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Vibration analysis in the assessment of conservatively managed tibial fractures
VIBRATION ANALYSIS IN THE ASSESSMENT OF CONSERVATIVELY MANAGED TIBIAL FRACTURES L. Nokes’,
W.J. Mintowt-Czyz*,
J.A. Fairclought,
I. Mackie 5 and J. Williams*
ABSTRACT
applied to the study of 22 tibiulfktures. Real time vibration analysis will allow quantitative comparisons of werent methods of non-operative fracture managemen& a& in addition to poviakg a uniquely pOwe@l research tool, may have value in aiding clinical management dzci&zs.
A simple and quantitative method for the assessment offracture healing has been developed this method &@nds on a technique of vibration analysis evolved from a study of30 intact human tibtie and has been Keywords:
Bone, tibia, fracture healing, vibration
analysis, attenuation
factor
INTRODUCTION
The clinical assessment of fracture union is useful once the point of union has been reached, but has little value in the prediction of the behaviour of a fracture in its progress to union. In other words, one can tell when union has occured but not whether it will occur. The advent of clinical radiology allowed the fracture surgeon to see an image of the developing callus on the road to union, but since that image relies for its production on the mineralisation of callus, the radiographic appearance lags behind the actual evolution of the callus mass. A more important failing of radiographs is that they are an unreliable predictor of failure of union. For example, some fractures fail to unite even in the presence of abundant callus. It is desirable to have a method of assessing fracture union which records at a s ecific time, the actual state of the callus in terms o f! its mechanical properties. It is further desirable that the method of assessment should allow the early and accurate prediction of failure of progress to union, so that treatment designed to augment healing may be instituted without the delay which is inevitable with current clinical techniques of fracture healing assessment.
tibial tubercle by dropping onto it a 28 g steel ball down a perspex tube. The resulting acceleration of the tibia was measured at two points, the first 60 mm distal to the tibial tubercle and the other, 60 mm proximal to the medial malleolus. At each of these points on the antero-medial subcutaneous surface of the tibia, an accelerometer (Bruel & Kjaer 4369) was positioned and preloaded with a vertical force of between 3.2 and 6 N according to the method of Nokes et al’. The accelerometer outputs were displayed on a Gould 4000 oscilloscope which allows the simultaneous display of two traces. A permanent record of the signals was made on an x-y recorder. The apparatus is illustrated in Figure 1. Three groups of tibiae were studied. Group 1 was composed of 30 normal tibiae in 15 normal adults. These results were used to characterise the response of normal tibia and to compare the left and right bones in individual subjects. Group 2 numbered 20 patients with unilateral diaphyseal fractures and normal contralateral limbs. Measurements were obtained at various stages during healing, from immediately after injury till up to six months later. All these fractures were managed non-operatively and all went on to satisfactory clinical and radiological union. Group 3 consists of 2 patients with non-union.
The leg is a complex mechanical system, the properties of which are rofoundly altered by the resence of a fracture o the tibia, It is one K nction of the process of fracture repair to restore those mechanical properties to normal. The tibia’s vibratory response to an impulse has been studied and has been shown to change in a constant way as fracture healing proceeds. It is proposed that this change in vibratory response might form a method for the quantitative assessment of bone union.
F
MATERIALS,
PATIENTS
AND METHODS
A standard impulse of 0.045 Ns was applied to the *University of Wales Institute of Science and Technology, Cathays, Card%, UK *Prince of Wales Orthopaedic Hospital, Rhydlafar, Cardiff, UK tQueen’s Medical Centre, University Hospital, Nottingham, UK jThe Cardiff Royal Infirmary, Newport Road, Cardiff, UK 0 1985 Butteworth & Co (Publishers) 0141-5425/85/010040-05 $03.00 40
J. Biomed Eng. Vol. 7, January
Ltd
Figure 1 described
The apparatus
used to obtain the measurements
Vibration analysis: I_ Nokes et al
,+: Distaloccelmmeter
’ :.: signal
PA RBB Mainml amplitudes OfewhsjOml
SD 0.11; left leg: range 0.4 - 0.8, mean 0.54, SD 0.23). For a fractured tibia, regardless of the state of healing of the fracture, the trace from the proximal accelerometer is always normal (Figure 4). The difference in attenuation factor in the presence of a
A
Attenuation
,5ms
Factor = O-13
,
Acceleration recorded simultaneously from Figure 2 proximal and distal accelerometers over the intact right tibia of a 21 year old female
RESULTS The method used to apply a stimulus to the tibial a tubercle proved a reliable way of obtainin reproducible signal from both intact and isractured tibiae. A typical trace obtained from a normal tibia is illustrated in Figure 2. The ratio of the maximal amplitude of the distal accelerometer signal to the maximal amplitude of the proximal accelerometer signal (AA/BB Figure 2), is the attenuation factor (AI?.
