculated for the different levels of muscle weakness. The maximal capability gap reflects the maximal joint moment deficit observed during the spectrum of ADL analyzed in this study. The maximal capability gap was calculated for each level of muscle weakness.

Statistical analysis

Task requirements during ADL

The task requirements differ between ADL and joints (Figure 2). Based on the task requirements we can specify the maximal task requirements in terms of joint moments (Figure 3) and joint powers (Figure 4). At the ankle joint, the stair ascent task imposes the highest net plantarflexion moment (1.68 +/− 0.09 Nm/kg, p < 0.05) whereas gait imposes the highest dorsiflexion moment (0.11 +/− 0.02 Nm/kg, p < 0.05). At the knee joint, the stair ascent and descent tasks impose the highest extensor moment (1.30 +/− 0.30 Nm/kg, 1.31 +/− 0.25 Nm/kg, p < 0.05) whereas the stair ascent and gait tasks impose the highest flexor moment (0.40 +/−0.06 Nm/kg, 0.42 +/− 0.13 Nm/kg, p < 0.05). At the hip joint, the stair ascent task imposes the highest extensor moment (0.91 +/− 0.25 Nm/kg, p < 0.05) whereas gait imposes the highest flexor moment (0.63 +/− 0.10 Nm/kg, p < 0.05). In general, considering the selected ADL, the ankle plantarflexion moments are highest (p < 0.01).The maximal task requirements in terms of joint power are shown in Figure 4. The highest positive ankle power is present during stair ascent (4.66 +/− 0.63 W/kg) and the highest negative power is present during stair descent (3.74 +/− 0.95 W/kg). For the knee joint, stair ascent imposes the highest positive power (2.91 +/− 0.39 W/kg), whereas stair descent imposes the highest negative power (3.64 +/− 0.58 W/kg). For the hip joint, stair ascent (1.73 +/− 0.49 W/kg) and gait (1.33 +/− 0.42 W/kg) impose the highest positive power, whereas stand-to-sit imposes the highest negative power (1.26 +/− 0.41 W/kg). In general, considering the ADL, the ankle joint positive power and the ankle joint and knee joint negative power are highest.

Capability gap

Figure 5 illustrates the main differences between the ID and AAN approaches during a stair ascent task for 70% muscle weakness. Firstly, the ID approach requires a higher assistive ankle moment (1.53 Nm/kg) compared with the capability gap in the AAN approach (0.68 Nm/kg). Secondly, the ID approach delivers continuous support whereas the AAN approach targets the period where a capability gap occurs (i.e. 55%-65% of the stair ascent cycle). Figure 6 illustrates the influence of an increasing level of muscle weakness on the capability gap during stair ascent. Both the timing and the magnitude of the capability gap depend on the level of muscle weakness.Figure 2 illustrates the capability gap for different ADL and different levels of muscle weakness. For example in the presence of 70% muscle weakness, no ankle dorsiflexion moment deficit is found. The highest plantarflexion capability gap occurs during stair ascent (0.96 +/− 0.14 Nm/kg, p < 0.05). For the knee joint, the highest knee extensor capability gap occurs during stair ascent (0.36 +/− 0.09 Nm/kg, p < 0.05) and the highest knee flexion capability gap occurs during gait (0.16 +/− 0.03 Nm/kg, p < 0.05). For the hip joint, the highest extensor capability gap occurs during stair ascent (0.32 +/− 0.06 Nm/kg, p < 0.05) and the highest flexion capability gap during gait (0.25 +/− 0.09 Nm/kg, p < 0.05).

A capability gap is found from 30% of muscle weakness onwards: from this level the ankle plantarflexion function during stair ascent and stair descent becomes insufficient and ideal moment generators assist. During gait, a capability gap is found when 40% of muscle weakness is present, and plantarflexion function is lacking. The sit-to-stand and stand-to-sit movements are less affected by overall muscle weakness: the knee and hip extension functions are only impaired when 70% of muscle weakness is present for the sit-to-stand task and when 80% of muscle weakness is present for the stand-to-sit task.

