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relationship between the arm–crutch loading, leg restriction, and motor paralysis, and reported that large reaction forces occurred at the crutches when the.
Original Article

Studying the effect of kinematical pattern on the mechanical performance of paraplegic gait with reciprocating orthosis

Proc IMechE Part H: J Engineering in Medicine 0(0) 1–12 Ó IMechE 2012 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0954411912447717 pih.sagepub.com

Koorosh Nakhaee1, Farzam Farahmand2,3 and Hassan Salarieh2

Abstract Paraplegic users of mechanical walking orthoses, e.g. advanced reciprocating gait orthosis (ARGO), often face high energy expenditure and extreme upper body loading during locomotion. We studied the effect of kinematical pattern on the mechanical performance of paraplegic locomotion, in search for an improved gait pattern that leads to lower muscular efforts. A three-dimensional, four segment, six-degrees-of-freedom skeletal model of the advanced reciprocating gait orthosis-assisted paraplegic locomotion was developed based on the data acquired from an experimental study on a single subject. The effect of muscles was represented by ideal joint torque generators. A response surface analysis was performed on the model to determine the impact of the kinematical parameters on the resulting muscular efforts, characterized by net joint torques. Results indicated that a lateral bending manoeuvre at the trunk would facilitate the foot clearance by reducing the torque requirement of the whole body lateral tilting. For swing leg advancement, the trunk posterior bending manoeuvre was found to be more effective and efficient than the whole body axial rotation, owing to the coupled reciprocal action of the advanced reciprocating gait orthosis. It was hypothesized that a modified gait pattern, with larger trunk movements and no axial rotation, could improve the energy expenditure and upper body loading during advanced reciprocating gait orthosis-assisted locomotion. More detailed modelling and experimental studies are needed to verify this hypothesis and evaluate its potential effects on the soft tissue strains.

Keywords Spinal cord injury, advanced reciprocating gait orthosis, dynamic modelling, parametric study, gait pattern

Date received: ; accepted: 11 April 2012

Introduction A spinal cord injury leads to an impairment of motor function below the level of the injury. Although for those with paralysis of the legs but not at arms, the primary means of mobility post injury is the manual wheelchair, there are many physiological and psychological advantages to standing and walking, e.g. improvement of respiratory function, prevention of osteoporosis in non-weight-bearing lower limbs, and avoiding joint contracture, muscle atrophy, spasticity, and pressure sore.1,2 There are three major categories of accessory devices to help individuals with paraplegia to stand and walk, including mechanical orthoses, functional electrical stimulation systems, and a combination of both, i.e. hybrid orthoses. Mechanical orthoses in the general forms of knee–ankle–foot orthoses (KAFOs) and hip– knee–ankle–foot orthoses (HKAFOs) are routinely

used to help paraplegic gait. They physically encompass the joints of the lower limb to provide mechanical control and stability during the weight-bearing stance phase of the gait cycle. Usually, walking aids, e.g. crutches, are also used to improve the stability and balance and provide a part of the propulsion required. A major concern in using the mechanical orthoses for ambulation of paraplegic individuals is the high energy expenditure involved. It has been reported that

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Department of Biomechanics, Science and Research Branch, Islamic Azad University, Iran 2 School of Mechanical Engineering, Sharif University of Technology, Iran 3 RCSTIM, Tehran University of Medical Sciences, Iran Corresponding author: Farzam Farahmand, School of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, Tehran, Iran. Email: [email protected]

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the energy cost of walking of individuals with paraplegia can be as high as three to nine times of that of the normal population.3,4 This is particularly important for high-thoracic lesion paraplegic patients who often suffer from disturbed cardiovascular regulation.5 Furthermore, the high upper body loading during walking with mechanical orthoses might be detrimental for paraplegic individuals considering their high prevalence and risk of wrist and shoulder pathology.6 These facts have been recognized by biomechanics and orthotics investigators and several versions of KAFOs and HKAFOs have been developed to improve the performance of the mechanical walking orthoses with respect to the energy expenditure, upper body loading, and user friendliness, e.g. easy donning and doffing. Some examples are Parwalker or hip guidance orthosis,7 the reciprocating gait orthosis,8 and the advanced reciprocating gait orthosis (ARGO).9 More recently, sophisticated orthotic joints, e.g. linked knee and ankle flexing joints, stance-control knee joint, etc., have been developed to improve the gait manoeuvres of individuals with paraplegia and provide lower energy expenditure and higher walking speeds.10–13 The efficiency and performance of the mechanical walking orthoses has been often evaluated based on experimental examination.3,4,7–14 Such tests provide valuable information on the kinematics, dynamics, and energy costs of the paraplegic gait when using different orthotic designs. However, it is often difficult, or even impossible, to achieve general conclusions from experimental data owing to the small size of the test subjects available and the large interindividual differences between.15 An alternative approach is mathematical modelling that can provide a better understanding of the role and significance of each individual relevant factor, affecting the efficacy and performance of the orthosis. There are a few mathematical models of the paraplegic gait available in the literature. A pioneer work belongs to Tashman et al.16 who developed a three-dimensional (3D) four-segment model of the RGO-assisted paraplegic ambulation and showed that the upper body forces and body deceleration are reduced substantially if a ballistic swing could be produced using functional electrical stimulation. Zefran et al.17 modelled the gait of a paraplegic individual when using crutches as a parallel robot and investigated the effect of different quadrupedal walking patterns on the efficiency of the gait. Greene and Granat18 conducted a kinematical analysis on a simple twodimensional (2D) mathematical model of the paraplegic gait to demonstrate the importance of the ankle dorsiflexion accomplished with knee flexion for increasing the foot clearance. Kagawa et al.19 addressed the relationship between the arm–crutch loading, leg restriction, and motor paralysis, and reported that large reaction forces occurred at the crutches when the ankle and knee joints were restricted. Nakhaee and Farahmand20 developed a simple 3D three segments model with five-degrees of freedom (DOF) to analyse

