Jorarirnl of Orthopedic Research
18912-Yl9 ' f i e Journal of Bone and Joint Surgery. Inc.
02000 Orthopaedic Research Society
Quantitative Assessment of In Vivo Bone Regeneration
Consolidation in Distraction Osteogenesis
Henning Windhagen, "Stefan Kolbeck, "Hermann Bail,
*Arne Schrneling, and *Michael Raschke
Department of Orthopedic Surgery, Hannover Medical School, Hanmvel; and
"Depiwtment of Trauma Surgery, Chariti, Huniboldt- University Berlin. Berlin, Germany
Summary: We present a new method for quantitatively assessing the consolidation of bone regeneration by
performing distraction osteogenesis in micropigs. We measured in vivo stiffness using a newly developed. re-
volving, bone-healing meter. After the micropigs were killed, we obtained maximum torsional moment data
for the regenerated bones by destructive mechanical testing, and we then correlated these data with the data
for stiffness. We found a highly significant regression between in vivo stiffness and maximum torsional moment (r' = 0.80), suggesting that monitoring stiffness may be useful for the prediction of bone regeneration
in distraction osteogenesis. Therefore, our method may be a reliable tool for future quantitative monitoring
of healing progress in patients with healing bones or in animal studies addressing treatments to increase
bone formation in long-bone defects.
~
Distraction osteogenesis creates bone mass through
controlled distraction of vital bone surfaces. It has
been used successfully for bridging bone defects in
trauma and bone tumor surgery. Its advantages over
bone-grafting techniques include its low infection risk
and its virtually unlimited bone mass; however, its major disadvantage is the long duration of treatment. In
general, for each millimeter of length gained in distraction, the patient needs roughly 3 days of treatment. At a distraction rate of approximately 1 mm/
day, the patient requires 1 day for distraction and 2
days for consolidation. A 10-cm-long defect-as seen
in tumor and trauma surgery-requires a distraction
phase of about 100 days and roughly 200 days of consolidation. Thus, this treatment often lasts longer than
a year. Although the distraction rate has been shown
to be constantly successful for different regions of the
body and for different patients, large differences in
consolidation time are obvious. Secondary to the long
time of consolidation is the difficulty deciding when t o
remove the stabilizing frame that the patient is required to carry during distraction and consolidation.
Several authors have focused their work on the value
of regenerate-zone imaging for prediction of consolidation: Eyres et al. (13), Blane et al. ( 3 ) ,Walker et al.
(39), and Minty et al. (25) demonstrated the qualita-
tive value of radiography, ultrasonography, and dual
energy x-ray absorptiometry for detecting the stage of
Consolidation. Quantitative assessments in fracture
regeneration were performed by Panjabi et al. (28)
and Nicholls et al. (27), who showed difficulties in
monitoring early stages of healing. Considering these
methodological problems, clinical diagnostic tools are
needed to accurately predict the actual load-bearing
capacity of the consolidating bones and to determinc
when the external fixator should be removed.
Several studies on force measurements during the
healing process in distraction osteogenesis have been
published. However, most of these studies focus on
the distraction phase and measure forces or strain
generated during different regimens of bone lengthening (1,21,22,36,38,40,42,43). On the other hand,
only a few attempts focus on the consolidation phase
and quantify the load-bearing capacity of the consolidated bone (10).
Although bone fractures and distraction osteogcnesis exhibit differcnt characteristics in cellular and
mechanical regeneration, the principles of quantifying the consolidation of fracture regeneration may be
applicable for distraction osteogenesis as well. Manual biomechanical methods for measuring bone rigidity under minimal forces have been developed by
Matthews et al. (24). Hammer et al. ( 2 5 ) assessed
stiffness from radiographs taken under bending moments. Other authors (2,4,6,18) instrumented external fixators with micrometers. strain gauges, or load
cells and measured the axial stiffness of fracture sites.
Received May 28, 1999; accepted February 1. 2000.
Address correspondence and reprint requests to H. Windhagen at Department of Orthopaedic Surgery, Hannover Medical
School. 30625 Hannover. Germany. E-mail: windhagenmannastift.
de
912
M E A S U R E M E N T S OF B O N E TORSIONAL STIFFhTESS
91.3
FIG. 1. Radiographic view of thc extcrnal fixator sctup with double ring, pin-fixation and osteotomy.
