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Stress analysis of compression plate fixation and its effects on long bone remodeling
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STRESS ANALYSIS OF COMPRESSION PLATE FIXATION AND ITS EFFECTS ON LONG BONE REMODELING EDWARD J. CHEAL. WLLSON C. HAVES and AUGUSTUS A. WHITE III Orthopaedic Biomechanics Laboratory, Institute. Beth Israel Hospital
Department and Harvard
of Orthopaedic Surgery. Medical School, Boston.
Charles A. Dana Research MA 01215. U.S.A.
and STEPHAN M. PERREN Laboratorium
fur Experimentelle
Chirurgie.
Schweizerisches Schweiz
Forschungsinstitut.
CH-7270
Davos.
Abstract-A three-dimensional finite element model is generated for an intact plexiglass tube with an attached six-hole stainless steel compression plate. The results for a wide range of loads. including cyclic external loads and static tensile preloads in the plate and screws, are examined as specifically related to plateinduced osteopenia. The model demonstrates that disuse osteopenia, resulting from a reduction in magnitude ofcyclic axial stress, should be limited to the central region between the inner screws. Also, the addition of a static preload negates any reduced axial stress levels in this region, thus raising questions on the relative importance of static and cyclic stresses for the internal remodeling of bone.
INTRODlKTIOK
In the early stages of fracture repair, the function of an internal fixation device is to rigidly immobilize the fracture fragments. This allows bony union to proceed and encourages functional utilization of the injured extremity. In the late stages of fracture repair, however, a loss of bone mass may occur. Many researchers attribute this loss to decreased stresses in the bone tissue during functional loading of the plate-bone system. Another possibility raised more recently is that ‘plate induced osteopenia’ is the result of vascular insufficiency (Gunst, 1980). Previous workers have demonstrated that the bone remodeling response is at feast in part a function of the plate mechanical characteristics. More rigid internal fixation, through increased plate elastic modulus (Akeson et al., 1976; Tonino et al., 1976; Woo et ol., 1976). increased plate thickness and elastic modulus (Moyen et al., 1978). or through the addition of a porous ingrowth layer (Pilliar er al., 1979). generally results in greater bone loss. However, literature reports of regional changes in cyclic bone stresses have not correlated well with the distribution of morphological changes. Also, the type and sequence of remodeling, such as increased porosity or cortical thinning. has been inconsistent. Akeson
et al. (1976) and
Woo
er al. (1976) examined
bone remodeling in response to IWO plates of different rigidities. Vitallium plates and less rigid graphite fiber methylmethacrylate (GFMM) plates were fixed to the anterior aspect of intact canine femora. At 9 and 12 months following plate application, mechanical, histological and cortical thickness studies were performed. Receired ? I Marc/l
1983; in rerisedjornl
7 June 1984. 141
The mechanical studies indicated that the bones beneath the Vitallium plates were structurally weaker than the bones beneath the GFMM plates. However, the bone material properties were similar for both groups of plated bones. The weakening of the bones resulted from a reduction ofcortical thickness, through enlargement of the medullary canal. especially in the anterior (plated) aspect. No significant difference existed in percentage of unlabeled old bone, in tetracycline labeled new bone, or in cortical porosity beneath the different plates. Furthermore, the cortical porosity was found to be in the normal range for canine long bones. Decreased bone blood perfusion following plate application was demonstrated by Gunst (1980). Large ischemic areas were found directly beneath fixation plates 1 day following application lo intact rabbit and sheep tibiae. A 10 week period was required for the complete restoration of bone blood supply. Correspondingly. remodeling activity was first observed in the third week, and reached a peak at seven to eight weeks following plate application. At 10 weeks, the metabolic activity. characterized as predominantly Haversian remodeling. continued, but at a reduced level, leaving a weakened and porous cortex. To explore the decreased stress hypothesis, investigators have used composite beam theory (Carter et al., 1981a, b) and finite element models (Woo er al., 1977; Simon er al., 1978) to predict the cyclic bone stresses following plate fixation. The predicted stress resultants were then related to the observed remodeling response (Woo et a/., 1976; Carter et al., 1981a) or parametric analyses were performed to predict the remodeling response (Simon et al., 1978). An alternate approach was to measure directly the in riro locomotor strains and relate the strain reductions to the observed remodeling (Baggott er al., 1981).
142
E. J. CHEAL. W. C. HAYES, A. A. WHITE Ill and S. M. PERREN
WOO TVal. (1977) used a one-dimensional beam finite element model to predict the cyclic bone stresses in an intact plated human femur. The model results were correlated to the long term remodeling response of intact canine femora to two plates of different rigidities. The bone morphological response was as reported earlier by Akeson et a/. (1976) and Woo et al. (1976). For the more rigid Vitallium plate, the model predicted significant stress reductions, especially directly beneath the center of the plate. For the less rigid GFMM plate the stress reductions were considerably less. These results were correlated with the observed cortical thinning which occurred directly beneath the rigid Vitallium plate. Carter et ~1. (198la) correlated predicted changes in bone stresses with the remodeling responses in several previously reported experimental studies using plates fixed to canine femora (Uhthoff and Dubuc, 1971; Akeson et ul., 1976; Tonino et a/., 1976; Wooer al., 1976; Moyen ct n/., 1978; Bradley et al., 1979; Pilliar et al., 1979). Calculations of thealterations in the in cico cyclic bone stresses due to external loading were made using composite beam theory, after determining the bone and plate sectional properties. Examples were presented wherein significant differences in bone loss were observed for plates of different rigidity. The maximum reductions in predicted cyclic bone stresses, however, were approximately 1 MPa, from normal stress levels in the range of 2.3 MPa tension to 5.1 MPa compression. They concluded that bone remodeling is very sensitive to small changes in cyclic bone stresses. There are limitations associated with the use of composite beam theory for predicting stress resultants in bone-plate systems. As we have shown previously, composite beam theory is relatively accurate for predicting the axial stress component in the cross-section at the center of the plate for externally applied axial and bending loads (Cheal et al., 1984). However, static stress fields due to plate and screw pretension must be determined using more complex models. Static stress fields are also difficult to monitor over long periods of time using in rim strain gage techniques. In addition, to properly relate the complete resultant stress fields to the observed remodeling responses, both circumferential and longitudinal variations in stress and remodeling must be established. Thus, only a three-dimensional analysis can completely relate altered stress resultants to the remodeling response. The objective of this investigation was to characterize the resultant stress fields for a geometrically idealized compression plate fixation system. A threedimensional finite element model of a six-hole, selfcompressing stainless steel plate applied to an intact plexiglass tube was previously presented (Cheal et al., 1984). Comparisons with strain gage data from a physical model and a composite beam theory solution were included. along with other relevant data, such as model deflection patterns and screw resultant forces. In this paper, the results for a range of applied loads, including plate and screw pretension, are examined as
specifically related to plate-induced osteopenia. The current hypotheses for plate-induced osteopenia are reviewed to establish a relationship between the controlling factors and the tissue response.