Proc IMechE Part H: J Engineering in Medicine 0(0) the kinematics and dynamics of the paraplegic gait and showed that an individual with low lesion level might be able to walk using appropriately designed mechanical orthosis and trunk manoeuvres, without the need of a propulsion supply from the hands through crutches. The aim of the present study was to investigate the effects of the kinematical pattern on the mechanical performance of the paraplegic locomotion. A 3D four segment 6-DOF model of a paraplegic subject wearing an ARGO was developed based on the data acquired from an experimental study on a single subject. It was then analysed using response surface methodology (RSM) to recognize the most relevant kinematical factors affecting the total and the upper body muscular efforts during the swing phase. The results were employed to provide recommendations on how the ARGO users can improve their energy expenditure and upper body loading by adopting a modified gait pattern.

Materials and methods A 3D model was developed to study the effects of the gait kinematical parameters on the mechanical performance of the paraplegic locomotion. The geometrical and kinematical dataset needed for simulation of the model, as well as its validation, was obtained in an experimental study involving motion capturing of a single paraplegic subject while wearing a bilateral ARGO and using two crutches. The orthosis locked the knee and ankle joints of the subject and restricted the hip joints to move only in the sagittal plane. Furthermore, by means of a cable link, it restricted the bilateral hip motion to a reciprocal action, so that flexion of the hip joint was coupled to the extension of the other.9 Considering the motion constraints imposed by the lesion and the ARGO, we used a four-segment model to describe the paraplegic gait (Figure 1). The body parts, superior to the lesion, were represented by a trunk segment that also included the head and arms. The pelvis and the part of the trunk inferior to the lesion were represented by a pelvis segment. Finally, a leg–foot segment, including the thigh, shank, and foot, was considered for each of the two legs.

Experimental study An experimental study was conducted on the ARGOassisted locomotion of a single spinal cord injury subject to analyses of the kinematics and dynamics of the gait cycle. The paraplegic subject was a 28-year-old male, 96 kg weight, and 180 cm height, with the lesion level T10. The process of the test was described for the subject and he signed an informed consent, according to the human subjects review committee of the university. The subject used a commercially available bilateral ARGO (Hugh Steeper Ltd, London, UK) and two aluminium forearm crutches for locomotion. During the

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3 occlusion, was repaired using cubic spline interpolation. The three marker sets, attached to each of the four segments, were used to define a local reference system, which was then employed to describe the rotations of the embedding segment with respect to the global system, using Cardan sequence (X-Y-Z).

Modelling study

Figure 1. The test subject during ARGO-assisted walking. A simple model, including trunk (L1), pelvis (L2 and L3), and left and right leg–foot (L4) segments, was used to describe the paraplegic ambulation.

tests, 24 reflective markers were fixed onto his anatomical landmarks, including the left and right posterior calcaneus (heels), second metatarsal head (toes), lateral malleolus (ankle joints), greater trochanter (hip joints), anterior and posterior superior iliac spine, acromion process (shoulder joints), the seventh cervical vertebra (C7), and the tenth thoracic vertebra (T10) (Figure 1). The subject was instructed to walk at his comfortable speed on a level surface, along a 10 m walk way. Twenty trials were recorded using a six-camera VICON motion analysis system (Oxford Metrics, UK) at 100 Hz. The 3D coordinate data of the markers was obtained in the global reference system, with the X, Y and Z being the coordinates in the anterior/posterior, media/lateral, and inferior/ superior directions, respectively. Among the recorded trials, 12 with the most complete tracking data were selected to be analysed. The data was first filtered through a low-pass filter with a cut-off frequency of 5 HZ, to reduce the measurement noises. Also, the missing data, owing to the marker

