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EVALUATION OF CLOSED-LOOP CONTROL SYSTEM FOR RESTORING STANDING AND SITTING FUNCTIONS BY FUNCTIONAL ELECTRICAL STIMULATION CHENG-LIANG LIU1, CHUNG-HUANG YU2, SHIH-CHING CHEN3, CHANG-HUNG CHEN4 1
Department of Mechanical Engineering, National Taiwan University, Taipei Institute of Rehabilitation Science and Technology, National Yang-Ming University, Taipei 3 Department of Physical Medicine and Rehabilitation, Taipei Medical University and Hospital, Taipei 4 Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 2
ABSTRACT Functional electrical stimulation (FES) is a method for restoring the functional movements of paraplegic or patients with spinal cord injuries. However, the selection of parameters that control the restoration of standing up and sitting functions has not been extensively investigated. This work provides a method for choosing the four main items involved in evaluating the strategies for sit-stand-sit movements with the aid of a modified walker. The control method uses the arm-supported force and the angles of the legs as feedback signals to change the intensity of the electrical stimulation of the leg muscles. The control parameters, Ki and Kp, are vary for different control strategies. Four items are collected through questionnaires and used for evaluation. They are the maximum reactions of the two hands, the average reaction of the two hands, largest absolute angular velocity of the knee joints, and the sit-stand-sit duration time. The experimental data are normalized to facilitate comparison. Weighting factors are obtained and analyzed from questionnaires answered by experts and are added to evaluation process for manipulation. The results show that the best strategy is the closed-loop control with parameters Ki=0.5 and Kp=0. Biomed Eng Appl Basis Comm, 2005(February); 17: 19-26. Keywords: FES, sit-stand-sit, evaluation, closed-loop control
a successful application to solving the gait problem. This approach has been applied to some patients with spinal cord injuries (SCI) who suffered problems with sit-to-stand movement. An early study applied electrical stimulation to a paralyzed lower limb to stimulate the hip muscles and quadriceps to enable a T3 patient stand from a sitting position [2]. The treatment involved electrical stimulation to actuate the muscle to cause functional movement in a process called functional electrical stimulation (FES). Some commercial products have been developed for the paralyzed upper limbs such as Handmaster, ETHZ-
1. INTRODUCTION Liberson et al. used electrical stimulation to improve the drop foot of hemiplegia [1]. It seems to be Received: May 24, 2004; Accepted: Jan 25, 2005 Correspondence: Cheng-Liang Liu, Professor Department of Mechanical Engineering, National Taiwan University, No.1, Section 4, Roosevelt Rd. Taipei 106, Taiwan E-mail:
[email protected]
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moments of the arm while FES was applied to the lower limb, to help an SCI T6 patient stand up and sit down. The design of an efficient FES controller for standing and sitting is an important area of research. Riener and Fuhr designed a patient-driven motion reinforcement controller [14]. They measured the position and speed of upper limb joints to control the FES of lower limbs to help SCI patients stand up and sit down, and reduce the calculation time of the controller. Some other researchers used switches to divide standing and sitting processes into several steps to simplify the design of the controller [15-16]. With so many methods and strategies for controlling standing and sitting, their performance evaluations are very important. Qualitative and quantitative data obtained through instrument readings are frequently used for evaluation, such as in the rehabilitation of patients with total hip replacement [17]. Triolo et al. developed a means of estimating the capacity to free the upper extremities from support and balancing tasks, while the patient is upright. He assessed and recorded the performance of 18 tasks, as well as the total elapsed standing time. [18]. However, the subjects had considerably different figures, making the comparison inappropriate. Bonaroti et al. used a measure of functional independence to compare patients who used FES and a long leg frame. Several evaluation items were tested and measured on a seven-point scale. The total score will reflect the better one or the worse. However, only one item related to the sit-to-stand task [19]. The Analytic Hierarchy Process (AHP) was introduced to support multi-criteria decision-making. Candidates are arranged hierarchically and a symmetric pair-wise comparison matrix would tell contradiction while arranging priority [20]. The AHP approach has also been used in many estimation methods. A transformed Saaty matrix, can be solved as an eigenvalue problem and supports the estimation of priorities [21-22]. Many articles have proven the accuracy of the AHP method [23-24]. This work is aims to determine the optimal value of parameters for a closed-loop control system that restores standing and sitting functions to paraplegics using FES. Therefore, a method for evaluating such system is required. The whole work consists of three phases. They are experimental setup, clinical trial and evaluation. The first phase, experimental setup, is to equip the subject with sensors and apparatus, which measure forces, torques, and postures. The second phase, clinical trial, stimulates the subjects using electric pulses with different valued parameters. The third phase, evaluation, involves a questionnaire, to set weighting factors and determine optimal values for the parameters that associated with FES.
