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A parametric analysis of bone fixation plates on fractured equine third metacarpal
1. Biomcchmks.
Vol. 4. pp. 163-174.
paEMon
RCSS. 197 1.
Printed in Gmt
Briprn
A PARAMETRIC ANALYSIS OF BONE FIXATION PLATES ON FRACTURED EQUINE THIRD METACARPAL* D. R. RAY.t W. B. LEDBElV2R.S D. BYNUM$ and C. L. BOYDll Texas A&M University, College Station. Texas 77843, U.S.A. Aba&met- A series of tests of the relative strengths of conventional bone fixation platedesigns as compared to the strength of unfractured equine third mctacafppl bones of the same age was performed. The tests involved a full factorial experimental design on three variabks: plate length. lateral hok pitch. and fastener size. AU tests were conducted in lkxtue. a concentrated
load being applied on the posterior surface of the bone at mid-spM.withthe fixation plate in each caseattachedto the anterior bone surface. The most signScant parameterwas found to be plate kngtb since an increase in length from 3 to 6 in. approximately doubled the capacity of the reconstructed bone spacimcn. Fastener size and lateral hok pitch pn&uced no sign&ant change in oveti capacity for the structure. It was concluded that. in generai. the use of a single Axation &ate for fracture fixation of eauine third metacarpal would not provide adequate support
for weight bearing during osteogen&s. 1. IN’IRODUCIION
time, attempts at using various metallic devices have ensued with varying degrees of success. Fracture fixation using screws alone occurred as early as 1902 (Jacobs and Guten. 1%7), but many other types of fixation devices, empioying a wide range of metallic materials, were also being investigated and tried clinically. The earliest types of metal plates to be used were made of nickel-steel, iron, or silver (Guthrie, 1903). These early plates were generally attached to the fractured bone with ivory pegs which were allowed to protrude from the wound to facilitate an easy removal of the device, usually after 3 or 4 weeks. Removal was generally required whenever metals other than silver were used or when devices of dissimilar metals were employed. The resulting electrochemical corrosion that occurred within the electrolytic environment of the body tissues was unforseen at the time and resulted in infection or other gross tissue reactions. It soom became evident that silver screws in conjunction with silver plates produced the most favorable results. Thus. silver
material in this paper pertains to the experimental evaluation of the structural rhtegrity of fractured equine third metacarpal bones (lower forelegs of the horse). reconstructed with fixation plates of various designs and tested in flexure. Specificaliy, the relative strengths of bone fixation plates and fasteners installed on fractured equine third metacarpals, to include the effects of varying the length of the plate. the lateral pitch between screw holes. and the size (diameter) of screw. were investigated and compared to the strengths of unfractured whole bone of the same age. From this analysis design recommendations for more optimum combinations of fastener size and plate dimensions were made.
THE
2. BACKGROUND Internal fixation of fractures in human medicine dates back at least to ‘1775 (Guthrie. 1903 : Hodgkinson. 196 11 when Lepeyode and Sicre used silver wire to achieve immobilization in fractures of the long bones. From that
‘Received I i June 1970. ?Engineering Research Associate. Texas Transportation Institute. ZAssociate Professor. Departments of Civil and Aerospace Engineering. $Assistant Research Engineer. Texas Transportation Institute. “Associate Professor. Veterinary Medicine and Surgery. College of Veterinary Medicine. 163
BM Vol. 4 No. 3-A
164
D. R. R4Y
the most commonly used implant material for several years. Stainless steel was first introduced under a British patent in 19 13 as the result of a search for a non-corrosive material to be used in the manufacture of naval guns (Hodgkinson 1961). Since that time. various types of stainless steels have been investigated for internal use and. primarily through a process of trial and error, stainless steels of types 3 16 and 3 17 have emerged as the most acceptable for implantation in the body. In 1962. the British Standards Association took steps to standardize the materials used in the manufacture of metal surgical implants and related tools (Weisman, 1968). The British Standard 353 1: 1962 was later amended to include pure titanium. Currently, within the United States, ASTM (American Society for Testing and Materials) Committee F-4 is in the process of developing standards and specifications for cast and wrought cobalt-chromium alloys, stainless steel, pure titanium and required surface finishes on these materials (Weisman, 1968). The Standards Association of Australia is taking similar steps. No standards could be found from any country for the testing and acceptance protocoi for surgical implants. Most of the testing of fixation units has been co&red to tests of the fixation plate and appropriate screws separately. The work of Martz (1956) and Lindahl ( 1962, 1964, 1967) represents much of the literature that has been published to date concerning the performance of fixation devices on whole bone. Both authors dealt primarily with observing the. loads required to produce failure of the composite structure, but convey little meaningful engineering information that can be used to make design recommendations. Both tested existing fixation devices (plates and screws), but neither investigated the effects of varying the basic designs. Fracture fixation in human medicine has progressed to the point at which relatively good success can be achieved with current became
er al.
types of fixation devices. provided the patient rigorously follows the post operative advice of his physician. Even so. failures which are structural in nature do occur. The problem of structural failures is not confined to human medicine alone. Indeed. the problem becomes accentuated in veterinary medicine. The practice of forbidding weight bearing following fracture fixation may be a convenient means of avoiding structural failure whiie osteogenesis occurs in the human species. but it becomes impractical if not impossible when dealing with fractures incurred in large domestic animals such as the horse (Lundvall. 1960). All of the fixation devices used to attempt the repair of fractures in large animals have been borrowed from human medicine. The largest plates, intended for fixation of the femur in humans, are the only sizes available to attempt the fixation of fracrCLredlong bones in animals as large as the horse. and these plates are rarely adequate. In the past, veterinarians had little choice but to sacrifice large animals that had developed fractures in the long bones. Little improvement in this situation exists today. In cases where fixation has been attempted in the horse with currently available fixation plates at the Large Animal Clinic of the College of Veterinary Medicine at Texas A&M University, failure of the composite bonefixation plate structure has generally occurred within a matter of hours from the time of implantation. Thus the veterinary orthopedic surgeon is faced with a frustrating dilemmato continue to attempt fixation with devices that are apparently inadequate, or to sacrifice the animal. In order to try to eiiminate this diiemma. veterinary orthopedic surgeons and materials and structural engineers at Texas A & M have teamed together to analyze and evaluate existing plate designs and to make recommendations for their improvement. The work reported here was an integral part of that program.
165
A parametric analysis of bone fixation plates 3. THWXETICAL
CONSIDERATIONS
In order to obtain useful information from the data, several assumptions had to be made. The validity of some of these assumptions may appear questionable in a strict sense, but it is believed that their use. nonetheless. yields meaningful results. The reconstructed bone specimen was assumed to be a beam. simply supported. with a concentrated load at the mid-span. The fixation plate was attached to the anterior surface of the bone and the concentrated load was applied to the posterior bone surface. The fixation plate was. therefore. on the tension side of the beam. In all cases the mid-length of the fixation plate, mid-span of the beam, and mid-length of the bone were coincident. To account for differences in bone size among the specimens, the applied load was normalized on the mid-shaft geometry of the bone by means of the flexure equation.