II
Attenuation
The measured attenuation factors in Group 1 (i.e. normal tibiae) are given in the histogram illustrated in Figure 3. It is clear that the range of results follows a normal distribution. There was no difference between the left and right legs of individuals (right leg: range 0.4 - 0.8, mean 0.57, NORMAL
CONTROL
II
HISTOGRAMS
Attenuation
IO
n
No. of Tibiae
8
Factor = 0~ 32
Factor = 0.44
Attenuation
Factor = 053
6
Proximal accrkarmier AA6 BB
0.4
Histogram Figure 3 normal tibiae
0.6
0.7
Attenuation
factor
0.5
of attenuation
0.8
factors obtained from 30
t
5mr
hbrlmal mpltfudes of each sianal
Recordings taken from the patients with tibial shaft Figure 4 fractures at various stages of healing. (a) male age 27; left tibia at 2 weeks; (b) male age 17; left tibia at 8 weeks - moderate callus on X-ray; (c) male age 80; right tibia at 12 weeks tenuous radiological union; (d) male age 22; right tibia at 18 weeks - clinically and radiologically solid
1 Rinmed
Eng.
1985,
Vol.
7, [anuary
41
s
Vibration analysis: L Nokes et al
fracture is therefore entirely due to a diminished amplitude in the trace recorded from the distal accelerometer.
Attenuation
In a fresh fracture, such as that recorded in Figure 4a, minimal transmission of vibration occurs and the distal accelerometer signal has a very low amplitude. The attenuation factor is therefore also very low (0.13). As healing progresses, vibration is increasingly transmitted across the fracture site so that the amplitude of the distal accelerometer signal increases, as does the AF. Examples taken from fractures at 8 and 12 weeks are given in Figures 4b and c. When the fracture is clinically and radiologically united, the AF approaches the value for the normal intact limb (Figure 4d).
,‘-,
5ms
Figure 6 illustrates the trace obtained from a case of
hypertrophic non-union at 32 weeks. There is very little transmission of vibration across the fracture and the AF of 0.1 falls well below the curve in Figure 5. An exactly similar trace was obtained from a case of atrophic non-union seen at six months from injury. DISCUSSION It has been demonstrated* that the speed of sound in a material is a function of its elastic properties (in particular, Young’s modulus). Mathe showed that the strength of a bone was related to its geometry and Young’s modulus, and it was these fundamental observations that enabled Jurist?d to construct a series of models for the vibratory characteristics of the human ulna. From these, Jurist’ went on to make some observations on the relationship between bending stiffness, breaking
h
O-8. 0 7. Attenuotnn factor lh)
0 5.
strain and mineral content of bone and he related this work to osteoporosis. Pugh*, using a piezoelectric accelerometer to record the effects of an impulse applied to the heel, used Fourier spectral analysis to deduce a possible resonant frequency for the tibia of about 200 Hz. Using a similar technique to monitor fracture healing in humans, Lewis and Tati found that the swelling in the fractured limb created problems which made comparison with the normal limb difficult. These problems were investigated by Saha and LakeslO and later by Ziegert and Lewis”. In both papers it was concluded that the soft tissue was an important part of the system but the authors held contradictory views on how the accelerometers should be loaded so as to overcome soft tissue effects. Our own studies’ of this soft tissue problem have led us to conclude that it is necessary to preload the recording accelerometers sufficiently to overcome the damping effects of soft tissue, and that the re uired preload is proportional to the so9t tissue thickness.
iy+===a L
,.
2
,,,.,..,.
4
6
,
8
IO
12 14
I6
18 20 22
No of weeks Figure 5 Graph of time after fracture, plotted against attenuation factor for those tibiae that went on to satisfactory clinical union. 0 Test data; 0 model
42
I
In addition to the difficulties inherent in obtaining reproducable data from living bone, calculation of the frequency response of bone from its reaction to an impulse is problematic, not least because of the lack of any satisfactory theoretical model for the interpretation of the data. From the practical point of view, until recently fast Fourier transforms required mainframe computing facilities to get to a meaningful result within the few minutes that the routine clinical situation allows. It was for these reasons that we chose to ignore the actual frequency of the impulse response and to look instead at its pattern of propagation in real time.
