Archives of Orthopaedic and Traumatic Surgery
Arch Orthop Trauma Surg (1984) 102: 242-247
© Springer-Verlag 1984
The Stability of Union in Tibial Shaft Fractures: Its Measurement by a Non-Invasive Method P Edholm l, R Hammer2, S Hammerby', and B Lindholm' Departments of 'Diagnostic Radiology and 2 Orthopedic Surgery, Link 6 ping University Medical School, S-58185 Link 6ping, Sweden
Summary The stability of the union in tibial shaft fractures was followed by repeated non-invasive radiographic measurement of a deflection induced in the area of the fracture By means of a Shift Comparator the difference in the angle between the two fragments before and during application of the deflecting force can be measured The relative measure of the strength of the union is furnished by a quantity, the deflection ratio, which is based on the quotient of the induced deflection by the magnitude of the applied bending moment When this ratio falls below a certain value the union is considered to be stable enough for full weight bearing during walking A plot of the deflection ratio against time, with logarithmic scales on both axes had a negative slope and was more or less linear. This graph can serve as an aid in detecting the course of union, in deciding when the cast should be removed, and in detecting any irregularity in the process of union In the management of 207 fractures of the tibial shaft 508 such deflection measurements were performed. Zusammenfassung Die Stabilitiitsentwicklung von 207 Tibiafrakturen wurde mit einer nichtinvasiven Untersuchung verfolgt Vom Unterschenkel werden in einem standardisierten Verfahren ap-R 6 ntgenaufnahmen mit und ohne Biegemoment gemacht Diese werden in einem optischen Apparat (Komparoscop) verglichen Der Deformationswinkel kann so mit gro13 er Sicherheit bestimmt werden Aus dem Biegemoment und dem Winkel ergibt sich eine DruckDeformationsbeziehung Dieser Wert wird fuir das Gewicht des Patienten korrigiert Wir nennen ihn ,Deflektionsrate" Nach unseren Erfahrungen ist die Stabilitit bei kleineren Werten als 0,08 ftir volle BeOffprint requests to: R Hammer, MD (address see above)
lastung beim Gehen ausreichend Die ,,D-Raten" werden in ein doppellogarithmisches Koordinatensystem eingetragen Die meisten Frakturen zeigten dabei eine gradlinige Stabilitatsentwicklung Ein Abweichen vom geraden Verlauf ist als Hinweis auf eine Pseudarthrosenentwicklung zu verwerten. The process of union in tibial shaft fractures is not infrequently disturbed l1,6,12,14 l Despite the many clinical and experimental investigations on this type of fracture and the excellent review articles dealing with its etiology and classification l 12 l, its initial treatment and complications l 10l, there is still no universally accepted definition of the state of stable union l2,5,7l This deficiency stands in the way of reliable evaluation of the available methods of treatment. Because clinical evaluation l2,11l and conventional X-ray examination furnish insufficient information concerning the mechanical properties of the fracture callus l13l a number of methods for evaluating the state of union have been designed, and a critical evaluation of some of these was presented by Hayes in 1980 l7l. Direct measurement of the stability of union of tibial shaft fractures in vivo presents a number ofpractical difficulties For example, the soft tissue covering and adhering to the tibia makes it difficult to detect the small deformations that must be induced and measured in the mechanical testing of stability. Repeated determination of the stability of union was performed directly in vivo in two extensive investigations conducted by Jernberger in 1970 l8l, and J 6rgensen in 1972 l9l Interesting basic information concerning the process of union was derived, but both methods suffer from the disadvantage that they entail the use of pins inserted directly into the fragments.
P Edholm et al : Stability of Union in Tibial Shaft Fractures
243
In the present study, a non-invasive technique for progressive measurement of the stability of the union was examined With this method it is possible to determine this stability in the case of fractures treated conservatively or with an external fixation device.
