Journal of Pediatric Orthopaedics Part B 10:248᎐254 䊚 2001 Lippincott Williams & Wilkins, Inc., Philadelphia

Fracture Stiffness in Callotasis Determined by Dual-Energy X-Ray Absorptiometry Scanning George Tselentakis, F.R.C.S.,U P. Julian Owen, F.R.C.S.,† James B. Richardson, M.D.,U Jan Herman Kuiper, Ph.D.,U Mike J. Haddaway, Ph.D.,U Jonathan S. M. Dwyer, F.R.C.S.,U and Gwyn A. Evans, F.R.C.S.U U

Robert Jones and Agnes Hunt Orthopaedic Hospital, Oswestry, Shropshire, UK; and †St. George’s Hospital NHS Trust, Blackshaw Road, Tooting, London, UK

Summary: Assessing healing after distraction limb lengthening is essential to manage patients undergoing callotasis for leg lengthening or bone transport. Direct measurement of fracture stiffness can assess healing but the equipment may not be available. In addition, it requires removal of the fixator, which may be complicated for ring fixators. The present study investigates whether an equivalent measure of healing can be based on the mineral density pattern from dual-energy X-ray absorptiometry ŽDXA. scans. Nine consecutive patients undergoing callotasis were studied. Bending stiffness of the distraction segment was measured and DXA scans were performed

regularly starting 6 weeks after completing distraction. In all, 23 simultaneous readings of bending stiffness and DXA scans were obtained. All density patterns showed a distinct minimum value of bone mineral density. We found a high and significant correlation between fracture bending stiffness and the square of the total mineral content at the location of minimum bone density Ž r 2 s 0.77, P0.001.. We conclude that DXA scans can be used reliably and effectively to determine fracture bending stiffness, valuable for determining both time of frame removal and delay in union. Key Words: DXAᎏAbsorptiometryᎏCallotasisᎏFracture stiffness ᎏNonunion.

Timing frame removal is a particular problem for fractures managed by external fixation. De Bastiani et al., using an Orthofix for tibial fractures, reported refracture as one of the few major complications, affecting 3% of patients Ž4.. Other workers report rates of 5% to approximately 11%, depending on the method of external fixation used Ž14,24,25.. In limb lengthening procedures, exact timing of frame removal is even more important. Ilizarov remarked that ‘‘leaving the apparatus on for longer than is necessary is as harmful as removing the fixator too early’’ Ž13.. Measuring fracture bending stiffness has provided a useful method to monitor healing of fractures and distraction segments and to time frame removal Ž5,22.. The authors of these studies suggested the probable safe limit for frame removal was a stiffness of 15 Nmrdeg in the tibia and 20 Nmrdeg in the femur. Dual-energy X-ray absorptiometry ŽDXA. scans

provide an alternative method of assessing healing. They can be taken during limb lengthening procedures to monitor bone formation Ž7,8.. In an animal study, nonunion could be predicted with high sensitivity on the basis of DXA scans Ž17.. For mature bone, relations between bone density and bone stiffness have been well established Ž1,21.. In a canine model of tibial lengthening, these same relations were shown to hold for the healing distraction segment Ž21.. The objective of the present study is to investigate whether a correlation exists between bending stiffness of a healing lengthening segment and the mineral density pattern as obtained from DXA scans. MATERIALS AND METHODS Patients Nine consecutive patients undergoing leg lengthening or bone transport procedures were studied ŽTable 1.. Five patients had a congenital shortening of either the femur or the tibia. In four patients, the shortening was because of trauma. Their age ranged

Address correspondence and reprint requests to G. Tselentakis, F.R.C.S., 74 Rowan Croft, Clayton Le Woods, PR6 7UX, UK.

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TABLE 1. Data on patients, comparison of healing times using direct stiffness measurements and dual-energy X-ray absorptiometry (DXA)-deri¨ ed ¨ alues and correlation between minimimr maximum DXA ¨ alue and fracture stiffness on indi¨ idual patients Case

1 2 3 4 5 6 7 8 9

Age Žyears.

Sex

Site

Diagnosis

Lengthening Žmm.

Direct stiffness Žweeks.

DXA derived Žweeks.