I4$,
=037(
Distal accelerometer
Recordings taken from a male patient with a Figure 6 hypertrophic non-union at 32 weeks from injury. The AF = 0.1
When the attenuation factors for those tibiae that went on to satisfactory union are plotted against time after fracture (Figure 5), a curve results which rises rapidly in the first 8 weeks before tending to a plateau at 24 weeks. The extrapolated plateau is reached at the mean normal level illustrated in Figure3, which is derived from normal tibiae.
0.9.
factor
J. Biomed Eng. Vol. 7, January
24
Because the tibia is essentially a damped system, a proportion of the input energy is lost along the length of the intact bone and less energy is recovered at the distal end than was measurable at the proximal end. Thus the normal value for the attenuation factor of the intact tibia by this technique is in the region of 0.57 and is not unity.
Vibration analysis: L Nokes et al
A predetermined anatomical site for the lacement of the accelerometers was decided upon f!or this study. It is apparent that the chosen fured points, 60 mm distant from bony landmarks, results in a transfer distance that varies from patient to patient and which is proportional to the height of the individual. The error introduced by an inconstant transfer distance is small in practice, and in fact is insignificant in relation to the changes occasioned by the presence of the fracture. What is more, in the event of any doubt in an individual case, as to the significance of a particular result, it may be compared to the normal contralateral limb over the same transfer distance. A rising attenuation factor, as illustrated in Figure 4, correlates well with the clinical and radiological evidence of union. Figure Z, which is constructed from the results in tibiae that healed normally, forms a model against which the healing of tibial diaphyseal fractures can be measured. The curve ap roaches a plateau at 24 weeks at which time sur;-icient consolidation of the fracture has taken place to render the mechanical response of the bone normal. The plateau is reached at the level predicted by the observations made on the normal tibia (i.e. 0.57, Figure 3). Initially the curve rises rapidly so that by 8 weeks, nearly two thirds of the expected rise in attenuation factor has already occured. What the actual strength of the bone is at this time is not yet known and there are practical difficulties in making measurements of strength or stiffness in living subjects. Clearly, testing of human fracture to destruction is not possible and there are dangers in inferring too much from animal studies. None the fess, we confidently expect that some quantitative point on the healing curve will prove to be a reliable indicator of the time at which a healing fracture may be left unsplinted, so minimising the time for which the injured limb is immobilised. The two cases of non-union suggest that the attenuation factor might be an indicator of this complication of fracture healing. However, we have yet to show that failure to follow the normal healing curve occurs sulficiently reliably and suficiently early for the technique to have a useful predictive value for the behaviour of fractures. The apparatus used for this study has been somewhat clumsy in use but has been modified since and is now much easier to use. Measurements have been made at routine plaster changes although it is quite possible to position the accelerometers through small holes in the plaster. We have no data on the influence of a whole leg plaster cast on the transfer of vibration along the bone but suspect that it would be slight. Patients with removable braces pose no problems. In the first few weeks following injury, oedema damps the output signals and requires relatively high accelerometer preloads which can be uncomfortable for the patient.
As a method of following the progress of fracture union, this technique has the great advantage over radiography that it avoids the time lag that is built into X-ray dependence on the mineralisation of healing tissue. Any inference from radiographs, about the mechanical state of the fracture, is necessarily subjective and in reality only relates to the visible mineralized callus and not the whole callus mass. In the first six weeks, when the changes at the fracture site are most rapid, radiographs may yield no useful information except about the position of the fracture fragments, while at the same time the AF mi ht have risen half way to normal. Conversely, i P at two months the X-ray shows abundant callus but the AF is low, then perhaps a hypertrophic non-union might be predicted. The technique described is likely to be invalid as a method of assessing fracture callus in the presence of an implant used to secure fixation of the fracture since, under these conditions, vibration may pass along the implant, even in the absence of any bone contact. The results obtained using this technique would seem to allow quantitative comparisons of differing methods of non-operative fracture management. CONCLUSIONS The pattern of vibration transmission along the fractured tibia changes with time in a way that reflects the healing of the fracture. The technique described has promise, both as a research tool for the quantitative comparison of non-operative methods of fracture management, and as a clinical aid to decision making.