With no bending moment applied to the leg, a radiograph is exposed in ap projection Without any other change in the conditions a weight is placed on the holder, and the second radiograph is exposed When first measured, the selected weight is always low (2 kg) The deflection is measured with the patient still on the examination couch. Measuring Procedure
Method An elastic body to which a force is applied undergoes deformation For small and moderate deformation there is a direct linear relationship between the magnitude of the deformation (the strain) and the applied force (the stress), and the quotient of strain by stress is proportional to the elasticity of the material l3l Callus may be regarded as an essentially elastic material, and during union its rigidity increases gradually to that of the intact bone l9l. The principle of the method presented here is that during union a bending moment is applied to the site of fracture so as to produce a small deflection of one fragment in relation to the other This deflection is then measured The quotient of the deflection by the bending moment multiplied by a weightstandardizing factor is directly related to the strength of union. This measure is arrived at in three stages, the first of which is an X-ray examination in which films of the lower leg are exposed before and during application of a bending moment to the site of fracture The second stage is the measuringprocedure, in which the deflection is measured by comparing the two radiographic images with the aid of an instrument known as a Shift Comparator The X-ray examination and the measuring procedurehave been described in an earlier publication l4 l and are essentially the following:
X-Ray Examination The patient is placed on an examination couch in the supine position The foot of the fractured leg is immobilized in a shoelike holder on a small carriage that can move in the mediolateral direction (Fig 1) The safety line is slack enough to permit a deflection of a few degrees.
The measurements are performed with a specially designed instrument, the Shift Comparator l4l, which consists of two light-boxes, one on each side of a semi-transparent mirror. On each light-box one of the films is placed, one of them the right way around and the other reversed The semi-transparent mirror brings the mirror image of the reversed film into coincidende with the image of the second film The two lightboxes are automatically switched on and off so that the two films are shown alternately in the same optical position On one of the light-boxes there is a film carrier by means of which the position of the film can be adjusted The carrier consists of a ring with two sharp points; these are pressed on the film which is thus affixed to the ring By means of three screws the film carrier together with the film can be translated in two perpendicular directions and rotated about the center of the carrier ring. By means of the carrier one of the films is adjusted in the Comparator so that the image of the proximal fragment of the tibia appears to remain stationary The deflection of the distal fragment of the tibia will then be perceived as an oscillatory rotation about a center located in or near the space between the two fragments (Fig 2). The carrier is placed over the fracture space where the center of rotation is considered to be located This movement is now eliminated by rotating the film under the carrier in the opposite direction about this center The distal fragment will then appear to be stationary, and it is now the previously stationary proximal fragment that moves The relative displacement of the two fragments can be measured as the angle of the compensatory rotation of the film carrier This angle is taken as a measure of the deflection at the site of union. If the observed deflection is less than 0 50 the procedure is repeated with a larger bending moment until the deflection exceeds 0 50 or until a weight of 8 kg has been applied If, however, the patient should report pain the examination should be discontinued. The third stage consists in the calculationof a measure of the stability of union, the deflection ratio (DR).
-
I
-F
IF Fig 1 The device used for inducing deflection of the tibia shaft Two films are exposed, one before and a second during application of a bending moment to the site of fracture
Fig 2 The deflection of the tibia shaft seen in the Shift Comparator is perceived as an oscillatory rotation about a center located in the fracture space
244
P Edholm et al : Stability of Union in Tibial Shaft Fractures
Calculation
Table 1 Distribution of the 207 patients and 508 measurements by number of measurements performed in each
The deflection ratio is calculated from the expression DW Deflection ratio (DR) = M 75 is the deflection in degrees where D M is the bending moment, in Newton meters W is the weight of the patient, in kilograms, and W/75 is a weight-standardizing factor The bending moment Mis the product of the tension in the traction line and the distance from the point in the fracture that is taken as the center of motion, to the tip of the lateral malleolus, at which level the traction line is fastened to the carrier of the patient's foot The forces acting at the site of union when the leg is bearing the whole body weight are proportional to this weight For this reason, the quotient D/M has been corrected for the weight of the patient by multiplying it by a standardizing factor, W/75 For a body weight of 75 kg the deflection ratio thus gives the deflection for a bending moment of 1 Nm.