L.=F, where. L, = normalized loaiL ksi. it4 = applied moment, in.-kips, c = distance from bone cross-section centroid to extreme bone fiber, in., I = moment of inertia of bone cross section about its centroidal axis (perpendicuJar to applied ioad), in4 The mid-shaft cross section of the bone was assumed to be that of an eccentric elliptical annulus (Fig. 1). Com-
SURFACE
Fig. 1. Assumed bone cross-section at mid-length.
parison with the actual bone cross-section (Fig. 2) illustrates that the assumption is quite good. Calculus was used to derive the moment of inertia for such a cross-section. which is given.by I = $ (LI,~,~- a,bz3 - 4azb2d,2) - ra2zb,2d,2 a&, - a,b,
where the symbols are defined in Fig. i. The location of the section’s centroid with respect to the intersection of the diametrical axes of the outer ellipse is given by. X=
-a,b,d? (a,b,-a2bz)’
‘=
- &b,d, (a,b,-a,bp)’
It must be noted here that the normalized load, L,, is not regarded as a stress since the dimensions of the plate and fasteners and thus the load they carry do not enter directly into the analysis. Rather. it was believed that the effects of varying the plate and fastener combination would be evidenced by the observed moments required to produce failure of the composite structure. Most certainly a complex stress state exists within the specimen. especially in the vicinity of the fasteners, and the analysis presented here represents an experimental evaluation of the various plate designs rather than a comprehensive theoretical structural analysis. It has been shown that the composition and mechanical properties of bone vary somewhat with position along its length (Evans er al. 195 I, 1964, 1969). and the magnitude of error introduced by assuming the bone to be homogeneous and isotropic for analytical purposes is not known. The nature of the problem does not lend itself to a straightforward exact mathematical solution that accounts for all the variables. An initial consideration was to analyze the structure using the principles of reinforced concrete design. The assumption that the
0. R. RAY et al.
166
bone below the neutral axis carries no tensile stress is quite good since the specimen is sawed through. It cannot be assumed, however, that the steel is uniformly bonded to the bone since a’non-uniform stress state prevails in the region of the fasteners. Because of the high modular ratio (approximately 15) that exists between the steel and the bone, the true neutral surface of the structure in bending will shift from the centroidal axis of the bone cross-section to a point closer to the centroidal axis of the steel plate. The exact location of the shifted axis is not accounted for in this analysis and no solution could be found in the literature for its location. Another variable that must be considered is bone age. Figure 3 illustrates that animal age influences the mechanical properties of equine bone (Bynum et al. 1969). In order to reduce the effect of bone age, the ultimate normalize load, $, was compared to the modulus of rupture of an unfractured bone of the same age by expressing $ as a per cent capacity. C, of the strength of the unfractured bone. Values for the strength of the unfractured bones were taken directly from the curves in Fig. 3. Nowhere in this analysis was the effect of animal nutrition considered. although nutrition must certainly be a factor influencing the mechanical properties of horse bone. It is, no doubt, one of many factors that contribute to the ,characteristic data scatter associated
o0
,
1
5
IO
4. ExPEmMEFdTk
PRocEDumS
Design of experiments, plates andfasteners
Because of the prohibitive cost of standard bone fixation plates and the accompanying fasteners, it was decided to fabricate the necessary plates from mild steel flat bar stock and to use a conventional ty@e of self-tapping screw. The type of screw used was a Type A (sheet metal) screw of mild steel with a conventional American Standard thread design. The decision to use mild steel for the test plates and fasteners rather than the universally accepted Type 316 stainless steel for orthopedic implants was based on their similarity in mechanical .properties and the absence of necessity of concern for recipient rejection mechanisms associated with the properties of mild steel. A full factorial experimental design on three variables was employed, providing 27 different combinations of plate dimensions and fastener size (Fig. 4). Typical plate dimensions appear in Fig. 5. By employing a constant end margin of 0.375 in. ‘and a constant
I
15 AGE.
Fig. 3. Strength to age
with the evaluation of these properties. This scatter was observed to carry over into the results of this work. It is doubtful that a high degree of accuracy can be readily obtained in evaluating the effects of age and nutrition on the bone properties of large animals without an extensive research program.
I
1
20
25
YEARS
relationshipfor whole cr al. 1969).
bone (Bynum
50
A parametricanalysis of bone fixation plates
PLATE
I
LENGTH ( in. I I ( 6 HOLES)
4.5
8
12
14
8
12
14
8
12
14
8
167
1
12
14
8
I2
14
8
12
14
PLATE WIDTH (in)
, ~FLi~$t~ 8
12
14
‘T’ 8
n
1
,!
l4
Fig. 4. Flow chart of factorial experiment.
longitudinal pitch. g, of O-75in. between holes, a variation in plate length provided a variation in the number of fasteners required (i.e. 4 screws for 3 in. plate, 6 screws for 4.5 in. plate. 8 screws for 6 in. plate). Similarly. by employing a constant edge margin of O-025in., a variation in plate width provided a variation in lateral pitch, p, (i.e. 0 for 0.5 in. plate. /
L
0.25 for. O-75in. piate, 0.5 for I in. plate). Three fastener sizes were used (Table 1). Ah fastener holes were dri&d in the plates with a drill press and countersunk to a depth of O*I25in. with a conventional American Standard countersink (82 degrees included angle). All tests ‘were performed on an Instron Floor Model Testing Machine (20.000 pound capacity). Each specimen was tested in flexure as a simply supported beam with a concentrated load at the mid-span, the fixation plate being on the tension side of the beam. This loading condition was selected for evaluating the various plate designs because Aexure was beheved to be the most critical loading situation in the absence of combined loads. Furthermore. it was believed that the greatest resistance to loading would be observed with the fixation plate attached to the tension side Table 1. Screw dimensions
Screw size
Fig. 5. General plate design.
No.8 No. 12 No. 14
Major diameter Du. (in.1
Minor diameter D,. (in.)
I5 11
0.168 o-221
0.116 0*155
1.75 1.75
oval oval
10
0.34
O-178
2.00
fiat
Threads per in.
screw length
w
Head
design
168
D. R. R4Y et al.
of the beam. To preclude rate effects. all tests were conducted at a common rate of deformation of 0.20 in./min. Replicate tests were conducted on one plate-fastener combination (3 in. by 1 in., No. 12) in order to obtain a general idea of the reliability of the test data The. selection of the combination used in the replicate tests was based upon the results of the initial 27 tests.
A detailed discussion of the initial 27 tests and the 4 replicate tests is presented later in the discussion.
Preparation of bone specimens with plates
Table 2. Bone drill sizes and intierences Fastener Fastener Size
No. 8 No. 12 No. 14
Minor diameter D,, (in.)
Bone drill drill size
0*.116 9164 O*lY No. 11 0.178 No. 1
Major diameter &, (in.)
Interference.
0.141 0.191 O-228
i, D,l& 0.89, O-81 0.78
tency in the make-up torque. The ‘C’ clamp was then removed Final preparation of the specimen consisted of trimming the anterior surface of the bone ends so that good bearing could be achieved in the test apparatus. It
All bone specimens were equine third metacarpals (lower forelegs) placed in a freezer following animal death. In order to simulate the properties of fresh dead bone, no more than 24 hours elapsed between removal from the freezer and the completion of a test. Immediately following the thaw period, all surrounding muscuiatur6, including periosteal tissue, was stripped from the bone. A transverse sawcut (approximately 0.05 inches widt) was made through the center of the bone at mid-length to simulate fracture. The severed bone ends were then butted together and held with a large ‘C’ clamp in order to achieve a compression fixation similar to that employed in actual practice by orthopedic surgeons. A standard compression was achieved in the specimen by bringing the ‘C’ clamp down snugly on the ends of the bone
4. In order to gain information regarding the influence of plate length, fastener size, and lateral hole spacing (plate width), the data is presented in the form of curves relating the per cent capacity, c, of each specimen to each of the three variables under consideration. Recall that the per cent capacity is de-
then applying an additional one-quarter turn. Appropriate holes for the fastener size to be used were th6n marked and drilled through the
fined to be the ratio of the strength of the bone specimen to the strength of an unfractured bone of the same age, ex-
bone with a drill press. Drill sizes used for driliing pilot holes in the bone for the appro-
pr6SS6d in per Cent. Inspection of Fig. 6 suggests some interesting observations concerning the influence of fastener size. A stratification of the data is immediately apparent separating the 6 in. long plates from the 3 and 4.5 in. long plates. This stratification suggests that plate length may have a considerable effect upon the capacity of the composite structure. Within each strata, however, the capacity of a particular plate size is only slightly affected by varying
priate fastener sizes employed were sclccted such that the resulting interferences were relatively constant (Table 2). Interftrence was defined to b6 the ratio of the minor diameter of the fixation screw to the diameter of the bone drill A fixation plate was then attached to the
anterior surface of the bone, the screws being driven down with. a brace and then handtightened to maintain approximate consis-
was believed that by freezing the bone specimens with the flesh intact their moisture content could be maintained at approximately the same level as at the time of death. Visual inspection during preparation r6V6al6d no frctze cracks. and after testing the bone fragments were still moist. 5. DISCUSSION OF RE!WL’IS
The various types of failures observed and the test results are pr6Sent6d in Tables 3 and
r6COnStIUCt6d
A parametric analysis of bone fixation plates Tabie 3. Observed failure mechanisms Plate and fasteners
Tvoe offailure observed
Test no.
