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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, SEPTEMBER 1975

Quantitative Gait Evaluation of Hemiplegic Patients Using Electrical Stimulation Orthoses MIROLJUB KLJAJIC, TADEJ BAJD, AND UROS STANIC Abstract-Although the functional electrical stimulation orthosis is one of the most recent approaches to the rehabilitation of hemiplegic patients, the quantitative estimate of its influence on the patients walking is not satisfactorily solved. In this communication the variables necessary for gait evaluation are defined and two quantitative methods for their interpretation are given. The second method was tested on eight hemiplegic patients. The results show the applicability of the described techniques of evaluation.

INTRODUCTION The bipedal gait, so simple at first sight, represents a very complicated problem in the study of human locomotion. The extreme complexity of the locomotor mechanism makes it difficult to choose the parameters necessary for a simple mathematical definition of the gait. The reason for studying locomotion arises from the desire to build homomorphic machines-robots, to develop prosthetic and orthotic devices, and finally, to estimate their influence on the patient's gait. Damage to lower extremity functions must be restored by artificial braces, prostheses or orthoses. To obtain the best interface with the human body these devices must have certain mechanical and dynamic properties. The problem of the construction of prostheses and their effect on patient gait has been studied before [ 1 ]-44]. One of the diseases that causes lower extremity disfunction is hemiplegia, which is a type of disability that derives from lesion to the cerebral motor area 4 where the control of voluntary movements is organized. One of the techniques of hemiplegic patient rehabilitation is a functional electrical stimulation (FES) [ 5 1. Under the influence of special electrical pulses on the paretic muscle or appropriate nerve, it is possible to activate this muscle again and to obtain some functional movements. FES orthosis represents a very modern and efficient tool in the rehabilitation of hemiplegic patients. Although the FES brace is accepted for rehabilitation, the quantitative evaluation of its effect on the gait pattern has not been yet satisfactorily solved. By adjusting the duration, amplitude, and beginning of stimulation with respect to heel-off, it is possible to obtain more or less successful corrections of the patient's gait. Our aim is to find out the stimulation sequence that maximally normalizes the gait. Such a sequence is called optimal. For this purpose a quantitative method is naturally advantageous with respect to a qualitative one because it allows an objective and selective way of defining the best FES orthosis parameters. The goal of this communication is to define the necessary variables, and to define adequate methods for quantitative gait evaluation. Using these methods we have evaluated the gait of six hemiplegic patients. Each of them was measured under three different conditions. Firstly the patient walked without orthosis, secondly using an implanted FES peroneal brace of type RPB-l [6 ], and finally with a new FES peroneal brace [ 7 ]. We also evaluated the gait of two patients using a three channel stimulator [81. Manuscript received January 18, 1973; revised January 7, 1975. This work was supported in part by the Boris Kidric Foundation of Slovenia, Yugoslavia, and in part by the Department of Health, Education, and Welfare, Social and Rehabilitation Service, Washington, D.C., under Grant 19-P-58415-F-01. The authors are with the J. Stefan Institute and Faculty for Electrical Engineering, University of Ljubljana, Ljubljana, Yugoslavia.