ANALlTICAL
METHODS
We analyzed a six-hole, self-compressing, 3 16L stainless steel plate. The plate was 10.3 cm long, 1.2cm wide, and 0.38 cm thick, fixed by six standard stainless steel cortical screws. The screws passed through the plate and both sides of a plexiglass cylinder. The compression plate was applied to the center of a 29cm long plexiglass tube with an inside diameter of 1.90 cm and an outside diameter of 2.54 cm. One quarter of a symmetrical model was analyzed with the mesh shown in Fig. 1. Symmetry was maintained by displacement constraints on the nodes in the planes of symmetry. The tube was represented by 128 twenty-node three-dimensional isoparametric solid elements (Bathe and Wilson, 1976) and the plate by 10 twenty-node solid elements, for a total of 963 nodal points. It was possible to use elements with poor aspect ratios (approximately 27:l) in the tube beyond the plate since this was outside the main region of interest. Only linear elastic isotropic elements were used. An elastic modulus of 3.1 GPa and Poisson’s ratio of 0.2 were used for the plexiglass tube, which represent properties for low to moderate load under static conditions. For the stainless steel compression plate and fixation screws an elastic modulus of 196 GPa and a Poisson’s ratio of 0.3 were used. The compression plate and plexiglass tube interact indirectly through the screws and directly through plate-tube contact along the outer edges of the plate. For this study, stiff linear trusses were used along the line of contact between plate and tube. The trusses represented sliding contact, such that only axial truss forces (normal to the tube surface) were transmitted. This assumed that the shear forces transmitted through plate-tube friction were negligible. Ideally, nonlinear trusses, with a low elastic modulus in tension, could be separation possible. ‘stress-free’ making used, However, the addition of this nonlinearity would make the mode1 solution much more complex and expensive. This factor will be studied in future models.
Fig. I. Three-dimensional finite element mesh of the plexiglass tube/compression plate system. Hidden line option used to avoid excessive detail.
113
Stress analysis of compression plate fixation In the clinical application of compression plates. tensile stresses are generated in both plate and screws in order to create the desired compressive stresses at the fracture site. To simulate plate pretension, applied longitudinal displacements were used at the center of the plate. The magnitude was chosen to result in a longitudinal tensile load in the plate of approximately 490 N. The beam elements representing the screws were defined using the corresponding nodal points from the twenty-node solid elements. Two additional nodes, yielding one additional internal element, were used adjacent to the plate-tube interface for each screw. Tensile stresses in the screws were generated by imposing internal compressive forces in this element. Resulting axial screw forces of approximately 200 N were used in the region at the plate-tube interface. Thus. the beam elements were equivalent to surgically applied fixation screws threaded through both cortices. The applied loads were chosen to provide a general set of representative loading conditions. Six individual load cases were examined. as shown in Fig. 2. The five external load cases (A-E) represented possible modes of applied cyclic load, whereas the internal load case (F) represented a static load resulting from plate and screw pretension. The superposition of load cases A-E with load case F was also possible, since linear behavior was assumed throughout. The externally applied load cases are assumed to represent typical loading modes for plate-bone systems caused by the activities of daily
living. Such loads could be expected to be time varying as opposed to the static pre-stress generated by tensile loads in the screw and plate. The analyses were performed using ADINA. a finite element program for automatic dynamic incremental nonlinear analysis (ADINA Engineering. Inc.). Preand post-processing were accomplished using FEMGEN, a finite element mesh generator and FEMVIEW. a finite element mesh and result viewing program ( JAR Associates, Inc.). ADINA provided the interpolation of elemental integration point stresses to the nodal points. In-house software calculated the principal stresses and direction cosines and converted the data to the input format for FEMVIEW. FEMVIEW was then used to generate graphic plots of nodal displacements, stress contours. and principal stress vectors. All work was performed on a VAX I l/780 computer. The results of strain gage experiments designed to test the validity of the finite element model were previously reported (Chedl YI u/.. 1984). There was good correspondence for the longitudinal strain components for both axial compression and four-point bending. The finite element results were also contrasted to a composite beam solution. demonstrating the importance of relative motion between the plate and the tube. Both the finiteelement modeland the physical model indicated that relative motion does occur but composite beam theory does not allow for relative motion between sections. The mechanical properties of the plexiglass tube used in this investigation must be compared to the mechanical properties of bone. Table I contrasts the axial and bending rigidities of the tube to typical canine and human femur mid-diaphyseal rigidities. The plexiglass tube is most comparable to the canine femur. The tendency is for higher bending and lower axial rigidities with the plexiglass.
0 RESULTS
n1 CU
E
I I
1 j
B 0 -it-
--
F
The longitudinal, normal stress distributions for the tube cross-section beneath the center of the plate are shown in Fig. 3 for load cases Band C. Included are the predicted stress distributions for the unplated and the plated tube. The most obvious effect of plate application is a shift of the neutral axis towards the plate (the top of each figure). For uniform axial loading of the tube. this changes the constant stress state to a combination of axial and bending stress. This effect is minimized for an off-center axial load (load case B). For
(
(
Table 1. Axial and Rexural regidities
I
Fig. 2. Load cases A-F, respectively. Load cases A-E represent cyclic external loads, whereas load case F represents a static internal preload. From Cheal CI al. (1954).
Plexiglass tube Canine femur Human femur
Axial rigidity (MN)
Bending rigidity (Nm’)
0.7 2.1 6.0
50 26 390
144
E. J. CHEAL, W. C. HAYES, A. A. WHITE III and S. M. PERREN
(a)
b)
w J
Fig. 3. (a) Contour plots of the longitudinal normal stresses beneath the center of the plate for the unplated and plated tube. Shown is the unplated tube. load case B. All stresses are in MPa. (b) Plated tube, load case B. (c) Unplated tube, load case C. (d) Plated tube, load case C.
a highly off-center axial load, however, there is an upward shift of the neutral axis to the plate/tube interface. Plate application also reduces the magnitude of the longitudinal stresses, especially in the region directly beneath the plate. This ‘stress protection’, measured as a percentage of the stress level generated by the same load case applied to the unplated tube, ranges from an 80 to a 95 y0 decrease for load cases A, C, D and E, to a slight increase in magnitude in this region for load case B. To further examine the question of stress protection, the longitudinal, normal stress contours at the inner. middle, and outer screw locations are presented for the highly off-center axial load (load case C; Fig. 4a-c). Figure 3c and d represents the reference conditions for the unplated and plated tube beneath the center of the plate. At the inner screw location, there is still a 50% reduction in stress level compared to the unplated tube. This compares to an 83 % reduction at the center of the plated tube for this load case. At the middle screw location, however, there is a sharp horizontal gradient
reaching a local maximum which exceeds that predicted for the unplated tube. At the outermost screw, there is a three-fold increase in longitudinal stress, indicating a significant stress concentration. This is consistent with the high level of loading in the outermost screw (Cheal et al., 1984). The distribution of longitudinal normal stresses resulting from static pretension in the plate and screws (load case F) is markedly different from those resulting from the applied external loads. Figure 5 shows the induced static stresses on the tube cross-section bcneath the center of the plate. There is an approximately linear stress gradient going from tension, on the side opposite the plate, to compression, directly beneath the plate. The transition from compression to tension occurs at approximately two-thirds of the distance from the plate to the bottom of the tube. The superposition of a static preload with the individual external load cases was examined. The resulting stress distribution for load case C is shown in Fig. 6. With plate pretension, there are no longer
Stress analysis of compresston plate tixatton
Fig. 5. Longitudinal normal stress magnitudes for load case F beneath the center of the plate. All stresses are in MPa.