ACKNOWLEDGEMENTS This work was supported by a grant from the Endowment Fund for Research of the South Glamorgan Area Health Authority. The illustrations were prepared by the Department of Medical Illustration at the University Hospital of Wales. REFERENCES Nokes L., Fairclough J.A., Mintowt-Czyz W.J., Mackie I. and Williams J. Vibration analysis of human tibia: the effect of soft tissue on the output from skin mounted accelerometers. J Biomed Eng. 1984, 6, 223-229 Rowe R.G. Vibration apparatus for testing articles. US Patent No. 2,486,984; 1949 Mather B.S. Comparison of two formulae for in vivo prediction of the strength of the femur. Aerospace Med, 1967, 38, 1270-1272 Jurist J.M. Determination of the elastic response of bone: method of ulnar resonant frequency determination. Phys. Med. Biol 1970, 15, 417-426 Jurist J.M. In vivo determination of the elastic response of bone: ulnar resonant frequency in osteoporotic, diabetic and normal subjects. Phys. Med Bio/, 1971, 15, 427-434 Jurist J.M. and Kianian K. Three models of the vibrating u1na.J. Biomech, 1973, 6, 331-342
J. Biomed Eng. 1985, Vol. 7, January
43
Vibration analysis: L Nokes et al 7
8
9
44
Jurist J.M. Human ulnar bending stiffness, mineral content, geometry and strength. J Biomech, 1977, 10, 455-459 Pugh J.W., Streitman A. and Stanoch J.F. Studies of the impact response of human limbs. 28th ACEMB Meeting, New Orleans, Sept. 1975, 171 Lewis J.L and Tan R.R. Fracture healing assessment by
J. Biomed
E “g.
Vol. 7, January
10
11
impact response.,J. Bone Jt Surg., 1975,57A, 576 Saha S. and Lakes R The effect of soft tissue on wave propagation and vibration tests for determining the in vivo properties of bone. J. Biomech 1977, 10, 393-401 Ziegen J.C. and Lewis J.L. The effect of soft tissue on measurements of vibrational bone motion by skin mounted accelerometers. J Biomech 1979, 12, 218-220
W.J. Mintowt-Czyz*,
J.A. Fairclought,
I. Mackie 5 and J. Williams*
ABSTRACT
applied to the study of 22 tibiulfktures. Real time vibration analysis will allow quantitative comparisons of werent methods of non-operative fracture managemen& a& in addition to poviakg a uniquely pOwe@l research tool, may have value in aiding clinical management dzci&zs.
A simple and quantitative method for the assessment offracture healing has been developed this method &@nds on a technique of vibration analysis evolved from a study of30 intact human tibtie and has been Keywords:
Bone, tibia, fracture healing, vibration
analysis, attenuation
factor
INTRODUCTION
The clinical assessment of fracture union is useful once the point of union has been reached, but has little value in the prediction of the behaviour of a fracture in its progress to union. In other words, one can tell when union has occured but not whether it will occur. The advent of clinical radiology allowed the fracture surgeon to see an image of the developing callus on the road to union, but since that image relies for its production on the mineralisation of callus, the radiographic appearance lags behind the actual evolution of the callus mass. A more important failing of radiographs is that they are an unreliable predictor of failure of union. For example, some fractures fail to unite even in the presence of abundant callus. It is desirable to have a method of assessing fracture union which records at a s ecific time, the actual state of the callus in terms o f! its mechanical properties. It is further desirable that the method of assessment should allow the early and accurate prediction of failure of progress to union, so that treatment designed to augment healing may be instituted without the delay which is inevitable with current clinical techniques of fracture healing assessment.
tibial tubercle by dropping onto it a 28 g steel ball down a perspex tube. The resulting acceleration of the tibia was measured at two points, the first 60 mm distal to the tibial tubercle and the other, 60 mm proximal to the medial malleolus. At each of these points on the antero-medial subcutaneous surface of the tibia, an accelerometer (Bruel & Kjaer 4369) was positioned and preloaded with a vertical force of between 3.2 and 6 N according to the method of Nokes et al’. The accelerometer outputs were displayed on a Gould 4000 oscilloscope which allows the simultaneous display of two traces. A permanent record of the signals was made on an x-y recorder. The apparatus is illustrated in Figure 1. Three groups of tibiae were studied. Group 1 was composed of 30 normal tibiae in 15 normal adults. These results were used to characterise the response of normal tibia and to compare the left and right bones in individual subjects. Group 2 numbered 20 patients with unilateral diaphyseal fractures and normal contralateral limbs. Measurements were obtained at various stages during healing, from immediately after injury till up to six months later. All these fractures were managed non-operatively and all went on to satisfactory clinical and radiological union. Group 3 consists of 2 patients with non-union.