A skeletal model was developed to characterize the kinematics and dynamics of the ARGO-assisted paraplegic gait. The model included four rigid bodies, i.e. the trunk, the pelvis, the stance and the swing leg–foot segments (Figure 2(a)). A fixed contact point was assumed between the leg–foot stance and the ground and the resulting 3 DOF were described using rotation angles around the global coordinate system. These absolute angular coordinates, i.e. u1 , u2 , u3 , represented the axial rotation, lateral tilting, and forward inclination of the leg–foot stance around the ground contact point, respectively. However, considering the fact that a paraplegic patient has no direct control over his legs, they were attributed to the whole body (assuming all other DOF were fixed), to represent its axial rotation, lateral tilting, and forward inclination, respectively, around the ground contact point (Fig 2(b)). For segments other than the leg–foot stance, we used relative angular coordinates to describe their configuration with respect to their distal or proximal segments. The flexion of the pelvis was described using its angle with the leg–foot stance segment in sagittal plane, i.e. up , at the pin joint assumed at the leg hip stance. The configuration of the trunk was described using the posterior and lateral bending angles of the trunk over the pelvis, i.e. u4 and u5 , respectively, assuming a one DOF joint between the pelvis and the trunk in each of the sagittal and frontal plans (Fig 2(c)). Finally, the configuration of the swing leg was described using its flexion angle with respect to the pelvis, i.e. u6 , assuming a single-pin joint at the swing leg hip (Fig 2(c)). The resulting seven coordinates were then reduced to a set of six independent coordinates, considering the fact that the rotations of the two hip joints were coupled owing to the function of the reciprocal link of the ARGO u6  u3 = 2 3 up

ð1Þ

The dynamics of the model, as an inverted multi-link pendulum, was formulated based on the torque actions only, with the effect of external forces, e.g. groundreaction, crutch-reaction, and weight, represented by their resultant torques. Six independent ideal torque generators were considered to control the six rotational DOF of the model, including three between the leg– foot stance and the ground (t1 , t2 , t3 ), one between each leg and the pelvis (tp = t6 ; owing to the action of the reciprocal cable), and two between the pelvis and the trunk (t4 , t5 ). The controlling torques, assumed around the contact point of the leg–foot stance with

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Figure 2. (a) The skeletal model of ARGO-assisted paraplegic gait, consisting of four segments and six independent DOF, at reference anatomical configuration. (b) The model configuration after a sample whole body rotation around the ground contact point: 10° axial rotation (u1 = 108), 10° lateral tilting (u2 = 108), and 10° forward inclination (u3 = 108). (c) The model configuration after a sample rotation of the trunk: 10° posterior bending (u4 = 108), and –10° lateral bending (u5 = 108), and the swing leg: 10° hip flexion (u6 = 108).

the ground, are actually generated owing to the force interactions of the upper body with the ground through crutches. In fact, they represent the muscular effort made by the shoulders and hands in order to balance the body around the ground contact point, against all force/moment effects applied to it. The sufficiency of the proposed model to simulate the ARGO-assisted paraplegic gait was evaluated in two steps. At first, the distances between the markers attached to each segment were measured at different instants of the gait cycle. The results were then analysed to verify the rigid body assumption considered for the segment, and thus the sufficiency of a four segment model for simulation of the paraplegic locomotion. In the next step, a forward kinematics analysis was performed to evaluate the sufficiency of the six DOF considered for the model. The trajectories of a number of end effectors were obtained, based on the Denavit–Hartenberg approach (Table 1), and compared with those of the experiments. The end effectors considered, included C7, L-heel and R-heel (Figure 1).

RSM analysis The RSM is a collection of statistical and mathematical techniques used for design, analysis, and optimization of processes.21 The most usual application of the RSM is in situations where several inputs of a process, i.e. design variables, potentially influence its responses, i.e. performance measures. In a RSM analysis, experimental strategies and statistical models are employed to explore the space of each design variable and

performance measure, and to develop empirical relationships between them. In the present study, a RSM analysis was performed to recognize the most relevant kinematical factors affecting the mechanical performance of the paraplegic gait. The mechanical performance was evaluated using two measures: (1) energy expenditure, and (2) upper body loading. The energy expenditure was characterized based on the assumption that the most efficient gait is obtained when a given distance is travelled with the lowest muscular effort. So, with the step length kept fixed, we used the total muscular effort (TME) index to characterize the energy expenditure. However, considering the fact that, instead of individual muscles – the joint torque generators, which reflect the resultant effect of the contributing muscles, were represented in our model – we used the sum of squared torques of all joints as indicative of the TME TME index =

