Journal of Orthopaedic Research 9131-142 Raven Press, Ltd., New York 0 1991 Orthopaedic Research Society

Role of InterfragmenLaryStrain in Fracture Healing: Ovine Model of a Healing Osteotomy *E. J. Cheal, K. A. Mansmann, *A. M. DiGioia 111, *W. C. Hayes, and S. M. Perren Laboratory for Experimental Surgery, Davos, Switzerland; and *Orthopaedic Biomechanics Laboratory, Department of Orthopaedic Surgery, Charles A . Dana Research Institute, Beth Israel Hospital and Harvard Medical School, Boston, Massachusetts, U.S.A.

~~~~~~

~~

Summary: It has been hypothesized that the histological pattern of fracture healing is controlled at least in part by the local mechanical strains in the interfragmentary region. To test this “interfragmentary strain hypothesis,” we applied cyclic bending deformations to tibia1 osteotomies in 11 sheep. An instrumented flexible plate spanning a 1-mm osteotomy gap was deformed to create a gradient of tissue elongation from 10% under the plate to 100% at the opposite cortex. The cyclic deformations were applied three times per minute, 24 h per day, for 1-5 weeks. However, as a result of tissue differentiation, the bone-plate complex increased in stiffness with healing time, resulting in a marked reduction of the gap deformation at approximately 4 weeks. Fracture healing was evaluated using vascular injection of India ink and conventional histology. A nonlinear three-dimensional finite element model of the interfragmentary tissue at the initial stage of healing was used to predict the complex tissue strains. The ingrowth of vascularized soft tissue into the interfragmentary gap, as well as the subsequent differentiation of this tissue, occurred earlier and to a greater degree in regions of lower strain. In contrast, the proliferation of callus tissue was greatest at the periosteal and endosteal surfaces of the cortex opposite the plate. Direct comparison of the finite element predictions with the histology demonstrated that the spatial distribution of bone resorption at the fracture fragment ends directly corresponded to the locations of elevated tissue strain and stress. However, there was no consistent numerical relationship between the magnitude of these local peak strains and the corresponding volume of cortical bone resorption over the bone cross section. Key Words: Fracture healing-Secondary bone healing-Interfragmentary strain-Finite element analysis-Plate fixation.

There are morphological patterns of fracture healing - that are characteristic of different methods of treatment. In general, the degree of fragment imand the level Of interfragmentary motion, strongly influences these morphological patterns (12,15 >1,23,38). For example,-stable fixation with ‘Ontact Of the fracture fragments results in direct cortical reconstruction

Received February 8, 1988; accepted July 20, 1990. Dr. Mansmann’s Dresent address is 555 Reservoir Drive. San Diego, California, ~.S.A. Dr. DiGioia’s present address is Ferguson Laboratory for Orthopaedic Research, Department of Orthopaedic Surgery, University of Pittsburgh, - 986 Scaife Hall, Pittsburgh, - Pennsylvania, U.S.A. Address correspondence and reprint requests to Dr. Edward J. Cheal at Orthopaedic Biomechanics Laboratory, Beth Israel Hospital, 330 Brookline Ave., Boston, MA 02215, U.S.A.

