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Monitoring of movement with radio frequency transducers
MONITORINGOF MOVEMENTWTH RADIOf%EQUENCY TRANSDUCERS Keith M. Jackson
ABSTRACT Two approaches to the problem of monitoring human movement using radio frequency transducers are described. A simple two dimensional solution can monitor movement restricted to one plane, whilst a three dimensional transducer (linked to a computer), can follow movement in any Keywords
Goniometcr,
radio-frequency,
transducer, computer
INTRODUCTION Historically the movements of the human body have been monitored by either filming the movement in question or using goniometers attached to the surface of the human body. Taking a film record of a pattern of human locomotion can be done with either tine cameras or television cameras. Both of these methods have been used successfully but have many drawbacks:
(4
Without recourse to mirrors or multiple cameras, movement can only be monitored one plane.
04
Manual analysis of film on a frame by frame basis is very tedious and time consuming.
(4
Errors due to parallax are inevitable and must either be accepted or removed with complicated calculations.
(4
plane. In both cases, by measuring the magnetic field produced by a set of small coils powered with high frequency current it is possible to calculate their relative displacement. If the coils are attached to the surface of the human body they can thus be used as a monitor of human movement.
Movement can only be performed field of view of the camera.
in
within the
These drawbacks ensure that photography is of little use in clinical gait monitoring, but still enable it to play a major role in research studies of human gait’**.
This was amply demonstrated during a series of experiments designed to monitor the rotation of the upper limb in the sagittal plane during human locomotion. Flexion of the forearm at the elbow joint during locomotion is a movement which is not under the control of the musculature traversing the elbow joint. It occurs as a consequence of the muscle induced rotation of the upper arm about the shoulder joint, and acceleration transmitted up the torso from the lower limb. The amount of rotation which occurs is dictated by the interplay between these active force? and passive forces such as joint friction and inertia . A small li htweight potentiometer attached over the axis o f rotation was used in an attempt to measure rotation at the elbow joint. This was singularly unsuccessful as attachment of the potentiometer removed most of the movement under study. I shall return to this point later. Despite the effects of their physical presence, goniometers have been widely applied to movements of a less delicate nature than the aforementioned flexion of the elbow. Their great advantage is that a voltage proportional to angle of rotation is available directly from the goniometers thus allowing simple on-line movement monitoring.
Goniometry, the direct measurement of angles, has been used successfully as a means of studying patterns of human movement. Small light-weight low friction potentiometers have been developed that can be positioned over the relevant centre of rotation. These are attached to the limb segment on either side of the joint under study and rotate as the intermediary joint rotates3. Usage of many goniometers attached to the body over each axis of rotation enables three dimensional movement to be monitored. However, complex frameworks to support the goniometers can make the apparatus interfere with the movement under study.
In recent years,? olarized light goniometers have been developed which combine some of the advantages of photography and ordinary goniometers. Small detectors are attached to the limb under study and a polarized light beam is shone upon the subject. Such systems give an on-line measure of joint rotation combined with the simplicity of photographic techniques but, as with photography, movement out of the particular plane of rotation under study introduces errors, and the subject’s movement is confined to the area in front of the light beam. Polarized light goniometers are now available commercially, and are used clinically to monitor gait patterns and detect abnormalities of locomotion.
Physics Department, Guys Hospital Medical School, London Bridge, London SE 1 9RT, UK
Optoelectronic systems have been developed6 that a.re capable of monitoring three dimensional move-
o 1989 Butterworth & Co (Publishers) Ltd. 0141~5245/SS/O20117-OS $03.00
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magnetic dipole at distances away from the coil which are large in comparison with the dimensions of the coil. Thus the magnetic field components surrounding an air-cored coil are described (in cylindrical polar co-ordinates) by:
Although able to accurately monitor three dimensional movement, such systems are restricted in that the subject is constrained to move only within the field of view of the optoelectronic system. However, movement can be monitored relative to the surrounding spatial environment. The radio frequency transducer described in this paper does not force the subject to stay within a particular field of view but this is at the expense of only being capable of studying relative movement of parts of the body.
Be = 3%
RADIO
B,
ment.
FREQUENCY
TRANSDUCERS
From the above short resume of the available methods of objectively recording patterns of human movement, it is apparent that any system combining the advantages of a polarized light goniometer, and removing the necessity to stay within the confines of a light beam would be a considerable asset in monitoring human movement. Radio frequency transducers can provide such an alternative. A high frequency magnetic field is created by a coiI powered by high frequency alternating current. This magnetic field is then sensed by induction of a current in a sensing Ioop. A suitable sensor is constructed from many turns of copper wire symmetrically wound in a circular shape. At the frequencies used, human tissue has a permeability effectively the same as a vacuum and thus does not affect the operation of the transducer. Put another way, the transducer does not ‘see’ the presence of human tissue. The voltage induced in the sensor is dependent on: (a)
the current
flowing in the coil
(b)
the number
of turns on the coil
(c)
the frequency
(d)
the number
(e)
the spatial position
of the magnetic
field
of turns on the sensor of the sensor
If all these components except (e) are held constant then the voltage induced in the sensor is solely a function of the position of the sensor in the magnetic field. Components (a) and (c) are a function of the controlling electronics, whilst components (b) and (d) are a function of the physical construction of the coil and sensor, Thus holding components (a) to (d) constant within a given accuracy presents no real problem. A movement transducer working on this principle has been proposed before’ but no mention was made of the effectiveness, range or accuracy of the system. The technical problems involved in producing a working system are largely dictated by the nonlinearity of the transducers response, its sensitivity to movement in any plane, and the possible complexity of computer programs needed for data analysis. A coil which produces a magnetic field as a result of a current flowing within it, acts as a
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B,
$$
=
2c,c;3s e
(1)
_r
p0
c sine lr13
= 0
(3)
where r, 8 and 4 are the normal cylindrical polar co-ordinates, p. is the permeability of the surrounding medium and c is a constant whose magnitude is proportional to the number of turns and current flow of the coil. This does not give a linear relationship between the spatial location and the measured magnetic field. Two alternatives are available. Firstly, one can try and produce coils and sensors of such a size and location that for a given movement the transducer output is linear within a given accuracy’. Seco:ldly, the resulting data can be computer processed to overcome any non-linearities, and calculate the relative positions of the sensor and the coil. TWO DIMENSIONAL
MOVEMENT
A simple two dimensional system has been developed which has the advantage of producing an output linear with respect to angle of rotation over a range compatible with many joint movements. Figure 1 shows the layout of the system when used to monitor flexion of the elbow, and a block diagram of the associated electronics. In the case of elbow flexion the coil producing the magnetic field is attached proximal to the elbow joint on the upper arm, and the sensor is attached distal to the elbow joint on the forearm. Both are held in place with simple Velcro straps. As elbow flexion occurs effectively in one plane, any move-
arm
\
I
Sensor
Phase slgnal
I
Heel strike pulse
Recorder
I Two dimensional radio frequency transducer. The attachment of the coil and sensor to the joint under study (the elbow) is shown, along with a block diagram of the associated electronics. Figure
1
Monitoring
Sensor to elbow distance
ment (except when the forearm is pronated or supinated) can be considered as pure rotation. Thus any change in the voltage induced in the sensor is due to flexion of the elbow joint.