Length, L(ill.1
Width. W(h)
Screw no.
Fast eners
1% 194 195 193
3 3 3 3 3 3 3 3 3 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 6 6 6 6 6 6 6 6 6 3 3 3 3
0.5 O-5 0.5
8 12 14 8 12 14 8 12 14 8 12 14 8 12 14 8 I’ 1;; 8 I2 14 8 12 14 8 12 14 12 12 12 12
I 2 ...
iii 199 201 200 181 188 189 186 187 197 190 191 192 183 185 182 179 180 184 178 176 177 2% 297 298 299
0.75 0.75 o-75 1 I A.5 0.5 0.5 o-75 o-75 0.75 1 1 A.5 0.5 ::;5 0.75 0.75 1 1 1 1 1 1 1
aes
Plate
Bone
2 1 2 2 2 ... 2 5 ... 2 3 .. . 2 4 .. . 3 1 ... 4 2 ... 3 5 ... 3 3 3 2
OJ60
0.m
FASTEN3 MMOR D(PIYTER,D~,N
Fig. 6. Influence of fastener size on plate capacity.
169
the size of the fastener. That is, increasing the size of the fastener from a No. 8 to a No. 14 produces no substantial gain in the overall capacity. It can be seen from Table 3 that considerably more fastener failures were experienced in the tests involving No. 8 and No. 12 screws than were experienced in the tests where No. 14 screws were employed. It is possible that greater chance for screw failures exists among the two small sizes due to variations in strength as a result of the manufacturing processes and variations in the makeup torque applied as the screws were driven into the bone. A more probable explanation is that although more screw failures were observed with the smaher sizes, the No. 14 screws induced premature failure in the bone resulting in no substantial increase in the overall capacity. Therefore, the selection of screw size appeared to depend largely upon whether it is clinically less desirable to experience a large number of screw failures or risk a premature fracture of the already broken bone. (It should be pointed out that neither alternative will meet the requirements of adequate fracture fixation in large arm&s.) Similar observations can be made regarding the influence of plate width (lateral pitch). Stratification of the data is again apparent between plate lengths (Fig. 7). One might have expected the narrowest plates. those with screws in line, to effect the least perturbation of the force flux in the plate and in the bone, thus producing a greater overall capacity for the structure. The data for the 3 in. and 4.5 in. long plates implies, however, that increasing the lateral pitch, p, from 0 to 0.5 in. produced no net increase in capacity. This is most likely due to a combination of those reasons given regarding fastener size effects, coupled with a corresponding increase in the load carrying capability of the wider plate as the lateral hole spacing is increased. In any event, increases in plate width did not produce substantial increases in the capacity of the structure. Notably, the volume of material that can be placed within the fracture site is
0.5 0.5 0.75 0.75 0.75
f I
0.5
z::
1:: 4.5 4.5 4.5 t:;
::;
6
6 6 6 6 6
z 298 299
6 3 3 3 3
f
f
5 3 3 3 3 3
I93 198 202 199
z ISI 188 189 186 187 197 190 191 192 183 I85 182 I79 180 I84 178 176 177
0.5
3 3
1E 195
I I I I
i
I
0.75 0.75 0.75
;:: 0.75 0.75 0.75 I
with tV(in.)
Length L (in.)
Test no.
Plate 6. fastener
8 I2 14 8 I2 I4 8 I2 14 8 I2 I4 8 I2 I4 8 I2 I4 8 I2 I4 8 I2 I4 8 I2 I4 I2 I2 I2 I2
no.
SCrCW
:z
t I ~92 I.43 I-25 2.88 2.15 I .87 I.92 I *43 I.25 I .43 I -07 0.94 2.15 2.15 2.15 2.15
5.75 4.29 3.74 3.83 2.86 2-50 2.88 2.15 I a87 3.83 2.86 2.50 2.56
(LWDJ
s IO 9 I3 IO 9 8 8 5 5 5 5
:: 5 5 I3 5 5 2 2 I6 4 I7 I7
:
16
:
(YZ,
Bone
0.337 0.326 0.345 0.268 0.352 0.263 0.247 0.309 0.358 0.155 0401 0.195 0.244 0.292 0.3% 0.161 0.296 0.257 0.258 0.381 O-308 0.236 0.271 0.282 0.259 0.331 0.304 0.282 o-138 0.245 0.285
Mid-spaa de&lion a, (in.)
Tabled.
::z I.57 2.20 2.75 I.96 I.90 2.88 l-63 0.86 I.38 I.25
::: I.56 2-05 2.00
1.03 0.92 I.45 0.90 I.30 I.30 0.85 0.87 I.64 I.60 I.50 I.35 I.55 I.52
wt.
Plated bone
Test results
14.5 IO.8 II-2 12.4 14.8 IS.6 IO.8 8.2 IS.2 13.9 13.9 12.7 149 14.7 16.9 IO.8 12.5 18.1 22.7 21.4 19-o 16.8 20.2 24.9 22.5 24.8 34.2 II.6 6.1 13.0 12.6
Ultimale uorm. load Y (ksi)
Capacity c (%I 42.6 28-I 29.6 36.5 38.6 41.0 28.4 21.0 38.8 36. I 35.5 32.4 41.4 40.9 44.6 28.1 33.4 48.3 58.0 54.6 48.7 42.5 52.5 63.9 57.0 62.4 86.0 29.6 15.6 33.2 32.2
34.0 37.9 38.4 34.0 38.4 38.0 38.0 39.2 39.2 38.5 39.2 39.2 36.0 36-O 37.9 38.4 37.5 37.5 39.2 39.2 39.0 39.5 38.5 39.0 39.5 39-8 39.8 39.2 39.2 39.2 39.2
Of
rupture, MR (ksi)
MOdUlus
Unfractured bone
2.34 3.51 3.43 2.74 2.59 244 3.52 4.75 258 2.77 2.82 3.08 2.42 2.45 2.24 3.56 3.00 2.07 I.73 I.83 2.05 2.36 I90 I.57 I *76 I.61 I.17 3.38 6.41 3.02 3.11
Norm. load factor, k
7 7 7 7 7 8 7 7 8 8 8 7 7 7 7
Test span (in.)
A parametric analysis of bone fixation plates
B
1
F ;
I
60-
ii...
OL
Fig.
1
0.50
7.
0.75 PLATE WIDTH. W. IN.
Influence
of
plate
LOD
width
on plate
OlPacity.
restricted by the availability of sufficient tissue surrounding the site to enable adequate wound closure. It is questionable whether a 1 in. wide plate could be employed on equine third metac@pal in actual practice. Hence, it is signifkant to the veterinary orthopedic surgeon that a narrow plate may be used instead of a wider one to provide better wound closure without a substantial sacrifke of strength. Figure 8 illustrates one of the most significant findings in the experimental program, the notable effect that an increase in plate length I
LEilEK) PLA7E wlDn!_ It&
01
3.0
4.5 PLATE
Fig. 8. Influence
LENGTH.