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(22,25,31). If a gap exists with rigid immobilization, cortical reconstruction is preceded by radial filling of the gap with lamellar bone, a process termed “gap healing.” With less rigid immobilization, such as with casts, cast-braces, or most applications of external fixation, fracture repair is characterized by callus formation in which a collar of fibrous tissue, fibrocartilage, and hyaline cartilage is formed to stabilize the fracture fragments. In this indirect healing process, the callus is remodeled over time to form mature cortical bone. Finally, excessive interfragmentary motion can lead to delayed union or nonunion. While it is clear that the mechanical environment influences the morphology of the healing process, there are conflicting results for the measured return of fracture stiffness and strength as a function of the degree of fracture immobilization (1,4,14,30,37). To resolve these conflicts, Perren and co-workers proposed a hypothesis that allows refinement of the concept that fracture healing is controlled by the local mechanical environment (22,24). The “interfragmentary strain hypothesis” attempts to provide a unifying theory relating interfragmentary strain, and thus fracture immobilization or fixation rigidity, to the tissue response. The hypothesis is that a tissue can be formed or remain in the interfragmentary region of a healing fracture only if the involved tissue tolerates the local mechanical strains. This theory attempts to explain the sequence of tissue differentiation by relating the mechanical characteristics of the repair tissue to those of the different stages of fracture healing. Once a tissue has formed, it will in turn contribute to the fracture site rigidity and therefore alter the local mechanical environment, making possible the next step of tissue differentiation. This sequence of altered mechanical environment leading to further tissue differentiation is repeated until the fracture is bridged by bone. Thereafter the bone is remodeled under the influence of the mechanical stresses. Previous experimental work has not dealt directly with the role of interfragmentary strain in fracture healing. However, indirect support for the hypothesis has been obtained from a number of in vivo models. Previous investigators have used in vivo models to define the form of osseous repair associated with external fixation of varying stiffnesses (13,14,37). External fixation systems applied to intact and osteotomized long bones have also been used to examine the effects of compression and cyclic loading on the strength of osseous repair and

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bone remodeling in the long term (10,18,20,34,35). Similar studies with internal fixation have examined the effect of plate stiffness on the quality of osseous repair. The rigidity of internal plate fixation can be varied by changing the material from which a plate is constructed (4,33,36), by altering the plate geometry (12,16,19,36), or by applying compression across the fracture site (16). This work has been limited to studying the effect of grossly different and uncontrolled mechanical environments at a fracture or osteotomy site. N o attempt has been made to control or define the local interfragmentary strain field in a healing fracture. The objective of this investigation was to test the interfragmentary strain hypothesis using an experimental model of fracture healing. In this experimental model, the interfragmentary tissues of a plated osteotomy of the ovine tibia were subjected to controlled cyclic deformations during the early healing period. The hypothesis was tested by directly comparing the observed patterns of osseous repair to finite element predictions of the tissue strains within the interfragmentary region. Our specific aims were (a) to develop a reproducible model of fracture healing in which the mechanical environment of the interfragmentary region is monitored and controlled; (b) to predict the three-dimensional strains in the interfragmentary tissue in the initial stage of healing; and (c) to correlate the measured bone resorption and callus formation to predicted tissue strains. METHODS In Vivo Experimental Model

A modified stainless steel plate ( A 0 #227.181, Synthes, Paoli, PA) was used to fix an osteotomy of the mid-diaphysis of the sheep tibia. The plate was 145 mm long and contained a thinned central section (1.5 by 16 mm in cross section) extending 17.5 mm on either side of the osteotomy. Two rectangular strain gauge rosettes were mounted on the thinned section to measure the bending and torsional deformations of the plate. The gauges were wired to permit temperature-compensated measurements, water-sealed with two coats of rubber cement, and coated with silastic. Two 5-mm-diameter stainless steel pins with standard cortical threads were used to provide external coupling with a hydraulic actuator (Fig. 1). The lengths of the transcutaneous pins ranged from 89 to 93 mm to accommodate different tibia1 shaft thicknesses. A hydrau-

INTERFRAGMENTAR Y STRAIN IN FRACTURE HEALING

FIG. 1. Postoperative radiograph showing the parallel alignment of the osteotomy surfaces. The hydraulic actuator was coupled to two transcutaneous pins through a ball and socket joint and cyclically deformed the osteotomy gap in 2-s pulses three times a minute, 24 h a day, for up to 5 weeks.