Errors of the Method During the radiographic examination one or both fragments may be inadvertently rotated slightly about their longitudinal axes, with the result that during adjustment in the Shift Comparator it will be impossible to keep one of the fragments quite stationary. Its longitudinal axes, however, may be kept stationary, and the fragment will then appear to oscillate with a rotatory motion through a small angle about this axis Such a rotation will decrease the precision of deflection measurement because this must now be based on an adjustment in the Shift Comparator which keeps the axis of the fragment stationary instead of the fragment itself. This rotation has several possible causes First, the geometry of the fracture space may be such that the deflection at the site of the union does not occur about a sagittal axis through the space, but about an axis forming an angle with it Such a deflection may be resolved into two components, namely, a medial deflection-i e , a rotation about a sagittal axis-and a rotation about the longitudinal axis of the fragment. Another possible cause of the rotation lies in the fact that the direction of the tractive force in the radiographic examination does not pass through the extension of the axis of the proximal fragment, with the result that there is a turning moment which may rotate the lower leg slightly about his axis. Neither fragment can then be kept quite stationary in the Shift Comparator. Such a turning moment may be due to a ventral or dorsal angulation at the site of union Any small rotation due to such a malposition will be perceived as a deflection in the Shift Comparator. The observed deflection will then be larger than the true value A rotation of the tibial shaft can sometimes be detected by direct inspection during X-ray examination, and it can invariably be confirmed by measurement in the Shift Comparator Any turning moment may be eliminated by a dorsoventral adjustment of the point at which the traction line is secured to the carriage New films are then exposed It was always possible to reduce, if not eliminate, a turning moment in this way, and hence to determine the deflection. The accuracy of the deflection measurement is thus largely dependent on the extent to which a rotatory component can be avoided.
No of measurements No of patients
1 90
2 38
3 32
4 18
>4 29
Total no of measurements
90
76
96
72
174
From the material, radiographs relating to 11 deflection determinations were chosen for which the measurement presented varying degrees of difficulty The deflections were measured by four radiologists who had no knowledge of the results of the original measurements The standard deviation (SD) in these observed values were determined from the following expression: 11
4
i= 1 j=l
11 (4
1)
The SD of the deflection measurements was 0 190 This value was considered as an estimation of precision and will be referred to as one unit of SD of the method.
Patients and Material During the period from 1972 to 1981 a total of 508 measurements were carried out on 207 patients with 207 fractures of the tibial shaft (Table 1). During this period the measurements were not performed on all the fractures because the fracture treatment was carried out at two different departments of the hospital between which there was some difference in the principles applied In addition, the measurement method was not always available throughout the period This situation has probably resulted in a tendency to submit patients to stability measurements in cases where clinical and conventional radiographic examinations did not furnish a definitive evaluation.
Results To be able to follow the progress of union, as this is manifested by the deflection ratio, the recorded values of this variable were plotted against the time elapsing between the occurrence of the fracture and the performance of the measurement Logarithmic scales were used on both axes to furnish a more compact graph. The values of the ratio obtained for the patients have been plotted in five graphs (Fig 3), which correspond to the five groups in Table 1. Three stability limits are indicated by the three horizontal lines as deflection ratios of 0 3, 0 03, and 0.08 Above 0 3 the union is so unstable that values are unreliable This is presumably due to the fact that in these cases the bending moment to be applied is so small that the deflection is influenced by friction and other factors in a manner difficult to analyze.