6 X

t2i

ð2Þ

i=1

where ti represents the torque of the ith joint. Similarly, the upper body loading was characterized using the upper body muscular effort (UME) index, indicated as the sum of the squared moments of the upper body UME index =

3 X

t2i

ð3Þ

i=1

An inverse dynamic analysis was conducted to obtain the joint toques at five critical instants of the swing

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Table 1. Denavit–Hartenberg parameters of the robotic model of paraplegic gait. i (link number) 1 2 3 p 4 5 6

ai1

ai1

di

ui

0

0 0 0 L4 L2 0 0

0 0 0 0

(u1  p2 ) (u2 + p2 ) u3 up u4 (u5 + p2 ) urh

p 2 p 2

0 p

p 2

0

L3 2

0 L3

phase, determined using the experimental data. The modified Newton–Euler formulation for multi-body branched systems was used to obtain the model’s nonlinear equations of motion   ti = Fi uj , u_ j , € uj , i, j = 1, . . . :7 ð4Þ

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where ti and ui represent the torque and angle of the ith joint, respectively. In order to simplify the RSM analysis, the joint torques were found assuming static condiuj = 0: The anthropometric properties of tions, i.e. u_ j = € the model segments were obtained from the literature.22 The kinematical parameters of the gait pattern were considered as the design variables of the RSM analysis. They included all independent DOF of the model, except for the swing leg hip flexion, u6 , and the whole body axial rotation, u1 , which were assumed fixed to keep the step length unchanged. For each of the design variables, i.e. u2, u3 , u4 , u5 , a range of variation was considered, based on the results of our repetitive experimental tests. Considering the four design parameters, 24 = 16 analyses were performed at each critical instant of the swing phase to obtain the relationship between the design variables and each of the performance measures, i.e. TME and UAE indexes. The results of the RSM analysis were expressed using linear regression equations21 f ð uÞ = b1 + b 2  u2 + b3  u 3 + b 4  u4 + b5  u 5

ð5Þ

where f(u) represents a performance measure, and bi s are constant coefficients that reflect the impact of each of the design variables on the that measure.

Results Joints motions The mean and standard deviations of the angular motions of the joints of the paraplegic test subject during the swing phase are shown in Figure 3. A schematic representation of the resultant movements of the rigid body segments is also illustrated in Figure 4. At the beginning of the swing phase, the subject started inclining his body forward on the leg–foot stance (Figure 3(c)). This motion continued, with a nearly constant rate, during the entire swing phase, so that the body’s centre of mass could be shifted from behind to in front

of the ground contact point. The forward inclination of the body was accompanied with the increasing anterior bending of the trunk over the pelvis in the first half of the swing phase, up to 45° at 50% instant (Figure 3(e)). This caused the majority of the subject’s weight to be transferred from the leg–foot stance to the walking aids. The subject could tilt his body laterally, in order to elevate the swing-side pelvis upward, and provide the required foot clearance (Figure 3(b)). This manoeuvre was helped by the trunk lateral bending, which increased sharply up to 25% and then slowly up to 50% of the swing phase (Figure 3(f)). The advancement of the swing leg from 32° extension to 38° flexion with respect to the leg–foot stance (Figure 3(d)) was provided by the flexion of the swing hip joint. This motion was very small in the first half of the swing phase, since it was only contributed to by the axial rotation of the subject’s body around the ground contact point (Figure 3(a)). The resulting circumduction movement of the swing leg caused a small flexion at the swing leg hip, with a total magnitude of less than 5° at 50% instant. The main part of the swing hip flexion, and consequently the swing leg advancement, occurred in the second half of the swing phase. At about 50% instant, the subject started bending his trunk posteriorly (Figure 3(e)), so that his pelvis was extended and pushed forward. The lateral tilting continued (Figure 3(b)); this motion extended the leg hip stance, and thus produced flexion at the swing leg hip, owing to the coupled reciprocal action of ARGO. After a 75% instance of the swing phase, with the swing leg passed the contralateral leg–foot stance, the lateral bending of the subject’s trunk was changed to the medial bending (Figure 3(f)). Also, the lateral tilt of the body was replaced by a medial tilt (Figure 3(b)). These motions gradually diminished the foot clearance in preparation for a smooth ground contact.