Fig. 6. Longitudinal normal stress magnitudes for load case C with superposition of the static preload (load case F). All stresses are in MPa.
IC)
Fig. 4. (a) Longitudinal normal stress magnitudes for load case C at the three screw locations. Shown is the inner screw location. All stresses are in MPa. (b) Middle screw location. (c)Outer screw location.
reduced longitudinal stress levels in the region beneath the plate for load cases A through C. Load cases D and E retain longitudinal stress reductions of 2: y0 or less. Vector plots of the principal stresses in the plexiglass
tube were examined for load cases C, F and the combined loading C & F. Two representative views are presented in Figs 7 and 8. Maximum and minimum here refer to the algebraic maximum and minimum principal stress components (Pl and P3, respectively). This approach effectively separates the tensile stresses from the compressive stresses. Figure 7 corresponds to the maximum principal stresses for load case C in the region beneath the outer end of the plate. Figure 8 corresponds to the minimum principal stresses for the combined loading C & F in the region beneath the center of the plate. Load case C results in high magnitude axial tensile stresses at the screw locations, with the magnitude increasing from the innermost to the outermost screws. At the outermost contact point between plate and tube, there is a high magnitude tensile stress (7.0 MPa) directed approximately 30. off
E. J. CHEAL. W. C. H.&YES.A. A. WHITE III and S. M. PERREN
46
r ,___------_____ - ____ - _________ r ‘-p___-____-_________-____-_____;-‘,
r_;________‘__
8 . ,
Fig. 7. Vector plots of principal
____
-. . .l
_--r._
_______
____
____
______--__--__-‘-_~-____~
stress PI for load case C. The region around an expanded view.
the end of the plate is show-n in
Stress analysis
.______..-..__
. . . . . . -__
of compression
. . ..-
plate tixation
---e-L-
.
I
.
.
.
.1 4 I
8
Fig. 8. Vector plots of principal
stress P3 for load case F. The region beneath the center of the plate is shown in an expanded view.
148
E. I. CHEAL. W. C. HAYES. A. A. WHITE III and S. M. PERREN
vertical (Fig. 7). indicating a tendency for plate separation from the tube surface. The tensile stresses are highest in the region beneath the outer end of the plate (see Discussion). The minimum principal stresses (not shown) for load case C exhibited less longitudinal variation, with a linear gradient of axial compressive stresses occurring over most of the tube cross-section. There is, however, a significant longitudinal increase in magnitude at the level corresponding to contour F in Fig. 5a. The magnitude increases from 0.4 MPa at the plate end to 1.0 MPa at the plate center. Immediately beneath the plate, the minimum principal stresses are of low magnitude throughout the length. The maximum principal stresses for load case F are tensile, occur at the three screw locations, and are directed at an oblique angle between horizontal and vertical, as expected for the combination of plate and screw pretension. The minimum principal stresses display radially directed compressive stresses beneath the plate at the screw locations and along the line of plate contact, as a consequence of screw pretension. A static preload results in axial compressive stresses beneath the center of the plate, as seen in Fig. 8. The maximum principal stresses which result for the combined loading of C & F, are similar to those for load case F alone, indicating the dominance of resultant stresses due to plate pretension. The minimum principal stresses (Fig. 8) are similarly distributed, except for the lower region of the tube, where the axial compressive stresses of load case C assume importance.
DISCUSSION
A reduction in externally generated longitudinal stresses in the region under a compression plate is well documented. There have also been attempts to relate the predictions of stress reduction to the observed osteopenia beneath the plate. If, as has been implicitly assumed in all previous models for ‘stress protection’, osteopenia is related to a reduced level of longitudinal normal stress, then our results suggest that the relationship between compression plate fixation and the development ofosteopenia in the underlying bone may be more complex than previously thought. Our results demonstrate that the stress reduction in the tube is dependent upon the particular combination of externally applied load and plate pretension. Plating the tube does not result, for instance, in stress reductions beneath the plate for the case of off-center axial loading, a possible type of loading encountered in ciao. The results also demonstrate that the observed stress reduction is only significant between the innermost screws. At the middleand outer screws the longitudinal normal stress was actually increased in comparison to the unplated tube. In the long term response to plate fixation, cortical thinning due to reductions in stresses generated by external loads should be limited to the central region between the inner screws. The radiograph in the study of Moyen et al. (1978) confirms this
finding. The demonstrated cortical thinning beneath the more rigid plate is apparent primarily in the central region, between the inner screws. The finite element model further suggests that ‘stress protection’ is more completely described as an exchange which results in stress concentrations around the screws. The stress fields beneath the entire length of the plate are clearly altered. but only a relatively small region of bone displays reduced stress levels. In addition, in our model, high magnitude tensile stresses occur beneath the outer end of the plate. However, the presence of these tensile stresses in the clinical application of compression plates is dependent on the plate-bone interface characteristics. As mentioned above, the modeling technique employed in this investigation did not allow for stress-free plate-tube separation, since nonlinear interface elements would have been required. High magnitude stresses will result beneath the ends of plates which have a porous ingrowth surface, but it is unlikely that the same is true for other plate types. Szivek er a/. (1981) studied bone remodeling following internal fixation with metal-polymer laminated plates containing a porous ingrowth surface. Increased cortical thickness was in fact observed near the plate ends which they attributed to the higher bone stresses expected in this region. In an earlier study, Pilliar et al. (1979) demonstrated that metal plates with a porous ingrowth surface result in significantly greater bone resorption than similar plates having a smooth surface. The strong influence of changing plate-bone interface conditions suggests that further parametric studies of this interface are warranted. The surface boundary conditions are violated for a small region for load case C, as seen in Fig. 7. More specifically. the resultant stresses are not oriented tangential to the external surface for several nodes on the upper surface of the tube located one element length beyond the end of the plate. Beneath the plate, higher magnitude tensile stresses occur which also are not oriented tangential to the surface. However, these stress components are accounted for by the linear truss elements which simulate the sliding contact between the plate and the tube. The finite element method used in this analysis is displacement based and thus the element interpolation functions need only satisfy geometric boundary conditions. The geometric boundary conditions are specified at the boundaries of the continuum, in this case the two planes-of-symmetry, and the inter-element continuity conditions are maintained. A numerical consequence of this is the occurrence of stress resultants which may not satisfy the stress boundary conditions, especially immediately adjacent to externally applied loads. In this instance, rather than an external load, the stress resultant from the truss interface element at the end of the plate is responsible. However, the occurrence of this anomaly does not influence the stress distributions in other areas, such as in the tube beneath the center of the plate. Rather than invalidating the
Stress analysis of compression plate tixation
modeling
technique.
inexact
nature
this
of
is a demonstration
the
finite
element
of the
method
as
149
stresses. may be insufficient to predict response of bone to internal fixation.
the remodeling
implemented. Perren
et al.
