Transcript
A device for measuring plantar pressures R. P. T. under the sole of the foot Betts and
Duckworth
An apparatus is described which gives a rapid and detailed picture of the distribution of pressure under the foot with quantitative information, the pressure distribution being displayed as either a continuous grey scale or a colour contour map on a television monitor. A theoretical analysis of the operating principles is given with evidence for its validity, and the practical problems associated with the more detailed aspects of the equipment are discussed.
APPLIED PRESSURE
Introduction The Sheffield Children’s Hospital has for many years been involved in the investigation and management of paralytic disorders: in particular spina bifida and cerebral palsy. Many children have received corrective surgical treatment for these conditions over a number of years and the need has arisen for objective measurements of the results of these techniques. Attention has recently become concentrated on a number of specific difficulties, one of which is deformities of the feet. The most important factors contributing to satisfactory function in the foot are its shape, the distribution of pressure over the sole and the adequacy of sensibility. The shape of the foot may be assessed by photography, concentrating particularly on the contact area of the sole during standing and walking. However, it was felt that there was need for a more sophisticated device for measuring the distribution of plantar pressures rapidly and accurately, and that such a method should be applicable to large numbers of patients. Early attempts at obtaining the load distribution under the foot were qualitative measurements made from impressions in mud, clay or a suitably deformable substance (Beeley 1882). The problem with these methods is that, because the medium is deformable, they tend to measure the shape of the foot rather than the load distribution. Semi-quantitative methods have been used such as overlaying a rubber mat of paramidal projections with an inked fabric and layer of paper (Morton 1935). Deformation of the projections under load produces a crude pressure pattern. Unfortunately, the device only records the highest pressure that ever occurs at a given point under the foot when walking. A more sophisticated qualitative method has used a cinC camera under a glass plate to film the pressure distribution during foot to glass contact (Elftman 1934). More recently attempts to obtain quantitative measures of pressure distributions have been made using pressure transducers attached to strategic positions on the sole of the foot (Bauman and Brand 1963; Schwartz et a1 1964), or using beams, suspended from load cells, upon which the subject walks (Hutton and Drabble 1972; Stott et a1 1973). Scranton and McMaster (1976) made preliminary studies into the use of pressure sensitive liquid crystals with some success. Despite previous research the need still exists for a system which will give a rapid but detailed picture of the distribution of pressure under the foot with quantitative information. Chodera (1957) proposed a pressure measuring device and it is this system which has been used and extensively developed in the Department of Medical Physics, Sheffield.
Reflector \
I
Plastic Sheet
Light
Fig. 1 Simplified diagram of the basic pressure measuring device
Method The basic system (Fig. 1) uses a glass plate illuminated at its edges by strip lights. The top surface of the glass plate is covered with a thin sheet of opaque reflective plastic on which the subject stands. When viewed from below the areas of contact of the foot can be seen with a light intensity related to the applied pressure.
Fig. 2 A typical grey scale display of the foot pressure distribution photographed from the television monitor
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Fig. 3 Foot pressure distributionsphotographed from the colour monitor for: (a)Left Normal adult (body weight 62 kg; colour threshold to pressure calibration- white 1260 mb, red 900 mb, green 540 mb, blue 215 mb, yellow 100 mb, cyan 35 mb, magenta N 15 mb) (b) Above Child with spina bifda (body weight 16 kg; colour threshold to pressure calibration-white 570 mb, red 450 mb, green 340 mb. blue 240 mb, yellow I60 mb, cyan 100 mb, magenta = 15 mb) NB These are black and white reproductions of colour photographs; consequently the colour boundaries are not very well defined
Fig. 2 illustrates the type of image which can be observed underneath the plate when the subject stands on the plastic. The image may be viewed via a mirror with a monoLhrome television camera and displayed on a monochrome video monitor. This type of image is good for picking out high spots of pressure by eye and for observing gross changes in the pressure distribution, but it is difficult to interpret the more subtle changes and variations of pressure underneath the foot. For this reason an interface has been developed to convert the video information from the monochrome camera into a suitable form to drive a colour monitor. The video signal is first amplified and is then fed to a set of seven parallel voltage level comparators. These comparators split the video signal up into seven different levels. Each of these levels is assigned an appropriate colour and by combining the outputs of the comparators with the appropriate logic circuitry, the three guns of a colour monitor are driven to produce the desired colour whenever the video signal is within the given band. The resultant display on the colour monitor is a pressure contour map of the pressure distribution underneath the foot. Fig. 3a illustrates the type of display obtained on the colour TV monitor. Each of the reference levels set on the comparators is continuously and independently variable. Consequently, the levels can be adjusted manually to any desired setting
r --------I
PLATE
to maximize the amount of information from any given display. For example, a more detailed distribution of load within a high pressure area may be studied. Fig. 4 illustrates in block diagram form the complete system. The image from the glass plate is viewed with the monochrome TV camera and the video information is stored permanently on a video tape recorder. The image is passed simultaneously to the colour converter and the display is viewed on the colour monitor either in monochrome or as a colour contour map. A 35 mm colour slide is taken direct from the colour monitor to provide another permanent record. The information stored on the video tape recorder may be replayed at any further date, again the nature of the pattern being adjustable at will with the voltage level controls on the comparators.