The first clinically usable device to measure absolute
levels of stiffness with a removable force plate and
gonionieter for measuring bending stiffness was prcsented by Churches et al. (8) and further developed
by Evans et al. (12). Although this method provided
a promising principle and clinical usage was demonstrated (34). it had some disadvantages: the indirect
method by which $train was measured in the fixator
column exhibited large errors. whercas the direct
method required disassembly of the fixator for nieasurements. Furthermore, a high risk ot bone malalignment exists during mcasurcment and reassembly with
this procedure.
To address this problem, we developed a new de-
vice for measuring hone stil'Incss in vivo. The device
is integrated into an external ring fixator that is standardly used to stabilize bone fragments in distraction
osteogenesis. It allows in vivo measurements of torsional stiffness. from which the progress in bone healing can be estimated. In addition, the device can bc
used with various fixator designs and allows repetitive measurements during trcatment without the
need for fixator removal and the associated complications. As previously demonstrated in an in vitro study
using a rubber model for simulating fractures, thc
method exhibited an accuracy of 9% for stiffness
measurements between 0.1 and 2.4 NmP, where accuracy was defined as the mean difference between gold
FIG. 2. Principle of the in vivo torsional measurement system. With comprcssion of the grip, the two bone fragments are rotated against
each other. Moment and angular displaccmcnt are calculated from the longitudinal variable differenlial transduccr (LVDT) and load-cell
data rccording. (Printed with permission of Blsevier Science Tnc.)
914
H. WINDHAGEN ET AL.
FIG. 3. Measurement procedure: the animal is placed in a hangniat (A), the locking bolts are removed (B), the measurement grip is atlached to the fixalor (C), and measurements are performed by manual grip compression (D).
standard values and the observed stiffness values,
divided by the gold standard. Furthermore, a 1.76.0% precision-compared with a 0.32-4.60% precision for a materials testing machine over the same
load range-was demonstrated. where precision was
expressed as the coefficient of variation from repeated measurements (41).
This study sought to determine whether torsional
stiffness measurements made with this newly developed device accurately predict the failure load of
healing bones. With use of a porcine model of distraction osteogenesis, in vivo torsional stiffness measurements of bone under minimal forces were compared
with torsional strength measurements made ex viva
Nephews, Memphis, TN, USA.),connected with three 4.5-mrn
threaded rods to a 10-cm-diameter distal double ring. The double
rings were combined with a bearing machined from polycarbooate that allowcd rotation of the two half-rings against cach other
(Fig, 1), Rillg dimensions alld position of the ring holes
equal to a standard 100-nim ring of thc Jlizarov External Fixation
System (Smith and Nephews). Thus. hecause standard dimensions
werc used; the douhle ring could he connected LO any external
fixator.
MATERIALS AND METHODS
The left lower limbs of 30 micropigs (Charles River France,
Saint Aubiii Les Elbeuf, France) were osteotomized and fixed
with an external fixator. The micropigs were part of an unrclated
pharmacological study (32). All cxperinicnts wcrc performed according to the Principles of Laboratory Animal Care (National
Institutes of Health publication no. 86-23, revised 1985; and German Law "Tierschutzgesetz" 0351 abstract 18). Approval was
also obtained by the government review board. A fixator frame
was assembled with use of a lO-cm proximal half-ring (Smith and
FIG. 4. Mechanical test setup.
915
M E A S U R E M E N T S OF B O N E TORSIONAL STIFFNESS
0,o
5
0
10
15
20
25
35
30
maximum torsional moment (Nm)
FIG. 5. Linear regrcssion between data for stiffness and maximum torsional moment
The proximal ring of the double ring was connected to bone
parts proximal to the osteotomy gap. and the distal ring was connected to bone parts distal to the fracture gap. For locking purposes, i.e.. in the normal configuration when measurements are
not being made, four sagittal screws were bolted through the rings;
this prohibitcd rotation of tlie proximal and distal rings. 'Thc fixator frame was connected to tlie bones with usc of 5-nim stainlcsssteel pins (Synthes, Paoli. PA, U.S.A.). The lower limbs wcrc distractcd along thc thrcadcd rods at 2 midday for 10 days and then
wcre allowcd to consolidatc for 10 days. During thc last day of
consolidation, dynamic nieasurcments were made with a rcmovable measuring unit dcsigncd to fit thc doublc rings of the fixator.