INSTRUMENTATION The hip, knee, and ankle angles of both legs in a sagittal plane were measured by a simple goniometric system using analog methods with precision potentiometers [9]. Contacts between the ground and three points of the sole were also registered. The step length was calculated from the known joint angles and the distances between the potentiometers attached to the joints, using a simple trigonometric equation [11]. METHODS Variables Necessary for Gait Evaluation In walking from a starting point A to a destination point B a man takes into consideration the distance AB and the time required to cover it. He adapts the walking parameters to this a priori information. Let us describe the gait parameters, under stationary conditions, with the relation G=G(S, T,a) (1) where S represents the step length, T the step duration, and a means the quotient of stance phase and stride time. The average gait velocity is also an important parameter. Since it can be defined with the parameters S and- T, it will be omitted in our analysis. Now we shall try to define the qualitative relationship between the elements of (1) and the variables describing the gait state. The step length can be expressed as a function of joint angles qi(t) and anthropometric lengths of the legs 1i (2) S=S(qi,li), i=1,2,3. The joint angles qi must satisfy the equation of body motion d laL\ aL 3n =1, n dt aqi Mi where L = E - V is the Lagrangian function (E is kinetic energy and V the potential energy of the system), qi are the generalized coordinates (in our case joint angles in the sagittal plane), and Mi are the moments in the system. On the other hand, the system period T depends upon the forces generated by the muscles activating the system [right side of (3)]. The system is self optimizing and it performs its task in a condition of minimal energy dissipation (at a certain velocity) by choosing the optimal parameters T, S, a and optimal trajectory of the variables qi. This statement is partially proved by the results available from the literature [11], [21 . The coefficients of variation depending upon different gait parameters (swing phase duration, maximal value of knee joint angle, etc.) were studied as functions of cadence (steps per minute) [ 11]. These coefficients have an evident minimum at a cadence of 100 to 110 steps per minute, which corresponds to the free gait. The authors explain this fact as an optimal solution of locomotion with the minimum of energy consumption. We found the same results when the energy consumption per meter walked as a function of velocity was studied [21. It was concluded that the minimum of energy consumption corresponds to an average velocity 1.12 m.p.s., that is, 90 to 110 steps per minute. We can see that normal human walking as a complex biomechanical system has its proper optimal parameters. We must have this fact in mind when deciding which evaluation method is to be chosen. The gait parameters under stationary conditions (1) are defined during walking performed without the influence of transient conditions related to the starting and stopping of motion. These transient conditions are especially evident in the gait of patients adapting to a new orthotic device. Therefore each stationary gait parameter has to be defined with a

\WJi/

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corresponding mean value and standard deviation. In this way not only the gait state (parameters values) is estimated but also the quality of gait parameters (repeatibility), which is dependent on the patient's adaption to the orthotic device and vice versa. The variables qi (joint angles) and moments Mi (3) have to be defined statistically as well. As it is impossible to measure the moment and because it is a very difficult task to calculate them, in the gait evaluation only the ground reactions will be included. Let us define a vector Y consisting of elements of (1) and (3) and ground reactions components, which are the variables necessary for gait evaluation. The elements of this vector are step length; step duration; stride duration; stance phase duration; Ys,6,7 goniometric functions of hip, knee, and ankle; vertical ground reaction; Y8 horizontal ground reaction. y9 In normal locomotion these variables obey the principle of symmetry between the functions of left and right leg. Though human walking takes place in three dimensional space, we must emphasize that our equations describe only movements in the sagittal plane, i.e., in the plane of progression as the dominant one, and the most essential for walking. To simplify the measurement technique we did not evaluate movements in the horizontal and frontal planes. Indirect information concerning the movements in these planes can be acquired by measurements in the sagittal plane and by knowledge of the kinematic relationships among gait events. Yi Y2 Y3 Y4

Evaluation Criteria There are two possible kinds of evaluation for the variables defined. 1) The first is to measure the normalized variables Yi, i= 1, * ** n on a group of N normal subjects (N > 30) and find a statistical pattern of normal gait

(4) ,n. In (4), wi is the weighting factor of every variable Yio and it is a function of the coefficients of variation. The variable Yio, i= 1,*, n is the average value of the variablesyi defined in the population of N normal subjects I N , Yik, i= , ** * n Yio

Yn = Y(Wi, Yio ),

i=

1, *

=

Let us define

Yp as the patient pattern

Yp= Y(Wi,Yip).

(6)

The normalized difference of vectors Yn and Yp is the estimate of abnormality. Vector Yp must be measured simultaneously for the right and left leg and these two vectors must be compared with the normal pattern. The quotient of right and left difference expresses the degree of abnormality [4]. 2) The second method of gait evaluation is based on the symmetry between the variables of the right and left leg when one of them is subnormal. It is not difficult to prove the symmetry of the right and left leg functions allows the minimal energy consumption t Il, the greatest stability and also the comfortability of the considered gait type. Let us consider locomotion as a periodical pseudoconservative system converting potential energy into kinetic energy and vice versa. The energy loss due to the locomotor mechanism is replaced by the biochemical processes in the muscles. If one of the legs is disabled (hemiplegia) the system becomes unsymmetrical because the damaged leg cannot obtain kinetic

energy in the heel-on phase, nor can it give the necessary energy in the toe-off phase to continue the tempo begun in the preceding cycle. Therefore the gait functions are distributed between healthy and damaged leg so that the body movement is stable. With an adequate FES orthosis we try to restore the lost functions of the impaired leg. Let us define symmetry S as a set of particular symmetries Si of each variable yi

(7)

S= {Si}. Each particular symmetry is defined as

Si1m mk=1

(8)

YjR (k YiL

where indices R and L mean the right and left side of the patient's body and m is the number of the steps. For normal locomotion we have Si _ 1 and for the pathological one Si L 1. We can define the final criterion Sj= I - ASi

min Ai\S

=

I n

-E

abs (1

-

Sii) wii,

sii > O.