lic actuator, connected to the transcutaneous pins through a ball and socket joint, was used to apply cyclic displacements to the plated bone and osteotomy gap. The plate-actuator system was applied in 11 young adult (from 2 to 6 years old) Swiss mountain sheep. Following endotracheal general anesthesia with halothane, the right leg and back were prepared and draped. The sheep were placed on their right sides. A medial incision was made over the right tibia and sharply dissected to the periosteum. Hemostasis was obtained, and the periosteum was incised and reflected off the posteromedial aspect of the tibia. A special drill and saw guide were applied to the posteromedial aspect in the midshaft of the tibia. The screw holes for the guide corresponded to those of the modified plate. Screw holes for the two transcutaneous pins were drilled with the guide to permit a standardized application of these pins relative to the osteotomy gap and hydraulic actuator. An osteotomy was made under continuous cooling using a 0.6-mm saw blade and resulted in a 1.0-mm mid-diaphyseal defect. The plate was then applied with the osteotomy directly beneath the thinned center portion. The transcutaneous pins were threaded and tightened with a nut to provide firm coupling between the pins and the bone-plate system. A special washer was applied at the skinimplant junction of the pins to permit ingrowth of stable tissue and thus minimize the risk of retrograde infection. The osteotomy surfaces were adjusted to a parallel position and fixed with a temporary shim of 1.0 mm thickncss until the final connection was made to the hydraulic actuator. The

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strain gauge wires were tunneled subcutaneously to the back, where they exited the skin. To reduce uncontrolled loading of the osteotomy by musculature spanning the gap, the sheep were turned onto their left sides, and two Schanz screws were applied to the distal lateral aspect of the ipsilateral femur and fixed externally to permit suspension of the operated leg. In addition, the sheep were suspended in harnesses while under anesthesia to protect the operated leg. The harness allowed the sheep to stand erect, turn 180°, sleep while being suspended, and bear weight on the three nonoperated legs. Postoperative radiographs were obtained to verify the parallel alignment and thickness of the osteotomy gap. The hydraulic actuators deformed the osteotomy gap three times a minute, 24 h a day, from the first day following surgery to the time of sacrifice. Each displacement pulse was 2 s in duration from neutral to neutral position. This permitted an 18-s pause to allow equilibration of the tissues in the unloaded state. The force capacity of the actuator was approximately 500 N, with a moment arm of 50 mm, for a bending moment of approximately 25 Nm. The torsional and bending strains in the plate were measured twice a day, using a digital microstrain recorder, with a series of five measurements taken at each occasion. The magnitude of the plate strain was adjusted by varying the excursion of the hydraulic actuators. During early osseous repair, the interfragmentary motion resulted in a strain gradient that varied linearly from 5-10% simple elongation at the periosteal surface adjacent to the plate to a maximum of 100% elongation at the periosteal surface opposite the plate. A small degree of plate torsion was also measured. The magnitude of the resulting shear deformations were approximately 10% of the axial deformations. The sheep were sacrificed at time periods of 1-5 weeks, two animals at each 1-week interval. India ink was injected at the time of sacrifice to delineate the areas of revascularization. Standard radiographs were obtained to verify the geometry of the healing osteotomy gaps. The specimens were dehydrated with alcohol and fixed in methyl methacrylate. Histological sections, using hematoxylin-eosin stain, and microradiographs were prepared to determine the characteristics of the gap tissue during healing. A series of 1&12 parallel sections in the sagittal plane were prepared. The resorption of cortical bone adjacent to the osteotomy was measured using an image-process-

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ing system. The area of resorption was measured at each cortex adjacent to the osteotomy on the central histological section from each animal. To measure the areas, the geometry of the intact cortices was estimated by assuming straight line extensions of the adjacent surfaces. Each area provides a local two-dimensional measurement of the three-dimensional volume of resorbed cortical bone. The location of each area measurement was characterized using three parameters: near plate or far plate, endosteal or periosteal, and proximal or distal. However, a paired t test indicated no significant difference between the resorption areas at the adjacent proximal and distal locations, so these data were averaged. Thus, there was a total of four independent measurements on each section, with one section analyzed for each of the ten animals. Finite Element Analysis A nonlinear three-dimensional finite element model of the tissue in the interfragmentary region was developed to predict the strains during the initial stage of healing. The geometry of the finite element model was defined by superimposing a finite element mesh on a photographed cross section of a tibia from an adult sheep. Using displacement contraints on nodes at the mid-gap plane of symmetry, a half-thickness model was used to represent the full 1-mm gap. The finite element model represented the osteotomy gap of uniform thickness with 144 isoparametric 20 node brick elements and 985 nodal points. A linear, elastic, isotropic material with an elastic modulus of 10 MPa and Poisson’s ratio of 0.45 was used to model the gap during the initial stage of repair. Note that the predicted interfragmentary strains are insensitive to the assumed elastic modulus since the tissue is under displacement control. To represent the cyclic deformations, displacements were defined for the nodes at the bone-gap interface. These displacements produced (a) elongation of the interfragmentary tissue that varied linearly from 6% (0.06 mm) at the periosteal surface adjacent to the plate to 100% (1.0 mm) at the periosteal surface opposite the plate, and (b) torsion about the longitudinal axis of the plate producing a maximum torsional deformation of 10% (0.1 mm) at the periosteal surface opposite the plate. The large applied deformations result in geometric and material nonlinearities (9). In the present analyses, we assumed elasticity for the material while accounting for the kinematic nonlinearities.