Relative movement of the sensor and coil is thus detectable but the problem of linearity still remains. Two alternatives are possible. Either use a system with a non-linear response, obtain the relevant calibration curve and remove the non-linearity with subsequent data processing, or construct the sensor and coil of such a size and relative displacement that the transducer is linear over a range compatible with the movement being studied. The latter course is simpler to implement. computer program was written which could calculate the response of the total system to rotation. As the magnetic dipole approximation can only be used at distances from the coil which are large in comparison with the coil dimensions, the computer program was capable of calculating the magnetic field directly from first principles (i.e. from the magnetic vector potential). The field produced by the coil was then integrated across the surface area of the sensor. Thus, the transducer response could be predicted for any combination of coil, sensor, relative position and centre of rotation. A
Fipre 2 shows the resulting sensor response for various physical configurations. It can be seen that the linearity of the sensor’s response varies considerably with the chosen physical configuration. Most configurations are unsuitable in giving even an approximation to a linear response. However, careful choice of the sensor and coil dimensions, and their relative positions can produce a system with reasonable characteristics. The responses vary greatly in absolute magnitude as the distance between the coil and sensor is increased, but only
K.M. Jackson
(mm)
40
IO
The sensing electronics uses a synchronous detector which is fed with a signal at the same frequency (1 MHz) and in phase with the alternating magnetic field produced by the coil. Thus the detector only measures signals produced by the coil and discriminates against other extraneous fields. This greatly reduces the power needed to produce a magnetic field of measureable intensity at distances in the region of 20-25 ems. Provision has also been made to multiplex a pulse recording the occurrence of heel strike, so that the gait pattern can be related to the phase of the walking cycle. This was derived from a small brass plate, attached to the subject’s heel, making contact with the metal surface of the walkway. Suitable electronics detect the first occurrence of this contact. All signals were transmitted along a cable which trailed behind the subject as he walked. This did not produce any detectable artefact due to cable movement, but the long leads used for signal and power supply transmission did introduce some 50 Hz interference. This was filtered out using a sharp cut-off 50 Hz notch filter. The heel strike pulse was not unduly affected by this filter.
with R/F transducers:
70
IO
‘0
u
1
I
I
-900
0”
90”
Figure 2 Linearity of response for attachment of the sensor and coil at various distances from the intermediary joint. Each graph is a computer prediction of the response from -90 to +90°. All the results have been normalized to facilitate comparison.
relative magnitude for any one chosen configuration is important. Thus all the computer predictions of transducer response have been normalized to show a scale ranging from -1 to +l. Using a coil length of 45 mm, and diameter 9 mm, a sensor diameter of 20 mm, a coil to elbow distance of 30 mm and a sensor to elbow distance of 40 mm, the computer program predicted that the transducer response should be as shown in F&we 3. The actual response of a system with such a configuration is also shown in Figure 3. This was measured with the coils and sensor mounted upon plastic (non-magnetically permeable) rods, hinged together with a potentiometer attached to the axis of rotation measuring the angle of rotation. The measured transducer response and the associated computer prediction
8 Figure 3 Comparison of the transducer with the associated computer prediction. The dotted lie is the computer prediction of the transducer response. The open circles show the measured response. The transducer can be considered linear over the range denoted by the solid line within an accuracy of 2%.
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mounting the components which form the high frequency oscillator and driver on the rear of the coil in a small epoxy package.
Flexion
Elbow
11
Extension’ Triceps
Lot. dors1
LW
Post. delt
Strike
1 pl Ii
I 50 Percentage
I lO(
of walking cycle
Lift F
L. heel
R heel
Figure 4 Elbow flexion and extension along with associated electromyographic activity recorded at a cadence of 110 steps/min. This record is a tracing of a recording made on an ultra-violet recorder. The horizontal scale corresponds to one complete walking cycle. The occurrence of heel strike and lift-off of the right foot are shown by the marker pulses added to the record of rotation of the elbow joint. Electromyographic activity is present only in posterior deltoid (post. delt.) and latissimus dorsi (lat. dorsi). This activity is of a very low level and only at definite phases of the walking cycle.
I
I
The coil used in the working system was made from 80 turns of 0.05 mm copper wire, and the sensor from 50 turns of the same wire. This number of turns gave enough sensitivity at the distances used for measurement of elbow flexion. The application of this two dimensional transducer is illustrated by Figure 4 which shows flexion in conjunction with simultaneously recorded electromyograms from the associated musculature. The sensor was calibrated for this application by attaching a pendulum goniometer to the subject’s forearm, holding his upper arm vertical and asking him to move his forearm to various resting positions. Zero degrees was taken to be at the point of ‘elbow locking’ during hyperextension of the elbow joint. Figure 5 shows a typical calibration curve using this method of transducer calibration. THREE DIMENSIONAL MOVEMENT None of the problems of lack of stability of the transducer mountings, and movement out of a single plane, which cause errors in two dimensional movement sensors are unique to radio frequency transducers. They also occur to a greater or lesser extent when either filming of the movement or goniometers are used. The problem of the stability of any transducer mounting is too complex to be discussed here. Errors caused by movements performed outside one single plane can be removed by using an inherently three dimensional movement transducer. System design and construction
I
I
I
I
I
5
15
25
35
Elbow
flexion
(“)
Figure 5 Typical calibration record. The subject was asked to hold his arm at a fixed position whilst a calibration point was recorded from the transducer and a pendulum goniometer simultaneously. He then moved his arm freely before the next calibration point was recorded. The calibration record obtained in this manner not only reflects the linearity of the transducer, but also errors due to movement of the transducer and its associated armbands relative to the surface of the body. Thus it is representative of the actual errors involved in using this two dimensional radio frequency transducer.