(9)

The restriction Sii > 0 is always fulfilled in our case. Index i defines the measured variables and j E J defines the kind of orthosis used. The greatest value of integral symmetry Si indicates the optimal orthosis used. In (9) wi1 is the weighting factor defined by

wi1=I

+

9i.

Sii

(10)

In (10) uij means the standard deviation of each symmetry Sie. Equation (9) described the relation between the absolute deviation of the average symmetry Sii from the ideal symmetry Si = 1 and its variation coefficient ail/S11. This is very important because the variation coefficient describes the "perfection" of the system [ 11] . A small value of this coefficient means a smooth gait and satisfactory orthosis behavior.

RESULTS In the previous paragraph we described two different gait evaluation methods. The first one depends on the normal gait pattern of an adequate population and the second depends only on the parameters measured on one patient. In our experiments only the second method of evaluating the gait of hemiplegic patients using FES orthoses was tested. To a group of six hemiplegic patients using the implanted peroneal brace RPB-1 with the stimulation sequence shown in Fig. l(c), we applied a peroneal brace with a new stimulation sequence [Fig. 1(d)] [7]. The only difference between the stimulation sequences (c) and (d) is in the fact that the first one begins just after heel-off and stops before heel-on. The new stimulation sequence has a delay with respect to sequence (c). It starts a little before the ankle angle reaches the maximal plantar flexion [Fig. 1(b)], continues through the swing phase and is prolonged in the early stance phase. On the basis of EMG measurements on the appropriate muscle group and the ankle goniogram the stimulation sequence (d) can be supposed to be optimal [7]. Because of differences between hemiplegic patients, the stimulation sequence (d) was varied during the experiment (periods t1 - t2 and t3) around the initial sequence until the optimal stimulation was found according to the criterion (9). The gait of two patients using a three-channel stimulator [8] was also evaluated. The muscle groups stimulated were the dorsiflexors, plantar flexors, and knee extensors. The stimulation sequences were adjusted with respect to delay between heel-off and beginning of stimulation, stimulation

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, SEPTEMBER 1975

440 Oll/.

500/.

looll/.

ANKLE

DORSAL FLEXION

ANKLE

PLANTAR FLEXION Ust

t

Ust

t *

--

_,

l..

_

Fig. 1. (a) Foot switch function, (b) ankle joint goniogram, (c) RPB-1 stimulation sequence, (d) new stimulation sequence. TABLE I RESULTS OF GAIT EVALUATION OF HEMIPLEGIC PATIENTS USING FES ORTHOSIS intePATIENT

partial symmetry

Slj

|

2j

|

weighting factors

3j

wl;

|2j

gral

symme-

try 0

3j

Ij

step

length Y3 m

stand. dev. of

steP

lengrth.