(1969)
demonstrated
an exponential
decay with time in the static pretension
plate
and
screws
at the time
of
developed plate
in the
application.
a small region of reduced stress levels. Since the level of
A three-dimensional finite element model of compression plate fixation was used to study the mechanics of plate-induced osteopenia. The results were presented for a wide range of loads, with and without an internal preload in the plate and screws. The following conclusions may be drawn from this study: (1) disuse osteopenia should be limited to the central region between the inner screws: (2) a static tensile preload in the plate results in high magnitude compressive stresses in the adjacent bone. which should be considered in models of plate-induced osteopenia; and (3) the inter-
preload
dependence
However,
as demonstrated
the resultant period
static
are
highly
significant
stresses due to internal
plate tension
by the finite element model.
stresses during
with
relative
loading.
externally
the early to
fixation
the cyclic
The superposition
applied
of
loads effectively
negates any reduced stress levels in the region adjacent to the plate. For pure bending
with
the plate on the
tensile aspect (load case D). a common dition
encountered
changes from tension
loading
con-
the axial stress magnitude
in Gvo.
to compression,
resulting
in only
decays with time, it may be most instructive
create a ratio to internal predict
between
loading.
the level of external
This
ratio
may then be utilized
for a particular
the stress magnitude
to
loading to
plate does not elect
that a static preload
the remodeling
pattern
al., 1975). Slatis PI (I/. ( 1975) also examined static
compression
significant
on
difference
compression
bone
was the earlier
lary cavity, remains
appearance
response
was an increase in the outer
bone, with cortical
(Matter The
thinning.
and increased porosity.
as to the relative
of
of morpho-
regardless
of the
diameter
of the
enlargement
of the medul-
Thus, the question
importance
and
insufficiency
the subsequent
response warrants
further
followadaptive
consideration.
Acl;now/rdgpmmr-Supported by NIH RCDA AM 00749, AM 26740 and a research grant from SYNTHES Ltd.
et
only
associated with the application
logic changes. The overall preload
in the
the effects of
remodeling.
remodeling
the vascular
level of
preload. It has been demonstrated
between
ing plate application
of the applied
cyclic loads from daily activities and the static stresses resulting from plate pretension in the long term remodeling response to internal fixation. The results of this study support and expand on the results of a similar three-dimensional finite element model of plate fixation (Simon et al., 1977). Both studies demonstrated that the outer screws are most highly loaded, and that similar stress reductions occur beneath the center of the plate for axial and bending external loads. Our model employed a higher mesh density, with SO”/, more three-dimensional elements, and a wider range of applied loading conditions. The most significant new information provided by this investigation is theconsideration ofpreload in the plate and screws and a more detailed examination of the resultant stresses along the tube length. The long term bone response to compression plate fixation may be influenced by other mechanical factors besides the reduction of axial stress magnitudes. Altered stress fields of any sort may trigger a remodeling response, such as a change in ‘sense’ of the longitudinal stresscomponent (Carter et al. 1981b), the introduction of multi-axial stresses, or a reorientation of the principal stress axes. The results of this study thus demonstrate the complex nature of the altered bone stresses. suggesting that a one-dimensional analysis, which considers only the resultant axial bone
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L.. Coutts, R. D.. Gonslaves. M. and Amiel. D. (1976) The effects of rigidity of internal fixation plates on long bone remodeling. Acfa orrhop. stand. 47, 241-249. Baggott. D. G.. Goodship. A. E. and Lanyon. L. E. (1981) A quantitative assessment of compression plate fixation in vim: an experimentai study using the sheep radius. J. Biomechanics 14, 701-711. Bathe, K. J. and Wilson. E. L. (1976) Numerical Merhods in Finite Elrmrnr Ano!,sis. Prentice-Hall, Englewood Cliffs, NJ. Bradley, G. W.. McKenna. G. B., Dunn, H. K., Daniels. A. V. and Statton. W. 0. (1979) Effects of flexural rigidity of plates on bone healing. J. Bone Jr Surg. 61-A, 866872. Carter, D. R., Vasu, R. and Harris. W. H. (1981a) The plated femur: relationships between the changes in bone stresses and bone loss. Acta orrhop. stand. 52, 241-248. Carter, D. R.. Vasu, R.. Spengler, D. M. and Dueland. R. T. (1981b) Stress fields in the unplated and plated canine femur calculated from in LiVO strain measurements. J. Biomechanics 14. 63-70. Cheal. E. J.. Hayes, W. C.. White, A. A., and Perren. S. M. (1984) Three-dimensional finite element analysis of a simplified compression plate fixation system. J. biomech. Engny. 106, 295-301. Gunst. M. A. (1980) Interference with bone blood supply through plating of intact bone. Currenr Concepts o/lnrerna/ Fixation of Fractures. (Edited by Uhthoff. H. K.). pp. 268-276. Springer, Berlin. Matter, P.. Brenwald. J., and Perren S. M. (1975) The effect of static compression and tension on internal remodeling of cortical bone. He/c. chir. acta Suppl. 12. Moyen, B. J-L. Lahey. P. J.. Jr.. Weinberg, E. H.and Harris. W. H. (1978) Effects on intact femora ofdogs of the application and removal of metal plates. J. Bone Jr Surg. 60-A, 940-947. Perren, S. M., Huggler, A. Russenberger, M., Allgower, M.. Mathys. R., Schenk, R.. Willenegger, H. and Muller, M. E. (1969) The reaction ofcortical bone to compression. Acra. orrhop. scond. Suppl. 125. Pilliar, R. M., Cam&on. H. U., Binnington. A. G., Szibek, J. and Mac-Nob, 1. (1979) Bone ingrowth and stress shielding with a porous surface coated fracture fixation plate. J.
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biomed. mar. Res. 13, 799-810.
Simon. B. R., McCarthy, Evaluation ement and
Woo. S. L-Y.. Stanley, G. M., Olmstead. S. R.. M. P.. Jemmott, G. F. and Akeson, W. H. (1977) of one-two-. and three-dimensional finite elexperimental models of internal fixation plates,
J. Biomechanics 10, 79-86. Simon. B. R., Woo, S. L-Y.. McCarty,
M.. Lee, S. and Akeson. W. H. (1978) Parametric study of bone remodeling beneath internal fixation plates of varying stiffness. J. Bioengng 2, 543-556.
Slatis, P., Karaharju. E., Holmstrom, T., Ahonen, J. and Paavolainen, P. (1978) Structural changes in intact tubular bone after application of rigid plates with and without compression. J. Bone Jr Surg. 60-A, 516-522. Szivek, J. A. Weatherly, G. C.. Pilliar. R. M. and Cameron. H. U. (1981) A study of bone remodeling using metal-
polymer laminates. J. biomed. mat. res. 15, 853465. Tonino, A. J.. Davison, C. L., Klopper. P. J. and Lineau. L. A. (1976) Protection from stress in bone and its effects. J. Bone Jr Surg. 58-B. 107-l 13. Uhthoff. H. K. and Dubuc, F. L. (1971) Bone structure changes in the dog under rigid internal fixation. c/1,1. Orthop. Rel. Rex 81, 165-170. WOO, S. L-Y.. Akeson, W. H., Coutts. R. D., Rutherford. L., Doty. D., Jemmott, G. F. and Amiel, D. 11976) A comparison of cortical bone atrophy secondary to fixation with plates with large differences in bending stiffness. J. Bone Jr Surg. 58-A. 190-195. Woo.S. L-Y.. Simon. B. R.,Akeson, W. H.and McCarty. M. P. (1977) An interdisciplinary approach to evaluate the effect of internal fixation plate on long bone remodeling. J. Biomechanics
10. 87-95.