Thc measurement unit is dcsigncd in thc shapc of a grip with two
bars and two handles (Fig. 2); one bar of the grip fit to a fork at
the proximal ring. and the other bar fit to a fork at the distal ring.
The grip was instrumented with a 20-mm longitudinal variable differential transducer and a 500-N load cell (both: Hottinger Baldwin, Frankfurt, Germany). These sensors were connected to a
powcr amplifier and A/D signal conditioner, and digital signals
werc processcd with use of a standard personal computer and LA-
0
1
2
BTCCH software (Labtech 4: Labtech. Andovcr. MA, U.S.A.).
The longitudinal variable differential transducer was mounted between the grip bars in such a way that displacements and grip between the grip ends were mcasurcd. Thc load cell was placed at
one bai- end. thus nionitoring all forces transmitted from the grip
to thc ring system.
For mcasuremcnt, the grip was mounted with its bars attached
to both thc proximal and distal rings ol' the Cixator double ring
(Fig. 3 ) . Thc locking bolts were removed. To perlorm the dynamic
mcasurement. the test conductor carefully compressed the handlcs, thercby rotating the distal and proximal rings against each
other. Applicd forccs and resulting displacements were continuously monitored. Forccs and displaccment were automatically
converted into torsional moments and corrcsponding angular displacements. A moment-rotation curve was displayed in rcal tinic,
and the information from the test conductor was used to terniinate
tests at 6" of torsional angulation or 0.6 Nni of moment. whichever
parameter was reached first. The moment-displacement curves
had two portions divided by a sudden sharp increase in slope. A
linear regression was performed for datum points for the portion
3
4
5
6
Angu I ati on (degre e)
FTG. 6. A and B Typical inonicnt-angular displacement curves for rigidly fixed pins ( A = late hcaling phasc, B = early healing phase). C:
A typical moment-angular displacement curve for a loosencd pin.
H. W l N D I I A G E N E T A L
916
after the sharp increase in slope. The slope coefficient of this curve
was defined as the initial torsional stiffness.
Aftcr the micropigs were killed, thc tibia1 bones were removed,
embedded in methylmethacrylatc, and mounted in a materials
testing machine (Fig. I).An axial preload of 10 N was maintained
throughout the test. Torsional moments were applied t o the boncs
in displacement control at 10"imin. Failure was defined at thc first
decrease in nicasured torsional moment. The maximum measured
torsional moment for each bone was recorded.
Linear regressions were performed between maximum torsional moment as the independeiit variable and initial torsional
stirfness as thc dependent variable.
RESULTS
The in vivo initial torsional stiffness measurements
taken on the day the micropigs were killed were
highly significantly related to the maximum torsional
moment data observed from in vifro testing of the extracted bones. The relationship was linear (p = 0.001),
with a coefficient of determination of 0.80 (Fig. 5). At
death of the micropigs. the boncs exhibited a large variety in torsional failure loads-25 to 40 Nm-thereby
representing 40-80% of the failure loads of thc contralateral bones (Fig. 5).
The in vivo measurements exhibited an initial stiffness that ranged from 1 to 2 Nnii". The momentdisplacement curves showed a typical shape with a
low slope portion at the beginning, a sharp increase in
moment, and then a linear increase. Pin loosening was
observed in several of the micropigs. The momentangulation curves of these animals typically showed
an enlarged toe region before a sudden sharp increase
in slope (Fig. 6).
DISCUSSION
We asked whether torsional stiffness measurements
with a rotational external fixator would be able to
predict torsional strength of healing bones in distraction osteogenesis. The highly significant regression
between in vivo stiffness and torsional strength (coefficient of determination r' = 0.80) demonstrated the
ability of the device to monitor fracture healing with
the in vivo initial stiffness measuremcnt apparatus.
The method outlined here has the potential to be used
clinically for monitoring the healing of distracted
bone: its advantages over previous methods include
maintenance of bone axis and alignment, free combination with different fixator designs, and speed and
reproducibility in a conveniently applied procedure in
the absence of damaging radiation.
The method is based on a principle first described
by Pope and Outwater (31). who found a high correlation between stiffness and strength of healing bone.
Lettin (23) was one of the first to demonstrate the
increasing quantity and quality of bone during tissue
repair. More specifically, Perren (30) showed a 40,000fold increase in elastic modulus of bone tissue during
healing. Reichel et al. (33) and Sferra et al. (35)
analyzcd the mechanical properties of distracted callus of sheep and dogs, respectively, by densitometric
and biomechanical methods. Both found increasing
strength and stiffness over a period of 8 weeks.