Number of data points

Minimum DXA r2 value

P value

16 14 16 15 64 31 30 16 21

F F M F F M M M M

T F F T T T T T F

Congenital Congenital Congenital Congenital Nonunion Traumatic loss Infection Congenital Traumatic loss

40 64 39 44 16 90 37 43 60

28.9 18.2

27.2 18.8

0.998 0.79

0.001 0.043

0.98 0.87

0.008 0.02

19.7 22.3 18.9 21.9

21.7 22.1 21.7 22.2

4 5 1 1 1 2 2 4 3

0.97 0.97

0.017 0.11

0.84 0.999

0.084 0.003

Maximum DXA r2 value

P value

T, Tibia; F, Femur.

between 14 years and 64 years, with a mean age of 24 years. The average acquired length was 50 mm Žrange, 16᎐90 mm.. The Orthofix lengthening external fixator was used. A modified De Bastiani osteotomy was performed. Distraction of the bone started 10 days after the operation, at a rate of 1 mmrday by lengthening 0.5 mm twice a day. Mobilization of the patient started immediately postoperatively. The consolidation period was 6 weeks. Simultaneous measurements of fracture stiffness and DXA scans were obtained starting 6 weeks after the end of lengthening. Where scans and stiffness measurements were obtained on different days, those measurements were not included in the study. We used the estimated time of healing Ž22. to follow-up our patients unless otherwise clinically indicated. The fracture stiffness was used as the criterion to remove the fixators from the patients. We used 15 Nmrdeg and 20 Nmrdeg as end points for the tibia and femur, respectively Ž5.. Direct stiffness measurement The technique used involved temporary removal

FIG. 1. Method of fracture stiffness measurement.

of the fixator. Clamps were applied separately to each set of pins, enabling the attachment of a goniometer ŽPenny and Giles Biometrics Ltd., Blackwood, Gwent, UK. to measure angular displacement. A force plate was placed at a known distance from the distal margin of the distraction segment ŽFig. 1.. A force was applied manually to the distraction segment, and both bending angle and force were measured. The bending angle was kept between 0.5⬚ and 1⬚ for each assessment. The bending stiffness was taken as the quotient of applied bending moment and resulting bending angle. A series of five measurements was performed in the sagittal plane, and the average stiffness was calculated. A hand-held microcomputer Ž‘‘Orthometer’’; Orthofix, Verona, Italy. was used for this purpose. The thus determined fracture stiffness was used as a criterion to remove the fixators from the patients. We used 15 Nmrdeg and 20 Nmrdeg as end points for the tibia and femur, respectively Ž5.. DXA scanning protocol The principles of bone densitometry using DXA have recently been reviewed Ž20.. We used a Hologic QDR 1000 dual-energy X-ray absorptiometer ŽHologic, Waltham, MA, USA. to scan the distraction site of the patients. The patients were positioned supine with the limb held using the standard positioning frame used for DXA scanning of the hip. Repositioning for subsequent scans was achieved using this positioning frame. To ensure that approximately the same region was scanned every time, an individual landmark was chosen for each patient to aid repositioning for subsequent scans. Patients were scanned in the ‘‘hip mode’’, which means rectilinear scanning was performed in a head-to-foot direction. We used the ‘‘hip-metal removal’’ Žor ‘‘High Density Detection’’. analysis protocol, which omits areas of very high density Žfixator, pins. before calculating bone mineral densities. The calculated bone density distribution in the limb Žgrcm2 . was displayed and further analysed. J Pediatr Orthop Part B, Vol. 10, No. 3, 2001

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G. TSELENTAKIS ET AL. or linear density. This value has been used as predictor of whole bone strength Ž23.. The area under the profile, the squared area, the minimum DXA value along the axial line ŽFig. 2B. and the maximum DXA value along the transverse line ŽFig. 3B. were then correlated with the directly measured bending stiffness to determine a possible link. These four parameters express, in different degrees, the material and the geometric characteristics of the distraction segment in the selected area of interest.

FIG. 2. A: Dual-energy X-ray absorptiometry scan with axial analysis line. B: Axial bone mineral density profile. Arrow indicates the point of minimum density of distraction segment.