J Orthop Re,, Vol. 9, No. 1, 1991

To account for these nonlinearities, an incremental solution strategy and updated Lagrangian formulation were used (3). At each displacement increment, equilibrium iterations were performed to improve solution accuracy. The stiffness matrix was also reformed at each increment to insure numerical convergence. Note that while a nonlinear element formulation was used, the material constants were defined such that the material (stress-strain) behavior was linear throughout the solution process. Carter and colleagues have proposed an “osteogenic index” for predicting ossification of fibrocartilage in a healing fracture gap (8). For multiple cyclic loading conditions, this parameter is proportional to a linear sum of the peak octahedral shear stress and hydrostatic stress for each load, each multiplied by the number of loading cycles. In the present experiment, there is only a single cyclic loading condition, and thus Carter’s osteogenic index may be simplified to

I

(a,

+ kad)

(1)

where a, is the octahedral shear stress, a, is the hydrostatic stress, and k is an empirical constant. To normalize for different values of k, we present the “osteogenic index” as

I

= (a,

+ kad)/(l + k)

(2)

fork = 0.5 and k = 2.0. The ADINA finite element modeling package (ADINA Engineering, Inc., Watertown, Massachusetts), implemented on a VAX 11/750 computer, was used to perform the finite element analyses. Pre- and post-processing were accomplished using FEMGEN and FEMVIEW (Great West Technology Transfer, Minneapolis, Minnesota) and inhouse software. RESULTS In Vivo Experimental Model One of the 11 sheep developed an infection and was excluded from further analysis. Uncontrolled deformations of the plate due to the musculature spanning the osteotomy gap were less than 10% of the deformation applied by the hydraulic actuator (Fig. 2). As the fracture callus differentiated and calcified between 3 and 4 weeks, there was a characteristic decline in both the torsional and bending strains. Histological sections of the healing osteotomy

INTERFRAGMENTAR Y STRAIN IN FRACTURE HEALING &

bending .. ..*....-...... *-..... 2000

1000

torsion I

-11.11..

A *

LY-

1

2

... s

2

I + * *

3

.A

. ..*.. .I

A

.A

*

a

1

%

4

c

r

1

I

t (wk)

-

8

5

FIG. 2. Daily average bending and torsional strain rneasurements over a 5-week period. There was a characteristic stiffening of the osteotomy site between 3 and 4 weeks of healing.

