A study of bone remodeling using metal-polymer
laminates
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J. A. Szivek", G . C. Weatherly", R. M. Pilliart, and H. U. Camerod
Department of Metallurgy and Materials Science, University of Toronto, Toronto, Ontario,
Canada M5S l A 4
Bone remodeling due to stress-shielding has
been studied using a model system consisting of metal-polymer laminated fixation
plates securely fixed to canine femurs. The
plate stiffness was controlled by varying the
ratio of metal facing to polymer core thickness in the laminate design while secure
fixation to bone was achieved by providing
a porous bone interfacing surface for the
ingrowth of bone from the periosteal sur-
face. Observations of laterally and medially
placed plates indicated resorption in the area
of the periosteal and endosteal bone surfaces
respectively, for the higher stiffness composite plates used. The results indicate that
plate stiffness greater than approximately 70
GPa (axial) and 6 N m2 (flexural) will result
in extensive bone remodeling in the canine
femur after a six month implantation period.
INTRODUCTION
Resorption of cortical bone beneath metal fixation plates has been reported
by a number of investigator^.'-^ This phenomenon has been attributed to
"stress shielding," a reduction in stresses below physiological levels as a result
of stress transfer to a higher stiffness metal plate fixed to the surface of the
bone. In order to evaluate the effects of implant stiffness on bone resorption
because of stress shielding, Woo et al.4 bilaterally plated the femurs of dogs
using conventional stainless steel and carbon fiber-reinforced poly(methy1
methacrylate) plates for periods of nine and twelve months. Post-sacrifice
histology indicated extensive resorption of the femoral cortex under the stiff
metal plate while far less cortical thinning was noted under the more flexible
composite plate. Bone remodelings was also studied by Moyen et al.,5 using
intact dog femurs plated with either standard cast cobalt-chromium alloy plates
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* Department of Metallurgy and Materials Science Faculty of Engineering, University of Toron to,
Toronto, Ontario, Canada M5S 1A4.
t Faculty of Dentistry, Univcrsity of Toronto, Toronto, Ontario, Canada M5G 1'26.
t Faculty of Medicine, University of Toronto, Toronto, Ontario, Canada.
5 The term "remodeling" as used throughout this text refers to structural changes caused by altered
stressing of the bone as opposed to its normal connotation to describe dynamic bone turnover under
normal physiological stress conditions.
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Journal of Biomedical Materials Research, Vol. 15,853-865 (1981)
0 1981 John Wiley & Sons, Inc.
CCC 0021-9304/81/060853-13$01.30
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SZIVEK ET AL.
854
or thinner, more flexible Ti alloy plates. They concluded that only the stiffer
cobalt chromium alloy plates caused cortical bone thinning, predominantly
by endosteal resorption. A loss of 20 to 30% of the skeletal mass was recorded
below the stiffer fixation plates after the six month implantation period.
In these studies fixation was achieved by the use of standard bone screws.
In order to assure more effective and controlled stress transfer between bone
and plate, Pilliar et a1.6 used standard stainless steel plates with porous structured bone interfacing surfaces. Fixation of these porous surfaced plates to
the femurs of dogs was achieved by bone ingrowth. This resulted in firm attachment of the plate to the bone, leading to far more extensive bone resorption
beneath the plate than other studies had indicated. This exaggerated resorption was attributed to a greater transfer of stress to the metal plate as a result
of the strong interface bond between the plate and the underlying bone.
The purpose of the present investigation was to study bone remodeling
under laminated plates attached by bone ingrowth as a function of plate
stiffness and position of placement of the plate (lateral or medial bone surface).
It was felt that the firm fixation of the plates to bone by bone ingrowth would
result in a reproducible model for studying bone remodeling as a function of
plate stiffness and position.
EXPERIMENTAL PROCEDURE
Materials and methods
The facings of the laminates were fabricated from either 316L stainless steel
or Ti-6A1-4V sheet. To form the bone interfacing porous surface region, the
metal sheets were coated with cobalt-chromium alloy powder particles (for
the 316L substrate) or with Ti-6A1-4V powder particles. The powder particles
were bonded to the metal sheets using a high temperature reducing atmosphere heat treatment.7
For the stainless steel-cobalt alloy combination, earlier studied indicated
that for the six-month implantation period used and the test procedure employed, no detectable corrosion occurred as a result of the dissimilar metal
contact. Surgical grade polycarbonate and polypropylene were used as the
polymeric core materials.