agree with each other very closely, confirming that the transducing system measures correctly the magnetic field produced by the coil, and that the shape of the magnetic field around the coil is as predicted by classical electro-magnetic theory, no detectable artefact being produced by the nearby presence of wires and other components. The influence of extraneous fields from cables feeding the coil had already been minimized by
120 J. Biomed. Eng. 1983, Vol. 5, April
I
A three-dimensional radio frequency transducer has been developed working on the same physical principles as the two-dimensional transducer described above. Each sensor now comprises three mutually perpendicular coils. Each of these coils measures one component of the magnetic field surrounding the sensor. This enables the sensing system to measure the scalar magnetic field strength by simply squaring, adding and square rooting the three components of the magnetic field. The actual rotational orientation of the sensor is immaterial to the calculation of scalar magnetic field strength, as no matter how it is placed in the magnetic field, squaring, adding and square rooting, three mutually perpendicular vector components will always derive the scalar magnitude of the field. Each of these sensors measures the magnetic field produced by a matrix of four (see later) field producing coils which are situated in space at locations whose spatial separations are known. These coils are powered in sequence, thus allowing the sensing electronics to discriminate the magnetic field produced by one coil from that produced by the other coils. Figure 6 illustrates the layout of the three dimensional transducer. At the initiation of a sampling
Monitoring
Computer Sensors
III
Pre-amps
/
/’
/ // /’
KM. Jackson
plexed series of signals, produces a time sequence of voltage levels whose voltage is proportional to field strength. Note that only the absolute magnitude of voltage level is important as the sign will be positive or negative depending on whether the sensor orientation produces an in-phase or antiphase signal from any given component. The output from the phase sensitive detector, and a pulse output providing synchronization information for later data processing, are recorded on two separate channels of a frequency modulated (FM) recorder (these are labelied Output and Timing on Figure 7).
r
//
with RfF transducers:
Ill
Ill Multrplexer
Figure 6 Three dimensional monitoring. Each of the four coils shown produces a high frequency magnetic field which is detected by each of the three components of each sensor. The expanded section illustrates how the three mutually perpendicular components of a sensor are wound. The dotted line shows that the system can be linked direct to a computing system if this is experimentally possrble.
processing
of data
Although future versions of this three dimensional movement system will probably operate in realtime under the control of a mini-computerfmicroprocessor, the present system has all computer processing performed off-line. The feasibility of real-time operation depends solely on the speed of operation of the algorithms providing positional information from the magnetic field measurements, which is in turn dependent upon the inherent speed of the data processing system. The signals recorded on one track of an FM tape recorder are fed into an analogue-to-digital converter which samples the data under the control of synchronizing signals recorded on a second track of the FM tape recorder. The signals are then processed and stored in the memory of the minicomputer (Varian 62OL-100). At the end of each
I
cycle in the transducer, high frequency current is applied to coil number 1. The sensing electronics then samples in turn the three components of each of the sensors. This sequence is repeated for coils 2, 3 and 4. After a suitable delay, compatible with processing of the data, the whole cycle of measurement is repeated. Any relative movement of one of the sensors and the matrix of coils will produce a change in the magnetic field measured by that sensor. The problem which remains is to reconstruct the spatial location of the sensor from the measured magnetic field strengths. In order to simplify the construction of the sensing electronics the coils were powered with current at a frequency of 100 KHz. This is in contrast to the two dimensional transducer which operated at a frequency of 1 MHz. The penalty paid for this is reduced voltage induced in the sensors. After the signal from one component of the sensor has been chosen by the multiplexer, a phase sensitive detector monitors this signal and produces a voltage output proportional to the amplitude of the alternating signal. F&w~ 7 illustrates this process for two sensors. A current is induced in each component of the sensor for the duration that power is provided to one of the coils (20 ms). The phase sensitive detector, when fed with a time multi-
.lBE
1:2
c
I
2 3
I
1
I
Coils
A I
4 Tlmlng 1
I 2
I I
I
f
I
I
I
1
I
I
3
I 2 3 output
Figure 7
Phasic activity of the coils and two sensors (each of 3 components). Each sensor component is sampled under the control of the Timing signal. The Output and Timing signals are recorded for further analysis.
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section of recording, the processed data is stored in the mini-computer’s permanent storage for immediate or subsequent output to a mainframe computer. The need to use a large mainframe computer will be explained later. The data processing performed by the minicomputer comprises averaging to reduce the noise present in the signal, extraction of the absolute magnitude of each component of the sensor, squaring, adding and square rooting of these components to give the scalar magnitude of the magnetic field. This processing reduces the amount of data transferred to the main computer. The main computer program has to calculate the sensor position from the scalar magnetic field. The mathematics describing the spatial variation of the magnetic fields produced by the four coils does not seem to be solvable analytically. To obviate the need to produce an analytic solution, the main computer program uses a minimization technique. The method of producing a solution can best be explained by considering a two dimensional analogy. Consider the spatial grid shown in Fi&~e 8. From knowledge of the shape of the magnetic field surrounding the coils, the field strength at each intersection of the grid can be calculated. The sensor provides a measure of the magnetic fields (suitably calibrated) at an unknown point in space. A simple search round the points on the grid can provide an approximate answer but obtaining an accurate answer entails interpolation between the grid lines. The concept of the computer program is to perform a quick search around all the points available on the grid to find an initial approximate answer. Then assuming the magnetic dipole equations (l-3) are valid over small distances, the computer program takes a small step away from this initial grid intersection and computes whether the solution is more accurate or not. By controlling the
direction of its steps it minimizes the errors until it arrives at the point of minimum error. This minimization process can be performed very efficiently with readily available minimization algorithms9. The necessity to use such a minimization algorithm is the main reason for employing a mainframe computer, and not performing all the calculations locally. The actual three dimensional computer programs work as described in this two dimensional analogy except there are three sets of intersecting magnetic field lines. Unfortunately if only three coils are used, the minimization process can sometimes be upset by the multi-valued nature of the fields and produce erroneous results (usually along a mirror image path to the true path). This is why four, as opposed to the mathematically necessary three, coils have been used. A solution is calculated for each of the four possible combinations of any three coils from four. These four answers are then compared to see if they are spatially very close together. If they are, the answer is accepted and the computer program moves on to the next data set. If not, it discards any answer which does not closely match the others and retests the remaining answers. This process continues until two answers remain. If these still do not match each other, the computer program computes an approximate solution, marks it as being approximate, and then continues with the next data set. This is only a very short outline of the algorithm currently employed to compute the spatial position of the sensor. It has many other logical alternatives available which enabIe it to shorten the time needed to execute the computer program and provide an accurate answer. Once the relative position of the sensor and the coils has been calculated, simple mathematical transformations can present the resultant movement data in any desired form. This will be demonstrated with specific reference to movement of the knee. Accuracy
and frequency
response
The accuracy with which this three dimensional transducer can calculate the spatial position of a sensor is dictated by three different parameters:
Figure 8 Twodimensional representation of a pair of crossed magnetic fields (solid lines) and a spatial matrix of x and y values (dotted lines).