Theoretical analysis The principle by which the method operates is illustrated in Fig. 5 . Light which enters the glass plate from its edges is totally internally reflected between the top and bottom surfaces of the glass. Total internal reflection can, of course, only occur when the light ray travels from a high refractive index medium to a low refractive
1 y3c I-----------
CAMERA
1 I
INTERFACE
. - -.. .
AIR
COLOUR
Wh'R 4 < & for refraction 4 > & for tolal internal
MONITOR
reflection
a RECORDER
Fig. 4 Block diagram of theapparatus
Fig. 5
42' for crown glass
.-
..-
-
At the areas of contact there is refraction only, followed by reflections from the plastic Total internal reflectiom can only occur when passing from a medium of high relraclive index to one of 13wer relractive index
Diagrammatic representation of the physical principles of operation involved at the plastic/glass interface (/pa, pa, p p are the refractive indices of air, glass and plastic respectively; 8,, 8, are the angle of incidence and critical angle respectively)
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index medium, i.e. from glass to air. However, where the plastic sheet comes into contact with the glass total internal reflection can no longer occur since plastic has a higher refractive index than glass. At these points of contact therefore the light ray is refracted out of the glass and is scattered in all directions at the glass to plastic interface. When viewed from below the glass plate this scattered light can be observed. The plastic sheet on the microscopic scale, has an uneven but deformable surface, therefore when pressure is applied to the top surface of the plastic sheet the deformable surface of the plastic will be forced into more intimate contact with the glass plate, the amount of contact being dependent upon the applied pressure. Hence the greater the pressure that is applied, the more intimate contact there is between plastic and glass and therfore the more the total internal reflection of the light is broken down, so that when viewed from beneath the glass plate the brighter is the light intensity seen. An experiment has been set up to investigate the plastic to glass interface under pressure. The under surface of a glass block is viewed with a microscope while pressure is gradually applied to the top surface of the plastic via an air pressure device. As the pressure is gradually increased, small spots of light begin to appear which increase in number with pressure. The size of the spots of light also increases slightly. As the pressure is continuously increased the number of spots of light gradually increases until a single totally uniform bright image is produced at which point saturation has effectively been reached. If the small spots of light are viewed individually they consist of a uniformly bright area. Total internal reflection of light can be broken down by bringing an appropriate medium to within the order of a wavelength of the surface of the glass and the question did arise as to what contribution was coming through direct contact with the glass plate and what contribution was coming through a proximity effect. Measurements have shown the light intensity to be proportional to the number of spots of light and to the applied pressure. The appearance of the spots of light has also been positively correlated with the surface structure of the plastic by electron microscope studies. Detailed analysis of the experimental results supports the hypothesis that almost all the light output is due to intimate contact between plastic and glass, only an insignificant amount being due to breakdown of total internal reflection from proximity effects, and that the light output is related to applied pressure.
Practical considerations Although the basic principles of operation of this technique are relatively simple, in practice the problems associated with the more detailed aspects of the system are quite extensive and these are considered below.
Glass plate There are many types of glass available on the commercial market but there are certain criteria to be met in the choice of glass for this application. One of the most important is that the glass should be able to bear the weight of any subject who is to stand on it. The specification here will depend upon the size of the glass plate being used.