PrcuLtd
STRESS ANALYSIS OF COMPRESSION PLATE FIXATION AND ITS EFFECTS ON LONG BONE REMODELING EDWARD J. CHEAL. WLLSON C. HAVES and AUGUSTUS A. WHITE III Orthopaedic Biomechanics Laboratory, Institute. Beth Israel Hospital
Department and Harvard
of Orthopaedic Surgery. Medical School, Boston.
Charles A. Dana Research MA 01215. U.S.A.
and STEPHAN M. PERREN Laboratorium
fur Experimentelle
Chirurgie.
Schweizerisches Schweiz
Forschungsinstitut.
CH-7270
Davos.
Abstract-A three-dimensional finite element model is generated for an intact plexiglass tube with an attached six-hole stainless steel compression plate. The results for a wide range of loads. including cyclic external loads and static tensile preloads in the plate and screws, are examined as specifically related to plateinduced osteopenia. The model demonstrates that disuse osteopenia, resulting from a reduction in magnitude ofcyclic axial stress, should be limited to the central region between the inner screws. Also, the addition of a static preload negates any reduced axial stress levels in this region, thus raising questions on the relative importance of static and cyclic stresses for the internal remodeling of bone.
INTRODlKTIOK
In the early stages of fracture repair, the function of an internal fixation device is to rigidly immobilize the fracture fragments. This allows bony union to proceed and encourages functional utilization of the injured extremity. In the late stages of fracture repair, however, a loss of bone mass may occur. Many researchers attribute this loss to decreased stresses in the bone tissue during functional loading of the plate-bone system. Another possibility raised more recently is that ‘plate induced osteopenia’ is the result of vascular insufficiency (Gunst, 1980). Previous workers have demonstrated that the bone remodeling response is at feast in part a function of the plate mechanical characteristics. More rigid internal fixation, through increased plate elastic modulus (Akeson et al., 1976; Tonino et al., 1976; Woo et ol., 1976). increased plate thickness and elastic modulus (Moyen et al., 1978). or through the addition of a porous ingrowth layer (Pilliar er al., 1979). generally results in greater bone loss. However, literature reports of regional changes in cyclic bone stresses have not correlated well with the distribution of morphological changes. Also, the type and sequence of remodeling, such as increased porosity or cortical thinning. has been inconsistent. Akeson
et al. (1976) and
Woo
er al. (1976) examined
bone remodeling in response to IWO plates of different rigidities. Vitallium plates and less rigid graphite fiber methylmethacrylate (GFMM) plates were fixed to the anterior aspect of intact canine femora. At 9 and 12 months following plate application, mechanical, histological and cortical thickness studies were performed. Receired ? I Marc/l
1983; in rerisedjornl
7 June 1984. 141
The mechanical studies indicated that the bones beneath the Vitallium plates were structurally weaker than the bones beneath the GFMM plates. However, the bone material properties were similar for both groups of plated bones. The weakening of the bones resulted from a reduction ofcortical thickness, through enlargement of the medullary canal. especially in the anterior (plated) aspect. No significant difference existed in percentage of unlabeled old bone, in tetracycline labeled new bone, or in cortical porosity beneath the different plates. Furthermore, the cortical porosity was found to be in the normal range for canine long bones. Decreased bone blood perfusion following plate application was demonstrated by Gunst (1980). Large ischemic areas were found directly beneath fixation plates 1 day following application lo intact rabbit and sheep tibiae. A 10 week period was required for the complete restoration of bone blood supply. Correspondingly. remodeling activity was first observed in the third week, and reached a peak at seven to eight weeks following plate application. At 10 weeks, the metabolic activity. characterized as predominantly Haversian remodeling. continued, but at a reduced level, leaving a weakened and porous cortex. To explore the decreased stress hypothesis, investigators have used composite beam theory (Carter et al., 1981a, b) and finite element models (Woo er al., 1977; Simon er al., 1978) to predict the cyclic bone stresses following plate fixation. The predicted stress resultants were then related to the observed remodeling response (Woo et a/., 1976; Carter et al., 1981a) or parametric analyses were performed to predict the remodeling response (Simon et al., 1978). An alternate approach was to measure directly the in riro locomotor strains and relate the strain reductions to the observed remodeling (Baggott er al., 1981).
142
E. J. CHEAL. W. C. HAYES, A. A. WHITE Ill and S. M. PERREN
WOO TVal. (1977) used a one-dimensional beam finite element model to predict the cyclic bone stresses in an intact plated human femur. The model results were correlated to the long term remodeling response of intact canine femora to two plates of different rigidities. The bone morphological response was as reported earlier by Akeson et a/. (1976) and Woo et al. (1976). For the more rigid Vitallium plate, the model predicted significant stress reductions, especially directly beneath the center of the plate. For the less rigid GFMM plate the stress reductions were considerably less. These results were correlated with the observed cortical thinning which occurred directly beneath the rigid Vitallium plate. Carter et ~1. (198la) correlated predicted changes in bone stresses with the remodeling responses in several previously reported experimental studies using plates fixed to canine femora (Uhthoff and Dubuc, 1971; Akeson et ul., 1976; Tonino et a/., 1976; Wooer al., 1976; Moyen ct n/., 1978; Bradley et al., 1979; Pilliar et al., 1979). Calculations of thealterations in the in cico cyclic bone stresses due to external loading were made using composite beam theory, after determining the bone and plate sectional properties. Examples were presented wherein significant differences in bone loss were observed for plates of different rigidity. The maximum reductions in predicted cyclic bone stresses, however, were approximately 1 MPa, from normal stress levels in the range of 2.3 MPa tension to 5.1 MPa compression. They concluded that bone remodeling is very sensitive to small changes in cyclic bone stresses. There are limitations associated with the use of composite beam theory for predicting stress resultants in bone-plate systems. As we have shown previously, composite beam theory is relatively accurate for predicting the axial stress component in the cross-section at the center of the plate for externally applied axial and bending loads (Cheal et al., 1984). However, static stress fields due to plate and screw pretension must be determined using more complex models. Static stress fields are also difficult to monitor over long periods of time using in rim strain gage techniques. In addition, to properly relate the complete resultant stress fields to the observed remodeling responses, both circumferential and longitudinal variations in stress and remodeling must be established. Thus, only a three-dimensional analysis can completely relate altered stress resultants to the remodeling response. The objective of this investigation was to characterize the resultant stress fields for a geometrically idealized compression plate fixation system. A threedimensional finite element model of a six-hole, selfcompressing stainless steel plate applied to an intact plexiglass tube was previously presented (Cheal et al., 1984). Comparisons with strain gage data from a physical model and a composite beam theory solution were included. along with other relevant data, such as model deflection patterns and screw resultant forces. In this paper, the results for a range of applied loads, including plate and screw pretension, are examined as
specifically related to plate-induced osteopenia. The current hypotheses for plate-induced osteopenia are reviewed to establish a relationship between the controlling factors and the tissue response.