Sufficiency analysis of the model The results of measurement of the inter-marker distances of each of the four segments of the model during the entire gait cycle are illustrated in Table 2. In general the variation of the inter-marker distances was relatively small in comparison with the overall size of each segment. The largest normalized standard deviation against the segment length was associated with the height of the pelvis segment, L2, with a magnitude of only 2.8%. The results of the forward kinematics analysis of the model, in comparison with those of an experimental test, are illustrated in Figure 5, considering the pelvis segment as the reference. In general, there was a good agreement between the predictions of the model for the 3D trajectories of the end effectors and the experimental data. For C7, all the X, Y, Z coordinates, and for L-heel and R-heel, the X and Z coordinates of the 3D trajectories were nearly identical. The largest differences

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Figure 3. The means and standard deviations of the angular motions of the joints of the paraplegic subject during swing phase: (a) whole body axial rotation, u1 ; (b) whole body lateral tilting, u2 ; (c) whole body forward inclination, u3 ; (d) hip flexion of the swing leg, u6 ; (e) trunk anterior bending, u4 ; (f) trunk lateral bending, u5 . All motions have been described considering the joints’ configurations at anatomical position as the zero references, except for the hip extension of the swing leg that has been expressed with respect to the hip joint of the stance leg for clarity.

Figure 4. Stick figures of the four rigid body segments, i.e. trunk, pelvis, and two legs, based on the 3D coordinate measurements of the experimental study during a representative swing phase in sagittal plane (top) and frontal plane (bottom).

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Table 2. Variation of the inter-marker distances of each of the model segments (Figure 1) during the entire gait cycle. Segment

Min (mm)

Max (mm)

Mean (mm)

Standard deviation (mm) (% of segment length)

L1 L2 L3 L4

268 269 472 918

292 311 492 961

282 293 489 937

5.4 (1.9%) 8.3 (2.8%) 2.1 (0.4%) 6.2 (0.6%)

in the modelling and experimental results were found for the Y coordinates of the heels, which represented the lateral movements of the legs.

RSM analysis Considering the results of the kinematical analysis of the paraplegic gait (Figure 3), three critical instants of the swing phase were found to appear at about 25%, 50%, and 75% of the total swing phase duration. Two other critical instants were also considered close to the start and ending of the swing phase, i.e. at 5% and 95% instants, respectively. The ranges of variation of the design variables, i.e. u2, u3 , u4 , u5 , considered for the

RSM analysis are shown in Table 3 for each critical instant of the swing phase. These ranges were obtained assuming a wider domain (to at least 10°) than that of the experimental variation range of each design variable but with the same mean value. The magnitudes of the non-variable kinematic parameters of the model, i.e. u1 , u6 , at each critical instant of the swing phase are also indicated in Table 3, based on the experimental data (Figure 3). The results of the RSM analysis, indicating the relationship between the kinematical design variables and the muscular effort indexes, i.e. UME and TME, as the performance measures, are illustrated in Tables 4 and 5, respectively. The bi parameters are constant coefficients of the linear regression equations (equation (4)) of the UME and TME indexes. The sign of each bi , in combination with the sign of the relevant design variable, ui , at the same instant, determines whether it has an increasing or decreasing effect on the indexes, and its magnitudes reflect the level of its impact. The results of Table 4 indicate that the UME index was most sensitive to u3 and then u2 design variables. The whole body forward inclination, u2 , increased this index consistently during the entire swing phase (Tables 4 and Figure 3(b)). For the whole body lateral

Figure 5. Comparison of the 3D trajectories of the end effectors predicted by the model (solid lines) and obtained during an experimental test (dash lines) considering the pelvis segment as the reference: C7 (top), L-heel (middle), R-heel (bottom).

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Table 3. The ranges of variation of the design kinematical variables and the fixed magnitudes of the non-variable kinematical parameters at each critical instant of the swing phase. Kinematical parameter

5% instant

25% instant

50% instant

75% instant

95% instant

u1(deg) u2(deg) u3(deg) u4(deg) u5(deg) u6(deg)

23 [–9 –1] [–23 –8] [–22 –5] [–10 10] –9

12 [–13 –3] [–9 1] [–35 –15] [–20 0] –5

0 [–14 –4] [1 9] [–45 –25] [–25 –5] 0

12 [–15 –5] [7 17] [–50 –30] [–15 5] 5

–23 [–9 –1] [15 29] [–15 –5] [–10 10] 9

Table 4. The constant coefficients of the linear regression equations of the UME index at each of the five critical instants of the swing phase. Swing instant

b1

b2

b3

b4

b5

5% 25% 50% 75% 95%

9.1964 2.3337 2.8633 6.5218 15.751

2.0360 1.5712 1.2581 1.2935 2.083

–5.3139 –0.5564 1.4028 3.3546 7.340

0.3285 0.0489 –0.1106 –0.2090 –0.295

–0.2784 –0.1798 –0.1722 –0.1561 –0.283

Table 5. The constant coefficients of the linear regression equations of the TME index at each of the five critical instants of the swing phase. Swing instant