The capability gap differs significantly depending on the specific DOF: the ankle plantarflexion function is impaired from 30% weakness onwards, whereas the dorsiflexion function is only impaired when 90% weakness is present. For the knee and hip joint, the knee flexion/extension and hip flexion/extension functions are impaired during ADL from 50% muscle weakness onwards.Based on the capability gaps for the ADL, we can specify the maximal capability gap for the different DOF in term of joint moments (Figure 3) and joint powers (Figure 4). These figures show the maximal moment and power assistance that is needed to perform the ADL for the different levels of muscle weakness.When inducing more strenuous activities, the task requirements for several DOF increase (Figure 7). For example increasing the walking speed from 3 km/h to 5 km/h causes an increase in the task requirements for all the DOF.

Comparison between the ID approach and the AAN approach

Our findings confirm a substantial capability gap that depends on the specific ADL task and the level of muscle weakness. The capability gap is determined based on a joint moment deficit, illustrated in Figure 5. This figure emphasizes the difference between the ID approach and the AAN approach. The ID approach overestimates the required assistance as it relies solely on the demands of the task, whereas the AAN approach incorporates the capabilities of the subject. To date, several exoskeletons are designed based on a percentage of the peak joint moments that are calculated with the ID approach [13]. This method assumes that the capability of the subject is a constant percentage of the peak moment calculated with ID (Figure 8a). However, not only the task requirements, but also the angle dependency of the moment generating capacity around the joint and the task requirements of the adjacent joints will affect the capability gap. The use of MM–based dynamic simulations accounts for the force-length properties of the muscle fibers and for the change in moment arm of the muscle with the joint angle. Therefore, the moment generating capacity of the subject is not constant, but varies in magnitude during the motor task in the AAN approach and affects the capability gap (Figure 5 + Figure 8b). This causes a substantial difference between required assistance in the AAN approach and the (scaled) ID approach.

Capability gap during ADL

The simulation of muscle weakness allows us to identify to what extent the MM is able to cope with muscle weakness. The capability gaps are analyzed for the ankle and knee in the sagittal plane and for the hip in the sagittal, frontal and transversal plan. The MM is able to perform stair ascent until 30% of muscle weakness is present, which is caused by a plantarflexion capability gap. The tolerance of the MM-model to muscle weakness, i.e. level of muscle weakness for which the external demands imposed by gait, sit-to-stand, stand-to-sit and stair descent can no longer be met by active muscle force production, is respectively 40%, 70%, 80% and 30%. The tolerance level reported for gait agrees with previously reported simulation results [14]. The tolerance level for the sit-to-stand movement is comparable to the experimental results from Hughes et al. [15]. In the presence of a reduction of 63% in maximal isometric force, elderly had to deliver 97% of their available strength to rise from the chair. Despite this agreement with experimental work, the tolerance level of 70% of muscle weakness for the sit-to-stand movement is somewhat surprising as difficulties in executing sit-to stance maneuvers are frequent in the elderly population [15]. These results indicate that in the elderly population, instability and inadequate coordination strategies more than muscle strength impair task execution when rising from a chair, as previously suggested by [16].Several factors influence the assistance that is needed to perform ADL. Firstly, the level of muscle weakness determines the timing and the magnitude of the capability gap (Figure 6). Secondly, the magnitude of the capability gap varies between the tasks and the joints. The plantarflexion has the highest maximal capability gap for all the DOF. This is caused by the high plantarflexion moments that are imposed during stair ascent (1.70 Nm/kg). These results emphasize the importance of plantarflexion assistance in powered exoskeletons, in particular during stair ascent when muscle weakness is present. Furthermore, the high angular velocity during push off in combination with the high plantarflexion joint moments causes high positive joint powers. Therefore, generating sufficient plantarflexion moment and power will be an important challenge in the design of lower limb exoskeletons.The crucial activity for the dorsiflexion capability gap is gait. Despite the relative small dorsiflexion moment deficits during gait, assisting this DOF is important for patients with drop foot gait. Our results show that there is only 0.11 (+/−0.02) Nm/kg dorsiflexion moment required to assist persons with total central paralysis of the dorsiflexion muscles during the selected ADL. However, the required dorsiflexion moment increases with gait speed (Figure 7).