ParaCare and Freehand to performing grasping functions [3]. In Kralj and Bajd s book [4], Wilemon and Reswick implanted penetration electrodes near the femur and hip nerve. The stimulation of the muscles extended the knee joints and hip joints. A pair of ankle orthoses were then used to stabilize the ankle joints. Kralj and Bajd had also performed extensive FES research and concluded that a paralyzed lower limb could be used to stand only by applying the surface FES technique. Their work on walking also addressed the effect of the paralysis of a lower limb on changes in the pace of walking. In addition to conducting research on standing and walking, Petrofsky et al. designed a bicycle for patients with SCI [5]. Helped by FES, patients exercised their muscles and moved to a nearby destination required. Kralj and Bajd s work on standing and sitting by patients with SCI involved a series of electrical pulses that stimulated the quadriceps, gluteus maximus, gluteus medius, soleus and gastrocnemius [4]. However the electrical pulses were not altered by any feedback signals and so could not control the speed of standing and sitting. Ewins et al. also developed an open FES controller using a microprocessor that made the FES controller portable [6]. Graupe et al. then developed another portable open system controller, ParaStep, that helped the T4 ~ T12 patients to walk a little [7]. However, the continuous stimulation causes the quadriceps to fatigue quickly. Andrews et al. installed an inclinometer and a load cell to generate feedback information concerning standing posture, which enable the FES controller maintain the stability of a patient in the standing position [8]. Their system is a closed-loop control system. Davoodi and Andrews compared five different standing and sitting control systems by simulation and concluded that closed-loop control systems yielded better results than open-loop control systems [9]. Graupe et al. attempted to extract EMG signals from the shoulder, and controlled the movement of the lower limbs [10]. However, some movements of the shoulder caused unexpected movements of the lower limb. Kagaya et al. collected the positions of the joints and the forces exerted by the muscles of normal people. They then used these data on SCI patients to enable them to stand stably [11]. Although a lower limb paraplegic cannot move his or her legs but generally has normal upper limbs, Veltink and Donaldson proposed the application of FES to leg muscles in close cooperation with normal arm movements to enable the patients to control their standing consciously and simplify the development of the FES controller [12]. Donaldson and Yu were then designed an auxiliary system controlled by the deficit moment of handle reactions and the stimulated leg muscle [13]. The system measured the reactions and
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regulated by saturation and is thereby transformed back into another moment signal E3. The difference between the desired moment E1 and the regulated moment E3 is fed back to adjust the subsequent electrical stimulation. A method of evaluation is introduced to determine the optimal parameters, Kp and Ki, in this closed-loop control.
2. METHODS 2.1 Knee Joints Extension Tests Knee joints provide most of the torque in the sit-to-stand process. Their capability to extend legs is tested using a Cybex machine. The Cybex machine is used for evaluating rehabilitation; it incorporates a dynamometer which measures performance of a limb. The limb motion, measured by using a Cybex machine, is then transferred into analogue signals. In this work, isometric type of motion is chosen as a base to determine the threshold pulse width, saturation pulse width and maximum torque of the knee joint for closed-loop control. A data acquisition card can extract 16 analog signals and eight digital signals, sampling at 96000 Hz. A four-channel portable electrical stimulator is controlled using LabVIEW software so as to output electrical pulses to electrode pads on the human skin. The frequency of the electrical pulses applied to the subject is adjusted to 20 Hz. The pulse width is varied from 100 s to 300 s with the increment of 50 s. The electrical stimulation cycle is ON for five seconds and OFF for another five seconds to prevent muscle fatigue. After three cycles, the stimulation is stopped for one-minute. The knee joint test using the Cybex machine yield a joint moment versus pulse width curve and helps to determine the limiting intensity of electrical stimulation.