122 J. Biomed. Eng. 1983, Vol. 5, April
(4
The physical
size of the sensor
lb)
The accuracy and reproducibility sensing electronics
(4
The rate of movement of the sensor, which must be slow enough to allow the approximation that the sequentially sampled magnetic fields are effectively sampled at the same location in space.
of the
The physical size of the sensor is constrained by the necessity to maximize the number of turns and the cross-sectional area of each component of the sensor. This maximization produces a sensor which has enough sensitivity to operate at a reasonable distance from the coils. Conversely, the
Monitoring
size of the sensor must be kept as small as possible so that the measured magnetic field is not unduly affected by local field variations across the sensor. A small sensor also has the obvious advantage of being simpler to attach to the human body and less obtrusive once affixed. The sensors at present in use are a compromise between these two conflicting requirements. The outside diameter of the three mutually perpendicular components of the sensor is 14 mm. Each component is wound from 500-1000 turns of 0.5 mm diameter copper wire. The maximum operating range of the sensor from the coils is 400 mm with an inherent accuracy of 2-3 mm. Each of the four coils is powered for 20 ms during which a scan of the three components of each sensor is completed. Thus, sampling of all four coils is complete in 80 ms. In order that the assumption, that each coil was sampled whilst the sensor was at one single point in space, is not violated, the frequency of movement must not approach 1000/80 = 12.5 Hz. A safe absolute maximum with the present system is considered to be 5 Hz. The length of time for which each coil is provided with power is dictated by the time needed by the sensory electronics and the computer sampling hardware to measure the signal level present.
with R/F transducers:
,y
K.M. Jackson
;x
y =. _7 ro
-0.121 0
I
1 20
IO Time
(5)
Figure 9 Discrimination of movement along one coordinate. The stratification of the graphs is caused by usage of a line-printer graph plotting routine in producing records of movement versus time. Missing records are due to tape ‘drop-out’ in the FM tape recorder used for this particular
recording. The computer programs can recognise erroneous data and reject it.
CONCLUSIONS
Figure 9 illustrates
Two radio frequency transducing systems have been described, both of which are suitable for the study of human movement in both research and clinical environments. They are non-invasive and at the operating magnetic field strength and frequency used, there are no known adverse effects in any animal, including man.
Knee movement
A radio frequency transducer capable of monitoring a simple two dimensional movement can be constructed from readily available low cost components. Methods have been described which can make this type of transducer produce a linear response to rotation of an intermediary joint over a reasonable range. Even if movements are to be studied which lie outside this linear range, knowledge of the calibration curve for the transducer over the total range to be studied permits the user to calculate the angle corresponding to a given transducer output. This can either be done manually or by subsequent data processing of the signals.
the response of the system to sensor movement and its ability to discriminate movement in different planes. These results are from an experimental test where a sensor was moved along the x axis from -70 to -5 mm. The results show that the only detected movement is along the x axis. The values derived for the y and z co-ordinates stay substantially the same throughout the sequence of data points.
As a specific case of usage of this three dimensional radio frequency transducer, consider movement at the human knee joint. The coils are attached rigidly to a non-metallic frame which is attached to the anterior surface of the thigh by means of Velcro straps. Two sensors are attached to the anterior surface of the lower leg by means of similar straps. Small pre-amplifiers are mounted in close proximity to each of the sensors to mitigate against noise and interference. The movement sensed is obviously that of the sensors with respect to the coils and will be considered as movement of the leg with respect to the thigh, since both the coils and sensors have a firm secure mounting. The computer programs at present calculate the angle of flexion and extension and give statistical information on the maximum and minimum angles occurring. A typical output is shown in Figure 10. The angle of knee flexion is calculated by computing the positions of each of the sensors with respect to the coils. A simple mathematical transformation can then compute the angle of flexion of the knee joint.
Extension
Flewon
I 20 Time
(5)
Figure 10 Flexion of the knee joint. As in Figure 9 the stratification of the graph is due to the method of graph plotting employed. This record is a copy of a print out from a computer line-printer. From being initially stationary with the lower leg at right angles to the thigh, the knee joint is flexed, extended and flexed in quick succession. After a slow move to an extended position it returns to its original position.
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The main advantage of such a radio frequency transducer over conventional photographic or goniometric methods is that it combines the ease of usage associated with the attachment of photographic markers to the surface of the body, with the immediate availability of the signal from a goniometer. Each of the attached components weighs little more than a photographic marker disc. Thus none of the problems of interference with the movement under study associated with conventional potentiometric goniometers are encountered. A three dimensional transducer is simple to affix to the subject, simple to cahbrate and, as data processing techniques are intimately involved in the operation of the transducer_, it is relatively easy to present the final data m any suitable format. Calibration is simply a matter of placing each sensor in turn at a known location relative to the coils and taking a short recording. Although the three dimensional transducer needs a computer to analyse the data produced by the sensors, I believe this should be viewed as an asset and not as a hindrance to implementing the transducing system. Computing power is now readily available and can be used to present an analysis of human locomotion in any desired format. Although the usage of radio frequency transducers is not confined to studies of human locomotion, it is here that their inherent advantages can be fully realised. Systems recording simple joint movement whilst the subject is stationary are relatively easy to construct but do not lead themselves to use with moving subjects without undue interference or restriction upon the movement under study. There is of course no reason, apart from the availability of appropriate data sampling and recording systems, why the number of sensors employed in a three dimensional radio frequency transducer cannot be increased. These could then be attached at multiple points upon the surface of the human body, and
124 J. Biomed. Eng. 1983, Vol. 5, April
would provide a total view of how the human body moves relative to one particular reference location. ACKNOWLEDGEMENTS I would like to thank the following; Guy’s Hospital Endowment Fund for funding the early part of this work; Guy’s Arthritis Research Unit, especially Dr R. Grahame, and the Arthritis and Rheumatism Research Council for funding the development of the three dimensional transducer; Prof. J. Joseph and Prof. S.J. Wyard for encouragement and advice; and Guy’s Hospital Tower Computing Unit for the provision of computer facilities. REFERENCES Plagenhoef, S. in Patterns of human motion: a cinematographic analysis, Prentice-Hall, Englewood Cliffs 1971. Winter, D.A., Greenlaw, R.K., Hobson, D.A. Television-computer analysis of kinematics of human gait, Comput. Biomed. Res. 1972,5,498-504. Findlay, F.R., Karpovich, P.V. Electrogoniometric analysis of normal and pathological gaits, Res. Q. 1964,35,379-384. Jackson, K.M., Joseph, J., Wyard, S J. A mathematical model of arm swing during locomotion, J. Biomechanits 1978, 11, 277-289. Grieve, D.W. A device called Polgon for the measurement of the orientation of parts of the body relative to a fixed external axis,j. Physiol. 1969,201, 70 p. Woltring, H J. Calibration and measurement in 3dimensional monitoring of human motion by optoelectronic means, Biotelemety 1975,2, 169-196. Chandler, S.A.G., Nightingale, J.M., Sedgwick, E.M. A multi-channel R.F. goniometer,j. Physiol. 1972, 226, llp-12~. Jackson, K.M. The linearity of radio frequency transducers, Med. Biol. Eng. Comput. 1977, 15, 446-449. Powell, M J.D. A Fortran subroutine for solving systems of non-linear equations, Harwell Report AERE-R5947, H.M.S.O. 1968, [reprinted in: Numerical methods for non-linear algebraic equations, (Ed. P. Rabinowitz, Gordon and Breach, 1970)]
ABSTRACT Two approaches to the problem of monitoring human movement using radio frequency transducers are described. A simple two dimensional solution can monitor movement restricted to one plane, whilst a three dimensional transducer (linked to a computer), can follow movement in any Keywords
Goniometcr,
radio-frequency,
transducer, computer
INTRODUCTION Historically the movements of the human body have been monitored by either filming the movement in question or using goniometers attached to the surface of the human body. Taking a film record of a pattern of human locomotion can be done with either tine cameras or television cameras. Both of these methods have been used successfully but have many drawbacks:
(4
Without recourse to mirrors or multiple cameras, movement can only be monitored one plane.