In contrast with the ankle, the directional dominance of the assistance is less clear at the knee and hip joint: at the knee a slight dominance of knee extension assistance is confirmed whereas at the hip both flexion and extension require similar assistance. Furthermore, the level of weakness tolerated before introducing the moment generators is substantially higher at the knee and hip.

Limitations

The aforementioned results should be interpreted and used within the limitations of the methodology. Firstly, to assess the validity of the simulations, we have calculated the correlation between the simulated muscle activations and the measured muscle activity (Table 1). These results indicate that the simulated muscle activation of all the mono-articular muscles correlates significantly with the measured activity. It is known that the activity of the bi-articular rectus femoris (RF) is less well predicted in the simulation [17]. Secondly, we assume in our simulation that persons perfectly adapt to an assistive moment, i.e. subjects are assumed not to oppose the induced external moment by increasing their antagonistic muscle activity or change the joint kinetics pattern. Indeed, experiments with single joint powered exoskeletons have shown that there is no difference in joint kinetics with and without assistance in healthy subjects [18, 19]. Furthermore, there is no difference in antagonistic muscle activity but a decrease in agonistic muscle activity when walking with a powered exoskeleton [20, 21]. Therefore, the assumption seems to be valid. Thirdly, the current workflow assumes that the MM represents the subject specific impairments of user/patient. It is known that aging and pathologies cause changes in musculotendon properties and activation dynamics [22]. In order to estimate the capability for these populations, the MM should ideally be adjusted towards the target population. Fourthly, the presented results rely on one specific objective function. However, the influence of the cost function on the capability gap is limited. The capability gap is the moment deficit when muscles maximally contribute to the desired motion. Therefore the influence of the cost function, which merely defines the muscle force distribution and not the overall level of agonistic muscle activity, on the moment deficit is small. Lastly, this study does not account for the stabilization of joints, fatigue, potential losses in body mass due to weakness and it assumes that the kinematics remain constant despite the presence of muscle weakness.

Application of the results

Within the limitations of the study, the results can be used in the design of assistive devices that support ADL. Elderly and patients with sarcopenia have a reduction in maximal isometric force that ranges between 20%-40% [11]. Our results suggest that in these cases solely an assistive plantarflexion moment is required to perform ADL (Figure 3). However, this study does not include the influence of fatigue on the capability gap of the individual subject. An additional knee flexion/extension and hip flexion/extension moment is required when the level of muscle weakness increases to 50%. In the study of Stevens-Lapsley et al., there is a reduction of 50 +/− 20% in maximal isometric force in persons with severe Parkinson disease, with 68% of the patients with severe Parkinson disease have 70% or less reduction in maximal isometric knee extensor moment [23]. Assuming an upper limit of body mass that equals 92.9 kg [23], Figures 3 and 4 can then be used to determine the design requirements of an exoskeleton that is able to assist this population in ADL: The exoskeleton should be able to deliver peak moments of 89.1 Nm (254 W) at the ankle joint, 33.4 Nm (72.5 W) at the knee joint and 29.7 Nm (63.17 W) at the hip joint. Furthermore, the present simulation workflow can be used to select the actuators of an assistive device with specific design criteria. The relative cost of the ideal moment actuators at the hip, knee, and ankle will influence bi-articular muscle action and therefore the capability gap at the joints. Therefore, the relative costs can be optimized for specific design criteria. For example, one could increase the cost of using the ideal moment actuator at the ankle joint in order to minimize the actuator size at the ankle (at the cost of increasing the size at the knee and hip).

Further directions

Although the added value of the current results is without question, future work should concentrate on forward simulations that allow changes in the motor strategy during the task. For example, changing the strategy to stand up from a chair influences the kinematics and peak joint moments [24]. Hughes et al. described a difference in chair rise strategy in the functionally impaired elderly in order to increase their stability [16]. On the one hand, these differences in motor strategies could influence the required assistance during ADL. On the other hand, exoskeletons are designed to increase the physical performance of the user, in order to achieve or exceed a healthy motor function.

The current study provides sufficient proof-of-concept to consider the design of targeted functional protocols that allow tuning the control settings for the exoskeleton to the functional limitations in terms of muscle weakness of individual subjects. This AAN control will promote active participation of the user which is essential to prevent disuse and promote neuromotor rehabilitation.