245
P Edholm et al : Stability of Union in Tibial Shaft Fractures DR
Deg/Nm)
_ 0.5 r (03
0.1
0.05 0.0
0.01. 2
1
3
4
5
12 24 TIMEAFTER FRACTURE(Month)
6
a
1
D/I
d DR
(Oeg/Nm)
TIME AFTER FRACTURE(Month)
(Deg/Nm)
7 C
q.5
0.5
(0.3) -
(0.3)
+
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,
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++
++ *
++++ 4+++
++ +
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. 1
+
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0.05 (0.03) -
+
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.Ill
I
i
'11111
12 24 TIMEAFTER FRACTURE(Month)
e
111 2
3
4
5
,
12 24 TIMEAFTER FRACTURE(Month)
Fig 3a-e Variation of deflection ratio with time, i e , the period of union reckoned from the time of fracture a One measurement during union; 90 tibial shaft fractures b Two measurements during union; 38 fractures c Three measurements during union; 32 fractures d Four measurements during union; 18 fractures e More than four measurements during union; 29 fractures
DR
0.1
0.1
0.05
0.0 2 C
3
4
S
6
12 24 TIMEAFTER FRACTURE(Month)
On the other hand, at values below 0 03 the fractures are so stable that even with the maximum bending moment applied the deflection is so small in relation to the SD of the method that the deflection ratio values obtained here are unreliable, too When the
union has attained a level of stability, such that the true deflection ratio is 0 08 or less, it is considered strong enough for the patient to be permitted to load the leg with the full weight while walking, without any external supporting device If the calculated deflection ratio is less than 0 08 the union is classed as presumably stable The addition of one unit of SD ( 0 19° ) to the recorded deflection may, of course, bring the actual value above 0 08, but if it remains below 0 08, the union is considered to be probably stable If the value is still under 0 08 when two units of SD have been added to the deflection, the union is graded as definitely stable Analogously, three levels of stability can be constructed for values of the deflection ratio above 0 08.
246
P Edholm et al : Stability of Union in Tibial Shaft Fractures
NUMBER OF MEASUREMENT
In 21 patients on whom stability measurements were performed three radiographs were exposed, one before, a second during loading, and a third when loading had been discontinued The values of the deflection ratio ranged from 0 to 0 3 When the measurements were completed, the first and third images were compared in the Shift Comparator Any change in the position of a fragment caused by the deflection would have been observed as a small deflection in the Comparator In none of the patients was any such change seen The deflection thus produced no lasting deformation large enough to be observed in the Comparator. When process of union has commenced, stability seems to increase continuously, indicating that the measuring procedure itself did not affect the course of union.
;,
Fig 4 Histogram showing the frequency distribution of the 508 stability measurements by deflection
In the calculation of the deflection ratio in clinical practice one unit of SD (0 190) has been added to the deflection This implies a safety margin so that, in the case of fractures where the cast has been removed and the patient has begun to load the leg when walking, the union is classed as probably stable. In no case did full loading of the leg when the deflection ratio was less than 0 08 result in recurrence of the fracture In eight cases the ratio increased to more than 0 08 after full loading had been permitted; no dislocation or fracture line was detected in the radiograph In two of these eight patients the ratio increased to 0 28 and 0 31; both had disregarded instructions and overloaded the affected leg For one of them union occurred after prolonged cast immobilization, while for the other the fragments failed to unite, and surgical intervention was necessary. For the remaining six patients the deflection ratio had increased to between 0 12 ± 0 01 (mean ± 1 SD). The treatment consisted in partial relief of load by means of crutches At the next measurement the value was less than 0 08 The subsequent course was uncomplicated. The deflection induced in the 508 measurements ranged from 0 to 3 60, but it usually lay at 0 70 (Fig 4). Deflections measured when DR 0 08, and full unprotected weight bearing was permitted, ranged from 0 to 1 7° (O5 + O3 ; mean ± 1 SD) If the instructions for the measuring procedure had been strictly followed, no deflection would have exceeded 1 60 or thereabouts, and higher values are therefore probably due to departures from the measuring procedure No complications were recorded during the measuring procedure On no occasion was the deflection so large as to stretch the safety line.