Chehade et al. (7) compared strength and stiffness development during fracture healing in sheep. They concluded that stiffness measurements can accurately
monitor strength until stiffness reaches two-thirds of
the normal stiffness. The predictive capacity of stiffness decreases with increased healing timc. On the basis of the results. stiffness is hypothesized to be a
measure of the load-bearing capacity of bone. Therefore, knowledge of torsional stiffness and strength can
provide a powerful indicator of bone healing.
Although the method tested in this study represents
a distraction osteogenesis cnvironment, bone healing
of a fracture or gap bridging are similar in restoring
load-bearing capacity from a biomechanical point of a
view. We therefore present the results of this study
with respect to bone-healing research in general.
The concept of monitoring the healing process from
rigidity mcasurcments derived from the external fixator frame or externally connected meawring instruments is not new. Most representative developments
were made by BeauprC et al. ( 2 ) ,Burny et al. ( 5 ) , Jorgensen (IX), and Kaplan et al. (1Y) using instrumented
fixators. These methods were overly complicated and
sensitive to a host of additional variables, such as individual geometry of the fixatorb, fragment size, and influence of bone-implant interfaces. Therefore. Evans
et al. (12), Kenwright et al. (20), Richardson et al.
(34), and Cunningham et al. (9) prescnted methods
using a removable measuring unit. They used a goniometer and a force plate to measure resulting forces
and bone deflection under bending loads, thus using
fracture bending stiffness for monitoring purposes.
These developments represent a large step toward appropriate clinical monitoring of healing, and this approach has been applied in a clinical study examining
212 patients (24). However, serious criticism may be
leveled at this approach because it requires removal
of the fixators. with the risk of potential damage to the
regenerated bone or nialalignment of thc bone and
axis. As a consequencc, this method cannot be used in
the early phase of fracture healing.
To our knowledge, this study is the first to predict
load-bearing capacity by comparing in vivo measurements of healing bones with actual load-bearing capacities of the bones measured ex vivo. Previously,
many authors used stiffness as a predictor of bone
healing; however, none correlated the data for in vivo
measured stiffness with a measure of the actual loadbearing capacity. which is the parameter with the ultimate clinical relevance. Some previous studies were
based on the immediate clinical use in which the authors (12) were forced to derive healing from repeti-
M E A S U R E M E N T S 0 F B 0N E 1'0R S l 0 N A L STIFFNESS
tive measurements of stiffness without knowledge of
the actual load-bearing capacity. They instead used
empirical data from clinical studies to establish a
threshold of loading at which failure of fracture healing no longer occurs. Similarly, several authors performed validation tests using either simulations or
artificial models (15,17,18).
The study of Chehade et al. (7) also addressed the
major research question of the current experiment.
Strength and stiffness of healing fractures in sheep
were compared after death at different timc points.
The authors concluded that stiffness was load dependent and that high-load stiffness was more strongly
related to strength than was low-load Stiffness. Furthermore, they found that stiffness predicts strength
recovery of a healing fracture until two-thirds of the
stiffness is reached. For low-load stiffness at early
healing phases, they found a correlation coefficient of
r = 0.89, which equals a coefficient of determination of
r' = 0.79; for very late healing stages, they found decreasing coefficients at r = 0.24. In this experiment, we
found a coefficent of determination of r2 = 0.80, suggesting that we performed our measurements at a
rather early healing phase. However, Chehade et al.
tested a fracture model, whereas we used a distraction
model. Bone development in distraction osteogenesis
exhibits differences with rather homogenous bone development compared with that in fracture healing;
thus, the prediction of strength may be more accurate
and precise even in advanced healing phases of distraction osteogenesis. Our findings and those of Chehade et al. support the idea of predicting strength of
healing bone from stiffness, but uncertainty exists
about the accuracy and precision in later healing
stages.
On interpretation of the results from the current
study, several factors must be taken into consideration. First, the moment-displacement curves determined from the minimal rotation of the bone
fragments exhibit a typical shape with two portions of
different slope. We interpret the first portion with low
slope to reflect the initial setting of the fixator and the
second portion with increased slope to reflect the mechanical response of the bone fragments. The data for
measured stiffness represent the torsional stiffness of
not only the healing bone fragments but also that of
the fixator and grip. The exact stiffness of the bone
fragment can be assessed by subtraction of the angulation caused by fixator bending from the overall angulation. We measured torsional stiffness of a relatively
flexible healing bone (k = 50.6 Nm/") with a rigid
fixator-grip systcm (k = NmP). Therefore, the crror
caused by the measurement system was negligible.