2.4 Evaluations Experts suggest that four relatively important items in evaluating standing and sitting using FES. They are the maximum forces applied by hands, the average force applied by hand, the angular velocity of the knee joint while sitting, and the standing and sitting time. The maximum force applied by hand may reflect the instantaneous deficit moment induced by the electrical stimulation on leg muscles. The average force applied by hand reflects deficit moment induced by the electrical stimulation on leg muscles throughout the period of standing. The angular velocity of the knee joint while sitting represents the smoothness of the sitting action. The total duration of standing measures the difficulty to the subject of the standing process. These four items seem to be able to specify whether the control system is good or bad. Three methods of comparison are provided to check consistency. The first method is to rank the four items by using ordered weight. The second is ranked by using scored weight. The last is ranked by analytic hierarchy process (AHP). The four items are weighed in terms of factors derived from the questionnaires. Twenty experts, comprising physicians, physical therapist, and biomechanical researchers, were asked to answer the questionnaire. The four items were weighted from 1 to 4 according to their importance. The most important item was ranked 1 and the least important, 4 . The overall rank of each item was then obtained by summing the ranks in the responses to the 20 questionnaires. They are listed in the third row of Table 1. More important items are assigned a larger weighting, so the rank totals are divided by 20 to yield
2.2 Sit-Stand-Sit Experiments The subject is equipped with measuring transducers. They include three pairs of electronic goniometers at the ankles, the knee joints, and the hip joints. Two dynamometers transferring forces and moments via a pair of handles held by the hands, feed back reactions and torques as electric signals. Therefore, the body posture of the subject at any moment can be determined [25]. The aforementioned signals are collected using a DAQ card for data processing. The electrode pads are stuck on the knee extensors. The electrical pulses are applied to extend the knee joint at the same time that an effort is made to move the upper limb.
2.3 FES Closed-Loop Controller The FES controller used in this work is a closedloop PI control system, as shown in Fig. 1 [14]. The input deficit moment is multiplied by Kp and Ki. Accordingly, the moment required to induce extension E1 of the knee, is generated. E1 is then transformed into an output pulse width, which drives the electrical stimulator. The width of the output pulse width may be
Fig. 1 Closed-loop PI control system [13]
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average ranking. The fourth row lists the reciprocals of these rankings. The fifth row lists the normalized weights of the four items, adjusted to sum to unity. The scored weights of the four items are from 1 to 10. The grade total of each item is obtained by summing the grades in the responses to the 20 questionnaires, and is listed in the third row of Table 2. The summation of the grade total of each item is 558. The sum is normalized to unity and then the weighting factor of each item is scaled down proportionally; they are listed in the fourth row of Table 2. The analytic hierarchy process is a method for evaluating the weighting factors of parameters in a group. Its first step is to compare every pair of parameters and compare the importance of the first parameter to that of the second parameter in the figure. For example, the first parameter is three times more important than the second parameter; the comparison is recorded as three. The second step is to ask the same group of experts to state the relative importance of the same four items. The third step is to create a square evaluation matrix whose rank is the number of parameters. All the elements on the diagonal of the matrix are 1 because every parameter is as important as itself. The upper right triangle of the matrix is the relative importance of each pair of parameters. The lower left triangle of the matrix is filled with elements determined by symmetry with the
upper right triangle, by dividing 1 by the corresponding elements, as in Eq. (1).