Another important consideration is the light absorption properties of the glass and the refractive index, since this will affect the transmission of the light by total internal reflection along the plate from its illuminated edges. In this application the glass used was a 460 mm square piece of toughened glass of 10 mm thickness which was supported on all four edges. The maximum allowable vertical load in the centre was calculated as 1290 kg. This was ordinary commercial glass which contains many impurities, including iron, which results in a green image being formed. This type of glass also has greater light absorption properties than some of the clear white glasses that are available. However, the clear white glasses are considerably more expensive and as our experiments have shown are not absolutely necessary. This is shown more fully under the section on flatness checks. The green image is acceptable since many camera tubes are most sensitive to the green wavelength of light. An improvement in the amount of light available within the glass could be made by sophisticated devices to direct the light into the edges of the glass to strike the faces at the desired angle. However, this was again felt to be unnecessary.
Plastic sheet The plastic sheet presents perhaps the greatest problem with the apparatus. One naturally requires a deformable plastic which will give a reasonable image grey scale over the required pressure range, (approximately 0-2000 mb). If one looks at a whole range of plastic sheets available on the market one finds that they have considerably different properties when used on the device. Certain plastics give a very bright image at relatively low pressures giving very little dynamic range. These plastics also tend to be the ones which stick to the glass plate after the pressure is removed and also leave a greasy deposit behind on the glass surface. At the other extreme, certain plastics give very dull images, again giving a very low dynamic range, but these types of plastic do not stick to the plate or leave deposits behind. Ideally the plastic would give a linear dynamic range with light intensity increasing with increasing pressure, although a saturation point must be reached where the plastic cannot be deformed into more intimate contact with the glass plate. Ideally the plastic should also recover very rapidly after the release of pressure giving no image retention and also should leave no deposit on the glass. It is very difficult to obtain information of the more detailed aspects of the manufacture of plastics in terms of their composition. The types of plastics which stick to the plate tend to be the ones which contain large amounts of plasticizer which extrudes out onto the glass plate under pressure. This also has the effect of producing a liquid interface between plastic and glass which results in a saturated image at very low pressure levels. At the other extreme hard coarse plastics containing small amounts of, or no, plasticizer cannot be deformed sufficiently to produce a reasonable dynamic range. Clearly a compromise has to be found which suits the given application. The overall thickness of the plastic is not critical so long as it is kept within the range of a few thousandths of an inch. Naturally the thicker plastic sheets will not faithfully reproduce the applied pressure pattern onto
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By curve fitting techniques the equation relating the fall-off of light is a good approximation to: I, = I, exp ( - 0 . 1 5 ~ )(correlation coefficient = 0.99) where I,, = light intensity at edge of plate I, = light intensity at point x x = distance from edge of plate Therefore, for a glass plate illuminated at two opposite edges the available light intensity at any given point on the plate is given by the equation: 2 I I
Fig. 6
I
do
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200 3hl 4hl POSITION ON GLASS (m) Graphs illustrating the vanation of light output for constant 0
160
presrure applied at points along the pressure plate surface
MATT B L X K &PER
/
POSITION ON GLASS Irnrn)
Fig. I
Graph illustrating the variation of applied pressure lo give a constant light output measured at intervals along the pressure plate surface
CAI . _ IRRATION _ -
PRESSURE TRAYSDUCER
U
t
COMPRESSED A I R CYLINDER
Fig. 8
Diagrammatic representation ofthe calibration apparatus
the glass, i.e. there is a loss of resolution. The plastic sheet is, in the end, the limiting factor on resolution. For the plastic in use, measurements have shown the resolution to be better than 1 mm.
Flatness checks It is important to ensure that the brightness of the image produced under the plate for a given pressure is constant over the total working area of the plate. For this reason it is necessary to make some measurements of the light absorption properties of the glass. Fig. 6 shows the falloff in light intensity of an image produced by a constant pressure when moving away from the illuminated edge. The strip light from the opposite edge has been removed for the purposes of these measurements.