60 L.
IN
of plate length on plate capacity.
171
produces. It can be seen that, regardless of the width of the plate or the size of fastener employed, the 6 in. long plates demonstrate approximately twice the capacity of the 3 in. long plates. It is felt that such an increase in capacity was a result of the capability of the longer plates to better distribute the stresses in the composite structure over a greater length of bone. That is, in order for the structure to maintain its integrity, the tensile forces below the neutral surface of the structure must be transferred from one side of the fiatture to the other via the fasteners and the plate. When this transfer must be completed over a smaU distance, as was the case with the 3 in. long plates, a higher stress concentration will exist than would be present if the forces were transferred over a greater length of bone. Certainly, substantial stress concentrations existed in the vicinity of all the screws, regardless of the length of plate used, but the net effect of distributing the forces over a greater portion of bone produced a corresponding increase in the capacity of the structure. In Fig. 8 an exceedingly high capacity was observed for the largest plate-fastener combination (6 in. by 1 in., No. 14). It is felt that this data point may not be characteristic of the capacity one could generally expect from a plate of these dimensions. A more reliable value would probably lie between 60 and 70 per cent, based upon the general trends discussed earlier. The fact that plate length is the most important variable influencing the capacity of the structure may produce somewhat of a dilemma for the veterinary orthopedic surgeon Because of the variation in bone cross-section and the fact that the average length of equine metacarpus bone is approximately 10 in., an increase in plate length above 6 in. does not appear to be feasible. Furthermore, because a primary tendon traverses the anterior surface of the bone and generally cannot be detached without permanent damage, the fixation plate in actuai practice is attached to the bone slightly to either side of this tendon.
171
D. R. R.4Y et al.
The cross-section of the bone varies considerably along its length and the surface possessing the least curvature is the anterior one. All surfaces possess considerable curvature at the distal and proximal ends and therefore any substantial increase in plate length would require that the plate be contoured to the recipient surface. No general design can be expected to serve all possible geometries and hence, the only practical alternative remaining would seem to be to bend the plate to fit the individual bone. This means installing a plate that has already been yielded, which can be undesirable from a structural aspect. Thus. 6 in. may be considered an upper bound on plate iength for use on equine third metacarpal. Because the 1 in. wide plate has questionable application, the capacity of the fixation . device’ is limited to approximately 60 per cent of the unfractured bone strength. This is readily apparent by inspection of Fig. 8. From Fig. 8 it can be seen that, disregarding the largest plate-fastener combination (6 in. by 1 in., No. 14). the capacity of the composite structure for the 6 in. long plate is not likely to be greater than approximately 60 per cent. This represents the maximum support that could normally be expected, using the largest feasible plate under the described loading condition. That is, the bone is a simply supported beam loaded at the mid-span with the fixation plate on the tension side of the structure. It is improbable that this particular loading condition would be encountered outside of the laboratory. Most likely, combined loading conditions would prevail in actual practice, and therefore the capacity of the structure could be substantially reduced. For example, if the animal attempts to rise from a prone position, the metacarpus will probably experience a simultaneous compression and ficxure loading Similarly, if a turning maneuver is attempted, it is possible that the metacarpus will experience torsion, compression, and flexure. Where combined loading conditions exist, a decrease in capacity would be expected.
In order to consider the combined effects of all three plate design variables. it was necessary to determine a suitable means of presenting the data as a function of the platefastener characteristics simultaneously. It was found that by plotting the per cent capacity of a particular plate-fastener combination against an arbitrary function, the reciprocal of the product of plate length, plate width, and fastener minor diameter, a failure envelope for all tests could be obtained (Fig 9). In general, Fig 9 suggests that for a particular combination of plate and fastener a capacity of not less than the value denoted by the curve may be expected. It is quite possible that the value will be greater than is indicated by the curve, but not likely to be less. Of the 27 tests conducted, test 202 (3 in. by 1 in., No. 12) appeared to be considerably lower than the failure envelope would indicate. It was decided to test the reliability of this data point, and four additional tests of this plate fastener combination were conducted. Values of C for all five tests ranged between 156 and 33.2 per cent (Table 4). Tests 296, 298. and 299 exhibited close agreement among test results but test 297 appears quite low. It was noted during the testing of specimen 297 that 3 of the 4 screws failed, two breaking simultaneously and the third shortly there-
0
I
2
3 I ~Wki’.
4
5
IN.-’
Fig. 9. Failure envelope for ail tests.
6
A
parametricanalysis
after. Fracture of the bone was not observed, and hence, it is believed that this test is the least characteristic since bone fracture was observed in each of the other tests. Such a spread of data does serve to illustrate the variation in results that may occur. It also suggests that to achieve results possessing a high degree of statistical reliability would require a large number of tests. Since only two specimens can be obtained from one animal, the presence of differences in health and nutrition among animals also dictates that the number of tests be large. Hence, the discussion presented here must be regarded as observations of only the general trends that occur as a result of varying plate length, plate width, and fastener size. Insuficient replication was obtained to determine reliability. In addition, this discussion concerns results obtained for one condition of loading, specifically Aexure with the fixation plate on the side of the bone opposite the applied load. In all probability, this configuration wifl offer the greatest resistance to loading Thus, the values presented here represent the best performance that can normally be expected where singular tiation plates are employed. In the general case, combined loading conditions on a single plate wiIl probably produce a more critical situation. Thus. it is tentatively conduded that. except for extraordinary cases, it is doubtful that the use of a single fixation ‘plate would provide adequate structural sup port during the period when osteogenesis is occurring in large animals, such as the horse. This conclusion is supported by clinical results obtained at the College of Veterinary Medicine. Texas A&M University. where within the past two years fracture fixation has been attempted in 15 horses using the largest commercial plates and screws available, with only one success. In most cases, failure has occurred within a matter of hours after implantation when the anesthetic wore off and the animal attempted to stand. The use of dual plates has been suggested (Lindahl, 1967) and tried (Peterson and
of bone fixation plates
173
Reeder, 1963; Murray ef al. 1964) in a few selected cases in human medicine. However, the problem of infection is compounded ,with this method, and hence the results of its use are diicult to evaluate despite the apparent gain in mechanical advantage. No mention could be found within the literature of attempts at fracture fixation in the horse using two plates. It is hypothesized, however, that two small plates placed medially and laterally on the anterior surface of the bone may provide more efficient support in the combined loading condition than can be achieved with a single plate. Another factor aggravating the structural aspects of the problem is the presence of gross mis-match in the elastic moduli of bone and steel. This factor may contribute to the failure of the composite structure, resulting in the low to moderate capacities. Thus it is believed that a fiber reinforced polymer (e.g. fiberglass) possessing an elastic modulus more closely matched with bone would enhance the integrity of the composite structure. Several such materials have been developed by the aerospace industry within recent years that possess tensile strengths in excess of stainless steel. Polymers are used as implant materials in many situations in human and veterinary medicine but have been rarely regarded as structural materials. It is conceivable that a highly * inert polymer, reinforced with high strength fibers. could serve as a better material for fixation devices than conventional stainless steel. provided adverse tissue reactions do not occur. 6. CONCLUSIONS (.1) For a particular size of fixation plate. increasing the screw from No. 8 to No. 14 produced no substantial increase in the capacity of the composite structure. (2) Increasing the plate width (lateral hole pitch) from O-5in. to 1 in. produced no significant increase in the overall capacity of the composite structure. (3) For the loading condition described. in-