gap through the midsagittal plane parallel to the long axis of the bone (Figs. 3 and 4) showed that at 1 week (Fig. 3A), there was no evidence of an organized cellular healing response either within the osteotomy gap or for a limited distance from the gap at the fracture surface. At 2 weeks (Fig. 3B) the soft tissue at the margin of the osteotomy gap was beginning to organize. The first evidence of bone resorption was found at the fracture surface adjacent to the gap tissues (Fig. 4A). Endosteal and periosteal callus had formed and consisted predominantly of fibrous connective tissue. Ossification of soft tissue was first noted at the near plate endosteal cortex proximal and distal to the osteotomy gap. Nowhere at this stage of healing was ossified callus observed in the plane of the osteotomy gap. At 3 weeks (Fig. 3C), bone resorption had progressed at the near-plate endosteal and opposite endosteal and periosteal cortices and was limited to the cortical surfaces of the osteotomy that were in contact with vascularized soft tissue outside the gap (Fig. 4B). There was also a greater amount of periosteal and endosteal callus around the far-plate cortex than around the near-plate cortex. Ossification continued to be more advanced in tissues at the near-plate endosteal cortex. Following 4 weeks of healing (Fig. 3D), ossification of the callus overcame the force capacity of the hydraulic actuator, rcsulting in significant rcductions in the levels of deformation applied to the in-

135

terfragmentary tissues. Ossification proceeded in the peripheral areas of callus and advanced toward the osteotomy gap. The ossification front at the opposite periosteal cortex continued to lag behind the near-plate endosteal callus, which was almost completely calcified at 4 weeks. At 5 weeks (Fig. 3E), osseous repair was advanced, and the endosteal callus was nearly completely ossified. However, even at this time, there was no evidence of calcified tissue within the osteotomy gap, and calcification of the periosteal callus had not completely bridged the osteotomy. The means of the areas of bone resorption, as a function of the experimental time period, are shown in Fig. 5. In general, there was an increase in the area of bone resorption with time over the 5-week period. However, the most striking difference between the different locations was the greater degree of bone resorption at the endosteal surfaces in comparison to the corresponding periosteal surfaces, rather than the differences between the far-plate and near-plate cortices. A multivariate repeated measures analysis of variance was performed to evaluate the statistical significance of these variations. The grouping factor was the experimental period, in weeks, and the trials factors were the periosteal/endosteal surface and the near-plate/far-plate location. This analysis indicated that the number of weeks (p = 0.002) and the periosteaUendostea1 surface location (p = 0.002) were significantly related to the amount of bone resorption. However, the near-plate/far-plate location was not significant (p = 0.170). As demonstrated in Fig. 5 , the amount of bone resorption at 3 weeks or more was always greater for the periosteal far-plate surface in comparison to the periosteal near-plate surface. However, the bone resorption at the endosteal surfaces was generally greater and more variable than the bone resorption at the periosteal surfaces. Finite Element Analysis The largest predicted deformations of the tissue in the osteotomy gap corresponded to the periosteal surface opposite the fixation plate (Fig. 6). Because of the Poisson effect, there was a marked contraction of the gap tissue, greatest at the mid-gap plane. On the plane of the bone-gap interface, the interfragmentary tissue translated with the cortical bone fragmcnt. Conscqucntly, thcrc were severe angular deformations of the elements adjacent to the bone-

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E. J . CHEAL ET AL.

136 (A)

(D)

FIG. 3. Histological sections taken from the midsagittal plane parallel to the long axis of the bone for healing periods of 1 (A), 2 (B),3 (C), 4 (D), and 5 (E) weeks.

Fixation Plate

2

gap interface, especially at the periosteal and endosteal surfaces. To examine the interfragmentary tissue strains, principal strain data were plotted in vector form on the mid-gap plane of symmetry and at the bone-gap interface (Fig. 7). On the mid-gap plane, the maximum principal strains (Pl) were tensile, oriented parallel to the longitudinal axis of the bone, and had a roughly linear gradient across the section with the greatest strains opposite the plate. On the same plane, the minimum principal strains (P3) were compressive and oriented in the radial direction. The tensile strains on this plane were in direct proportion to the applied deformations, and the compressive strains corresponded to the Poisson con-

J Orthop Res, Vol. 9, No. I , 1991

traction of the interfragmentary tissue. However, at the bone-gap interface, there were high magnitude tensile and compressive strains at the inner and outer surfaces, indicating high shear strains. A maximum tensile strain of 193% occurred at the periosteal surface opposite the plate, which was almost twice the maximum longitudinal relative displacement of the bone surfaces. The maximum compressive principal strain of 144% occurred at the same location on the bone-gap interface. To further examine tissue deformations, contour plots of the hydrostatic stress (ad)and octahedral shear stress (a,)at the bone-gap interface and midgap plane of symmetry were generated (Fig. 8). These stress invariants displayed a combination of

INTERFRAGMENTAR Y STRAIN IN FRACTURE HEALING (A)

(B)

137 (C)

~~

Endosteum Near-Plate Cortex

Endosteum F a r - Pla t e Cortex

Periosteum Far- Plate Cortex

FIG. 4. Magnification of the histological sections taken through the midsagittal plane for regions including the endosteum near-plate cortex, endosteum far-plate cortex, and periosteum far-plate cortex. The healing periods were 1 (A), 3 (B),and 4 (C) weeks.