ANALlTICAL
METHODS
We analyzed a six-hole, self-compressing, 3 16L stainless steel plate. The plate was 10.3 cm long, 1.2cm wide, and 0.38 cm thick, fixed by six standard stainless steel cortical screws. The screws passed through the plate and both sides of a plexiglass cylinder. The compression plate was applied to the center of a 29cm long plexiglass tube with an inside diameter of 1.90 cm and an outside diameter of 2.54 cm. One quarter of a symmetrical model was analyzed with the mesh shown in Fig. 1. Symmetry was maintained by displacement constraints on the nodes in the planes of symmetry. The tube was represented by 128 twenty-node three-dimensional isoparametric solid elements (Bathe and Wilson, 1976) and the plate by 10 twenty-node solid elements, for a total of 963 nodal points. It was possible to use elements with poor aspect ratios (approximately 27:l) in the tube beyond the plate since this was outside the main region of interest. Only linear elastic isotropic elements were used. An elastic modulus of 3.1 GPa and Poisson’s ratio of 0.2 were used for the plexiglass tube, which represent properties for low to moderate load under static conditions. For the stainless steel compression plate and fixation screws an elastic modulus of 196 GPa and a Poisson’s ratio of 0.3 were used. The compression plate and plexiglass tube interact indirectly through the screws and directly through plate-tube contact along the outer edges of the plate. For this study, stiff linear trusses were used along the line of contact between plate and tube. The trusses represented sliding contact, such that only axial truss forces (normal to the tube surface) were transmitted. This assumed that the shear forces transmitted through plate-tube friction were negligible. Ideally, nonlinear trusses, with a low elastic modulus in tension, could be separation possible. ‘stress-free’ making used, However, the addition of this nonlinearity would make the mode1 solution much more complex and expensive. This factor will be studied in future models.
Fig. I. Three-dimensional finite element mesh of the plexiglass tube/compression plate system. Hidden line option used to avoid excessive detail.
113
Stress analysis of compression plate fixation In the clinical application of compression plates. tensile stresses are generated in both plate and screws in order to create the desired compressive stresses at the fracture site. To simulate plate pretension, applied longitudinal displacements were used at the center of the plate. The magnitude was chosen to result in a longitudinal tensile load in the plate of approximately 490 N. The beam elements representing the screws were defined using the corresponding nodal points from the twenty-node solid elements. Two additional nodes, yielding one additional internal element, were used adjacent to the plate-tube interface for each screw. Tensile stresses in the screws were generated by imposing internal compressive forces in this element. Resulting axial screw forces of approximately 200 N were used in the region at the plate-tube interface. Thus. the beam elements were equivalent to surgically applied fixation screws threaded through both cortices. The applied loads were chosen to provide a general set of representative loading conditions. Six individual load cases were examined. as shown in Fig. 2. The five external load cases (A-E) represented possible modes of applied cyclic load, whereas the internal load case (F) represented a static load resulting from plate and screw pretension. The superposition of load cases A-E with load case F was also possible, since linear behavior was assumed throughout. The externally applied load cases are assumed to represent typical loading modes for plate-bone systems caused by the activities of daily
living. Such loads could be expected to be time varying as opposed to the static pre-stress generated by tensile loads in the screw and plate. The analyses were performed using ADINA. a finite element program for automatic dynamic incremental nonlinear analysis (ADINA Engineering. Inc.). Preand post-processing were accomplished using FEMGEN, a finite element mesh generator and FEMVIEW. a finite element mesh and result viewing program ( JAR Associates, Inc.). ADINA provided the interpolation of elemental integration point stresses to the nodal points. In-house software calculated the principal stresses and direction cosines and converted the data to the input format for FEMVIEW. FEMVIEW was then used to generate graphic plots of nodal displacements, stress contours. and principal stress vectors. All work was performed on a VAX I l/780 computer. The results of strain gage experiments designed to test the validity of the finite element model were previously reported (Chedl YI u/.. 1984). There was good correspondence for the longitudinal strain components for both axial compression and four-point bending. The finite element results were also contrasted to a composite beam solution. demonstrating the importance of relative motion between the plate and the tube. Both the finiteelement modeland the physical model indicated that relative motion does occur but composite beam theory does not allow for relative motion between sections. The mechanical properties of the plexiglass tube used in this investigation must be compared to the mechanical properties of bone. Table I contrasts the axial and bending rigidities of the tube to typical canine and human femur mid-diaphyseal rigidities. The plexiglass tube is most comparable to the canine femur. The tendency is for higher bending and lower axial rigidities with the plexiglass.
0 RESULTS
n1 CU
E
I I
1 j
B 0 -it-
--
F
The longitudinal, normal stress distributions for the tube cross-section beneath the center of the plate are shown in Fig. 3 for load cases Band C. Included are the predicted stress distributions for the unplated and the plated tube. The most obvious effect of plate application is a shift of the neutral axis towards the plate (the top of each figure). For uniform axial loading of the tube. this changes the constant stress state to a combination of axial and bending stress. This effect is minimized for an off-center axial load (load case B). For
(
(
Table 1. Axial and Rexural regidities
I
Fig. 2. Load cases A-F, respectively. Load cases A-E represent cyclic external loads, whereas load case F represents a static internal preload. From Cheal CI al. (1954).
Plexiglass tube Canine femur Human femur
Axial rigidity (MN)
Bending rigidity (Nm’)
0.7 2.1 6.0
50 26 390
144
E. J. CHEAL, W. C. HAYES, A. A. WHITE III and S. M. PERREN
(a)
b)
w J
Fig. 3. (a) Contour plots of the longitudinal normal stresses beneath the center of the plate for the unplated and plated tube. Shown is the unplated tube. load case B. All stresses are in MPa. (b) Plated tube, load case B. (c) Unplated tube, load case C. (d) Plated tube, load case C.
a highly off-center axial load, however, there is an upward shift of the neutral axis to the plate/tube interface. Plate application also reduces the magnitude of the longitudinal stresses, especially in the region directly beneath the plate. This ‘stress protection’, measured as a percentage of the stress level generated by the same load case applied to the unplated tube, ranges from an 80 to a 95 y0 decrease for load cases A, C, D and E, to a slight increase in magnitude in this region for load case B. To further examine the question of stress protection, the longitudinal, normal stress contours at the inner. middle, and outer screw locations are presented for the highly off-center axial load (load case C; Fig. 4a-c). Figure 3c and d represents the reference conditions for the unplated and plated tube beneath the center of the plate. At the inner screw location, there is still a 50% reduction in stress level compared to the unplated tube. This compares to an 83 % reduction at the center of the plated tube for this load case. At the middle screw location, however, there is a sharp horizontal gradient
reaching a local maximum which exceeds that predicted for the unplated tube. At the outermost screw, there is a three-fold increase in longitudinal stress, indicating a significant stress concentration. This is consistent with the high level of loading in the outermost screw (Cheal et al., 1984). The distribution of longitudinal normal stresses resulting from static pretension in the plate and screws (load case F) is markedly different from those resulting from the applied external loads. Figure 5 shows the induced static stresses on the tube cross-section bcneath the center of the plate. There is an approximately linear stress gradient going from tension, on the side opposite the plate, to compression, directly beneath the plate. The transition from compression to tension occurs at approximately two-thirds of the distance from the plate to the bottom of the tube. The superposition of a static preload with the individual external load cases was examined. The resulting stress distribution for load case C is shown in Fig. 6. With plate pretension, there are no longer
Stress analysis of compresston plate tixatton
Fig. 5. Longitudinal normal stress magnitudes for load case F beneath the center of the plate. All stresses are in MPa.