1, = I, exp [ - 0 . 1 5 ~ 1+ I, exp [ -0.15 (a-x)] where a = width of plate between lights. The relationship governing fall-off in light intensity will of course depend upon the parameters of the glass in use. Combining the intensity fall-off from the two opposing lights by summation of the two curves in Fig. 6, or by solving the above equations for the particular glass plate under test, shows that over the working area of about 250 mm square in the centre of the glass, the light intensity for a given pressure is substantially the same. In quantitative terms, the error approaches 70 mb at the edge of the working area but is much less than this inside the working area. Since the fall-off in light intensity is exponential in form, if one assumes lower absorption properties of the glass, then the errors in flatness would be much smaller. This could be one advantage of using clear white glass. The choice of glass would depend upon the particular application and desired working area. However, the dimensions of the glass plate are critical in determining the distribution of light intensity, larger or smaller sized plates changing the summated intensity from two opposing light sources. The flatness was also checked by having both strip lights connected and plotting similar curves to Fig. 6 across the face of the plate both from strip light to strip light and from unilluminated edge to unilluminated edge. Again these curves show (Fig. 7) that over the central portion of the plate the light intensity for a given pressure is consistent, but this consistency falls down very rapidly outside of this area. Naturally close to the strip lights the light intensity for a given pressure is high relative to the central area of the plate, compounded by light escaping due to the low angle of incidence at the edge, and conversely towards the unilluminated edges the light intensity falls off for a given applied pressure. This central working area of the plate is quite acceptable for the types of measurements under investigation, i.e. the distribution of pressure underneath the foot. Great care has to be taken to ensure that one does not stray outside the working area otherwise the pressure patterns which are produced give erroneous data which can be quite catastrophic in terms of the interpretation for a clinical condition. This is easily avoided by masking techniques.
Ca Iibrat ion of plate The methods used for assessing the working area of the plate and for calibrating the different types of plastics is illustrated in Fig. 8. It is important to obtain a uniform
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pressure loading for calibration purposes and for this reason an air pressure system was used. The basic jig consists of a metal block with a blind hole of 2.87 cm diameter drilled in the bottom surface. The blind hole may be pressurized from a compressed air cylinder and the pressure reading noted from a pressure transducer and amplifier system accurate to within 1 per cent. This gives very accurate readings of the pressure levels applied to the glass surface. Rather than monitor the actual light output from underneath the plate in absolute terms the calibration is normally done by noting the change-over levels from one colour band to the next using the colour monitor display. By this method of calibration a pressure level may easily be assigned to each of the colour bands produced on the colour monitor whatever the reference level set on the voltage comparators. Fig. 9 shows the calibration curve for the experimental equipment used in the foot pressure measurements.
Equipment The monochrome television camera used was an EM1 Surveyor I1 camera fitted with a silicon diode tube. The silicon diode tube has advantages over conventional videcons in that it will monitor images at much lower light levels (an order of magnitude down) and the voltage output of the tube is directly related to the light input. The automatic gain control used inside the camera has to be disconnected and the camera used at a fixed gain so as to ensure faithful reproduction of the grey scale image. The monochrome camera has a video output bandwidth of 7 MHz. If this resolution is to be maintained the colour interface system must have comparators and logic components which have very rapid switching times (< 100 ns). Comparators were used with switching times of the order of 40 ns and similarly the Schottky TTL logic components had switching times in the order of 20 ns. Signal to noise ratios from television cameras are very poor compared to other scientific instrumentation, typical values being around 40 dB. This means that for a 1 V signal output from the camera there is approximately 10 mV of noise. One of the major problems is that the high quality comparator used will switch on voltages of the order of a millivolt or less. Consequently the electronic noise from the camera produces poor colour boundary definition on the monitor. For this reason the bandwidth of the signal passing through the colour interface was reduced at the video amplifier to the order of 1 MHz. This reduces the noise sufficiently to be of no problem. The effect of filtering is to cause a very small picture shift across the monitor screen. The picture shift was calculated as 0 . 2 5 per cent of total picture width (see Appendix) and was found to be undetectable by eye on the colour monitor. The video information for the monochrome display was unfiltered since the noise from the camera cannot be seen by eye when observing a continuous grey scale image. The video tape recorder used was a Sony AV-3670 CE model (resolution better than 300 lines; video signal to noise ratio better than 40 dB). Video tape recorders in general always reduce the quality of the recorded signal but under the interface specifications the image produced on the colour monitor was acceptable whether it was
'1 1000 2000 PRESSURE (mb) Fig. 9 Graph showing the light output of the device plotted against applied pressure
displayed directly or indirectly via the video tape recorder. Again the automatic gain control system in the video tape recorder has to be disconnected and the system worked under a fixed gain condition to avoid distortion of the image. The colour monitor used was a Hitachi Model CM181AE monitor (horizontal resolution 380 lines at centre, vertical resolution 300 lines at centre). This was used in preference to a commercial television since it avoids the necessity of internal modifications, direct RGB inputs are available with simple switching to PAL and also the scientific monitor has a higher specification.