two gradients over these surfaces. One gradient was from the cortex near the plate to the opposite cortex, corresponding to the gradient of applied deformation. The second gradient was from the inner and outer surfaces to the central region. For the hydrostatic stress at the mid-gap plane, and the octahedral shear stress at the bone-gap interface, the gradient from the surfaces to the central region was especially dominant. A maximum shear stress of 9.5 MPa was predicted to occur at the periosteal surface opposite the plate at the bone-gap interface. A maximum hydrostatic stress of 16.2 MPa was predicted to occur at the same location. The octahedral shear stresses away from this plane were of relatively low magnitude, whereas the hydrostatic stresses were more constant in the direction parallel to the long axis of the bone. Contour plots of the osteogenic index (Eq. 2) were also generated (Fig. 9). The distributions of the osteogenic index were intermediate to the distributions of hydrostatic stress and octahedral shear stress since the osteogenic index was defined as a

linear sum of these effective stresses (8). When the empirical constant (k) was equal to 0.5, the distribution of the osteogenic index closely resembled the distribution of octahedral shear stress (Fig. 8). When k was increased to 2.0, the distribution of the osteogenic index closely resembled the distribution of hydrostatic stress (Fig. 8). Finally, the measured bone resorption at the endosteal and periosteal cortical surfaces was examined as a function of the predicted stresses in the adjacent interfragmentary tissue. The bone resorption as a function of the predicted hydrostatic stress and octahedral shear stress is shown in Figs. 10 and 11. These graphs demonstrate no consistent relationship between the predicted stresses in the interfragmentary tissue and the amount of cortical bone resorption during the 5-week experimental period. Note, however, that this is a global comparison; the finite element model did predict a local elevation of the octahedral shear stress at the endosteal and periosteal surfaces (Fig. 8), which was where the bone resorption was observed (Figs. 3 and 4).

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E. J . CHEAL ET AL.



I

E

BONE-GAP INTERFACE

++ Far periosteal 4

- Far endosteal

-

-Near endosteal

MID-GAP PLANE

- - 0- Near periosteal

I

I

0

1

2

3

4

5

Time [weeks]

FIG. 5. Mean areas of bone resorption (?SEM), normalized to the cortical thickness, on the central longitudinal section. “Far” and “near” indicate the location relative to the modified fixation plate.

DISCUSSION

The interfragmentary strain hypothesis implies that if an existing tissue cannot tolerate the local mechanical conditions, the biological response will be to reduce the tissue strains to allow fracture healing to proceed. This response consists primarily of tissue proliferation and differentiation, as in callus formation. However, bone resorption can also result in reduced tissue strains by reduction of the

FIG. 6. Original (A) and deformed (B) finite element mesh, with hidden lines removed. The mesh is rotated 75” about a vertical axis from the plane of view. The mid-gap plane is the visible surface, facing to the right.

J Orthop Res, Vol. 9, No. 1, 1991

FIG. 7. Predicted tensile (Pl)and compressive (P3)principal strain vectors. Crossbars on the vectors indicate compression. Each surface is rotated 70” about a vertical axis from the plane of view. Max = 1.93;min = - 1.44.