Analysis of the DXA scan In the computed density distribution, a line was drawn along the bone axis and through the distraction segment ŽFig. 2A.. Along this line, an axial profile of bone mineral density Žgrcm2 . versus position was determined ŽFig. 2B.. Each density value on this profile is the average mineral density over a width of 19 mm, which is approximately the full bone width. This averaging procedure was chosen to ensure consistency and reduce noise. At the level of minimum density, which was considered the weakest level, a transverse line was centred. Along this line, a transverse mineral density profile was determined ŽFig. 3B.. The transverse profile was again calculated as the average bone density over a width of 19 mm. The transverse profile was captured and from it the width of the distraction section, the maximum density value and the area under the profile were determined using image analysis software ŽNIH image, http:rrrsb.info.nih.govrnih-imager.. The area under the profile represents the total calcium content per unit of bone length Žgrcm. in the cross-section,

FIG. 3. A: Dual-energy X-ray absorptiometry scan with transverse analysis line. B: Transverse bone mineral density profile at the level of minimum density. J Pediatr Orthop Part B, Vol. 10, No. 3, 2001

Comparison between healing times derived from direct stiffness measurements and DXA parameters During healing, the bending stiffness of a fracture and a distraction segment rise exponentially in time Ž5,22.. By fitting an exponential equation through the time versus stiffness data, one can pinpoint the time since end of lengthening to reach a specific bending stiffness. A tibia with a stiffness of 15 Nmrdeg, or a femur with 20 Nmrdeg, is regarded healed and the time has been defined as healing time Ž5,22.. For each patient with at least two measurement points Žthe minimum to fit an exponential equation., we calculated a healing time on the basis of both the directly measured stiffness and the DXA-derived stiffness. For the latter calculation, we used the DXA-derived parameter, which provided the best overall correlation to direct stiffness. RESULTS We obtained 23 simultaneous measurements of fracture stiffness and DXA scans. Fourteen of the measurements were on tibial segments and 9 were on femoral segments. Fifteen of the measurements were on segments with congenital conditions and 8 were on segments with traumatic conditions. All density patterns were characterized by a region of lower density at the location of the distraction segment with a distinct minimum value of bone mineral density. Linear correlations were determined for directly measured stiffness versus minimum axial and maximum transverse density, and versus area and squared area ŽFigs. 4᎐7 and Table 2.. All correlations were highly significant. The highest correlation between measured stiffness and DXA-derived parameters Ž r 2 s 0.77, P- 0.001. was found using the squared area, i.e., the squared total calcium content per unit of length or squared linear density. The best-fit line between this parameter and stiffness was: stiffness s 1.81= Žlinear density. 2 . Although minimum axial and maximum transverse density did not correlate well with measured stiffness when all patients were lumped, there was a high and, in most cases, significant correlation for all

FRACTURE STIFFNESS IN CALLOTASIS

FIG. 4. Linear correlation between area 2 , as derived from dual-energy X-ray absorptiometry scan, and fracture stiffness.

individual patients of whom we had acquired at least three simultaneous measurements Žthe minimum number to make a correlation; Figs. 8 and 9, and Table 1.. On the basis of the best DXA-derived parameter Žsquared area., we calculated healing time. Healing time based on DXA was, in most cases, slightly longer than the time based on direct stiffness measurements ŽTable 1.. The average absolute difference between the two methods was 8.8 days Žaverage difference, 4.6 days., compared with an average healing time of 151 days. DISCUSSION Many authors have studied noninvasive methods to determine the mechanical properties of bone Ž7,8,12,16,18,19.. The potential uses of these noninvasive techniques include the monitoring of fracture Ž16᎐19. and callotasis Ž7,8. healing. DXA scanning is now established as the most common method of determining the degree of mineralization of bone Ž6,10.. Compared with other noninvasive methods, DXA has many advantages, including low radiation dose, short scanning time, increased image resolution and improved precision Ž3.. Measuring healing times or timing fixator removal, however, requires a definite end point. Eyres et al. attempted to derive a criterion based on DXA

251

FIG. 6. Linear correlation between maximum density (max. dens.), as derived from dual-energy X-ray absorptiometry scan, and fracture stiffness.