Discussion The above apparatus gives a display in either black/ white, or in the form of a colour contour map, and gives a very rapid and detailed picture of the distribution of pressure under the foot with quantitative information. The current work involves the collection of normal data to try and assess the range of normality in both children and adults. In pathological conditions, in particular spina bifida, the relative load bearing areas of the foot, and changes with time are being observed, the distributions of pressure under the foot before and after operation are being compared and an assessment is being made of the success of various procedures such as the use of splints. As an example of the clinical use of the apparatus, Fig. 3b shows the pressure recording from the deformed feet of a child with spina bifida. The pressure is abnormally concentrated over the outer border of the soles and the child is at risk of developing pressure sores in these areas. The device at present provides a static and not a dynamic picture of the loading of the foot. Preliminary studies have shown that it is quite feasible to use the system dynamically and a walkpath is being built to use the system under dynamic conditions. The video recorder in use has slow motion facilities, enabling the detailed analysis of the foot step at some time after the recording. A fully automated microprocessor system to provide on-line information on the loadings of various parts of the foot throughout the foot step is under construction. 227
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Acknowledgements The equipment outlined in this paper was purchased with the aid of a grant of f3500 from the National Fund for Research into Crippling Diseases. The authors are pleased to acknowledge the advice and constructive criticism of colleagues in the Department of Medical Physics and in particular, the technical assistance provided by Mr D. J. Turner, and the help of Dr I . G. Austin, Mr S. Crocker and Mr S. Moore (Physics Department, Sheffield University) in the investigation of the plastic to glass interface under pressure.
Appendix For a simple RC parallel network
f,= l/2nRC where
f,= lower 3 dB frequency Iff, is set to 1 MHz RC = 159 ns TD= Delay time for step response to reach 50 per cent of final value (Kuo 1966) = RC Television line scan rate = 1 line in 64 ps
Therefore Delay T D = 0 . 2 5 per cent of picture width i.e. horizontal picture shift will be in the order of one television line which is better than the resolution of the colour monitor.
References Banman, J. H., and Brand, P. W. (1963) Measurement of pressure between foot and shoe. The Lancet, March 23rd, 629-632. Beeley, F. (1882) Zur Mechanik des Stehens. Uber die Bedentung des Fussgewolbes beim Stehen. Langenbecks Archiv f u r klinische Chirurgie, 21,457. Chodera, J. (1957) Examination methods of standing in man. FU CSAVPraha., Vols. 1-3. Elftman, H. (1934) A cinematic study of the distribution of pressure in the human foot. Anat. Rec., 59,481-491. Hutton, W. C., and Drabble, G . E. (1972) An apparatus to give the distribution of vertical load under the foot. Rheum. Phys. Med., 11, 3 13-3 17. Kuo, F. F. (1966) Network analysis and synthesis. John Wiley and Sons Inc. Morton, D. J. (1935) The human foot. Columbia University Press, New York. Schwartz, R. P., Heath, A. L., Morgan, D. W., and Towns, R. C. (1964) A quantitative analysis of recorded variables in the walking pattern of normal adults. J. Bone Jt Surg., 46A, 324-334. Scranton, P. E., and McMaster, J. H. (1976) Momentary distribution of forces under the foot. J. Biomech., 9 , 4 5 4 3 . Stott, J. R. R., Hutton, W. C., and Stokes, 1. A. F. (1973) Forces under the foot. J. Bone Jt Surg., 55B, 335-344.
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