b1

b2

b3

b4

b5

5% 25% 50% 75% 95%

9.2863 2.5667 3.2071 6.7791 15.822

2.0339 1.5652 1.2544 1.2912 2.081

–5.2602 –0.5019 1.4477 3.4017 7.322

0.3112 0.0120 –0.1423 –0.2457 –0.305

–0.2708 –0.1659 –0.1728 –0.1508 –0.275

tilting, u3 , we found a changing, but always increasing, effect on the UME index (Table 4 and Figure 3(c)). The trunk kinematical variables affected the index with much lower impacts in comparison with those of the whole body movements. The trunk anterior bending, u4 , increased the UME index relatively consistently. However, the trunk lateral bending, u5 , had a reducing effect on the UME index of up to 75% instant of the swing phase, but an increasing effect afterwards. Results of Table 5 indicate that the relationship between the design variables and the TME index was quite similar to what observed for the UME index. The coefficients of the design variables in the linear regression equations of the TME and UME indexes were found to be nearly identical.

Discussion Human walking is a fundamental and well-learned coordinated movement that enjoys an efficient and relatively consistent pattern in normal conditions. For individuals with neuromusculoskeletal disorders, e.g. paraplegic patients, lower limb amputees, etc., however, performing an efficient gait pattern, not only

requires effective orthoses/prostheses, but also needs training on how the muscles functions and joints movements to be coordinated.23 Pure experimental examinations cannot provide a deep understanding of the factors affecting the efficacy and performance of the walking orthoses and the associated gait patterns. This is mainly owing to their inadequate research methodology in view of the large variance in populations who use a particular orthosis, the significant impact of heterogeneity within each population, and the resultant small number of potential subjects available to participate in research that would meet strict inclusion and exclusion criteria required to minimize this heterogeneity.15 Computer modelling of the gait pattern, however, provides a detailed description of the role and significance of each individual relevant factor affecting the kinematics, dynamics, and energy expenditure of the gait. This is obviously of great importance for the interpretation of the experimental data, which normally reflects the results of a combination of several determinants, e.g. subject’s conditions, orthotic design, and gait pattern. However, the most attractive feature of computer modelling in gait biomechanics may be its capabilities for parametric

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studies, as well as synthesis of new motion patterns, which are not possible to be achieved experimentally.24 The previous modelling studies of the paraplegic gait have often been concerned with the efficacy and performance of the mechanical walking orthoses in combination with the functional electrical stimulation.16,17 However, the use of such hybrid devices for ambulation of individuals with paraplegia has not yet evolved practically owing to several limitations, e.g. long term infection of tissues around implanted electrodes, fast muscles fatigue associated to the use of surface electrodes, long don and doff times, high set-up and maintenance costs, etc.15 Similarly, the hybrid systems based on the external electrical or pneumatical actuators are not yet in practical use owing to the need to external energy sources, long don and doff times, and high maintenance costs.25 In the present study, we focused on ARGO mechanical orthoses, which are routinely used by paraplegic individuals for locomotion.14,15 We studied the kinematics of the ARGO-assisted paraplegic gait in detail in search for an improved gait pattern that provides lower energy expenditure and upper body loading. For the first time, the RSM was employed to explore the relationship between the kinematical parameters, considered as design variables, and the total and upper body muscular efforts, defined as performance measures. Then, by identification of the impacts of each kinematical parameter, practical guidelines were revealed for paraplegic patients to obtain a more advantageous gait pattern. The kinematic results of this study for ARGOassisted paraplegic gait are in general agreement with the data reported in the literature, in spite of the significant effect attributed to the heterogeneity of the test subjects. Similar to our study, other researchers4,14,16,26 have found lateral tilting over the stance leg, at the beginning of the swing phase and extension of the trunk and pelvis, in the mid swing. Our detailed kinematic data, however, provide more insight into the biomechanics of the paraplegic locomotion, and in particular, characterizes two main strategies for the swing phase. The first strategy arises from the need for foot clearance, i.e. the swing leg shall be functionally shorter than the stance leg to avoid colliding with the ground and being able to pass the stance leg. In natural walking, this requirement is satisfied by knee flexion and ankle dorsiflexion. In paraplegic individuals, with the knee and ankle locked by the orthosis, a lateral tilting strategy is adopted to elevate the swing-side pelvis upward, and provide the foot clearance. The results of our kinematical investigation (Figure 3(b) and (f)) suggest that this strategy is implemented by the contribution of a main and an assistant manoeuvre, i.e. the whole-body lateral tilting and the trunk lateral bending, respectively. By performing a whole-body lateral tilting manoeuvre, the patient can tilt his pelvis as a direct kinematical effect through the body-orthosis linkage system (Figure 2(b)). As a result, the swing hip would be elevated upward providing the required foot