174
D. R. RAY et al.
creasing the plate length from 3 in. to 6 in. approximately doubled the capacity of the composite structure. (4) Where the largest feasible plate was employed (i.e. 6 in. by 0.75 in., No. 14), the maximum capacity that can normally be expected under loading conditions similar to that described is approximately 60 per cent. (5) In general, the use of a single fixation plate for fracture fixation of equine third metacarpal will not provide sufiicient strength for weight bearing during osteogenesis. 7. RBcoMMplDATlONS
(1) The possibility of using two small tixation plates placed medially and laterally on the anterior bone surface should be investigated. (2) The possibie use of a fiber reinforced polym~ as a fixation plate material should be investigated for strength and modulus compatibility, as well as tissue tolerance in the host. (3) In conjunction with the use of polymeric fixation plates, a more efficient method of fastening the plate to the bone should be investigated (e.g. biind rivets, bolts with lock nuts, nylon or other polymeric fasteners). (4) An analytical method of structurally analyzing the compositive under various loading conditions should be devised to facilitate the proper design of fixation plates. (5) Standards for testing and acceptance protocol are needed to help prevent structural failures due to inadequate designs of current fixation plates and other devices. Acknowledgement-The
metcrial for this paper was excerpted from a thesis by D. R. Ray submitted to the Graduate College of Texas A&M University in partial fuhlllment of the requitements for a Master of Science in CiviI Engineering degree.
NOMBNCLATURB Symbol L ti f i
Typical Variable Imits notmakedload ksi in.-hips appliedmoment distance from bone cross-section cenin. troid to extreme bone fiber moment of inertia of bone crosssection about its ccntroidal axis in.’ (perpendicular to applied load)
half majordiameter of outer ellipse in. half minor diameter of outer ellipse in. half major diameter of inner ellipse half minor diameter of inner elliose . vertkatoffset ofinner ellipse with respect to outer ellipse in. hotizontai offset of inner ellipse with respect to outer ellipse in. centroid coordinate of bone crossin. section centroid coordinate of bone cross-
section modulus of rupturefor whole bone ultimate norm&& load capacity, reconstructed bone longitudinai hole pitch lateral hoie pitch ;a$e major screw diameter
minor screw diameter. boaedrilidbmeter
ei ksi per ant m. m. in. in. in. in. in.
REFERENCES
Bynum. D., Jr., Ledbeuer, W. 9.. Boyd C. L. and Ray, D. R ( 1969) Flexural proputk of equine metacarpus. Paper submitted to 1. Biotncd. Mark Res. Evans, F. G. and Lebow, M. (1951) Regionaldilkence in some of the physical properties ofthe human femur. 1. appl. Phyriol. 3.563-572. Evans, F. G. (1964) Signikant ditTerencein the tensile strength of adult human compact bone. Proc. Firs? Europa~ Bone and Tooth Symposium. pp. 3 19-33 1. Evans, F. G. and Vhtcent&, R. (1969) R&ion of cdlagen fiber orientation to some mschankaJ propettks of human cortical bone. J. Biomcchanics 2.63-7 1. Guthrie, G. W. (1%3),Direct hxation in fractures. Am. Med. 5,376-379.
Hodgkinson. R. (l%l) Internal fixation of fktures of long bones with metallic devices. Med. J. Aust. 46, 691-693.
Jacobs. P. A. and Guten, G. N. (1967) Compression furationofbone. Wk. med.J. 66.412417. Lindahl, 0. (1962) Rigidity of immobiion of tmnsverse bXures.Acta orthop. scand.32 237-246. Lii, 0. (1961) Rigidity of immobilization of oblique fmctures. Rcta orrhop. stand. 35.39-50. Lindahl, 0. (1967) The rigidity offrectum immobihzation withpiates.Actaorrhop.rcund.38,101-141. Lundvall. R. L. (1960) Observations on the treatment of &actures of the long bones in large animals. J. Am. vet. med. Ass. l37,308-3 12. Mart& C. D. (1956) Stress tolerance in bone and metal. 1. BoneJ. Surg. 3% 827-834. Munay, W. R., Lucas. D. B., and Inman. V. T. (1964)
Treatment of non-union of fractures of the long bones by the two-pkate method. J. Bone Jt Surg. 46.4. 1027Peizn. L. T. and Reeder. 0. S. (1963) Dual Slotted plates in fixation of fractums of the femoral Shaft J. Bone Jt Sutlr. 4W 430-43 1. Weisman, S. (I%@ Metals for implantation in the human body.dnn. N. Y.Acad. Sci.146,80-85.
Vol. 4. pp. 163-174.
paEMon
RCSS. 197 1.
Printed in Gmt
Briprn
A PARAMETRIC ANALYSIS OF BONE FIXATION PLATES ON FRACTURED EQUINE THIRD METACARPAL* D. R. RAY.t W. B. LEDBElV2R.S D. BYNUM$ and C. L. BOYDll Texas A&M University, College Station. Texas 77843, U.S.A. Aba&met- A series of tests of the relative strengths of conventional bone fixation platedesigns as compared to the strength of unfractured equine third mctacafppl bones of the same age was performed. The tests involved a full factorial experimental design on three variabks: plate length. lateral hok pitch. and fastener size. AU tests were conducted in lkxtue. a concentrated
load being applied on the posterior surface of the bone at mid-spM.withthe fixation plate in each caseattachedto the anterior bone surface. The most signScant parameterwas found to be plate kngtb since an increase in length from 3 to 6 in. approximately doubled the capacity of the reconstructed bone spacimcn. Fastener size and lateral hok pitch pn&uced no sign&ant change in oveti capacity for the structure. It was concluded that. in generai. the use of a single Axation &ate for fracture fixation of eauine third metacarpal would not provide adequate support
for weight bearing during osteogen&s. 1. IN’IRODUCIION
time, attempts at using various metallic devices have ensued with varying degrees of success. Fracture fixation using screws alone occurred as early as 1902 (Jacobs and Guten. 1%7), but many other types of fixation devices, empioying a wide range of metallic materials, were also being investigated and tried clinically. The earliest types of metal plates to be used were made of nickel-steel, iron, or silver (Guthrie, 1903). These early plates were generally attached to the fractured bone with ivory pegs which were allowed to protrude from the wound to facilitate an easy removal of the device, usually after 3 or 4 weeks. Removal was generally required whenever metals other than silver were used or when devices of dissimilar metals were employed. The resulting electrochemical corrosion that occurred within the electrolytic environment of the body tissues was unforseen at the time and resulted in infection or other gross tissue reactions. It soom became evident that silver screws in conjunction with silver plates produced the most favorable results. Thus. silver
material in this paper pertains to the experimental evaluation of the structural rhtegrity of fractured equine third metacarpal bones (lower forelegs of the horse). reconstructed with fixation plates of various designs and tested in flexure. Specificaliy, the relative strengths of bone fixation plates and fasteners installed on fractured equine third metacarpals, to include the effects of varying the length of the plate. the lateral pitch between screw holes. and the size (diameter) of screw. were investigated and compared to the strengths of unfractured whole bone of the same age. From this analysis design recommendations for more optimum combinations of fastener size and plate dimensions were made.