Table 1 Summation and normalization of Orderedweighting factors
where is the largest eigenvalue, and N is the rank of the matrix. In this work, is 4.0531 and N is 4. RI , which is an index subject to change according to different rank of a square matrix, was suggested to be 0.9 by Satty for N =4. From Eq. (2), CI is 0.0177, which is much smaller than the acceptance value 0.1 [22]. From Eq. (3), CR is 0.0197, which is also smaller than the acceptance value 0.1. The weighting factors obtained from the questionnaire can be regarded reasonable [20]. The above three methods of evaluation are compared in Fig. 2, where figure 1 to 4 in the horizontal axis represent item 1 to 4 and the vertical axis scales the weightings. The figure shows that in all three methods, item 1 is the most important, followed by items 2, 3 and 4. The difference among the weightings of item 1 is largest and that of item 2 is least.
Evaluation matrix =
(1)
This square evaluation matrix is then solved to obtain its eigenvalues and eigenvectors. The elements of the eigenvector, corresponding to the largest eigenvalue, are thus the weighting factors that weigh each item. The largest eigenvalue solved from Eq. (1) is 4.0531. The third row of Table 3 lists its corresponding eigenvectors. These weighting factors are then normalized by proportional adjustment to sum to unity. The results fill in the fourth row, as AHP weighting factors for items 1 to 4, respectively. Satty suggested the use of a consistency index (CI) and a consistency ratio (CR) to check the acceptability of the weighting [20]. The value of CI and CR can be obtained from the following equations. (2) (3)
Table 2 Summation and normalization of scored weighting factors
2.5 Experiment on Knee Extension Moment A normal male, subject Chonn, aged 27, 173 cm tall, 70 kg weight, was recruited as a volunteer to participate in this knee extension experiment. The experiment was performed on both legs. Electrical stimulation of five pulse widths - 100, 150, 200, 250, 300 s - were applied on the right leg. Figure 3 plots the knee extension moment vs. electrical pulse width.
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Table 3 AHP weighting factors
Fig. 3 Knee extension moment vs. electrical pulse width vertical double-dashed line, which plots the times when the standing or sitting processes were completed. In the experiment, the subject moves from the sitting position to the standing and then back to the sitting without ES, as shown in Fig. 4. Then an openloop control ES was also applied to the subject, during sit-stand-sit experiments yielding the results shown in Fig. 5. The line descriptions are almost the same as in Fig. 4, except that the two vertical dashed lines Es give the times at which the electrical stimulation is turned ON and OFF. Figure 6 refers to the closed-loop control ES sitstand-sit experiment, involving the subject with Ki=2.0, Kp=0. The ES is on at the moment indicated by the vertical dashed line. The ES is then applied throughout the sit-stand-sit process. In closed-loop control, there are some more figures to present the pulse width and the deficit of the knee joint moment at both legs shown in Fig. 7. The line descriptions Pw and Md in the figure are of pulse width and deficit moment. The sit-stand-sit experiments with closed-loop control ES were also performed using different sets of parameters (Ki=1.0, Kp=0), (Ki=0.5, Kp=0), (Ki=1.5, Kp=0), (Ki=2.0, Kp=0), (Ki=1.0, Kp=0.5) and (Ki=1.0, Kp=1.0). Table 4 presents the results of the evaluation. One set of parameters (Ki=1.0, Kp=1.0) is excluded because the subject could not perform any sit-stand-sit movement at all. The first column in Table 4 presents four evaluation items, stated in paragraph 2.5. In Table 4, the first experiment was performed without any electrical stimulation (ES). The second one was performed with open-loop control ES. The last five experiments involved closed-loop control ES with various control parameters Ki and Kp.
Fig. 2 Weighting factor comparison among the three evaluation methods The approximate slope of the curve can be calculated by dividing the largest moment at 300 s by the difference between the largest and smallest pulse widths, 300-100=200( s). The slope is thus 0.41047 (Nm/ s). The same experiment was also performed on the left leg, yielding a slope of 0.323 (Nm/ s). Hence, the strengths of the right and the left knee joints of this subject differ.