9 clearance. This manoeuvre, however, might be facilitated through a dynamic effect if a trunk lateral bending manoeuvre is performed simultaneously. This assistant manoeuvre transfers the body’s centre of mass towards the lateral, reducing the torque requirement of the whole body lateral tilt. Thus, the swing foot clearance could be achieved by lower energy expenditure and upper body loading. The assisting contribution of the trunk lateral bending manoeuvre on the foot clearance strategy is confirmed by the results of our RSM analysis (Tables 4 and 5), which indicate a reducing effect on the UME and TME indexes for u5 . This suggests that an improved gait pattern can be obtained by the paraplegic patients if they adopt a larger lateral bending manoeuvre at the trunk during the swing phase. This conclusion is in good agreement with our previous modelling study20 indicating a major contribution for the trunk kinematics in the dynamics of the paraplegic locomotion. However, it needs more detailed modelling studies, as well as experimental investigations, to be verified. The second strategy within the ARGO-assisted paraplegic gait arises from the need for advancement of the swing leg, while the hip flexor muscles do not function owing to the neurological problems. The kinematical results of our study suggest that this strategy can be implemented using two independent manoeuvres, i.e. trunk posterior bending and whole-body axial rotation around the ground contact point. However, we found the latter manoeuvre to cause only a small flexion at the swing leg hip (Figure 3(a) and (d)), probably owing to the restricting action of the ARGO’s cable link. On the contrary, the coupled reciprocal action of the ARGO caused the trunk posterior bending to significantly contribute to the swing leg hip flexion (Figure 3(e) and (d)) and its consequent advancement, with a small impact on the muscular effort indexes (Tables 4 and 5). This suggests that for ARGO users, the advancement of the swing leg can be effectively and efficiently accomplished by the trunk posterior bending manoeuvre and that the whole-body axial rotation shall be avoided owing to its inefficacy and inefficiency. Again, more detailed modelling and experimental studies are needed to verify this hypothesis. Finally, the results of our RSM analysis (Tables 4 and 5) indicate that the coefficients of the design variables in the linear regression equations of the TME and UME indexes were nearly identical. This might suggest that the quantities that these two performance measures represent, i.e. the total and upper body muscular efforts, are close to each other. Thus, one might conclude that in our test of the ARGO-assisted paraplegic gait, the subject mostly used his upper body segments to provide the required muscular effort, with minor contribution from the trunk muscles. In spite of the interesting observations discussed, care must be taken in making general conclusions from the results, in view of the several limitations involved in

10 the methodology of this study. First of all, we only considered the single support phase of the paraplegic gait and ignored the contribution of the double support phase in providing a part of the body propulsion. The main cause of this limitation was the fact that the double support phase of locomotion forms a closed-loop kinetic chain problem that is difficult to solve using conventional robotic methods. Also, we assumed a fixed contact point between the leg–foot stance segment and the ground, in order to facilitate the formulation of the model. This is obviously a simplification of the normal gait behaviour in which the foot contact point moves from the heel, at the start of the stance phase, to the toes, at its final stages. We have addressed a solution for a more realistic model of gait, including the double support phase and moving ground contact point, in a previous study on amputee locomotion.27 However, the results are much more sensitive to the assumptions made for modelling of the foot–ground contact. The experimental data basis of our study was obtained from a single individual with a specific level of injury and wearing a particular type of orthosis. The model was also simple and included a limited number of rigid segments and rotational DOF. In spite of these limitations, our model was capable of reproducing the essential kinematical and dynamical characteristics of the single support phase of the ARGO-assisted paraplegic. The basic structure of the model, with four segments for representation of the trunk, pelvis, and two legs, was consistent with our test configuration and might also be applied to a wide range of spinal cord injury individuals wearing other types of KAFOs and HKAFOs. The small variation of the inter-marker distances of each segment in repetitive experimental tests (Table 3) indicate that the number of segments was rather sufficient and the rigidity assumption considered for them was not unrealistic. The largest normalized standard deviation we observed was less than 3% of the segment length, and was associated with the shortest segment of the model, i.e. the height of the pelvis segment. The six DOF assumed for the joints of the model correspond to the basic motion restrictions imposed by the ARGO, i.e. sagittal plane reciprocal motion of the hip joints. However, the results of the forward kinematics analysis (Figure 5) suggest that the lateral rigidity of the hip joints of the orthosis might be inadequate to completely restrict the subject’s joints from frontal plane motions, i.e. adduction and abduction, in practice. This suggests that, for a more realistic simulation of the ARGO-assisted paraplegic gait, it might be necessary to include a lateral DOF with appropriate stiffness at the hip joints of the model. However, such stiffness data is not yet available in literature and needs to be generated from experimental examinations. Obviously, if other types of HKAFOs are to be modelled, more changes in the model’s rotational DOFs would be required.