Metal facing-polymer core bonding was achieved by forming a porous region on the polymer interfacing metal sheet surface and subsequently pressure
bonding this to the polymer core using the pressure molding conditions indicated in Table I. Intrusion of the polymer into the porous metal surface layer
during pressure molding resulted in a micromechanical bond at the metalpolymer interface (Fig. 1). By this method a laminated composite plate was
formed without the use of chemically active adhesives. Plates of several different stiffnesseswere produced using this procedure and were modeled on
standard six-hole fixation plates. Table I1 indicates the relative stiffnesses of
the plates fabricated, the thickness of each component and the facing and core
materials.
BONE REMODELING
855
TABLE I
Pressure Molding Conditions for Bonding Metal Facings to Polymer Core
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Material Characteristics
Polycarbonate
Polypropylene
Molding Parameters
Platen preheat temperature
Pressure during molding
Time to melting of polymer surface
Mold cooling time
Mold cooling technique
240-250 "C
0.7 MPa
7-8 min
4-5 min
water quench
18O-19O0C
0.7 MPa
7-8 min
3-4 min
water quench
Laminated plates were produced for both mechanical testing (plate characterization) and for animal implantation. Both outer surfaces of the plates
used for mechanical testing were smooth. A set of smooth surfaced plates for
animal implantation was also produced. These plates were attached to bone
by screws only, and therefore, served as a control set in our experiments to
compare the effect of fixation by bone ingrowth to normal screw fixation on
bone remodeling. All plates were gas sterilized prior to implantation.
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Figure 1. Scanning electron micrograph of the metal-polymer interface
showing the interdigitation of the polymer i n the porous metal surface structure (250X).
TABLE I1
Description of Laminated Plates Fabricated
Facing Description
Approx.
Thickness
Material
(mm)
316L
Ti-6A1-4V
316L
Ti-6A1-4V
1.3
1.5
1.o
1.o
Core Description
Approx.
Thickness
Material
(mm)
Polypropylene
Polypropylene
Polycarbonate
Polvcarbonate
1.5
1.0
3.0
2.0
Plate Type
high stiffness
medium stiffness
low stiffness
low stiffness
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SZIVEK ET AL.
856
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Characterization of plates
In order to evaluate the stiffnesses of plates used in the animal studies,
smooth surfaced plates of the same configuration were tested axially in compression and by three point bending using an Instron Universal Test Machine.
Tests were carried out at two strain rates, 9 X 1W6and 75 X
s-l. It was
felt that tests over this range of strain rates would correspond to the strain rates
encountered during gait. The strains were measured using strain gauges attached to the outer surface of the plates.
Animal testing
Eight adult mongrel dogs were used in this study. Plates were attached
using standard aseptic surgical procedures to the intact femurs of the dogs and
for all plates initial fixation was achieved using self-tapping bone screws. For
all the animals a porous surfaced plate was attached to one femur and a smooth
surfaced plate of similar stiffness was placed on the contralateral limb. Plates
were attached as nearly as possible to either the lateral or medial aspect of bone.
The animal test protocol used is outlined in Table 111. All the animals were
observed to be active shortly after surgery. A normal gait appearance and the
retention of muscle mass suggested that the dogs were actively loading the
operated limbs.
Following surgery the animals were radiographed at regular intervals.
After sacrifice at 6 months, the femurs were excised and placed in formaldehyde prior to dehydration and embedding in poly(methy1 methacrylate) for
histological sample preparation. A transverse section was cut from the center
of each bone-fixation plate sample and the remainder of the sample was sectioned longitudinally. The transverse sections were thinned for examination
by transmitted light microscopy, while the longitudinal sections were polished
and viewed using reflected light microscopy.
A computer aided analysis of the percentage porosity observed in the cortical
bone below the higH stiffness plates was carried out. For this purpose, part
of the program reported by Nagurka and Hayes* for determination of bone
sectional properties was used. The calculations were performed on a Tektronix
4051 Minicomputer with a Graphics Tablet and Digitizer. The four segments
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TABLE 111
Implantation Protocol
Laterally plated
Medially plated
Number of
Stiffness Test Animals
Facing and
Core Material
Plate Type
Facing Thickness
316-L-Polypropylene
Ti-6Al-4V-Polypropylene
316L-Polycarbonate
Ti-6Al-4V-Polycarbonate
thick
thick
thin
thin
high
medium
low
low
2
316L-Polypropylene
316L-Polycarbonate
thick
thin
high
low
1
1
1
2
1
BONE REMODELING
857
of each longitudinal section were enlarged to facilitate accurate definition of
the regions of resorption. The cortical bone below the plate was divided into
two halves, namely, the periosteal envelope extending from the plate surface
to the midline of the cortex and the endosteal envelope extending from the
midline to the endosteal surface of the cortex. Percentage porosity calculations
were carried out for each region.