04
Manual analysis of film on a frame by frame basis is very tedious and time consuming.
(4
Errors due to parallax are inevitable and must either be accepted or removed with complicated calculations.
(4
plane. In both cases, by measuring the magnetic field produced by a set of small coils powered with high frequency current it is possible to calculate their relative displacement. If the coils are attached to the surface of the human body they can thus be used as a monitor of human movement.
Movement can only be performed field of view of the camera.
in
within the
These drawbacks ensure that photography is of little use in clinical gait monitoring, but still enable it to play a major role in research studies of human gait’**.
This was amply demonstrated during a series of experiments designed to monitor the rotation of the upper limb in the sagittal plane during human locomotion. Flexion of the forearm at the elbow joint during locomotion is a movement which is not under the control of the musculature traversing the elbow joint. It occurs as a consequence of the muscle induced rotation of the upper arm about the shoulder joint, and acceleration transmitted up the torso from the lower limb. The amount of rotation which occurs is dictated by the interplay between these active force? and passive forces such as joint friction and inertia . A small li htweight potentiometer attached over the axis o f rotation was used in an attempt to measure rotation at the elbow joint. This was singularly unsuccessful as attachment of the potentiometer removed most of the movement under study. I shall return to this point later. Despite the effects of their physical presence, goniometers have been widely applied to movements of a less delicate nature than the aforementioned flexion of the elbow. Their great advantage is that a voltage proportional to angle of rotation is available directly from the goniometers thus allowing simple on-line movement monitoring.
Goniometry, the direct measurement of angles, has been used successfully as a means of studying patterns of human movement. Small light-weight low friction potentiometers have been developed that can be positioned over the relevant centre of rotation. These are attached to the limb segment on either side of the joint under study and rotate as the intermediary joint rotates3. Usage of many goniometers attached to the body over each axis of rotation enables three dimensional movement to be monitored. However, complex frameworks to support the goniometers can make the apparatus interfere with the movement under study.
In recent years,? olarized light goniometers have been developed which combine some of the advantages of photography and ordinary goniometers. Small detectors are attached to the limb under study and a polarized light beam is shone upon the subject. Such systems give an on-line measure of joint rotation combined with the simplicity of photographic techniques but, as with photography, movement out of the particular plane of rotation under study introduces errors, and the subject’s movement is confined to the area in front of the light beam. Polarized light goniometers are now available commercially, and are used clinically to monitor gait patterns and detect abnormalities of locomotion.
Physics Department, Guys Hospital Medical School, London Bridge, London SE 1 9RT, UK
Optoelectronic systems have been developed6 that a.re capable of monitoring three dimensional move-
o 1989 Butterworth & Co (Publishers) Ltd. 0141~5245/SS/O20117-OS $03.00
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magnetic dipole at distances away from the coil which are large in comparison with the dimensions of the coil. Thus the magnetic field components surrounding an air-cored coil are described (in cylindrical polar co-ordinates) by:
Although able to accurately monitor three dimensional movement, such systems are restricted in that the subject is constrained to move only within the field of view of the optoelectronic system. However, movement can be monitored relative to the surrounding spatial environment. The radio frequency transducer described in this paper does not force the subject to stay within a particular field of view but this is at the expense of only being capable of studying relative movement of parts of the body.
Be = 3%
RADIO
B,
ment.
FREQUENCY
TRANSDUCERS
From the above short resume of the available methods of objectively recording patterns of human movement, it is apparent that any system combining the advantages of a polarized light goniometer, and removing the necessity to stay within the confines of a light beam would be a considerable asset in monitoring human movement. Radio frequency transducers can provide such an alternative. A high frequency magnetic field is created by a coiI powered by high frequency alternating current. This magnetic field is then sensed by induction of a current in a sensing Ioop. A suitable sensor is constructed from many turns of copper wire symmetrically wound in a circular shape. At the frequencies used, human tissue has a permeability effectively the same as a vacuum and thus does not affect the operation of the transducer. Put another way, the transducer does not ‘see’ the presence of human tissue. The voltage induced in the sensor is dependent on: (a)
the current
flowing in the coil
(b)
the number
of turns on the coil
(c)
the frequency
(d)
the number
(e)
the spatial position
of the magnetic
field
of turns on the sensor of the sensor
If all these components except (e) are held constant then the voltage induced in the sensor is solely a function of the position of the sensor in the magnetic field. Components (a) and (c) are a function of the controlling electronics, whilst components (b) and (d) are a function of the physical construction of the coil and sensor, Thus holding components (a) to (d) constant within a given accuracy presents no real problem. A movement transducer working on this principle has been proposed before’ but no mention was made of the effectiveness, range or accuracy of the system. The technical problems involved in producing a working system are largely dictated by the nonlinearity of the transducers response, its sensitivity to movement in any plane, and the possible complexity of computer programs needed for data analysis. A coil which produces a magnetic field as a result of a current flowing within it, acts as a
118
J. Biomed.
Eng.
1983,
Vol.
5,
April
B,
$$
=
2c,c;3s e
(1)
_r
p0
c sine lr13
= 0
(3)
where r, 8 and 4 are the normal cylindrical polar co-ordinates, p. is the permeability of the surrounding medium and c is a constant whose magnitude is proportional to the number of turns and current flow of the coil. This does not give a linear relationship between the spatial location and the measured magnetic field. Two alternatives are available. Firstly, one can try and produce coils and sensors of such a size and location that for a given movement the transducer output is linear within a given accuracy’. Seco:ldly, the resulting data can be computer processed to overcome any non-linearities, and calculate the relative positions of the sensor and the coil. TWO DIMENSIONAL
MOVEMENT
A simple two dimensional system has been developed which has the advantage of producing an output linear with respect to angle of rotation over a range compatible with many joint movements. Figure 1 shows the layout of the system when used to monitor flexion of the elbow, and a block diagram of the associated electronics. In the case of elbow flexion the coil producing the magnetic field is attached proximal to the elbow joint on the upper arm, and the sensor is attached distal to the elbow joint on the forearm. Both are held in place with simple Velcro straps. As elbow flexion occurs effectively in one plane, any move-
arm
\
I
Sensor
Phase slgnal
I
Heel strike pulse
Recorder
I Two dimensional radio frequency transducer. The attachment of the coil and sensor to the joint under study (the elbow) is shown, along with a block diagram of the associated electronics. Figure
1
Monitoring
Sensor to elbow distance
ment (except when the forearm is pronated or supinated) can be considered as pure rotation. Thus any change in the voltage induced in the sensor is due to flexion of the elbow joint.