3. RESULTS MATALAB was used to manipulate raw data obtained from the handle dynamometers and the electronic goniometers. The angular velocities and deficit moments of each knee joint is thus calculated. Three experiments were conducted on the normal subject Chonn; Fig. 4 to 7 plot the corresponding curves. The line type description in the upper right frame of each figure, Ha means hand; A, ankle; K, knee; Hi, hip; R, right; L, left; Fx, force component in the anterior-posterior direction (N); Fy, force component in the upper-lower direction (N); M, moment (N-m); Md, deficit moment (N-m); Ag, angle (deg); Va, angular velocity (deg/sec), and Pw, pulse width ( s). The line Es points out the times at which the ES was switched ON and OFF during the experiments. The line Stand is a
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Fig. 4 Sit-stand-sit experiments without the aid of ES
Fig. 7 Pulse width and the deficit of knee joint moment in sit-stand-sit experiments with the aid of closed-loop control (Ki=2, Kp=0) Table 4 Results for evaluation
Fig. 5 Sit-stand-sit experiments with the aid of open-loop control ES in Fig. 4, that lists maximum hand force, is 452 (N). The first datum of the row, 527.498 (N), is then divided by 452 (N). The normalized value is 1.166 (N) and is presented in Table 5. The ordered weightings of each evaluation item in Table 1 are added into Table 6 for calculation. Each normalized datum is then multiplied by its corresponding weighting factor to its left in the same row; the values in each column are then summed. Each sum is included the row, total. The last row lists the ranks of the seven experiments, according to the value of the row, total. A similar manipulation is performed by replacing the column of ordered weighting factors in Table 5 by scored factors (from Table 2) or AHP weighting factors (from Table 3), yielding the total and rank in Table 6 and Table 7. For convenience of comparison, Fig. 8 presents the total and rank values in Tables 5, 6 and 7. OP and CL in Fig.8 represent open and closed loop control. The lowest total in each line is the rank 1. The highest value is the rank 7. All the three methods of evaluation in Fig. 8 imply that Ki=0.5 and Kp=0 are the most appropriate parameters of closed-loop control for sit-stand-sit
Fig. 6 Sit-stand-sit experiments with the aid of closed-loop control ES(Ki=2, Kp=0) The experimental data concerning the four evaluation items are so diverse, so normalization is applied. Each datum in Fig. 4 is divided by the average of the row to which it belongs. Table 5 lists the normalized data. For example, the average of the row
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Table 7 Ranks evaluated by using AHP weighting
electrical stimulation. However, the three evaluations are not wholly consistent with each other, while (Ki, Kp) valued (1.5, 0) and (2.0, 0). After all, the weightings were obtained from human responses to questionnaires.
4. DISCUSSION In this work, three methods are used to evaluate the closed-loop control system for restoring standing and sitting functions by functional electrical stimulation. It is found that the ranking of the three methods are almost the same. It can be used as a contrast to confirm the correctness of the ranking and assure that the evaluation process is reliable. There does not indicate the availability of each evaluation method. However, through the evaluation of the three different methods the consistency of the results will lead to high confidence. This evaluation approach is applied on a normal subject because the potential errors whether they may be contributed from the subject or the method itself are Table 5 Ranks evaluated by using ordered weighting
Fig. 8 Comparison by three methods of weighting for different control methods and different Ki and Kp values willing to be separate. Fortunately, the results of this newly developed evaluation are quite consistent and some further tests for patients could be planned later on.
5. CONCLUSIONS This work demonstrated three methods of evaluation, using four items to rank the appropriate ES parameters for sit-stand-sit process. The three methods of evaluation yield consistent rankings, in most cases. Their results are reasonable. The subject was a normal person who was electrically stimulated and the experiment showed that closed-loop control with Ki=0.5, Kp=0 was the most satisfactory method.
Table 6 Ranks evaluated by using scored weighting
ACKNOWLEDGEMENT The authors would like to thank the National Science Council of the Republic of China for financially supporting this research under the Contract No. NSC-90-2213-E-038-009.
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