In preparing the longitudinal samples for these measurements, care was
taken to section the bone-plate complex as nearly as possible through the
longitudinal axis of the plate. This insured that the region of most extensive
resorption invariably found along that axis was used in the analysis.
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RESULTS
Elastic property measurements
The results of the axial modulus and bending stiffness measurements for
the different laminate geometries used in the animal tests are shown in Figure
2. The theoretical axial and bending stiffnesses included in this figure were
determined from the following relationships:
Axial modulus:
E,
Bending stiffness: EI = 2E,(zu,ti/
+ VrEr
12 + wmt,d2) + E,(w,t;/ 12)
= V,,E,
(1)
(2)
where Ec,m,p = elastic modulus of composite, metal, polymer; Vm,,= volume
fraction of metal, polymer; I = area moment of inertia; t,,, = thickness of metal,
polymer; w,,~ = width of metal, polymer; and d = distance between neutral
axis and centroidal axis of metal facings.
As can be seen in Figure 2, the experimentally determined stiffnesses were
in good agreement with the theoretical predictions.
It is evident from Figure 2 that an increase in the polymer core to metal
facing ratio resulted in a greater reduction in the axial modulus ( E ) , than in
the bending stiffness (EI). Although not critical for our model studies this
would be a desirable design for a clinical fracture fixation plate since it would
allow the maintenance of a relatively high bending stiffness (useful for fracture
stabilization) while providing a lower axial plate stiffness.
Animal studies
Radiography proved to be an insensitive technique for the study of changes
in bone structure below the plates. Only post-sacrifice histology could,
therefore, be used to assess bone remodeling. Transverse histological sections
from the midlength region of the plated bones were examined for both bone
ingrowth (porous surfaced plates) and for evidence of bone remodeling (resorption and formation).
The interface region of a high stiffness porous surfaced plate and the
underlying bone is shown in Figure 3. Osteocytes are visible up to and within
858
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SZIVEK ET AL.
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v)
W
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LL
3 1 6 L S S Polymer Laminate
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9-
N
.
.
1
0
Strain r a t e
A
Strain rate 7 5 p s t r a i n
Spstrain,
T I - B A I - ~ V Polymer Laminait
8-
8
7-
Straln r a t e
\Strain
gpstrain,
rate 75 psirain,
6--
LL 5I-
-I
4-
a
5x
3-
2
2-
w
1-
(b)
__ - 3 1 6 L S S
____ T i - 6 A I - 4 V
0 1
I
0
1
P o l y m e r L a m i n a t e s (theoretical)
Polymer Laminates (theoretical)
I
2
1
3
4
P O L Y M E R CORE T H I C K N E S S ( m m )
Figure 2(a). Axial modulus of laminates as a function of polymer core thickness. (b) Bending stiffness of laminates as a function of polymer core thickness.
the porous surface region of this plate. Similarly, ingrowth of bone was observed into at least some regions of the porous surface layers for all the porous
surfaced plates. For some of the specimens fibrous tissue was observed toward
the edges of the implants (specifically for lower stiffness plates). However,
there was sufficient area of bone ingrowth for all the plates to ensure that the
BONE REMODELING
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859
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Figure 3. Interfacial region of high stiffness laminate and bone showing
bone ingrowth into the porous surface layer of the laminate (250X).
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plates were rigidly fixed. Any attempt to physically remove the plates resulted
in either their delamination or failure through the bone. The interface itself
remained intact. Effective stress transfer, thus, was assured between bone
and all the different stiffness composite plates.
For the laterally plated femurs the most severe resorption occurred below
the thick stainless steel faced plates, i.e., the high stiffness composite plates.
This is demonstrated in Figure 4(a). In the transverse section of the bone
plated with a high stiffness laminate [Fig. 4(a)] it is seen that resorption has
occurred directly below the plate at the periosteal surface. The area of bone
resorption extends only part way through the cortex with dense cortical bone
being retained at the adjacent zone toward the endosteal surface. The longitudinal section indicates that the bone resorption occurred below the plate
from the most proximal to the most distal screw. Regions of bone formation
are also evident below this high stiffness plate. Extensive new bone was
formed below the edges of the plate and at the periosteal surface of the diametrically opposed cortex [regions A and B, respectively, in Figure 4(a)]. Only
minor amounts of intracortical osteoporosis are seen below the medium
stiffness Ti-6A1-4V faced laminate [Fig. 4(b)]. Again evidence of additional
bone formation is apparent beneath the edges of the plate and peripherally
on the opposite cortex. Less new bone formation is observed in this case as
compared to that observed below the higher stiffness plates. The transverse
and longitudinal sections of a bone plated with a low stiffness stainless steel
faced laminate indicate that negligible remodeling (resorption and formation)
occurred and both the cortical thickness and density were retained throughout
the region below the plate [Fig. 4(c)].