Relative movement of the sensor and coil is thus detectable but the problem of linearity still remains. Two alternatives are possible. Either use a system with a non-linear response, obtain the relevant calibration curve and remove the non-linearity with subsequent data processing, or construct the sensor and coil of such a size and relative displacement that the transducer is linear over a range compatible with the movement being studied. The latter course is simpler to implement. computer program was written which could calculate the response of the total system to rotation. As the magnetic dipole approximation can only be used at distances from the coil which are large in comparison with the coil dimensions, the computer program was capable of calculating the magnetic field directly from first principles (i.e. from the magnetic vector potential). The field produced by the coil was then integrated across the surface area of the sensor. Thus, the transducer response could be predicted for any combination of coil, sensor, relative position and centre of rotation. A
Fipre 2 shows the resulting sensor response for various physical configurations. It can be seen that the linearity of the sensor’s response varies considerably with the chosen physical configuration. Most configurations are unsuitable in giving even an approximation to a linear response. However, careful choice of the sensor and coil dimensions, and their relative positions can produce a system with reasonable characteristics. The responses vary greatly in absolute magnitude as the distance between the coil and sensor is increased, but only
K.M. Jackson
(mm)
40
IO
The sensing electronics uses a synchronous detector which is fed with a signal at the same frequency (1 MHz) and in phase with the alternating magnetic field produced by the coil. Thus the detector only measures signals produced by the coil and discriminates against other extraneous fields. This greatly reduces the power needed to produce a magnetic field of measureable intensity at distances in the region of 20-25 ems. Provision has also been made to multiplex a pulse recording the occurrence of heel strike, so that the gait pattern can be related to the phase of the walking cycle. This was derived from a small brass plate, attached to the subject’s heel, making contact with the metal surface of the walkway. Suitable electronics detect the first occurrence of this contact. All signals were transmitted along a cable which trailed behind the subject as he walked. This did not produce any detectable artefact due to cable movement, but the long leads used for signal and power supply transmission did introduce some 50 Hz interference. This was filtered out using a sharp cut-off 50 Hz notch filter. The heel strike pulse was not unduly affected by this filter.
with R/F transducers:
70
IO
‘0
u
1
I
I
-900
0”
90”
Figure 2 Linearity of response for attachment of the sensor and coil at various distances from the intermediary joint. Each graph is a computer prediction of the response from -90 to +90°. All the results have been normalized to facilitate comparison.
relative magnitude for any one chosen configuration is important. Thus all the computer predictions of transducer response have been normalized to show a scale ranging from -1 to +l. Using a coil length of 45 mm, and diameter 9 mm, a sensor diameter of 20 mm, a coil to elbow distance of 30 mm and a sensor to elbow distance of 40 mm, the computer program predicted that the transducer response should be as shown in F&we 3. The actual response of a system with such a configuration is also shown in Figure 3. This was measured with the coils and sensor mounted upon plastic (non-magnetically permeable) rods, hinged together with a potentiometer attached to the axis of rotation measuring the angle of rotation. The measured transducer response and the associated computer prediction
8 Figure 3 Comparison of the transducer with the associated computer prediction. The dotted lie is the computer prediction of the transducer response. The open circles show the measured response. The transducer can be considered linear over the range denoted by the solid line within an accuracy of 2%.
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mounting the components which form the high frequency oscillator and driver on the rear of the coil in a small epoxy package.
Flexion
Elbow
11
Extension’ Triceps
Lot. dors1
LW
Post. delt
Strike
1 pl Ii
I 50 Percentage
I lO(
of walking cycle
Lift F
L. heel
R heel
Figure 4 Elbow flexion and extension along with associated electromyographic activity recorded at a cadence of 110 steps/min. This record is a tracing of a recording made on an ultra-violet recorder. The horizontal scale corresponds to one complete walking cycle. The occurrence of heel strike and lift-off of the right foot are shown by the marker pulses added to the record of rotation of the elbow joint. Electromyographic activity is present only in posterior deltoid (post. delt.) and latissimus dorsi (lat. dorsi). This activity is of a very low level and only at definite phases of the walking cycle.
I
I
The coil used in the working system was made from 80 turns of 0.05 mm copper wire, and the sensor from 50 turns of the same wire. This number of turns gave enough sensitivity at the distances used for measurement of elbow flexion. The application of this two dimensional transducer is illustrated by Figure 4 which shows flexion in conjunction with simultaneously recorded electromyograms from the associated musculature. The sensor was calibrated for this application by attaching a pendulum goniometer to the subject’s forearm, holding his upper arm vertical and asking him to move his forearm to various resting positions. Zero degrees was taken to be at the point of ‘elbow locking’ during hyperextension of the elbow joint. Figure 5 shows a typical calibration curve using this method of transducer calibration. THREE DIMENSIONAL MOVEMENT None of the problems of lack of stability of the transducer mountings, and movement out of a single plane, which cause errors in two dimensional movement sensors are unique to radio frequency transducers. They also occur to a greater or lesser extent when either filming of the movement or goniometers are used. The problem of the stability of any transducer mounting is too complex to be discussed here. Errors caused by movements performed outside one single plane can be removed by using an inherently three dimensional movement transducer. System design and construction
I
I
I
I
I
5
15
25
35
Elbow
flexion
(“)
Figure 5 Typical calibration record. The subject was asked to hold his arm at a fixed position whilst a calibration point was recorded from the transducer and a pendulum goniometer simultaneously. He then moved his arm freely before the next calibration point was recorded. The calibration record obtained in this manner not only reflects the linearity of the transducer, but also errors due to movement of the transducer and its associated armbands relative to the surface of the body. Thus it is representative of the actual errors involved in using this two dimensional radio frequency transducer.