However, for measurements with more rigid healing
bones and limited dimensions of the fixator and grip,
the deflection of the fixator has to be assessed for all
917
loading levels, and the overall measurements should
account for that error.
Second, due to the indirect assessment of bone stiffness over sensors at the fixator, the bone-pin connection may affcct accuracy and precision of the
measurements. However, we found that pin loosening
resulted in an enlarged first portion of the momentangulation curve without affecting the second portion, which was taken to calculate stiffness. This first
portion reflects the initial setting and bending of the
fixator under preliminary loading. With greater pin
loosening. the pins will edge within their holes to a
greater degree until they finally lock and transmit
forces from the fixator to the bone fragments. At the
point of locking, the slope increases rapidly and represents the mechanical properties of the bone.
Third, distraction was performed at 2 mmiday.
which is higher than the distraction rate of 1-1.5 mmi
day generally used in humans. We observed premature consolidation in a pilot series of animals distracted at 1 mm/day. Therefore, the model had to be
adjusted for the porcine model.
The device presented here has several advantages
over conventional designs, with a variable ring construct that can be easily integrated into conventional
ring external fixators. In its locked configuration, the
system provides a standard external fixator. Unlocking by removal of a bolt guarantces the exact maintenance of the length and rotation position after testing.
With the removable measuring unit, we could assess
fracture torsional strength by a single fixator twist of
6". However, pin-associated infection and pin loosening may influence the measurement. Due to uncontrolled influences, such as soft-tissue resistance and
the elastic properties of the fixator and pins, use of the
apparatus in its current design is recommended only
for relative measurements with a zero measurement
at the initial surgery. This study included a large population of 30 micropigs, with broad differences in the
healing stage and the achieved strength of the regeneration; however. with this study we cannot prove
whether strength of the regeneration can be predicted
at a very early healing phase. Tn addition, we have not
determined whether the applied minimal forces may
influence the healing process. As a semi-invasive dynamic measurement system with torsional angulation
of as much as 8", some strain will be applied to the regenerating collagen fibers. This strain will depend
largely on the size of the fracturc or distraction gap:
the smaller the gap, the larger the strains. Whether the
displacements under these circumstances are damaging to the newly developed fibers cannot be answered
with this study. and further research addressing this
problem is required.
Mechanical testing of the fracture zone was performed with use of torsional testing. However, other
J Ortliop K e s Vol 18. N o 6, 2000
H. W l N D HAGEN E l ’ A L .
918
principles exist to measure the mechanical properties
of bone or fracture callus. Tensile tests can provide
very accurate methods for measuring bone properties
(37); however, large forces are required to distract
whole bones in tensile testing. Therefore, tensile tests
are mostly used for assessing material properties of
smaller specimens. Compressive testing is a popular
method for testing cancellous bones (26), especially in
regions that are loaded in compression (e.g., vertebrae). Pure shear tests (16) are sensitive to measurement errors and are hardly useful for testing whole
bones. Whole long bones are tested mostly in either
bending or torsion. Bending can be applied with either three or four-point loading (37). For accurate
measurements, three-point bending requires a relatively large span of the specimen with respcct to its
width. Four-point bending requircs cqual loading
points, which are hard to establish in irregularly
shaped specimens. Furthermore, the axial orientation
of irregularly shaped bones such as the tibia considerably influences the bending stiffness. Therefore, torsional tests are often used to measure strength of
whole bones (11,14). Torsional tests are less sensitive
to axial orientation of the irregularly shaped long
bones. They are relatively independent of specimen
span, and embedding the bone ends in polyrnethylmethacrylatc kecps the length of the test specimen
constant. Furthermore, torsion creates a mix of shear
and tensional stresses (29). which mimics the typical
loading conditions of long bones during active life.
Our results thus far are connected with the animal
model and special design of our fixator: thus, no interpretations can be drawn from this study to the validity
of other torsional stiffness measurement systems that
use a measuring principle similar to ours but with different designs and test models.