For the rnedially plated femurs the most extensive remodeling is also ob-
860
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SZIVEK ET AL.
(a)
(b)
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(C)
Figure 4(a). A transverse section of a bone plated on the lateral aspect with
a high stiffness 316L facing laminate. Oseoporotic bone is clearly evident at
the periosteal surface of the plate below the center of the plate. Regions A
and B are regions of bone formation (3X). (b)A transverse section of a bone
plated on the lateral aspect with a medium stiffness Ti-6A1-4V laminate.
Some intracortical osteoporosis is visible below the plate. Regions of bone
formation can also be seen below the plate and on the diametrically opposite
periosteum (3X). (c) A transverse section of a bone plated on the lateral aspect with a low stiffness 316L laminate. No resorption has occurred below
this plate. Cracks in the polycarbonate core are an artifact of the histological
preparation process (3X).
served below the high stiffness plate [Fig. 5(a)]. Resorption below this plate,
however, occurred at the endosteal surface of the bone and throughout most
of the cortex with dense cortical bone being retained near the periosteal surface. Bone formation at the plate edges and on the lateral periosteal surface
is also evident. No obvious regions of resorption are seen below the low
stiffness laminate, as seen in Figure 5(b) and, although a thin bone spur appears
to have formed posteriorly, this is not extensive.
Observations of the contralateral limbs that were plated with smooth surfaced plates attached by screws only demonstrated negligible remodeling of
bone in all instances, regardless of plate stiffness. This result is consistent with
our earlier studies on higher stiffness, all-metal plates? in that there was much
less resorption under the plates attached using screws only.
The quantitative analysis of the porosity below the midline regions of the
high stiffness plates is shown in Figure 6. Porosity below the two laterally
plated cases is greater in the periosteal envelope than in the endosteal envelope. In the first laterally plated case, it should be noted that although the
difference in percent porosity is not very great the average percentage porosity
for the whole section is very high. For the medially plated bone the porosity
is significantly higher in the endosteal envelope than in the periosteal envelope.
BONE REMODELING
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861
(a)
Figure 5(a). A transverse section of a bone plated on the medial aspect with
a high stiffness 316L laminate. Gross endosteal resorption is evident below
the center of the plate. Extensive bone formation is also visible below the
edges of the plate and on the periosteum of the diametrically opposite cortex
(5X). (b) A transverse section of a bone plated on the medial aspect with a
low stiffness 316L laminate. N o visible resorption has occurred below this
plate. The cracks in the polycarbonate core of the plate are an artifact of the
histological preparation process (5X).
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DISCUSSION
During gait, the femur is stressed as a result of axial, bending, and torsional
components of the applied Ioad and muscle forces. The bending component
a ) LATERAL
b)
C)
LATERAL
MEDIAL
P
-
P
E
P
E
P
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Cortical Bone
Percent
b e l o w Plate
Porosity
P e r i o s t e a l Envelope
E -Endosteal Envelope
--
I
65.3 %
57.4 %
7.9 %
55.5 %
30.9 %
24.6 %
22.5 %
40.3 %
70.0 %
L-!
A%
- Cortical Bone
-
Resorption Cavities
Figure 6. A schematic diagram of porosity in the cortex below high stiffness
plates for laterally and medially plated cases. Percent porosity is shown for
the periosteal envelope and endosteal envelope of each section. The A% indicates the difference in porosity between the two regions.
SZIVEK ET AL.
862
will result in a variation of stress across the cortex with a maximum tensile
stress occurring toward the lateral periosteal surface and a lower level of stress
at the endosteal surface. On the medial surface a maximum compressive stress
acts at the periosteum with a lower amplitude stress on the endosteal surface.
The axial stress component imposes a compressive stress on the femur. Superposition of the bending and axial stress components results in an anterior-lateral displacement of the neutral surface, i.e., the plane on which
bending stresses are zero. In addition, a torsional stress component, which
imposes a circumferential shear stress, and transverse shear stress components
will act on the bone. Superposition of all of these components would define
a region of low stress within the femur at every position during the gait
cycle.