agree with each other very closely, confirming that the transducing system measures correctly the magnetic field produced by the coil, and that the shape of the magnetic field around the coil is as predicted by classical electro-magnetic theory, no detectable artefact being produced by the nearby presence of wires and other components. The influence of extraneous fields from cables feeding the coil had already been minimized by
120 J. Biomed. Eng. 1983, Vol. 5, April
I
A three-dimensional radio frequency transducer has been developed working on the same physical principles as the two-dimensional transducer described above. Each sensor now comprises three mutually perpendicular coils. Each of these coils measures one component of the magnetic field surrounding the sensor. This enables the sensing system to measure the scalar magnetic field strength by simply squaring, adding and square rooting the three components of the magnetic field. The actual rotational orientation of the sensor is immaterial to the calculation of scalar magnetic field strength, as no matter how it is placed in the magnetic field, squaring, adding and square rooting, three mutually perpendicular vector components will always derive the scalar magnitude of the field. Each of these sensors measures the magnetic field produced by a matrix of four (see later) field producing coils which are situated in space at locations whose spatial separations are known. These coils are powered in sequence, thus allowing the sensing electronics to discriminate the magnetic field produced by one coil from that produced by the other coils. Figure 6 illustrates the layout of the three dimensional transducer. At the initiation of a sampling
Monitoring
Computer Sensors
III
Pre-amps
/
/’
/ // /’
KM. Jackson
plexed series of signals, produces a time sequence of voltage levels whose voltage is proportional to field strength. Note that only the absolute magnitude of voltage level is important as the sign will be positive or negative depending on whether the sensor orientation produces an in-phase or antiphase signal from any given component. The output from the phase sensitive detector, and a pulse output providing synchronization information for later data processing, are recorded on two separate channels of a frequency modulated (FM) recorder (these are labelied Output and Timing on Figure 7).
r
//
with RfF transducers:
Ill
Ill Multrplexer
Figure 6 Three dimensional monitoring. Each of the four coils shown produces a high frequency magnetic field which is detected by each of the three components of each sensor. The expanded section illustrates how the three mutually perpendicular components of a sensor are wound. The dotted line shows that the system can be linked direct to a computing system if this is experimentally possrble.
processing
of data
Although future versions of this three dimensional movement system will probably operate in realtime under the control of a mini-computerfmicroprocessor, the present system has all computer processing performed off-line. The feasibility of real-time operation depends solely on the speed of operation of the algorithms providing positional information from the magnetic field measurements, which is in turn dependent upon the inherent speed of the data processing system. The signals recorded on one track of an FM tape recorder are fed into an analogue-to-digital converter which samples the data under the control of synchronizing signals recorded on a second track of the FM tape recorder. The signals are then processed and stored in the memory of the minicomputer (Varian 62OL-100). At the end of each
I
cycle in the transducer, high frequency current is applied to coil number 1. The sensing electronics then samples in turn the three components of each of the sensors. This sequence is repeated for coils 2, 3 and 4. After a suitable delay, compatible with processing of the data, the whole cycle of measurement is repeated. Any relative movement of one of the sensors and the matrix of coils will produce a change in the magnetic field measured by that sensor. The problem which remains is to reconstruct the spatial location of the sensor from the measured magnetic field strengths. In order to simplify the construction of the sensing electronics the coils were powered with current at a frequency of 100 KHz. This is in contrast to the two dimensional transducer which operated at a frequency of 1 MHz. The penalty paid for this is reduced voltage induced in the sensors. After the signal from one component of the sensor has been chosen by the multiplexer, a phase sensitive detector monitors this signal and produces a voltage output proportional to the amplitude of the alternating signal. F&w~ 7 illustrates this process for two sensors. A current is induced in each component of the sensor for the duration that power is provided to one of the coils (20 ms). The phase sensitive detector, when fed with a time multi-
.lBE
1:2
c
I
2 3
I
1
I
Coils
A I
4 Tlmlng 1
I 2
I I
I
f
I
I
I
1
I
I
3
I 2 3 output
Figure 7
Phasic activity of the coils and two sensors (each of 3 components). Each sensor component is sampled under the control of the Timing signal. The Output and Timing signals are recorded for further analysis.
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section of recording, the processed data is stored in the mini-computer’s permanent storage for immediate or subsequent output to a mainframe computer. The need to use a large mainframe computer will be explained later. The data processing performed by the minicomputer comprises averaging to reduce the noise present in the signal, extraction of the absolute magnitude of each component of the sensor, squaring, adding and square rooting of these components to give the scalar magnitude of the magnetic field. This processing reduces the amount of data transferred to the main computer. The main computer program has to calculate the sensor position from the scalar magnetic field. The mathematics describing the spatial variation of the magnetic fields produced by the four coils does not seem to be solvable analytically. To obviate the need to produce an analytic solution, the main computer program uses a minimization technique. The method of producing a solution can best be explained by considering a two dimensional analogy. Consider the spatial grid shown in Fi&~e 8. From knowledge of the shape of the magnetic field surrounding the coils, the field strength at each intersection of the grid can be calculated. The sensor provides a measure of the magnetic fields (suitably calibrated) at an unknown point in space. A simple search round the points on the grid can provide an approximate answer but obtaining an accurate answer entails interpolation between the grid lines. The concept of the computer program is to perform a quick search around all the points available on the grid to find an initial approximate answer. Then assuming the magnetic dipole equations (l-3) are valid over small distances, the computer program takes a small step away from this initial grid intersection and computes whether the solution is more accurate or not. By controlling the
direction of its steps it minimizes the errors until it arrives at the point of minimum error. This minimization process can be performed very efficiently with readily available minimization algorithms9. The necessity to use such a minimization algorithm is the main reason for employing a mainframe computer, and not performing all the calculations locally. The actual three dimensional computer programs work as described in this two dimensional analogy except there are three sets of intersecting magnetic field lines. Unfortunately if only three coils are used, the minimization process can sometimes be upset by the multi-valued nature of the fields and produce erroneous results (usually along a mirror image path to the true path). This is why four, as opposed to the mathematically necessary three, coils have been used. A solution is calculated for each of the four possible combinations of any three coils from four. These four answers are then compared to see if they are spatially very close together. If they are, the answer is accepted and the computer program moves on to the next data set. If not, it discards any answer which does not closely match the others and retests the remaining answers. This process continues until two answers remain. If these still do not match each other, the computer program computes an approximate solution, marks it as being approximate, and then continues with the next data set. This is only a very short outline of the algorithm currently employed to compute the spatial position of the sensor. It has many other logical alternatives available which enabIe it to shorten the time needed to execute the computer program and provide an accurate answer. Once the relative position of the sensor and the coils has been calculated, simple mathematical transformations can present the resultant movement data in any desired form. This will be demonstrated with specific reference to movement of the knee. Accuracy
and frequency
response
The accuracy with which this three dimensional transducer can calculate the spatial position of a sensor is dictated by three different parameters:
Figure 8 Twodimensional representation of a pair of crossed magnetic fields (solid lines) and a spatial matrix of x and y values (dotted lines).