Discussion The direction of the tractive force applied to the distal fragment was chosen on the basis of the findings of a pilot study conducted on 11 fractures Lateral, ventrolateral, ventromedial, medial, and dorsal directions were tested In all the experiments, however, the tractive force was directed perpendicular to the longitudinal axis of the tibial shaft. The reproducibility of the measurements was best for the medial and lateral directions During traction the sling stabilizes the proximal fragment With the lateral direction the effect of the sling was poorer because the soft tissues laterally on the lower leg are resilient With the medial directions of the tractive force, on the other hand, the stabilizing effect of the sling on the proximal fragment was good because the sling could be applied directly against the medial surface of the tibia The medial direction of traction was therefore chosen for the study. The choice of the 0 08 level of the deflection ratio was in principle based on empirical factors, with some support from the values published by Jrgensen in 1972 l 9l. However, Jrgensen did not correct the deflections for the weight of the patient, and only fractures treated by Hoffman's external fixation device were measured. In 90 cases (Fig 3a), stability measurements were performed on only one occasion during the process of union In all these cases determination of the deflection ratio was done because the stage of union, when based on clinical examination and conventional X-ray images, did not furnish definitive evaluation In 77 cases, deflection ratio was calculated to be less than
P Edholm et al : Stability of Union in Tibial Shaft Fractures
247
0.08, and in all these cases the cast was abandoned, full weight bearing permitted, and the subsequent course was uncomplicated Based on medical documentation for these 77 fractures, cast immobilization would have been prolonged if the stage of union had been based on conventional clinical methods. Since in the graphs plotted with logarithmic scales the deflection ratio for most of the patients appears to have decreased more or less linearly with time, it is possible to determine by extrapolation the time at which stability of union may be expected to have increased to the point where the ratio is below 0 08. In the few patients where the curve deviated from linearity there was presumably a disturbance of the process of union This type of graph therefore furnishes the possibility of detecting any such anomaly. In cases of delayed union, unnecessary surgical measures can be avoided when repeated determinations of the deflection ratio indicate progressive increase in stability It is thus possible to distinguish between delayed union and true non-union.
analysis of very small movements Acta Radiol Scand 24: 267-272 Edwards P, Nilsson BER (1965) Graphic representation of healing time in fractures of the shaft of the tibia Acta Orthop Scand 36:104-111 Edwards P (1965) Fracture of the shaft of the tibia: 495 consecutive cases in adults Acta Orthop Scand lSuppll 76 Hayes WC (1980) Biomechanics of fracture treatment In: Heppenstahl RB (ed) Fracture treatment and healing. Saunders, Philadelphia, pp 124-172 Jernberger A (1970) Measurement of stability of tibial fractures A mechanical method Acta Orthop Scand lSuppll 135 Jorgensen TE (1972) Measurements of stability of crural fractures treated with Hoffman-osteotaxis II Measurements on crural fractures Acta Orthop Scand 43 :2 07-218. -III The uncomplicated terminal phase of healing of crural fractures Acta Orthop Scand 43: 264-279 IV The complicated terminal phase of healing of crural fractures. Acta Orthop Scand 43: 280-291 Karlstr 6m G, Olerud S (1974) Fractures of the tibial shaft-a critical evaluation of treatment alternatives Clin Orthop 105: 82-115 Matthews LS, Kaufer H, Sonstegard DA (1974) Manual sensing of fracture stability A biomechanical study Acta Orthop Scand 45:373-381 Nicoll EA (1964) Fractures of the tibial shaft, a survey of 705 cases J Bone Joint Surg lBrl 46: 373-387 Nicholls PJ, Berg E, Bliven FE, Kling JM (1979) X-ray diagnosis of healing fractures in rabbit Clin Orthop 142: 234-236 Watson-Jones R, Coltart WD (1943) Slow union of fractures with a study of 804 fractures of the shafts of the tibia and femur Br J Surg 30: 260-276
References
5 6 7 8 9
10 11 12 13
1 Bauer GCH, Edwards P, Widmark PH (1962) Shaft fractures of the tibia Etiology of poor results in a consecutive series of 173 fractures Acta Chir Scand 124: 386-395 2 Brown PW (1974) The early weight-bearing treatment of tibial shaft fractures Clin Orthop 105 :167-178 3 Carter D, Spengler D (1978) Section III Basic science and pathology Mechanical properties and composition of cortical bone Clin Orthop 135 :192-217 4 Edholm P, Hammer R, Hammerby S, Lindholm B (1983) Comparison of radiographic images; a new method for
14
Received November 8, 1983