An analysis to determine the exact position of this low stress region in a
bone, (with or without plate), would require strain determinations during gait
using in vivo strain gauging techniques which were beyond the scope of this
study. A qualitative explanation of the observed remodeling is, however,
possible and will be presented here.
Since the main objective of this study was an investigation of the effect of
stress shielding on bone resorption a discussion of the observed resorption
below the plates will be dealt with first. The new bone formation noted will
be discussed thereafter.
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Bone resorption
When a plate is fixed to the surface of the femur, the bone-plate complex
can be considered an eccentrically loaded composite column. The redistribution of stress between the plate and the bone will depend on the plate
stiffness, its position on the surface of the bone and the nature of the bond
between the implant and bone. Secure attachment of a high stiffness plate
to the lateral aspect of the femur will result in a reduction in the normal tensile
stress component due to bending acting in the cortex just under the plate, as
well as a reduction in the axial compressive stress component, torsional stress
component and transverse shear component under the plate. The result of
these altered stress components is a shift of the low stress region in the lateral
direction. As a result, the low stress region occurs near the lateral periosteal
surface for the femurs with high stiffness plates fixed to the lateral aspect. The
effect of the low stress state in this region is the observed bone resorption under
the plate at the lateral periosteal surface and part way through the cortex [Fig.
4 ~ 1 .
For the medially attached plate, similar reasoning will indicate a shift in the
low stress region. For this case, the neutral axis shift is in the medial direction.
Because the neutral axis for the unplated bone is lateral to the centroidal axis,
the position of the neutral axis for the medially plated bone is medial to, but
closer to the femoral axis. From the observed remodeling for the medially
placed, high stiffness composite plate, the resulting low stress region occurs
near the medial endosteal cortical bone surface. Again, after six months the
resorption was only partly through the cortex [Fig. 5(a)].
BONE REMODELING
863
For lower stiffness plates or poor plate-bone bonding, the stress shielding
effect on the bone is lessened. In our study, this resulted in less bone loss.
In an earlier study6 using porous surfaced metal plates attached by bone
ingrowth to the lateral surfaces of dog femurs extensive loss of cortical bone
was also observed. In that experiment, the six-month implantation of the
higher stiffness stainless steel plates resulted in resorption virtually completely
across the cortex immediately under the plates. The high stiffness composite
laminates used in the present study were about 0.5 times as stiff axially and
0.85 times as stiff in flexure as the all-metal plate used in that earlier study.
This difference in stiffness was apparently sufficient to result in the partial
intra-cortex resorption that was observed. This also allowed us to observe a
subtle difference in remodeling for the laterally and medially placed
plates.
The computer aided porosity analysis of the longitudinal sections verified
that this difference occurred along the length of the bone section and was not
a sectioning effect noted at the midlength only. The difference in osteoporosis
as a function of position in the cortex (i.e., endosteal vs. periosteal envelope)
is significant for femurs (b) and (c) in Figure 6. The changes in femur (a) although indicating the same trend were less dramatic. This sample, however,
showed the greatest overall porosity suggesting that the load history for this
animal was such that the particular plate stiffness used in the experiment
masked any differences in remodeling at six months, i.e., the plate stiffness
was too high to clearly indicate the differences shown by femurs (b) and (c).
This gross overall loss of bone was also noted in an earlier study using higher
stiffness (all metal) plates.6
Our observations support the hypothesis that a minimum stress is required
to prevent gross bone resorption. Other studies of resorption after prolonged
recumbency, immobilization or weightlessness have also indicated that a
minimum stress is required to prevent resorption and other physiological
change~.~-l~
A determination of the minimum stress necessary to maintain a healthy bone
structure would be highly desirable, not only for the design of load-bearing
implants, but also for an appreciation of patient treatment during prolonged
bed rest. It would also be useful for the definition of gravity simulation
conditions required in space to avoid physiological and anatomical changes
in man. Such an analysis could not be made in this study because of limited
information regarding the exact load-strain history acting on the femur during
normal animal activity. Such an analysis should be possible with refined
experimentation.
Bone formation
It was noted that toward the edges of the higher stiffness plate extensive
new bone had formed. Additionally, cortical thickening was observed at the
ends of these plates. These regions correspond to zones in which stresses are
transferred between bone and plate and as such are regions of higher stress
SZIVEK ET AL.
864
concentration. The buildup of bone in these regions is thus a response to the
increased stresses in the area.