The newly developed measuring system and its validation in an animal model suggest that the regeneration strength of healing bones can be assessed in vivo
by measurements of torsional stiffness. Compared
with several other methods, this method may provide
a more useful device-with less danger of complications-to monitor healing progress in patients treated
with distraction osteogenesis.
Acknowledgment Thc authors thank Novo-Nordisk N S . Gentoftc, Iknmark, and Smith and Nephews, Memphis, TN. U.S.A.,for
support. They also thank Karl-Eugen Windhagen, MD, for photographic documentation.
4. Briggs BT. Chao EY The mechanical performance of the
5
6
7
8
9
10
11
12
13
14
15
36
17
18
19
20
21
22
23
24
REFERENCES
1. Aronson J: Experiincntal and clinical experience with distraction osteogencsis. Cleft Palate Craniofac J 31 :473-481, 1994
2. Beaupre t i S , Hayes WC, Jofe MH, White AA 3rd: Monitoring fracture site properties with cxternal fixation. J Biomech
Eng 105:120-126, 1983
3. Blanc CE. Hcrzenbcrg JE, DiPietro MA: Radiographic imaging for Ilizarov limb lengthening in children. Pedirrtr Rndiol
21:117-120. 1991
25
26
27
28
standard Hoffmann-Vidal external fixation apparatus. J Bone
hint Surg [Am] 64566-573. 1982
Burny F, Moulart F, Bourgois R: Mesure de la deformation
des implants “in vivo.” Rcsultats d‘une Ctude portant sur dix
patients traitis par clouplaque.
42(Suppl
. Belgicn
..
- . Actu Orthop
1152-61, 1976
Burny F, Bourgois R, Donkerwolcke M, Moulart F: Utilisation clinique de jauges de contrainte: situation actuelle et perspectives d’avenir. Acta Orthop Belgica 44:89.5-920, 1978
Chehade MJ, Pohl AP. Pearcy MJ, Nawana N: Clinical implications of stiffness and strength changes in fracture healing.
J Bone Joint Surg [Br] 79:9-12, 1997
Churches AE. Tanner KE, Evans M. Gwillim J: Fracture healing assessment with external fixation. Eng Med 14:13-20.1985
Cunningham JL. Richardson JB, Soriano RM. Kenwright J
A mechanical assessment of applicd compression and healing
in knee arthrodesis. Clin Ortlzop 242956-264, 1989
Dwyer JS, Owen PJ, Evans GA, Kuiper JH. Richardson JB:
Stiffness measurements to assess healing during leg lengthening: a preliminary report. J Bone Joint S7rrg [Br] 78:286-289,
1996
Einhorn TA, Wakley GK, Linkhart S, Rush EB. Maloney S,
Faiernian E, Baylink DJ: Incorporation of sodium fluoride
into cortical bone does not impair the mechanical properties
of the appendicular skeleton in rats. Culcif Tissue Int .51:127131. 1992
Evans M, Kenwright J, Cunningham JL: Design and performance of a fracture monitoring transducer. .I Bionied Eng
10:64-69, 1988
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] 75:358-364. 1993
Forwood MR, Parker AW: Effects of exercisc on bone
growth: mechanical and physical properties studied in the rat.
Clin Biornech 2:185-190, 1987
Hammer R, Edholm P. Lindholm B: Stability of union after
tibial shaft fracture: analysis by a non-invasive technique.
J Bone Joint Surg [BrJ 66529.534, 1984
Iosipescu N: New accurate procedure for single shear testing
of metals. J Muter 2537-566, 1967
Jernberger A: Measurement ol stability of tibial fractures: a
mechanical method. Acru Orthop Scnnd Srrppl 135:l-88, 1970
Jorgenscn TE: Mcasuremcnts of stability of crural fractures
treated with Hoffmann osteotaxis. I. Method and measuremcnts of deflection on autopsy crura. Actn Oufhop Scund
43:188-206, 1972
Kaplan SJ, Hayes WC, Stone JL, BeauprC GS: Tensile
strength of bovine trabecular bone. .I Riomech 1 X:723-727.