scans, and suggested removal of the fixator when the density of the newly formed bone has reached 75% of the normal density Ž7.. Fracture stiffness has been shown to be a reliable end point for fracture healing Ž22., and preliminary work shows it to be equally useful in callotasis Ž5.. In addition, fracture stiffness serves to compare the healing progress between patients and can identify slow healers. We believe that this is the first study to correlate clinically measured values of fracture stiffness and DXA-derived parameters to establish the potential of DXA as an endpoint. In the present study, we found that the minimum DXA value in the axial direction or the maximum DXA value in the transverse direction correlated well with bending stiffness for individual patients, with a coefficient of determination r 2 s 0.8 and higher. These two DXA values represent the calcium content of the most flexible part of the segment. The most flexible part is the main determinant of bending stiffness. Our results suggest that these two DXA-derived parameters are useful to monitor patients on an individual basis. The coeffi-

FIG. 7. Linear correlation between area, as derived from dual-energy X-ray absorptiometry scan, and fracture stiffness. TABLE 2. Correlation between fracture stiffness and dual-energy X-ray absorptiometry (DXA)-deri¨ ed parameters

FIG. 5. Linear correlation between minimum density (min. dens.), as derived from dual-energy X-ray absorptiometry scan, and fracture stiffness.

Parameter

r2

P value

2

0.77 0.73 0.58 0.55

3.67= 10 ᎐ 8 1.93= 10 ᎐ 7 5.22= 10 ᎐ 5 2.54= 10 ᎐ 5

Area Area Minimum DXA value Maximum DXA value

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FIG. 8. Linear correlation between minimum (min.) density, as derived from dual-energy X-ray absorptiometry scan, and fracture stiffness on individual patients.

cient of determination dropped to r 2 s 0.58 when we combined the values of all patients. These two DXA-derived parameters are therefore not very useful to compare between patients. The most likely cause for the drop in correlation is the influence of the segment geometry. For each patient, the geometry does not change significantly during healing, but there is a wide spectrum of callus shapes in different patients. Bending stiffness combines the influence of material stiffness and geometry ŽAppendix A.. Because our transverse DXA profiles give information on the calcium distribution along the geometry, parameters based on this profile are likely to correlate better with stiffness. Indeed, we found that measured stiffness correlated well with the area under the profile Žtotal calcium content. and the square of this value. Based on theoretical considerations, the good correlation between the squared area and the bending stiffness can be understood ŽAppendix A.. Given that this study combines results from a wide range of age, diagnosis and segment location, an r 2 value of 0.77 between bending stiffness and mineral density pattern is surprisingly high. Our measurements are fairly accurate: bending stiffness measurements have an accuracy of 97% Ž11., and DXA scans predict bone density patterns with high accuracy Ž6,10.. However, laboratory studies relating bone

FIG. 9. Linear correlation between maximum (max.) density, as derived from dual-energy X-ray absorptiometry scan, and fracture stiffness on individual patients. J Pediatr Orthop Part B, Vol. 10, No. 3, 2001

density to Young’s modulus show an amount of scatter that is similar to our results Ž1,15.. This would suggest that all scatter may well be explained by the fundamental inability of bone density to fully predict Young’s modulus. Other parameters, such as bone architecture, should be taken into account to improve the power of densitometry to predict Young’s modulus and thus fracture stiffness. Our theoretical analysis ŽAppendix A. is based on the assumption of a constant ratio of height and width in the cross-sections of newly formed bone. This is obviously not true but, because the scatter in our results is so close to that in laboratory studies relating bone density to Young’s modulus, this assumption seems justified. Although better methods might be conceivable to take into account segment geometry, this consideration suggests it would improve the correlation only marginally. We can now analyse the suggestion of Eyres et al. to base fixator removal on a bone density at the distraction segment, which is 75% of the normal density Ž7.. The value they used is equivalent to the maximum DXA value in the transverse plane in our study. The relatively low correlation between this particular parameter and bending stiffness Ž r 2 s 0.55. suggests that the criterion of Eyres et al. can probably be improved upon. Markel and Chao found a low correlation between torsional stiffness and DXA Ž16.. They supposed that the resolution provided by DXA is insufficient to correlate DXA results with bone stiffness. Our findings suggest that their low correlation was more likely owing to the fact that Markel and Chao did not take into account the geometry of the fracture, rather than a lack of resolution. We routinely use direct stiffness measurements to monitor callotasis healing and to time fixator removal Ž5.. If we were to base our healing time on a DXA-derived stiffness, healing times would increase by an average of only 4.6 days ŽTable 1.. Compared with the average healing time of 151 days, this represents a small difference. With regards to refracture risk, we believe that these frames could have been safely removed based on a DXA-derived stiffness. However, a large study would be needed to independently confirm that DXA-derived stiffness is sufficient to determine frame removal. It is only the strong correlation with fracture stiffness that allows this DXA-derived stiffness to be used as objective information towards the decision on removing a frame. On the basis of our results, it would appear that linear densities of 2.8 grcm and 3.2 grcm correspond to stiffness levels of 15 Nmrdeg and 20 Nmrdeg, respectively. These levels are, however, guidelines, and several factors must be considered including alignment, fracture level and the weight of the patient Ž5,22.. We have concentrated our study on bone regeneration using callotasis. There are more applications