number of

steps

0,lj

n

kind or orthoj

1

1.29 1.34 1.27

0.79 0.81 0.82

0.86 0.74 0.86

1.03 1.06 1.10

1.05 1.06 1.06

1.08 1.10 1.06

0.77 0.72 0.79

0.49 0.51 0.51

0.080 0.070

0.067

35 27 33

1 2 3

2

1.04 0.99 1.06

0.63 0.67 0.73

0.77 0.79 0.84

1.09 1.09 1.07

1.05 1.07 1.15

1.13 1.06 1.07

0.76 0.80 0.82

0.46 0.53 0.57

0.030 0.050 0.040

31 25 39

1 2 3

3

0.58 0.81 1.03

0.57 0.54 0.64

0.68 0.74 0.76

1.08 1.15 2.12

1.05 1.13

1.06

1.06

1.04

0.59 0.66 0.77

0.50 0.44 0.53

0.168 0.074 0.067

54 47

93

1 2 3

4

1.30 1.27 1.43

0.64 0.61 0.78

0.94 0.87 0.79

1.07 1.10 1.09

1.04 1.06 1.79

1.05 1.07 1.05

0.75 0.72 0.64

0.-56 0.54 0.48

0.080 0.070 0.090

31 31 33

1 2 3

5

1.38 1.06 1.21

0.81

0.87 0.81 0.77

1.06 1.06 1.10

1.05 1.07 1.08

1.03 1.04

0.75 0.82 0.71

0.58 0.61 0.58

0.096 0.030 0.070

39 34 40

1 2 3

123

0.92 0.87

1.07 1.05 1.05

1.09 1.13 1.07 1.14 1.05

0.71 0.76

0.61 0.58 0.64 0.52 0.60

0.070 0.070

0.88 0.76

1.08 1.09 1.13 1.11 1.18

0.81 0.82

7

0.80 0.80 0.92 0.69 0.63

1.07

1.15 0.98 1.34 0.97

0.090 0.040

39 88 40 51 43

2 3 1 4

8

0.84 0.94

0.82 0.92

1.16 0.85

1.24 1.18

1.13 1.08

1.14 1.10

0.80 0.89

0.37 0.41

0.060 0.040

52 52

1 4

6

0.76 0.68

0.§4

1.06

1.07

1.08

0.95

0.050

1

Note: In the last column j = 1 means gait without orthosis,j = 2 with implantable orthosis RPB-1, j = 3 with new orthosis, andj = 4 with a three channel stimulator.

duration, and stimulation amplitude. Using the mentioned criteria we discovered the best combination of stimulation sequences (Table I, patients No. 7 and 8). Comparing the evaluated gait parameters when the patient walked without any orthosis and with the application -of different kinds of orthoses, we can objectively decide which is the best one for the patient considered. We studied the following gait parameters defined by (1): 1) the average value of the step lengthy1; 2) the distance symmetry Sl1 expressed as the quotient of the step length of disabled leg yIp and the step length of the normal one Y in; 3) the time symmetry S2j expressed as the quotient of step duration of the disabled leg Y2p and the normal leg Y2n; 4) the sym-

metry S3j expressed as the quotient of stance phase duration of the disabled leg y4p normalized with the stride duration of the same leg Y3p and the stance phase Y4n of normal leg normalized with Y3nIn Table I the following results are given: partial symmetry, weighting factors, and integral symmetry calculated according to (8), (10), and (9) respectively, the average value of the step length and its standard deviation. The most interesting columns are the integral symmetry and-the step length. Student's significance test was used to find whether the prolongation of the step length is a consequence of the FES orthosis or whether these changes are random. Studying the results of patients 2, 3, and 6 using the standard peroneal FES

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brace RPB-1 and the new one, we found out that the step length prolongation was significant at the 0.05 level, when the new FES peroneal brace was used. The results on patient 2 are even significant at the 0.01 level. Significant improvement at the 0.05 level for patient 5 is reached using the standard brace RPB-1. The results of patient 1 are not significant. With patient 4 using the new brace significant reduction of step length at the 0.05 level was obtained and there was no significant improvement when RPB-1 was applied. There is a significant prolongation at the 0.01 level for patients 7 and 8, as a result of the three channel FES orthosis used. From Table I it can be concluded that the maximal value of integral symmetry occurs where the step length is maximal. These results are underlined in Table I and the corresponding orthosis is considered as optimal. Such a result agrees with our idea that the symmetry of the system is the consequence of maximal stability and minimal energy consumption. The increase of the impaired leg's step length is only one proof of such an assumption. CONCLUSION In this communication the variables necessary for gait evaluation were defined and two methods of estimating the gait of patients were described. We proved that the most important three parameters are the step length, the step duration, and stance phase to stride time ratio. The symmetry of the variables necessary for gait evaluation is defined as the main principle for both evaluation methods. The second method was tested on a group of eight hemiplegic patients using FES orthoses and the following advantages for this method were found: 1) The method is very simple; it has its own optimum which is independent of the normal population pattern. 2) The symmetry defined as a quotient of the parameters of the disabled and the normal leg normalizes the gait parameters, and makes them independent regarding the type of walking. 3) The weighting factor helps us to estimate the functionality of the orthosis used. With this quantitative method the optimal stimulation sequence for each patient was found. Analysis of goniometric functions was omitted because at the time of the experiment there was no possibility to process the data. Besides this, we assume that the goniograms contain no essential new information. The measured step length is a consequence of the goniometric functions. Therefore the information contained in goniograms is automatically expressed by the step length. For technical reasons to now we have had no possibility of measuring the ground reactions during the walking of the subject. With the force-plate it is hard to get good statistical results. However, the deficit of measured variables does not reduce the objectivity of the results in Table I. The variables omitted would only complete our conclusions and make the method more sensitive, but certainly they would not change them. An optimal stimulation sequence can be defined for each patient by applying the method described. Whether such an optimal sequence is modified by exercising remains to be investigated. REFERENCES [11 B. Bresler, C. W. Radcliffe, and F. R. Berry, "Energy and power in the legs of above-knee amputees during normal level walking," Lower-extremity Amputee Research-Project, IER, Univ. of California, Berkeley, Report Series 11, Issue 31, May 1957. [2] E. Peizer, D. W. Wright, C. Mason, "Human locomotion," Bulletin of Prosthetics Research, BPR 10-1 2, pp. 48-105, Fall 1969. [3] L. A. Leavitt, J. C. Calvert, J. Canzoneri, and C. R. Peterson, "Gait patterns in above-knee amputees," Archives of Physical Medicine and Rehabilitation, volume 53, No. 8, pp. 373-382, August 1972.