THE
2. BACKGROUND Internal fixation of fractures in human medicine dates back at least to ‘1775 (Guthrie. 1903 : Hodgkinson. 196 11 when Lepeyode and Sicre used silver wire to achieve immobilization in fractures of the long bones. From that
‘Received I i June 1970. ?Engineering Research Associate. Texas Transportation Institute. ZAssociate Professor. Departments of Civil and Aerospace Engineering. $Assistant Research Engineer. Texas Transportation Institute. “Associate Professor. Veterinary Medicine and Surgery. College of Veterinary Medicine. 163
BM Vol. 4 No. 3-A
164
D. R. R4Y
the most commonly used implant material for several years. Stainless steel was first introduced under a British patent in 19 13 as the result of a search for a non-corrosive material to be used in the manufacture of naval guns (Hodgkinson 1961). Since that time. various types of stainless steels have been investigated for internal use and. primarily through a process of trial and error, stainless steels of types 3 16 and 3 17 have emerged as the most acceptable for implantation in the body. In 1962. the British Standards Association took steps to standardize the materials used in the manufacture of metal surgical implants and related tools (Weisman, 1968). The British Standard 353 1: 1962 was later amended to include pure titanium. Currently, within the United States, ASTM (American Society for Testing and Materials) Committee F-4 is in the process of developing standards and specifications for cast and wrought cobalt-chromium alloys, stainless steel, pure titanium and required surface finishes on these materials (Weisman, 1968). The Standards Association of Australia is taking similar steps. No standards could be found from any country for the testing and acceptance protocoi for surgical implants. Most of the testing of fixation units has been co&red to tests of the fixation plate and appropriate screws separately. The work of Martz (1956) and Lindahl ( 1962, 1964, 1967) represents much of the literature that has been published to date concerning the performance of fixation devices on whole bone. Both authors dealt primarily with observing the. loads required to produce failure of the composite structure, but convey little meaningful engineering information that can be used to make design recommendations. Both tested existing fixation devices (plates and screws), but neither investigated the effects of varying the basic designs. Fracture fixation in human medicine has progressed to the point at which relatively good success can be achieved with current became
er al.
types of fixation devices. provided the patient rigorously follows the post operative advice of his physician. Even so. failures which are structural in nature do occur. The problem of structural failures is not confined to human medicine alone. Indeed. the problem becomes accentuated in veterinary medicine. The practice of forbidding weight bearing following fracture fixation may be a convenient means of avoiding structural failure whiie osteogenesis occurs in the human species. but it becomes impractical if not impossible when dealing with fractures incurred in large domestic animals such as the horse (Lundvall. 1960). All of the fixation devices used to attempt the repair of fractures in large animals have been borrowed from human medicine. The largest plates, intended for fixation of the femur in humans, are the only sizes available to attempt the fixation of fracrCLredlong bones in animals as large as the horse. and these plates are rarely adequate. In the past, veterinarians had little choice but to sacrifice large animals that had developed fractures in the long bones. Little improvement in this situation exists today. In cases where fixation has been attempted in the horse with currently available fixation plates at the Large Animal Clinic of the College of Veterinary Medicine at Texas A&M University, failure of the composite bonefixation plate structure has generally occurred within a matter of hours from the time of implantation. Thus the veterinary orthopedic surgeon is faced with a frustrating dilemmato continue to attempt fixation with devices that are apparently inadequate, or to sacrifice the animal. In order to try to eiiminate this diiemma. veterinary orthopedic surgeons and materials and structural engineers at Texas A & M have teamed together to analyze and evaluate existing plate designs and to make recommendations for their improvement. The work reported here was an integral part of that program.
165
A parametric analysis of bone fixation plates 3. THWXETICAL
CONSIDERATIONS
In order to obtain useful information from the data, several assumptions had to be made. The validity of some of these assumptions may appear questionable in a strict sense, but it is believed that their use. nonetheless. yields meaningful results. The reconstructed bone specimen was assumed to be a beam. simply supported. with a concentrated load at the mid-span. The fixation plate was attached to the anterior surface of the bone and the concentrated load was applied to the posterior bone surface. The fixation plate was. therefore. on the tension side of the beam. In all cases the mid-length of the fixation plate, mid-span of the beam, and mid-length of the bone were coincident. To account for differences in bone size among the specimens, the applied load was normalized on the mid-shaft geometry of the bone by means of the flexure equation.
L.=F, where. L, = normalized loaiL ksi. it4 = applied moment, in.-kips, c = distance from bone cross-section centroid to extreme bone fiber, in., I = moment of inertia of bone cross section about its centroidal axis (perpendicuJar to applied ioad), in4 The mid-shaft cross section of the bone was assumed to be that of an eccentric elliptical annulus (Fig. 1). Com-
SURFACE
Fig. 1. Assumed bone cross-section at mid-length.
parison with the actual bone cross-section (Fig. 2) illustrates that the assumption is quite good. Calculus was used to derive the moment of inertia for such a cross-section. which is given.by I = $ (LI,~,~- a,bz3 - 4azb2d,2) - ra2zb,2d,2 a&, - a,b,
where the symbols are defined in Fig. i. The location of the section’s centroid with respect to the intersection of the diametrical axes of the outer ellipse is given by. X=
-a,b,d? (a,b,-a2bz)’
‘=
- &b,d, (a,b,-a,bp)’
It must be noted here that the normalized load, L,, is not regarded as a stress since the dimensions of the plate and fasteners and thus the load they carry do not enter directly into the analysis. Rather. it was believed that the effects of varying the plate and fastener combination would be evidenced by the observed moments required to produce failure of the composite structure. Most certainly a complex stress state exists within the specimen. especially in the vicinity of the fasteners, and the analysis presented here represents an experimental evaluation of the various plate designs rather than a comprehensive theoretical structural analysis. It has been shown that the composition and mechanical properties of bone vary somewhat with position along its length (Evans er al. 195 I, 1964, 1969). and the magnitude of error introduced by assuming the bone to be homogeneous and isotropic for analytical purposes is not known. The nature of the problem does not lend itself to a straightforward exact mathematical solution that accounts for all the variables. An initial consideration was to analyze the structure using the principles of reinforced concrete design. The assumption that the
0. R. RAY et al.
166
bone below the neutral axis carries no tensile stress is quite good since the specimen is sawed through. It cannot be assumed, however, that the steel is uniformly bonded to the bone since a’non-uniform stress state prevails in the region of the fasteners. Because of the high modular ratio (approximately 15) that exists between the steel and the bone, the true neutral surface of the structure in bending will shift from the centroidal axis of the bone cross-section to a point closer to the centroidal axis of the steel plate. The exact location of the shifted axis is not accounted for in this analysis and no solution could be found in the literature for its location. Another variable that must be considered is bone age. Figure 3 illustrates that animal age influences the mechanical properties of equine bone (Bynum et al. 1969). In order to reduce the effect of bone age, the ultimate normalize load, $, was compared to the modulus of rupture of an unfractured bone of the same age by expressing $ as a per cent capacity. C, of the strength of the unfractured bone. Values for the strength of the unfractured bones were taken directly from the curves in Fig. 3. Nowhere in this analysis was the effect of animal nutrition considered. although nutrition must certainly be a factor influencing the mechanical properties of horse bone. It is, no doubt, one of many factors that contribute to the ,characteristic data scatter associated
o0
,
1
5
IO
4. ExPEmMEFdTk
PRocEDumS
Design of experiments, plates andfasteners
Because of the prohibitive cost of standard bone fixation plates and the accompanying fasteners, it was decided to fabricate the necessary plates from mild steel flat bar stock and to use a conventional ty@e of self-tapping screw. The type of screw used was a Type A (sheet metal) screw of mild steel with a conventional American Standard thread design. The decision to use mild steel for the test plates and fasteners rather than the universally accepted Type 316 stainless steel for orthopedic implants was based on their similarity in mechanical .properties and the absence of necessity of concern for recipient rejection mechanisms associated with the properties of mild steel. A full factorial experimental design on three variables was employed, providing 27 different combinations of plate dimensions and fastener size (Fig. 4). Typical plate dimensions appear in Fig. 5. By employing a constant end margin of 0.375 in. ‘and a constant
I
15 AGE.
Fig. 3. Strength to age
with the evaluation of these properties. This scatter was observed to carry over into the results of this work. It is doubtful that a high degree of accuracy can be readily obtained in evaluating the effects of age and nutrition on the bone properties of large animals without an extensive research program.