FRACTURE STIFFNESS IN CALLOTASIS where a DXA-derived stiffness could be useful, such as normal fractures or the consolidation of spinal fusions. One major disadvantage of these alternative applications is, however, that the geometry is not as homogeneous as a distraction segment. A relation between DXA profile and mechanical stiffness might then be harder to find, as was discovered recently by Cattermole et al. Ž2.. In conclusion, we found a high correlation between fracture bending stiffness and a DXA-derived stiffness value. Use of this DXA-derived stiffness can give the same benefits in monitoring healing and predicting delayed union as directly measured stiffness. In addition, DXA scans may be used to allow the safe removal of fixators. This will reduce morbidity considerably, especially when ring fixators are used that are cumbersome and uncomfortable to remove. Acknowledgements: The authors thank Smith’s Charity for supporting G.T., the Wishbone Fund for supporting P.J.O., and the Medical Research Council for supporting J.H.K.

REFERENCES 1. Carter DR, Hayes WC. The behavior of bone as a two-phase porous structure. J Bone Joint Surg Am 1977;59:954᎐62. 2. Cattermole HC, Fordham JN, Muckle DS, Cunningham JL. Dual-energy X-ray absorptiometry as a measure of healing in fractures treated by intramedullary nailing. J Orthop Techniques 1997;10:563᎐8. 3. Cullum ID, Ell PJ, Ryder JP. X-Ray dual-photon absorptiometry: a new method for the measurement of bone density. Br J Radiol 1989;62:587᎐92. 4. De Bastiani G, Aldegheri R, Brivio LR. The treatment of fractures with a dynamic axial fixator. J Bone Joint Surg Br 1984;66:538᎐45. 5. Dwyer JSM, Owen PJ, Evans GA, Kuiper JH, Richardson JB. Stiffness measurements to assess healing during leg lengthening. J Bone Joint Surg Br 1996;78:286᎐9. 6. Eastell R. Assessment of bone density and bone loss. Osteoporosis Int 1996;6Žsuppl 2.:3᎐5. 7. Eyres KS, Bell MJ, Kanis JA. New bone formation during leg lengthening evaluated by DXA. J Bone Joint Surg Br 1993;75:96᎐106. 8. Eyres KS, Bell MJ, Kanis JA. Methods of assessing new bone formation during limb lengthening: ultrasonography, dual energy x-ray absorptiometry and radiography compared. J Bone Joint Surg Br 1993;75:358᎐64. 9. Gibson LJ, Ashby MF. Cellular solids. Structure & properties. Oxford: Pergamon Press, 1988. 10. Grampp S, Genant HK, Matthew A, et al. Comparisons of noninvasive bone mineral measurements in assessing age-related loss, fracture discrimination, and diagnostic classification. J Bone Miner Res 1997;12:697᎐711. 11. Hardy JRW, Richardson JB. Fracture stiffness. J Orthop Techniques 1994;2:177᎐90. 12. Harp JH, Aronson J, Hollis M. Noninvasive determination of bone stiffness for distraction osteogenesis by quantitative computed tomography scans. Clin Orthop Rel Res 1994;301:42᎐8. 13. Ilizarov GA. Clinical application of the tension᎐stress effect for limb lengthening. Clin Orthop Rel Res 1990;250:8᎐25. 14. Krettek C, Haas N, Tscherne H. The role of supplemental lag screw fixation for open fractures of the tibial shaft treated with external fixation. J Bone Joint Surg Am 1991;73:893᎐7.