severe material discontinuities and widening of the fracture gap (24). Resorption of the fragments ends may reduce the tissue strains to levels that permit completion of a bridging callus, allowing ingrowth of the soft tissue scaffold necessary for sequential differentiation, which ultimately results in bony union (22). In this preliminary study, we found a positive relationship between the local interfragmentary strains in the initial stage of healing and both the subsequent callus proliferation and bone resorption. It was particularly striking that the spatial distribution of bone resorption, namely the endosteal and periosteal cortical surfaces, directly corresponded to the maximum predicted tissue shear deformations. However, there was proportionally more bone resorption at the endosteal surfaces than would be predicted by the initial interfragmentary strains alone. There are several mechanisms by which the level of interfragmentary strain might influence fracture

INTERFRAGMENTAR Y STRAIN IN FRACTURE HEALING BONE-GAP INTERFACE

139 MID-GAP PLANE

2 + 4 r?

m 0

FIG. 8. Predicted hydrostatic stress and octahedral shear stress (MPa).A = 0.0; B = 2.0; C = 4.0; D = 6.0;E = 8.0;F = 10.0; G = 12.0; H

=

14.0; I

=

t.

16.0.

healing. First, there is a close association of blood supply and fracture healing (26,27,28,31); many newly formed capillaries are found in early fracture repair. During the early stages of repair there is also an associated increase in capillary fragility (26). Local deformations may disrupt early revascularization and interrupt the blood supply to the developing osteons. During early fracture repair the material discontinuities from cortical bone to soft tissue are severe. Olerud and associates (17) reported that bone formed in a fracture gap will have a weaker anchorage at the cortical surfaces. Local shear strain gradients at the bone-gap interface may thus play an important role in determining the establishment and patency of the periosteal and endosteal blood supply to the osteotomy gap or have a direct effect on the formation of Haversian system cutting cones. The influence of tissue strain at the cellular level may involve cell disruption, the generation of electric potentials, humeral factors, or membrane and calcification phenomena (2,5,11,29). In all likelihood there exists a multifactorial relationship during the different stages of osseous repair. The present experimental design resulted in two different phases during the healing period. In the first phase, each osteotomy was under displacement control, since the maximum displacement of the hydraulic actuators was limited. However, after approximately 4 weeks, the actuator could no

longer overcome the osteotomy stiffness, and the applied displacements were reduced. In this second phase, the osteotomy was under load control, since the maximum actuator load was relatively constant. The original intent of the experimental design was to maintain a constant maximum gap deformation throughout the experimental period. However, the reduction in the applied deformations was a direct consequence of the biological response, and, in turn, this reduction allowed the healing process to continue. In retrospect, this combination of displacement control in the early phase and load control in the later phase may be the most appropriate method for investigating the interfragmentary strain hypothesis. Healing was allowed to proceed, whereas continuous application of the original osteotomy deformation, with unlimited loading potential, would result in nonunion. The nonlinear three-dimensional finite element model demonstrated the complex nature of the interfragmentary strain field. Most important, severe shear deformations occurred at the endosteal and periosteal margins of the gap. In addition to the expected gradient of tensile strain from the periosteal surface adjacent to the plate to the periosteal surface opposite the plate, there are two local strain gradients that are critical: (a) variations through the thickness of the osteotomy gap and (b) variations radially from the endosteal to periosteal gap surJ Orthop Res, Vol. 9, No. 1, 1991

E. J . CHEAL ET AL.

I40

MID-GAP PLANE

BONE-GAP INTERFACE /

n

FIG. 9. Predicted osteogenic index (MPa). A = 0.0;B = 2.0;C = 4.0; D = 6.0; E = 8.0;F = 10.0; G = 12.0;H = 14.0; I = 16.0.