The formation of bone on the diametrically opposed periosteum (with respect to the plate position) can also be explained by enhanced stress levels. The
shift in the neutral surface caused by the plate, in addition to reducing stresses
on the plated surface by reducing the distance from the plate to the neutral
surface, would also increase the stresses on the diametrically opposed cortex.
The greatest amount of new bone formed (as expected) was on the bones plated
with high stiffness plates. The limited number of samples and the large
variation from one test animal to the next, however, warrants a note of caution
i n any quantitative judgment of this sort.
CONCLUSIONS
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(1) A comparison of high stiffness composite implants attached by bone
ingrowth to others attached conventionally using screws demonstrated more
extensive bone remodeling for the biologically attached implants.
(2) This remodeling was strongly dependent on implant stiffness with
negligible effects being observed for well-bonded plates with an axial stiffness
of about 0.3 times (70 GPa) and flexural stiffness of about 0.6 times (6N m2)that
of a stainless steel plate.
( 3 )For implants of a critical stiffness, a difference in remodeling, (principally
resorption), was demonstrated for plates attached to the lateral and medial
aspects of the femur.
The authors are grateful to the Atkinson Charitable Foundation for financial support
for the program. The assistance of the Ontario Ministry of Health through a Senior Scientist
Award is gratefully acknowledged by one of the authors (RMP). Additionally, we would
like to thank Deloro Orthopaedic, a division of Canadian Oxygen Ltd., and the Ontario
Research Foundation for assistance with materials supply and fabrication of parts.
References
1. T. Slatis, E. Karaharju, T. Holmstrom, J. Ahonen, and P. Paavolainen,
"Structural Changes in Intact Trabecular Bone after Application of Rigid
Plates with and without Compression," 1. Bone It. Surg., 60-A, 516-522
(1978).
2. A. J. Tonino, C. L. Davidson, P. J. Klopper, and L. A. Linclau, "Protection
from Stress in Bone and its Effects. Experiments with Stainless Steel and
Plastic Plates in Dogs," 1. Bone It. Surg., 58-B,107-113 (1976).
3. H. K. Uhtoff and F. L. Dubuc, "Bone Structure Changes in the Dog under
Rigid Internal Fixation," Clin. Orfkop. Relat. Res., 81, 165-170 (1971).
4. S. L-Y. Woo, Mi. H. Akeson, R. D. Coutts, L. Rutherford, D. Doty, G. F.
Jemmott, and D. Amiel, "A Comparison of Cortical Bone Atrophy Secondary to Fixation with Plates with Large Differences in Bending Stiffness,''
1. BoneJt. Surg., %-A, 190-195 (1976).
5. B. J-L. Moyen, P. J. Lahey, E. H. Weinberg, and W. H. Harris, "Effects on
Intact Femora of Dogs of the Application and Removal of Metal Plates,"
I . Bone It. Surg., 60-A, 940-947 (1978).
6. R. M. Pilliar, H. U.Cameron, A. G. Binnington, and J. Szivek, "Bone Ingrowth and Stress Shielding with a Porous Surface Coated Fracture Fixation Plate," 1. Biomed. Mafer. Res., 13,799-810 (1979).
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BONE REMODELING
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865
7. R. M. Pilliar, and H. U. Cameron, and I. Macnab, ”Porous Surface Layered
Prosthetic Devices,” Biomed. Eng., 10 (4), 126-131 (1975).
8. M. L. Nagurka and W. C. Hayes, “An Interactive Graphics Package for
Calculating Cross-sectional Properties of Complex Shapes,” J . Biomech.,
13,59-64 (1980).
9. D. P. Cuthbertson, “Influence of Prolonged Muscular Rest on Metabolism,”
Biochem. J., 23, 1328 (1929).
10. J. A. Gillespie, ”The Nature of Bone Changes Associated with Nerve Injuries and Disuse,” J . Bone Jt. Surg., 36-8,464-473 (1954).
11. E. R. Morey and D. J. Baylink, “Inhibition of Bone Formation during Space
Flight,” Science, 201,1138-1141 (1978).
12. J. E. Deitrick, G. D. Whedon, and E. Shorr, “Effects of Immobilization upon
Various Metabolic and Physiologic Functions of Normal Men,” Am. J. Med.,
4,3 (1948).
13. B. Issekutz, ”Effect of Prolonged Bed Rest on Urinary Calcium Output,”
J . AppZ. Physid., 21, 1013-1020 (1966).
Received September 26,1980
Accepted April 3,1981