Fig. 6. Longitudinal normal stress magnitudes for load case C with superposition of the static preload (load case F). All stresses are in MPa.
IC)
Fig. 4. (a) Longitudinal normal stress magnitudes for load case C at the three screw locations. Shown is the inner screw location. All stresses are in MPa. (b) Middle screw location. (c)Outer screw location.
reduced longitudinal stress levels in the region beneath the plate for load cases A through C. Load cases D and E retain longitudinal stress reductions of 2: y0 or less. Vector plots of the principal stresses in the plexiglass
tube were examined for load cases C, F and the combined loading C & F. Two representative views are presented in Figs 7 and 8. Maximum and minimum here refer to the algebraic maximum and minimum principal stress components (Pl and P3, respectively). This approach effectively separates the tensile stresses from the compressive stresses. Figure 7 corresponds to the maximum principal stresses for load case C in the region beneath the outer end of the plate. Figure 8 corresponds to the minimum principal stresses for the combined loading C & F in the region beneath the center of the plate. Load case C results in high magnitude axial tensile stresses at the screw locations, with the magnitude increasing from the innermost to the outermost screws. At the outermost contact point between plate and tube, there is a high magnitude tensile stress (7.0 MPa) directed approximately 30. off
E. J. CHEAL. W. C. H.&YES.A. A. WHITE III and S. M. PERREN
46
r ,___------_____ - ____ - _________ r ‘-p___-____-_________-____-_____;-‘,
r_;________‘__
8 . ,
Fig. 7. Vector plots of principal
____
-. . .l
_--r._
_______
____
____
______--__--__-‘-_~-____~
stress PI for load case C. The region around an expanded view.
the end of the plate is show-n in
Stress analysis
.______..-..__
. . . . . . -__
of compression
. . ..-
plate tixation
---e-L-
.
I
.
.
.
.1 4 I
8
Fig. 8. Vector plots of principal
stress P3 for load case F. The region beneath the center of the plate is shown in an expanded view.
148
E. I. CHEAL. W. C. HAYES. A. A. WHITE III and S. M. PERREN
vertical (Fig. 7). indicating a tendency for plate separation from the tube surface. The tensile stresses are highest in the region beneath the outer end of the plate (see Discussion). The minimum principal stresses (not shown) for load case C exhibited less longitudinal variation, with a linear gradient of axial compressive stresses occurring over most of the tube cross-section. There is, however, a significant longitudinal increase in magnitude at the level corresponding to contour F in Fig. 5a. The magnitude increases from 0.4 MPa at the plate end to 1.0 MPa at the plate center. Immediately beneath the plate, the minimum principal stresses are of low magnitude throughout the length. The maximum principal stresses for load case F are tensile, occur at the three screw locations, and are directed at an oblique angle between horizontal and vertical, as expected for the combination of plate and screw pretension. The minimum principal stresses display radially directed compressive stresses beneath the plate at the screw locations and along the line of plate contact, as a consequence of screw pretension. A static preload results in axial compressive stresses beneath the center of the plate, as seen in Fig. 8. The maximum principal stresses which result for the combined loading of C & F, are similar to those for load case F alone, indicating the dominance of resultant stresses due to plate pretension. The minimum principal stresses (Fig. 8) are similarly distributed, except for the lower region of the tube, where the axial compressive stresses of load case C assume importance.
DISCUSSION
A reduction in externally generated longitudinal stresses in the region under a compression plate is well documented. There have also been attempts to relate the predictions of stress reduction to the observed osteopenia beneath the plate. If, as has been implicitly assumed in all previous models for ‘stress protection’, osteopenia is related to a reduced level of longitudinal normal stress, then our results suggest that the relationship between compression plate fixation and the development ofosteopenia in the underlying bone may be more complex than previously thought. Our results demonstrate that the stress reduction in the tube is dependent upon the particular combination of externally applied load and plate pretension. Plating the tube does not result, for instance, in stress reductions beneath the plate for the case of off-center axial loading, a possible type of loading encountered in ciao. The results also demonstrate that the observed stress reduction is only significant between the innermost screws. At the middleand outer screws the longitudinal normal stress was actually increased in comparison to the unplated tube. In the long term response to plate fixation, cortical thinning due to reductions in stresses generated by external loads should be limited to the central region between the inner screws. The radiograph in the study of Moyen et al. (1978) confirms this
finding. The demonstrated cortical thinning beneath the more rigid plate is apparent primarily in the central region, between the inner screws. The finite element model further suggests that ‘stress protection’ is more completely described as an exchange which results in stress concentrations around the screws. The stress fields beneath the entire length of the plate are clearly altered. but only a relatively small region of bone displays reduced stress levels. In addition, in our model, high magnitude tensile stresses occur beneath the outer end of the plate. However, the presence of these tensile stresses in the clinical application of compression plates is dependent on the plate-bone interface characteristics. As mentioned above, the modeling technique employed in this investigation did not allow for stress-free plate-tube separation, since nonlinear interface elements would have been required. High magnitude stresses will result beneath the ends of plates which have a porous ingrowth surface, but it is unlikely that the same is true for other plate types. Szivek er a/. (1981) studied bone remodeling following internal fixation with metal-polymer laminated plates containing a porous ingrowth surface. Increased cortical thickness was in fact observed near the plate ends which they attributed to the higher bone stresses expected in this region. In an earlier study, Pilliar et al. (1979) demonstrated that metal plates with a porous ingrowth surface result in significantly greater bone resorption than similar plates having a smooth surface. The strong influence of changing plate-bone interface conditions suggests that further parametric studies of this interface are warranted. The surface boundary conditions are violated for a small region for load case C, as seen in Fig. 7. More specifically. the resultant stresses are not oriented tangential to the external surface for several nodes on the upper surface of the tube located one element length beyond the end of the plate. Beneath the plate, higher magnitude tensile stresses occur which also are not oriented tangential to the surface. However, these stress components are accounted for by the linear truss elements which simulate the sliding contact between the plate and the tube. The finite element method used in this analysis is displacement based and thus the element interpolation functions need only satisfy geometric boundary conditions. The geometric boundary conditions are specified at the boundaries of the continuum, in this case the two planes-of-symmetry, and the inter-element continuity conditions are maintained. A numerical consequence of this is the occurrence of stress resultants which may not satisfy the stress boundary conditions, especially immediately adjacent to externally applied loads. In this instance, rather than an external load, the stress resultant from the truss interface element at the end of the plate is responsible. However, the occurrence of this anomaly does not influence the stress distributions in other areas, such as in the tube beneath the center of the plate. Rather than invalidating the
Stress analysis of compression plate tixation
modeling
technique.
inexact
nature
this
of
is a demonstration
the
finite
element
of the
method
as
149
stresses. may be insufficient to predict response of bone to internal fixation.
the remodeling
implemented. Perren
et al.