[4] V. S. Ljalin, A. P. Matvejev, "Metod kompleksnoj statistickoj ocenki hodbi," Protezirovanie i protezostroenie, Sbornik trudov, Vipusk XXIX, pp. 103-108, Moscow, 1972. [51 L. Vodovnik, "Functional electrical stimulation of extremities," Advances in electronics and electron physics, vol. 30, pp. 283297, Academic Press, Inc., New York and London, 1971. [6] A. Jegli6, E. Vavken, M. Benedik, "Implantable muscle nerve stimulator as a part of an electronic brace," Advances in External Control of Human Extremities, Yugoslav Committee for Electronics and Automation, pp. 593-603, 1970. [7] A. Trnkoczy, U. Stani6, T. Jeglic, "Electronic peroneal brace with a new sequence of stimulation," Med. Biol. Engng., Pergamon Press, New York, in press. [8] A. Kralj, A. Trnkoczy, R. Aimovic, "Improvement of locomotion of hemiplegic patients with multichannel electrical stimulation," Proc. Conf. on Human Locomotor Engn., Sussex, England, pp. 60-68, 1971. [9] A. Trnkoczy, T. Bajd, "A simple electrogoniometric system and its testing," IEEE Transactions on Bio-Medical Engineering, vol. BME-22, pp. 257-259, May 1975. [101 T. Bajd, M. Kljajic, A. Trnkoczy, U. Stanic, "Electrogoniometric measurements of step length," Scand. J. Rehab. Med., 6, pp. 78-

80, 1974.

[11] A. S. Vitenzon, A.

V. Sarancev, "Statisticeskie zakonomernosti izmenenija biomehaniceskih i elektrofiziologiceskih parametrov pri raznih tempah hodbi," Protezirovanije i protezostroenije, Zbornik trudov, Vipusk XXIX, pp. 29-35, Moscow, 1972.

Precise Voltage to Frequency Converter for Telemetry Applications of Strain Gage Pressure Transducers THOMAS P. GROVER, MEMBER, IEEE Abstract-A voltage to frequency converter suitable for telemetric applications of strain gage pressure transducers is described and analyzed. The circuit uses a voltage reference IC and a temperature dependent op amp bias current to achieve zero pressure offsets less than 3 torr over a 250C temperature range and a 1 volt supply voltage range.

INTRODUCTION This communication describes a precise pressure to pulse rate converter. It forms part of a system intended for long term monitoring of intraocular pressure by scleral applanation tonometry. The transducer is a two arm, 5 mm. diameter diaphragm, silicon strain gage device with 12 ,V/V/torr sensitivity.1 With a normal pressure range of 15 to 30 torr [ 1 ,the system requirements for sensitivity and stability are severe. The pressure to pulse rate converter is incorporated in a telemetry transmitter; the pulse output modulates the RF circuits to encode pressure information. The transmitter is worn externally and must operate for several weeks, so considerable effort was expended to create a circuit which is insensitive to changes in battery voltage and temperature. This design has low offset and span errors and the component count is less than that needed by circuits meeting similar requirements but using AC transducer excitation [2] -[4]. Manuscript received May 13, 1974; revised October 22, 1974, and February 21, 1975. This work was supported by the National Eye Institute under Contract N01-EY-3-2115. The author is with the Utah Biomedical Test Laboratory, University of Utah Research Institute, Salt Lake City, Utah 84108. 1 Koningsberg Instruments, Pasadena, Calif.