The leg is a complex mechanical system, the properties of which are rofoundly altered by the resence of a fracture o the tibia, It is one K nction of the process of fracture repair to restore those mechanical properties to normal. The tibia’s vibratory response to an impulse has been studied and has been shown to change in a constant way as fracture healing proceeds. It is proposed that this change in vibratory response might form a method for the quantitative assessment of bone union.
F
MATERIALS,
PATIENTS
AND METHODS
A standard impulse of 0.045 Ns was applied to the *University of Wales Institute of Science and Technology, Cathays, Card%, UK *Prince of Wales Orthopaedic Hospital, Rhydlafar, Cardiff, UK tQueen’s Medical Centre, University Hospital, Nottingham, UK jThe Cardiff Royal Infirmary, Newport Road, Cardiff, UK 0 1985 Butteworth & Co (Publishers) 0141-5425/85/010040-05 $03.00 40
J. Biomed Eng. Vol. 7, January
Ltd
Figure 1 described
The apparatus
used to obtain the measurements
Vibration analysis: I_ Nokes et al
,+: Distaloccelmmeter
’ :.: signal
PA RBB Mainml amplitudes OfewhsjOml
SD 0.11; left leg: range 0.4 - 0.8, mean 0.54, SD 0.23). For a fractured tibia, regardless of the state of healing of the fracture, the trace from the proximal accelerometer is always normal (Figure 4). The difference in attenuation factor in the presence of a
A
Attenuation
,5ms
Factor = O-13
,
Acceleration recorded simultaneously from Figure 2 proximal and distal accelerometers over the intact right tibia of a 21 year old female
RESULTS The method used to apply a stimulus to the tibial a tubercle proved a reliable way of obtainin reproducible signal from both intact and isractured tibiae. A typical trace obtained from a normal tibia is illustrated in Figure 2. The ratio of the maximal amplitude of the distal accelerometer signal to the maximal amplitude of the proximal accelerometer signal (AA/BB Figure 2), is the attenuation factor (AI?.
II
Attenuation
The measured attenuation factors in Group 1 (i.e. normal tibiae) are given in the histogram illustrated in Figure 3. It is clear that the range of results follows a normal distribution. There was no difference between the left and right legs of individuals (right leg: range 0.4 - 0.8, mean 0.57, NORMAL
CONTROL
II
HISTOGRAMS
Attenuation
IO
n
No. of Tibiae
8
Factor = 0~ 32
Factor = 0.44
Attenuation
Factor = 053
6
Proximal accrkarmier AA6 BB
0.4
Histogram Figure 3 normal tibiae
0.6
0.7
Attenuation
factor
0.5
of attenuation
0.8
factors obtained from 30
t
5mr
hbrlmal mpltfudes of each sianal
Recordings taken from the patients with tibial shaft Figure 4 fractures at various stages of healing. (a) male age 27; left tibia at 2 weeks; (b) male age 17; left tibia at 8 weeks - moderate callus on X-ray; (c) male age 80; right tibia at 12 weeks tenuous radiological union; (d) male age 22; right tibia at 18 weeks - clinically and radiologically solid
1 Rinmed
Eng.
1985,
Vol.
7, [anuary
41
s
Vibration analysis: L Nokes et al
fracture is therefore entirely due to a diminished amplitude in the trace recorded from the distal accelerometer.
Attenuation
In a fresh fracture, such as that recorded in Figure 4a, minimal transmission of vibration occurs and the distal accelerometer signal has a very low amplitude. The attenuation factor is therefore also very low (0.13). As healing progresses, vibration is increasingly transmitted across the fracture site so that the amplitude of the distal accelerometer signal increases, as does the AF. Examples taken from fractures at 8 and 12 weeks are given in Figures 4b and c. When the fracture is clinically and radiologically united, the AF approaches the value for the normal intact limb (Figure 4d).