(1969)
demonstrated
an exponential
decay with time in the static pretension
plate
and
screws
at the time
of
developed plate
in the
application.
a small region of reduced stress levels. Since the level of
A three-dimensional finite element model of compression plate fixation was used to study the mechanics of plate-induced osteopenia. The results were presented for a wide range of loads, with and without an internal preload in the plate and screws. The following conclusions may be drawn from this study: (1) disuse osteopenia should be limited to the central region between the inner screws: (2) a static tensile preload in the plate results in high magnitude compressive stresses in the adjacent bone. which should be considered in models of plate-induced osteopenia; and (3) the inter-
preload
dependence
However,
as demonstrated
the resultant period
static
are
highly
significant
stresses due to internal
plate tension
by the finite element model.
stresses during
with
relative
loading.
externally
the early to
fixation
the cyclic
The superposition
applied
of
loads effectively
negates any reduced stress levels in the region adjacent to the plate. For pure bending
with
the plate on the
tensile aspect (load case D). a common dition
encountered
changes from tension
loading
con-
the axial stress magnitude
in Gvo.
to compression,
resulting
in only
decays with time, it may be most instructive
create a ratio to internal predict
between
loading.
the level of external
This
ratio
may then be utilized
for a particular
the stress magnitude
to
loading to
plate does not elect
that a static preload
the remodeling
pattern
al., 1975). Slatis PI (I/. ( 1975) also examined static
compression
significant
on
difference
compression
bone
was the earlier
lary cavity, remains
appearance
response
was an increase in the outer
bone, with cortical
(Matter The
thinning.
and increased porosity.
as to the relative
of
of morpho-
regardless
of the
diameter
of the
enlargement
of the medul-
Thus, the question
importance
and
insufficiency
the subsequent
response warrants
further
followadaptive
consideration.
Acl;now/rdgpmmr-Supported by NIH RCDA AM 00749, AM 26740 and a research grant from SYNTHES Ltd.
et
only
associated with the application
logic changes. The overall preload
in the
the effects of
remodeling.
remodeling
the vascular
level of
preload. It has been demonstrated
between
ing plate application
of the applied
cyclic loads from daily activities and the static stresses resulting from plate pretension in the long term remodeling response to internal fixation. The results of this study support and expand on the results of a similar three-dimensional finite element model of plate fixation (Simon et al., 1977). Both studies demonstrated that the outer screws are most highly loaded, and that similar stress reductions occur beneath the center of the plate for axial and bending external loads. Our model employed a higher mesh density, with SO”/, more three-dimensional elements, and a wider range of applied loading conditions. The most significant new information provided by this investigation is theconsideration ofpreload in the plate and screws and a more detailed examination of the resultant stresses along the tube length. The long term bone response to compression plate fixation may be influenced by other mechanical factors besides the reduction of axial stress magnitudes. Altered stress fields of any sort may trigger a remodeling response, such as a change in ‘sense’ of the longitudinal stresscomponent (Carter et al. 1981b), the introduction of multi-axial stresses, or a reorientation of the principal stress axes. The results of this study thus demonstrate the complex nature of the altered bone stresses. suggesting that a one-dimensional analysis, which considers only the resultant axial bone
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L.. Coutts, R. D.. Gonslaves. M. and Amiel. D. (1976) The effects of rigidity of internal fixation plates on long bone remodeling. Acfa orrhop. stand. 47, 241-249. Baggott. D. G.. Goodship. A. E. and Lanyon. L. E. (1981) A quantitative assessment of compression plate fixation in vim: an experimentai study using the sheep radius. J. Biomechanics 14, 701-711. Bathe, K. J. and Wilson. E. L. (1976) Numerical Merhods in Finite Elrmrnr Ano!,sis. Prentice-Hall, Englewood Cliffs, NJ. Bradley, G. W.. McKenna. G. B., Dunn, H. K., Daniels. A. V. and Statton. W. 0. (1979) Effects of flexural rigidity of plates on bone healing. J. Bone Jr Surg. 61-A, 866872. Carter, D. R., Vasu, R. and Harris. W. H. (1981a) The plated femur: relationships between the changes in bone stresses and bone loss. Acta orrhop. stand. 52, 241-248. Carter, D. R.. Vasu, R.. Spengler, D. M. and Dueland. R. T. (1981b) Stress fields in the unplated and plated canine femur calculated from in LiVO strain measurements. J. Biomechanics 14. 63-70. Cheal. E. J.. Hayes, W. C.. White, A. A., and Perren. S. M. (1984) Three-dimensional finite element analysis of a simplified compression plate fixation system. J. biomech. Engny. 106, 295-301. Gunst. M. A. (1980) Interference with bone blood supply through plating of intact bone. Currenr Concepts o/lnrerna/ Fixation of Fractures. (Edited by Uhthoff. H. K.). pp. 268-276. Springer, Berlin. Matter, P.. Brenwald. J., and Perren S. M. (1975) The effect of static compression and tension on internal remodeling of cortical bone. He/c. chir. acta Suppl. 12. Moyen, B. J-L. Lahey. P. J.. Jr.. Weinberg, E. H.and Harris. W. H. (1978) Effects on intact femora ofdogs of the application and removal of metal plates. J. Bone Jr Surg. 60-A, 940-947. Perren, S. M., Huggler, A. Russenberger, M., Allgower, M.. Mathys. R., Schenk, R.. Willenegger, H. and Muller, M. E. (1969) The reaction ofcortical bone to compression. Acra. orrhop. scond. Suppl. 125. Pilliar, R. M., Cam&on. H. U., Binnington. A. G., Szibek, J. and Mac-Nob, 1. (1979) Bone ingrowth and stress shielding with a porous surface coated fracture fixation plate. J.
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E. J. CHEAL, W. C. HAYES, A. A. WHITE III and S. M. PERRES
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J. Biomechanics 10, 79-86. Simon. B. R., Woo, S. L-Y.. McCarty,
M.. Lee, S. and Akeson. W. H. (1978) Parametric study of bone remodeling beneath internal fixation plates of varying stiffness. J. Bioengng 2, 543-556.
Slatis, P., Karaharju. E., Holmstrom, T., Ahonen, J. and Paavolainen, P. (1978) Structural changes in intact tubular bone after application of rigid plates with and without compression. J. Bone Jr Surg. 60-A, 516-522. Szivek, J. A. Weatherly, G. C.. Pilliar. R. M. and Cameron. H. U. (1981) A study of bone remodeling using metal-
polymer laminates. J. biomed. mat. res. 15, 853465. Tonino, A. J.. Davison, C. L., Klopper. P. J. and Lineau. L. A. (1976) Protection from stress in bone and its effects. J. Bone Jr Surg. 58-B. 107-l 13. Uhthoff. H. K. and Dubuc, F. L. (1971) Bone structure changes in the dog under rigid internal fixation. c/1,1. Orthop. Rel. Rex 81, 165-170. WOO, S. L-Y.. Akeson, W. H., Coutts. R. D., Rutherford. L., Doty. D., Jemmott, G. F. and Amiel, D. 11976) A comparison of cortical bone atrophy secondary to fixation with plates with large differences in bending stiffness. J. Bone Jr Surg. 58-A. 190-195. Woo.S. L-Y.. Simon. B. R.,Akeson, W. H.and McCarty. M. P. (1977) An interdisciplinary approach to evaluate the effect of internal fixation plate on long bone remodeling. J. Biomechanics
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