I
1
20
25
YEARS
relationshipfor whole cr al. 1969).
bone (Bynum
50
A parametricanalysis of bone fixation plates
PLATE
I
LENGTH ( in. I I ( 6 HOLES)
4.5
8
12
14
8
12
14
8
12
14
8
167
1
12
14
8
I2
14
8
12
14
PLATE WIDTH (in)
, ~FLi~$t~ 8
12
14
‘T’ 8
n
1
,!
l4
Fig. 4. Flow chart of factorial experiment.
longitudinal pitch. g, of O-75in. between holes, a variation in plate length provided a variation in the number of fasteners required (i.e. 4 screws for 3 in. plate, 6 screws for 4.5 in. plate. 8 screws for 6 in. plate). Similarly. by employing a constant edge margin of O-025in., a variation in plate width provided a variation in lateral pitch, p, (i.e. 0 for 0.5 in. plate. /
L
0.25 for. O-75in. piate, 0.5 for I in. plate). Three fastener sizes were used (Table 1). Ah fastener holes were dri&d in the plates with a drill press and countersunk to a depth of O*I25in. with a conventional American Standard countersink (82 degrees included angle). All tests ‘were performed on an Instron Floor Model Testing Machine (20.000 pound capacity). Each specimen was tested in flexure as a simply supported beam with a concentrated load at the mid-span, the fixation plate being on the tension side of the beam. This loading condition was selected for evaluating the various plate designs because Aexure was beheved to be the most critical loading situation in the absence of combined loads. Furthermore. it was believed that the greatest resistance to loading would be observed with the fixation plate attached to the tension side Table 1. Screw dimensions
Screw size
Fig. 5. General plate design.
No.8 No. 12 No. 14
Major diameter Du. (in.1
Minor diameter D,. (in.)
I5 11
0.168 o-221
0.116 0*155
1.75 1.75
oval oval
10
0.34
O-178
2.00
fiat
Threads per in.
screw length
w
Head
design
168
D. R. R4Y et al.
of the beam. To preclude rate effects. all tests were conducted at a common rate of deformation of 0.20 in./min. Replicate tests were conducted on one plate-fastener combination (3 in. by 1 in., No. 12) in order to obtain a general idea of the reliability of the test data The. selection of the combination used in the replicate tests was based upon the results of the initial 27 tests.
A detailed discussion of the initial 27 tests and the 4 replicate tests is presented later in the discussion.
Preparation of bone specimens with plates
Table 2. Bone drill sizes and intierences Fastener Fastener Size
No. 8 No. 12 No. 14
Minor diameter D,, (in.)
Bone drill drill size
0*.116 9164 O*lY No. 11 0.178 No. 1
Major diameter &, (in.)
Interference.
0.141 0.191 O-228
i, D,l& 0.89, O-81 0.78
tency in the make-up torque. The ‘C’ clamp was then removed Final preparation of the specimen consisted of trimming the anterior surface of the bone ends so that good bearing could be achieved in the test apparatus. It
All bone specimens were equine third metacarpals (lower forelegs) placed in a freezer following animal death. In order to simulate the properties of fresh dead bone, no more than 24 hours elapsed between removal from the freezer and the completion of a test. Immediately following the thaw period, all surrounding muscuiatur6, including periosteal tissue, was stripped from the bone. A transverse sawcut (approximately 0.05 inches widt) was made through the center of the bone at mid-length to simulate fracture. The severed bone ends were then butted together and held with a large ‘C’ clamp in order to achieve a compression fixation similar to that employed in actual practice by orthopedic surgeons. A standard compression was achieved in the specimen by bringing the ‘C’ clamp down snugly on the ends of the bone
4. In order to gain information regarding the influence of plate length, fastener size, and lateral hole spacing (plate width), the data is presented in the form of curves relating the per cent capacity, c, of each specimen to each of the three variables under consideration. Recall that the per cent capacity is de-
then applying an additional one-quarter turn. Appropriate holes for the fastener size to be used were th6n marked and drilled through the
fined to be the ratio of the strength of the bone specimen to the strength of an unfractured bone of the same age, ex-
bone with a drill press. Drill sizes used for driliing pilot holes in the bone for the appro-
pr6SS6d in per Cent. Inspection of Fig. 6 suggests some interesting observations concerning the influence of fastener size. A stratification of the data is immediately apparent separating the 6 in. long plates from the 3 and 4.5 in. long plates. This stratification suggests that plate length may have a considerable effect upon the capacity of the composite structure. Within each strata, however, the capacity of a particular plate size is only slightly affected by varying
priate fastener sizes employed were sclccted such that the resulting interferences were relatively constant (Table 2). Interftrence was defined to b6 the ratio of the minor diameter of the fixation screw to the diameter of the bone drill A fixation plate was then attached to the
anterior surface of the bone, the screws being driven down with. a brace and then handtightened to maintain approximate consis-
was believed that by freezing the bone specimens with the flesh intact their moisture content could be maintained at approximately the same level as at the time of death. Visual inspection during preparation r6V6al6d no frctze cracks. and after testing the bone fragments were still moist. 5. DISCUSSION OF RE!WL’IS
The various types of failures observed and the test results are pr6Sent6d in Tables 3 and
r6COnStIUCt6d
A parametric analysis of bone fixation plates Tabie 3. Observed failure mechanisms Plate and fasteners
Tvoe offailure observed
Test no.
Length, L(ill.1
Width. W(h)
Screw no.
Fast eners
1% 194 195 193
3 3 3 3 3 3 3 3 3 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 6 6 6 6 6 6 6 6 6 3 3 3 3
0.5 O-5 0.5
8 12 14 8 12 14 8 12 14 8 12 14 8 12 14 8 I’ 1;; 8 I2 14 8 12 14 8 12 14 12 12 12 12
I 2 ...
iii 199 201 200 181 188 189 186 187 197 190 191 192 183 185 182 179 180 184 178 176 177 2% 297 298 299
0.75 0.75 o-75 1 I A.5 0.5 0.5 o-75 o-75 0.75 1 1 A.5 0.5 ::;5 0.75 0.75 1 1 1 1 1 1 1
aes
Plate
Bone
2 1 2 2 2 ... 2 5 ... 2 3 .. . 2 4 .. . 3 1 ... 4 2 ... 3 5 ... 3 3 3 2
OJ60
0.m
FASTEN3 MMOR D(PIYTER,D~,N
Fig. 6. Influence of fastener size on plate capacity.
169
the size of the fastener. That is, increasing the size of the fastener from a No. 8 to a No. 14 produces no substantial gain in the overall capacity. It can be seen from Table 3 that considerably more fastener failures were experienced in the tests involving No. 8 and No. 12 screws than were experienced in the tests where No. 14 screws were employed. It is possible that greater chance for screw failures exists among the two small sizes due to variations in strength as a result of the manufacturing processes and variations in the makeup torque applied as the screws were driven into the bone. A more probable explanation is that although more screw failures were observed with the smaher sizes, the No. 14 screws induced premature failure in the bone resulting in no substantial increase in the overall capacity. Therefore, the selection of screw size appeared to depend largely upon whether it is clinically less desirable to experience a large number of screw failures or risk a premature fracture of the already broken bone. (It should be pointed out that neither alternative will meet the requirements of adequate fracture fixation in large arm&s.) Similar observations can be made regarding the influence of plate width (lateral pitch). Stratification of the data is again apparent between plate lengths (Fig. 7). One might have expected the narrowest plates. those with screws in line, to effect the least perturbation of the force flux in the plate and in the bone, thus producing a greater overall capacity for the structure. The data for the 3 in. and 4.5 in. long plates implies, however, that increasing the lateral pitch, p, from 0 to 0.5 in. produced no net increase in capacity. This is most likely due to a combination of those reasons given regarding fastener size effects, coupled with a corresponding increase in the load carrying capability of the wider plate as the lateral hole spacing is increased. In any event, increases in plate width did not produce substantial increases in the capacity of the structure. Notably, the volume of material that can be placed within the fracture site is
0.5 0.5 0.75 0.75 0.75
f I
0.5
z::
1:: 4.5 4.5 4.5 t:;
::;
6
6 6 6 6 6
z 298 299
6 3 3 3 3
f
f
5 3 3 3 3 3
I93 198 202 199
z ISI 188 189 186 187 197 190 191 192 183 I85 182 I79 180 I84 178 176 177
0.5
3 3
1E 195
I I I I
i
I
0.75 0.75 0.75
;:: 0.75 0.75 0.75 I
with tV(in.)