1Y85
Kenwright J, Richardson JB, Goodship AE. Evans M. Kelly
DJ, Spriggins AJ. Newman JH, Burroughs SJ. Harris JD,
Rowley DI: Effect of controlled axial micromovcment on
healing of tibial fractures. Lnncef 22:1185-1187, 1986
Kenwright J, Spriggins AJ, Cunningham JL: Kespoiise of the
growth plate to distraction close to skeletal maturity. Is fracture necessary? C h i Orthop 250:61-72, 1990
Leong JC. Ma RY, Clark JA, Cornish LS; Yau AC: Viscoelastic behavior of tissue in leg lengthening by distraction. Clin
Orthop 139102-109, 1979
Lettin AW The effects o f axial compression on the healiug
of cxpcrimcntal fractures of the rabbit tibia. Proc K Soc Med
58~882-886.1965
Matthews LS, Kaufcr H, Sonstegard DA: Manual sensing of
fracture stability: a biomechanical study. A m Orthop S c a d
451373-381,1974
Minty I. Maffulli N, Hughes TH, Shaw DG, Fixsen JA: Radiographic leatures of limb lengthening in children. Actu Rudid 35:555-559, 1994
Mosekildc L: Asscssing bone quality-animal models in preclinical osteoporosis research. Bone 17:343S-352S, 199.5
Nicholls PJ, Berg E, Bliven FE Jr, Kling JM: X-ray diagnosis
of healing fractures in rabbits. Clin Orrhop 142:234-236. 1979
Panjahi MM, Walter SD, Karuda M, White AA, Lawsoti JP:
M E A S U R E M E N T S OF BONE TORSIONAL' STlFFNESS
29.
30.
31.
32.
33.
34.
35.
Correlations of radiographic analysis of healing fractures with
strength: a statistical analysis o f experimental osteotomies.
J Orthop Rex 3:212-218. 1985
Park HC, Lakes RS: Cosserat micromechanics of human
bone: strain redistribution by a hydration sensitive constituent. J Biornech 9:38S-397. 1986
Pcrren SM: Physical and biological aspects of fracture healing
with special reference to internal rixation. Clin Orthop
138~175-196,1979
Pope MH, Outwater JO: The fracture characteristic of bone
substance. J Biomech 5:457-465, 1972
Raschke MJ, Rail H, Windhagen HJ, Kolbeck SF. Weiler A ,
Raun K, Kappelgard A, Skiaerbaek C, Haas NP: Recombinant growth hormone accelerates bone regenerate consolidation in distraction osteogenesis. Bone 24:82-88, 1999
Reichel H, Lebek S. Alter C. Hein W: Biomechanical and
densitometric hone properties after callus distraction in
sheep. Clin Orthop 357237-246, 1998
Richardson JB, Cunningham JL, Goodship AE, O'Connor
BT, Kenwright J: Measuring stiffness can define healing of
tibia1 fractures. J Bone Joint Surg [Br] 76389.394. 1994
Sferra J. Kanibic HE, Schickendantz MS. 'Watson J T Biomechanical analysis of canine bone lengthened by the callotasis
method. CIin Orrhop 311:222-226, lY95
919
36. Sleen H, Fjeld TO: Lengthening osteotomy in the metaphysis
and diaphysis: an experimental study in the ovine tibia. CIin
Orthop 247:297-305, 1989
37. Turner CH, Burr DB: Basic biomechanical measurements of
hone: a tutorial. Bone 14:595-608, 1993
38. Verkerke GJ, Schraffordt Koops H, Veth RP, Nielsen HK, van
den Kroonenberg HH, Grootenboer HJ, de Boer LJ. van
Krieken FM, Wagner H, Pock HG: Design of a load cell for
the Wagner distractor. Proc Inst Mech Eng [HI 203:91-96,
1989
39. Walker CW, Aronson J, Kaplan PA, Molpus WM, Seihert JJ:
Radiologic evaluation of limb-lengthening procedures. AJR
Am J Roentgenol 156:353-358, 1991
40. White SH, Kenwright J: The timing of distraction of an osteotomy. J Bone Joint Surg [Br] 72:356-361. 1990
41. Windhagen H, Bail H, Schmeling A, Kolbeck S, Weiler A,
Raschke M: A new device to quantify rcgenerate torsional
stiffness in distraction osteogenesis. J Biamech 323357-860,
1999
42. Wolfson N, Hearn TC, Thomason JJ, Armstrong PF: Force
and stiffness changes during Ilizarov leg lcngthening. C h Orthop 25058-60, 1990
43. Younger AS, Mackenzie WG, Morrison JR: Femoral lorces during limb lengthening in children. Clin Orthop 301:55-63, 1994
J Orrhop Res, Vul. 18, No.
6, 2000