faces. The longitudinal relative motion of the bone fragments is commonly referred to as the interfragmentary strain. However, the finite element model demonstrated that because of the complexities of the three-dimensional strain field during early osseous repair, it is not adequate to use simple longitudinal deformation as a basis for predicting the tissue response. The present finite element analysis was limited by several factors. Torzilli, Burstein, and co-workers showed that newly formed bone and cartilage behave like elastic-plastic materials (6,7,32). While the present model included nonlinear geometric behavior, nonlinear material properties were not included. Depending on the magnitude of the applied displacements, nonlinear stress-strain relationships may be more accurate, especially for the later stages of healing. The greatest limitation of the present analysis was the representation of a single point in time (the initial conditions following surgery). If the model were truly predictive of the biological processes, it should be possible to modify the model in an iterative manner based on the predicted tissue strains. However, an iterative model must include the adjacent cortical bone and possess the capability of gross changes in both the material properties and geometry of the various tissues. A direct comparison of the local tissue response with the finite element predictions is facilitated by

J Orthop Res, Vol. 9, No. 1 , 1991

employing effective stress criteria. It is essential that these criteria account for the multiaxial strains. Octahedral shear stresses are often correlated with failure of engineering materials. Carter and colleagues have proposed using a linear sum of the peak cyclic octahedral shear and hydrostatic stresses, termed the osteogenic index (8). We examined the global relationships between the measured bone resorption at the cortical surfaces and various effective stress parameters predicted by the finite element analysis. The only trend of note was the negative correlation between bone resorption after 5 weeks and the effective stress magnitude, if the periosteal surface beneath the plate is ignored (see Figs. 10 and 11). While the lack of bone resorption beneath the plate may be explained by such complicating factors as vascular interference by the plate, this negative correlation is contrary to the interfragmentary strain hypothesis. The present data do not support the application of any particular effective stress criterion for the prediction of cortical bone resorption, including hydrostatic stress, octahedral stress, or the combined osteogenic index. In conclusion, the present findings provide preliminary support for the interfragmentary strain hypothesis. The spatial distribution of bone fragment end resorption corresponded to areas of elevated tissue strain as predicted by the finite element

INTERFRAGMENTAR Y STRAIN IN FRACTURE HEALING

Acknowledgement: This study was supported by Swiss National Foundation for Scientific Research Grant 3.416.078, National Institutes of Health FIRST Award AR38869, the Harvard Medical School Student Research Fund, the A 0 Foundation, and the Maurice E. Mueller Professorship in Biomechanics at Harvard Medical School (WCH). We also thank Dr. Berton Rahn at the Laboratory for Experimental Surgery for assistance with the histological analyses and Dr. Elizabeth Myers at the Orthopaedic Biomechanics Laboratory for assistance with the statistical analyses.

o lweek - - oPweeks - e -3weeks

I

4

141

-4 weeks

q 0.5

REFERENCES O

C 0

2

4

6

6

10

12

14

16

Hydrostaticstress [MPa]

FIG. 10. Bone fragment end resorption as a function of the predicted hydrostatic stress.

model. This resorption may result in a decrease in tissue strain to tolerable limits. However, there was no consistent numerical relationship between the magnitude of the local peak predicted effective stresses (or strains) and the measured bone resorption at these locations of elevated tissue strain. Indirect healing by endosteal and periosteal callus formation was the predominate form of osseous repair. Ingrowth of soft tissue and vasculature into the interfragmentary gap occurred earlier and to a greater degree at the near-plate cortex where there were reduced strain magnitudes and less severe gradients. The differentiation of this tissue toward immature bone was also greater in the lower strain regions. Conversely, at the far-plate cortex, where the tissue strains were elevated, there was abundant endosteal and periosteal callus formation.

11

- -L)- 2 weeks

2-

- e -3 weeks

2.5

o lweek

N -

d

E E

-4 weeks

L

.c

1.5 -

P

9

??

1 -

1 -

0

Octahedralshear stress [MPa]

FIG. 11. Bone fragment end resorption as a function of the predicted octahedral shear stress.

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Role of interfragmentary strain in fracture healing: ovine model of a healing osteotomy.

It has been hypothesized that the histological pattern of fracture healing is controlled at least in part by the local mechanical strains in the inter...
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