Proc IMechE Part H: J Engineering in Medicine 0(0) Another major limitation of the present study arises from the fact that the equations of motion were solved assuming static conditions. This simplification was necessary for our RSM analysis in order to keep the number of design variables within an affordable range. Otherwise, the velocity and acceleration components of the current design variables should also have been treated as design variables, making the analysis too complicated (needing 212 = 4096 analyses at each critical instant of the swing phase). As a result, our model ignored the dynamic effects of the joints’ motions. In particular, the momentum produced by the whole-body axial rotation around the ground contact point, which is thought to contribute, in part, to the advancement of the swing leg,12 was not reflected in our model. This effect, however, is not expected to be significant in the ARGO-assisted paraplegic gait, in which the flexion– extension motion of the hip joints is controlled by the ARGO’s cable link. Nevertheless, the static joint torques, calculated in our model, are slightly smaller than those revealed by a dynamic analysis. Winter22 reported that the joints net moments raised about 10% when the normal subjects changed their speed of walking from slow to natural. Considering the relatively slow movements of the paraplegic patients during locomotion, we expect our static assumption to have caused errors in a similar order. In this study, we used the results of the RSM analysis to provide information on the muscular effort costs resulted from different manoeuvres involved in the paraplegic gait. The muscular effort was characterized in terms of the sum of squared joint torques, in view of the fact that the individual muscles were not included in our skeletal model and their resultant effect was represented by joint torque generators. Such a simplification is only a rough estimation of the muscular effort and cannot reflect the limited capacity of the muscles for force generation. Moreover, it is well documented in the biomechanical literature that the force produced by a muscle depends upon the muscle length and velocity, according to Hill’s modified model of muscle contraction.22 The similarity of our RSM results for UME and TME indexes is thought to be resulted from not considering such details in the estimation of the muscular effort costs. Further work is going on to develop a more sophisticated musculoskeletal model of the paraplegic gait, so that a more accurate assessment of the muscular effort and energy cost can be obtained. Finally, in our suggestion for a larger lateral bending manoeuvre of the trunk during paraplegic gait, we did not consider the soft tissue strain limitations of a real patient. Ligaments, muscles, and other soft tissues may experience high strains during movements that explore a wide portion of a joint’s normal range of motion. This effect is much more critical in paraplegic patients who often suffer from stiffened joints and reduced soft tissue strength. Thus, care must be taken in adopting such a modified kinematical pattern, with a large range

Nakhaee et al. of motion for the trunk, by these patients to avoid soft tissue tearing.

Conclusions In this study the muscular effort cost of different manoeuvres involved in the two main strategies of the swing phase of the paraplegic gait, i.e. foot clearance and leg advancement, were evaluated using a mathematical model and RSM analysis. The model predictions revealed that a large lateral bending manoeuvre at the trunk reduces the torque requirement of the whole body lateral tilting performed for the foot clearance. Also, the model predictions indicated that the swing leg advancement can be effectively and efficiently accomplished by the trunk posterior bending manoeuvre, by means of the coupled reciprocal action of the ARGO. It was further suggested that the ARGO users should avoid whole-body axial rotation, owing to its inefficacy and inefficiency for swing leg advancement. By adopting such modifications in the gait pattern, the paraplegic individuals are expected to achieve improved energy expenditure and upper body loading. However, further work, based on more sophisticated musculoskeletal models, and large-sample sized experimental tests are required to verify these conclusions. In particular, the effect of the suggested modified gait pattern on the strains and potential tearing of the patient’s soft tissues should be studied in detail. Funding This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. Acknowledgments The authors wish to thank the assistance of the staff of the Gait Analysis Lab, Department of Ergonomics, University of Social Welfare and Rehabilitation Sciences, and in particular the valuable support of Dr S Nakhaee, the president of the university. References 1. Mazur JM, Shurtleff D, Menelaus M, et al. Orthopedic management of high-level spinal bifida: Early walking compared with early use of a wheelchair. J Bone Joint Surg Am 1989; 71(1): 56–61. 2. Kunkle CF, Scremin AM, Eisenberg B, et al. Effects of standing on spasticity, contracture and osteoporosis in paralyzed males. Arch Phys Med Rehab 1993; 74(1): 73–78. 3. Cerny K, Perry J and Walker JM. Effect of an unrestricted knee-ankle-foot orthosis on the stance phase of gait in healthy persons. Orthopedics 1990; 13(10): 1121–1127. 4. Bernardi M, Canale I, Castellano V, et al. The efficiency of walking of paraplegic patients using a reciprocating gait orthosis. Paraplegia 1995; 33(7): 409–415.

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