122 J. Biomed. Eng. 1983, Vol. 5, April
(4
The physical
size of the sensor
lb)
The accuracy and reproducibility sensing electronics
(4
The rate of movement of the sensor, which must be slow enough to allow the approximation that the sequentially sampled magnetic fields are effectively sampled at the same location in space.
of the
The physical size of the sensor is constrained by the necessity to maximize the number of turns and the cross-sectional area of each component of the sensor. This maximization produces a sensor which has enough sensitivity to operate at a reasonable distance from the coils. Conversely, the
Monitoring
size of the sensor must be kept as small as possible so that the measured magnetic field is not unduly affected by local field variations across the sensor. A small sensor also has the obvious advantage of being simpler to attach to the human body and less obtrusive once affixed. The sensors at present in use are a compromise between these two conflicting requirements. The outside diameter of the three mutually perpendicular components of the sensor is 14 mm. Each component is wound from 500-1000 turns of 0.5 mm diameter copper wire. The maximum operating range of the sensor from the coils is 400 mm with an inherent accuracy of 2-3 mm. Each of the four coils is powered for 20 ms during which a scan of the three components of each sensor is completed. Thus, sampling of all four coils is complete in 80 ms. In order that the assumption, that each coil was sampled whilst the sensor was at one single point in space, is not violated, the frequency of movement must not approach 1000/80 = 12.5 Hz. A safe absolute maximum with the present system is considered to be 5 Hz. The length of time for which each coil is provided with power is dictated by the time needed by the sensory electronics and the computer sampling hardware to measure the signal level present.
with R/F transducers:
,y
K.M. Jackson
;x
y =. _7 ro
-0.121 0
I
1 20
IO Time
(5)
Figure 9 Discrimination of movement along one coordinate. The stratification of the graphs is caused by usage of a line-printer graph plotting routine in producing records of movement versus time. Missing records are due to tape ‘drop-out’ in the FM tape recorder used for this particular
recording. The computer programs can recognise erroneous data and reject it.
CONCLUSIONS
Figure 9 illustrates
Two radio frequency transducing systems have been described, both of which are suitable for the study of human movement in both research and clinical environments. They are non-invasive and at the operating magnetic field strength and frequency used, there are no known adverse effects in any animal, including man.
Knee movement
A radio frequency transducer capable of monitoring a simple two dimensional movement can be constructed from readily available low cost components. Methods have been described which can make this type of transducer produce a linear response to rotation of an intermediary joint over a reasonable range. Even if movements are to be studied which lie outside this linear range, knowledge of the calibration curve for the transducer over the total range to be studied permits the user to calculate the angle corresponding to a given transducer output. This can either be done manually or by subsequent data processing of the signals.
the response of the system to sensor movement and its ability to discriminate movement in different planes. These results are from an experimental test where a sensor was moved along the x axis from -70 to -5 mm. The results show that the only detected movement is along the x axis. The values derived for the y and z co-ordinates stay substantially the same throughout the sequence of data points.
As a specific case of usage of this three dimensional radio frequency transducer, consider movement at the human knee joint. The coils are attached rigidly to a non-metallic frame which is attached to the anterior surface of the thigh by means of Velcro straps. Two sensors are attached to the anterior surface of the lower leg by means of similar straps. Small pre-amplifiers are mounted in close proximity to each of the sensors to mitigate against noise and interference. The movement sensed is obviously that of the sensors with respect to the coils and will be considered as movement of the leg with respect to the thigh, since both the coils and sensors have a firm secure mounting. The computer programs at present calculate the angle of flexion and extension and give statistical information on the maximum and minimum angles occurring. A typical output is shown in Figure 10. The angle of knee flexion is calculated by computing the positions of each of the sensors with respect to the coils. A simple mathematical transformation can then compute the angle of flexion of the knee joint.
Extension
Flewon
I 20 Time
(5)
Figure 10 Flexion of the knee joint. As in Figure 9 the stratification of the graph is due to the method of graph plotting employed. This record is a copy of a print out from a computer line-printer. From being initially stationary with the lower leg at right angles to the thigh, the knee joint is flexed, extended and flexed in quick succession. After a slow move to an extended position it returns to its original position.
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The main advantage of such a radio frequency transducer over conventional photographic or goniometric methods is that it combines the ease of usage associated with the attachment of photographic markers to the surface of the body, with the immediate availability of the signal from a goniometer. Each of the attached components weighs little more than a photographic marker disc. Thus none of the problems of interference with the movement under study associated with conventional potentiometric goniometers are encountered. A three dimensional transducer is simple to affix to the subject, simple to cahbrate and, as data processing techniques are intimately involved in the operation of the transducer_, it is relatively easy to present the final data m any suitable format. Calibration is simply a matter of placing each sensor in turn at a known location relative to the coils and taking a short recording. Although the three dimensional transducer needs a computer to analyse the data produced by the sensors, I believe this should be viewed as an asset and not as a hindrance to implementing the transducing system. Computing power is now readily available and can be used to present an analysis of human locomotion in any desired format. Although the usage of radio frequency transducers is not confined to studies of human locomotion, it is here that their inherent advantages can be fully realised. Systems recording simple joint movement whilst the subject is stationary are relatively easy to construct but do not lead themselves to use with moving subjects without undue interference or restriction upon the movement under study. There is of course no reason, apart from the availability of appropriate data sampling and recording systems, why the number of sensors employed in a three dimensional radio frequency transducer cannot be increased. These could then be attached at multiple points upon the surface of the human body, and
124 J. Biomed. Eng. 1983, Vol. 5, April
would provide a total view of how the human body moves relative to one particular reference location. ACKNOWLEDGEMENTS I would like to thank the following; Guy’s Hospital Endowment Fund for funding the early part of this work; Guy’s Arthritis Research Unit, especially Dr R. Grahame, and the Arthritis and Rheumatism Research Council for funding the development of the three dimensional transducer; Prof. J. Joseph and Prof. S.J. Wyard for encouragement and advice; and Guy’s Hospital Tower Computing Unit for the provision of computer facilities. REFERENCES Plagenhoef, S. in Patterns of human motion: a cinematographic analysis, Prentice-Hall, Englewood Cliffs 1971. Winter, D.A., Greenlaw, R.K., Hobson, D.A. Television-computer analysis of kinematics of human gait, Comput. Biomed. Res. 1972,5,498-504. Findlay, F.R., Karpovich, P.V. Electrogoniometric analysis of normal and pathological gaits, Res. Q. 1964,35,379-384. Jackson, K.M., Joseph, J., Wyard, S J. A mathematical model of arm swing during locomotion, J. Biomechanits 1978, 11, 277-289. Grieve, D.W. A device called Polgon for the measurement of the orientation of parts of the body relative to a fixed external axis,j. Physiol. 1969,201, 70 p. Woltring, H J. Calibration and measurement in 3dimensional monitoring of human motion by optoelectronic means, Biotelemety 1975,2, 169-196. Chandler, S.A.G., Nightingale, J.M., Sedgwick, E.M. A multi-channel R.F. goniometer,j. Physiol. 1972, 226, llp-12~. Jackson, K.M. The linearity of radio frequency transducers, Med. Biol. Eng. Comput. 1977, 15, 446-449. Powell, M J.D. A Fortran subroutine for solving systems of non-linear equations, Harwell Report AERE-R5947, H.M.S.O. 1968, [reprinted in: Numerical methods for non-linear algebraic equations, (Ed. P. Rabinowitz, Gordon and Breach, 1970)]