,‘-,
5ms
Figure 6 illustrates the trace obtained from a case of
hypertrophic non-union at 32 weeks. There is very little transmission of vibration across the fracture and the AF of 0.1 falls well below the curve in Figure 5. An exactly similar trace was obtained from a case of atrophic non-union seen at six months from injury. DISCUSSION It has been demonstrated* that the speed of sound in a material is a function of its elastic properties (in particular, Young’s modulus). Mathe showed that the strength of a bone was related to its geometry and Young’s modulus, and it was these fundamental observations that enabled Jurist?d to construct a series of models for the vibratory characteristics of the human ulna. From these, Jurist’ went on to make some observations on the relationship between bending stiffness, breaking
h
O-8. 0 7. Attenuotnn factor lh)
0 5.
strain and mineral content of bone and he related this work to osteoporosis. Pugh*, using a piezoelectric accelerometer to record the effects of an impulse applied to the heel, used Fourier spectral analysis to deduce a possible resonant frequency for the tibia of about 200 Hz. Using a similar technique to monitor fracture healing in humans, Lewis and Tati found that the swelling in the fractured limb created problems which made comparison with the normal limb difficult. These problems were investigated by Saha and LakeslO and later by Ziegert and Lewis”. In both papers it was concluded that the soft tissue was an important part of the system but the authors held contradictory views on how the accelerometers should be loaded so as to overcome soft tissue effects. Our own studies’ of this soft tissue problem have led us to conclude that it is necessary to preload the recording accelerometers sufficiently to overcome the damping effects of soft tissue, and that the re uired preload is proportional to the so9t tissue thickness.
iy+===a L
,.
2
,,,.,..,.
4
6
,
8
IO
12 14
I6
18 20 22
No of weeks Figure 5 Graph of time after fracture, plotted against attenuation factor for those tibiae that went on to satisfactory clinical union. 0 Test data; 0 model
42
I
In addition to the difficulties inherent in obtaining reproducable data from living bone, calculation of the frequency response of bone from its reaction to an impulse is problematic, not least because of the lack of any satisfactory theoretical model for the interpretation of the data. From the practical point of view, until recently fast Fourier transforms required mainframe computing facilities to get to a meaningful result within the few minutes that the routine clinical situation allows. It was for these reasons that we chose to ignore the actual frequency of the impulse response and to look instead at its pattern of propagation in real time.
I4$,
=037(
Distal accelerometer
Recordings taken from a male patient with a Figure 6 hypertrophic non-union at 32 weeks from injury. The AF = 0.1
When the attenuation factors for those tibiae that went on to satisfactory union are plotted against time after fracture (Figure 5), a curve results which rises rapidly in the first 8 weeks before tending to a plateau at 24 weeks. The extrapolated plateau is reached at the mean normal level illustrated in Figure3, which is derived from normal tibiae.
0.9.
factor
J. Biomed Eng. Vol. 7, January
24
Because the tibia is essentially a damped system, a proportion of the input energy is lost along the length of the intact bone and less energy is recovered at the distal end than was measurable at the proximal end. Thus the normal value for the attenuation factor of the intact tibia by this technique is in the region of 0.57 and is not unity.
Vibration analysis: L Nokes et al
A predetermined anatomical site for the lacement of the accelerometers was decided upon f!or this study. It is apparent that the chosen fured points, 60 mm distant from bony landmarks, results in a transfer distance that varies from patient to patient and which is proportional to the height of the individual. The error introduced by an inconstant transfer distance is small in practice, and in fact is insignificant in relation to the changes occasioned by the presence of the fracture. What is more, in the event of any doubt in an individual case, as to the significance of a particular result, it may be compared to the normal contralateral limb over the same transfer distance. A rising attenuation factor, as illustrated in Figure 4, correlates well with the clinical and radiological evidence of union. Figure Z, which is constructed from the results in tibiae that healed normally, forms a model against which the healing of tibial diaphyseal fractures can be measured. The curve ap roaches a plateau at 24 weeks at which time sur;-icient consolidation of the fracture has taken place to render the mechanical response of the bone normal. The plateau is reached at the level predicted by the observations made on the normal tibia (i.e. 0.57, Figure 3). Initially the curve rises rapidly so that by 8 weeks, nearly two thirds of the expected rise in attenuation factor has already occured. What the actual strength of the bone is at this time is not yet known and there are practical difficulties in making measurements of strength or stiffness in living subjects. Clearly, testing of human fracture to destruction is not possible and there are dangers in inferring too much from animal studies. None the fess, we confidently expect that some quantitative point on the healing curve will prove to be a reliable indicator of the time at which a healing fracture may be left unsplinted, so minimising the time for which the injured limb is immobilised. The two cases of non-union suggest that the attenuation factor might be an indicator of this complication of fracture healing. However, we have yet to show that failure to follow the normal healing curve occurs sulficiently reliably and suficiently early for the technique to have a useful predictive value for the behaviour of fractures. The apparatus used for this study has been somewhat clumsy in use but has been modified since and is now much easier to use. Measurements have been made at routine plaster changes although it is quite possible to position the accelerometers through small holes in the plaster. We have no data on the influence of a whole leg plaster cast on the transfer of vibration along the bone but suspect that it would be slight. Patients with removable braces pose no problems. In the first few weeks following injury, oedema damps the output signals and requires relatively high accelerometer preloads which can be uncomfortable for the patient.