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15. Linde F, Nørgaard P, Hvid I, Odgaard A, Søballe K. Mechanical properties of trabecular bone. Dependency on strain rate. J Biomech 1991;24:803᎐9. 16. Markel MD, Chao EY. Noninvasive monitoring techniques for quantitative description of callus mineral content and mechanical properties. Clin Orthop Rel Res 1993;293:37᎐45. 17. Markel MD, Bogdanske JJ, Xiang Z, Klohnen A. Atrophic nonunion can be predicted with dual energy X-ray absorptiometry in a canine ostectomy model. J Orthop Res 1995;13:869᎐75. 18. Markel MD, Morin RL, Wikenheiser MA, Lewallen DG, Chao EY. Quantitative CT for the evaluation of bone healing. Calc Tiss Int 1991;49:427᎐32. 19. Markel MD, Wikenheiser MA, Morin RL, Lewallen DG, Chao EY. The determination of bone fracture properties by dual-energy X-ray absorptiometry and single-photon absorptiometry: a comparative study. Calc Tiss Int 1991;48:392᎐9. 20. Mirsky EC, Einhorn TA. Bone densitometry in orthopaedic practice. J Bone Joint Surg Am 1998;80:1687᎐98. 21. Rice JC, Cowin SC, Bowman JA. On the dependence of the elasticity and strength of cancellous bone on apparent density. J Biomech 1988;21:155᎐68. 22. Richardson JB, Cunningham JL, Goodship AE, O’Connor BT, Kenwright J. Measuring stiffness can define healing of tibial fractures. J Bone Joint Surg Br 1994;76:389᎐94. 23. Sarin VK, Loboa Polefka EG, Beaupre GS, Kiratli BJ, Carter DR, van der Meulen MC. DXA-derived section modulus and bone mineral content predict long-bone torsional strength. Acta Orthop Scand 1999;70:71᎐6. 24. Steinfield PH, Cobelli NJ, Sadler AH, Szporn MN. Open tibia fractures treated by anterior half-pin frame fixation. Clin Orthop Rel Res 1988;228:208᎐14. 25. Thakur AJ, Patankar J. Open tibial fractures: treatment by uniplanar external fixation and early bone grafting. J Bone Joint Surg Br 1991;73:448᎐51.

APPENDIX A The bending stiffness of a long bone depends on the material stiffness of the bone and the geometry of the cross-section. These are represented by the Young’s modulus, E, and the second moment of inertia, I. For bending around the horizontal x axis ŽFig. 10., the latter is equal to: Is

2

HHy d x d y

For a rectangular cross-section of width w and height h, I is equal to Ž1r12. wh 3 ; and for a circular crosssection with diameter D, I is equal to Ž␲r64. D 4 . Broadly generalizing, for a cross-section of width w, height h, and area A, I is proportional to wh 3 , or Ah2 . The Young’s modulus of bone is mainly determined by the bone density, ␳ Ž1,9,15,21.. Most workers found a power relation between density and modulus: Es c ␳ n where n equals 1 to 3. Rice et al. Ž21. reviewed a number of separate experiments. They found that a quadratic relation Ži.e., n s 2. provided a best fit through the pooled data of these experiments, and J Pediatr Orthop Part B, Vol. 10, No. 3, 2001

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G. TSELENTAKIS ET AL. We will now relate the DXA profile to bending stiffness. The second moment of inertia, I, is proportional to: I f A b h 2 f A2b

h w

On the basis of the quadratic relation between Young’s modulus, E, and density, ␳ , the Young’s modulus is: Ef ␳ 2 s FIG. 10. Transverse bone section and associated dual-energy X-ray absorptiometry (DXA) profile.

we will use that value here. The DXA value quantifies the total amount of calcium that has attenuated the passing X-rays. Assuming a homogeneous bone density ␳ Žgrcm3 ., the profile of DXA values Žgrcm2 . represents the product of bone height and bone density. The area under the profile of DXA values, A D Žgrcm., represents the product of the bone area, A b , and bone density.

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AD Ab

2

ž /

The total bending stiffness, EI, is then proportional to the square of the area under the DXA profile multiplied by the ratio of bone height and bone width: EI f

AD Ab

ž /

2

A2b

h h s A2D w w

Assuming a constant ratio of bone height and bone width, the bending stiffness will be proportional to the square of the area under the DXA profile.