As a method of following the progress of fracture union, this technique has the great advantage over radiography that it avoids the time lag that is built into X-ray dependence on the mineralisation of healing tissue. Any inference from radiographs, about the mechanical state of the fracture, is necessarily subjective and in reality only relates to the visible mineralized callus and not the whole callus mass. In the first six weeks, when the changes at the fracture site are most rapid, radiographs may yield no useful information except about the position of the fracture fragments, while at the same time the AF mi ht have risen half way to normal. Conversely, i P at two months the X-ray shows abundant callus but the AF is low, then perhaps a hypertrophic non-union might be predicted. The technique described is likely to be invalid as a method of assessing fracture callus in the presence of an implant used to secure fixation of the fracture since, under these conditions, vibration may pass along the implant, even in the absence of any bone contact. The results obtained using this technique would seem to allow quantitative comparisons of differing methods of non-operative fracture management. CONCLUSIONS The pattern of vibration transmission along the fractured tibia changes with time in a way that reflects the healing of the fracture. The technique described has promise, both as a research tool for the quantitative comparison of non-operative methods of fracture management, and as a clinical aid to decision making.
ACKNOWLEDGEMENTS This work was supported by a grant from the Endowment Fund for Research of the South Glamorgan Area Health Authority. The illustrations were prepared by the Department of Medical Illustration at the University Hospital of Wales. REFERENCES Nokes L., Fairclough J.A., Mintowt-Czyz W.J., Mackie I. and Williams J. Vibration analysis of human tibia: the effect of soft tissue on the output from skin mounted accelerometers. J Biomed Eng. 1984, 6, 223-229 Rowe R.G. Vibration apparatus for testing articles. US Patent No. 2,486,984; 1949 Mather B.S. Comparison of two formulae for in vivo prediction of the strength of the femur. Aerospace Med, 1967, 38, 1270-1272 Jurist J.M. Determination of the elastic response of bone: method of ulnar resonant frequency determination. Phys. Med. Biol 1970, 15, 417-426 Jurist J.M. In vivo determination of the elastic response of bone: ulnar resonant frequency in osteoporotic, diabetic and normal subjects. Phys. Med Bio/, 1971, 15, 427-434 Jurist J.M. and Kianian K. Three models of the vibrating u1na.J. Biomech, 1973, 6, 331-342
J. Biomed Eng. 1985, Vol. 7, January
43
Vibration analysis: L Nokes et al 7
8
9
44
Jurist J.M. Human ulnar bending stiffness, mineral content, geometry and strength. J Biomech, 1977, 10, 455-459 Pugh J.W., Streitman A. and Stanoch J.F. Studies of the impact response of human limbs. 28th ACEMB Meeting, New Orleans, Sept. 1975, 171 Lewis J.L and Tan R.R. Fracture healing assessment by
J. Biomed
E “g.
Vol. 7, January
10
11
impact response.,J. Bone Jt Surg., 1975,57A, 576 Saha S. and Lakes R The effect of soft tissue on wave propagation and vibration tests for determining the in vivo properties of bone. J. Biomech 1977, 10, 393-401 Ziegen J.C. and Lewis J.L. The effect of soft tissue on measurements of vibrational bone motion by skin mounted accelerometers. J Biomech 1979, 12, 218-220