Length L (in.)
Test no.
Plate 6. fastener
8 I2 14 8 I2 I4 8 I2 14 8 I2 I4 8 I2 I4 8 I2 I4 8 I2 I4 8 I2 I4 8 I2 I4 I2 I2 I2 I2
no.
SCrCW
:z
t I ~92 I.43 I-25 2.88 2.15 I .87 I.92 I *43 I.25 I .43 I -07 0.94 2.15 2.15 2.15 2.15
5.75 4.29 3.74 3.83 2.86 2-50 2.88 2.15 I a87 3.83 2.86 2.50 2.56
(LWDJ
s IO 9 I3 IO 9 8 8 5 5 5 5
:: 5 5 I3 5 5 2 2 I6 4 I7 I7
:
16
:
(YZ,
Bone
0.337 0.326 0.345 0.268 0.352 0.263 0.247 0.309 0.358 0.155 0401 0.195 0.244 0.292 0.3% 0.161 0.296 0.257 0.258 0.381 O-308 0.236 0.271 0.282 0.259 0.331 0.304 0.282 o-138 0.245 0.285
Mid-spaa de&lion a, (in.)
Tabled.
::z I.57 2.20 2.75 I.96 I.90 2.88 l-63 0.86 I.38 I.25
::: I.56 2-05 2.00
1.03 0.92 I.45 0.90 I.30 I.30 0.85 0.87 I.64 I.60 I.50 I.35 I.55 I.52
wt.
Plated bone
Test results
14.5 IO.8 II-2 12.4 14.8 IS.6 IO.8 8.2 IS.2 13.9 13.9 12.7 149 14.7 16.9 IO.8 12.5 18.1 22.7 21.4 19-o 16.8 20.2 24.9 22.5 24.8 34.2 II.6 6.1 13.0 12.6
Ultimale uorm. load Y (ksi)
Capacity c (%I 42.6 28-I 29.6 36.5 38.6 41.0 28.4 21.0 38.8 36. I 35.5 32.4 41.4 40.9 44.6 28.1 33.4 48.3 58.0 54.6 48.7 42.5 52.5 63.9 57.0 62.4 86.0 29.6 15.6 33.2 32.2
34.0 37.9 38.4 34.0 38.4 38.0 38.0 39.2 39.2 38.5 39.2 39.2 36.0 36-O 37.9 38.4 37.5 37.5 39.2 39.2 39.0 39.5 38.5 39.0 39.5 39-8 39.8 39.2 39.2 39.2 39.2
Of
rupture, MR (ksi)
MOdUlus
Unfractured bone
2.34 3.51 3.43 2.74 2.59 244 3.52 4.75 258 2.77 2.82 3.08 2.42 2.45 2.24 3.56 3.00 2.07 I.73 I.83 2.05 2.36 I90 I.57 I *76 I.61 I.17 3.38 6.41 3.02 3.11
Norm. load factor, k
7 7 7 7 7 8 7 7 8 8 8 7 7 7 7
Test span (in.)
A parametric analysis of bone fixation plates
B
1
F ;
I
60-
ii...
OL
Fig.
1
0.50
7.
0.75 PLATE WIDTH. W. IN.
Influence
of
plate
LOD
width
on plate
OlPacity.
restricted by the availability of sufficient tissue surrounding the site to enable adequate wound closure. It is questionable whether a 1 in. wide plate could be employed on equine third metac@pal in actual practice. Hence, it is signifkant to the veterinary orthopedic surgeon that a narrow plate may be used instead of a wider one to provide better wound closure without a substantial sacrifke of strength. Figure 8 illustrates one of the most significant findings in the experimental program, the notable effect that an increase in plate length I
LEilEK) PLA7E wlDn!_ It&
01
3.0
4.5 PLATE
Fig. 8. Influence
LENGTH.
60 L.
IN
of plate length on plate capacity.
171
produces. It can be seen that, regardless of the width of the plate or the size of fastener employed, the 6 in. long plates demonstrate approximately twice the capacity of the 3 in. long plates. It is felt that such an increase in capacity was a result of the capability of the longer plates to better distribute the stresses in the composite structure over a greater length of bone. That is, in order for the structure to maintain its integrity, the tensile forces below the neutral surface of the structure must be transferred from one side of the fiatture to the other via the fasteners and the plate. When this transfer must be completed over a smaU distance, as was the case with the 3 in. long plates, a higher stress concentration will exist than would be present if the forces were transferred over a greater length of bone. Certainly, substantial stress concentrations existed in the vicinity of all the screws, regardless of the length of plate used, but the net effect of distributing the forces over a greater portion of bone produced a corresponding increase in the capacity of the structure. In Fig. 8 an exceedingly high capacity was observed for the largest plate-fastener combination (6 in. by 1 in., No. 14). It is felt that this data point may not be characteristic of the capacity one could generally expect from a plate of these dimensions. A more reliable value would probably lie between 60 and 70 per cent, based upon the general trends discussed earlier. The fact that plate length is the most important variable influencing the capacity of the structure may produce somewhat of a dilemma for the veterinary orthopedic surgeon Because of the variation in bone cross-section and the fact that the average length of equine metacarpus bone is approximately 10 in., an increase in plate length above 6 in. does not appear to be feasible. Furthermore, because a primary tendon traverses the anterior surface of the bone and generally cannot be detached without permanent damage, the fixation plate in actuai practice is attached to the bone slightly to either side of this tendon.
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The cross-section of the bone varies considerably along its length and the surface possessing the least curvature is the anterior one. All surfaces possess considerable curvature at the distal and proximal ends and therefore any substantial increase in plate length would require that the plate be contoured to the recipient surface. No general design can be expected to serve all possible geometries and hence, the only practical alternative remaining would seem to be to bend the plate to fit the individual bone. This means installing a plate that has already been yielded, which can be undesirable from a structural aspect. Thus. 6 in. may be considered an upper bound on plate iength for use on equine third metacarpal. Because the 1 in. wide plate has questionable application, the capacity of the fixation . device’ is limited to approximately 60 per cent of the unfractured bone strength. This is readily apparent by inspection of Fig. 8. From Fig. 8 it can be seen that, disregarding the largest plate-fastener combination (6 in. by 1 in., No. 14). the capacity of the composite structure for the 6 in. long plate is not likely to be greater than approximately 60 per cent. This represents the maximum support that could normally be expected, using the largest feasible plate under the described loading condition. That is, the bone is a simply supported beam loaded at the mid-span with the fixation plate on the tension side of the structure. It is improbable that this particular loading condition would be encountered outside of the laboratory. Most likely, combined loading conditions would prevail in actual practice, and therefore the capacity of the structure could be substantially reduced. For example, if the animal attempts to rise from a prone position, the metacarpus will probably experience a simultaneous compression and ficxure loading Similarly, if a turning maneuver is attempted, it is possible that the metacarpus will experience torsion, compression, and flexure. Where combined loading conditions exist, a decrease in capacity would be expected.
In order to consider the combined effects of all three plate design variables. it was necessary to determine a suitable means of presenting the data as a function of the platefastener characteristics simultaneously. It was found that by plotting the per cent capacity of a particular plate-fastener combination against an arbitrary function, the reciprocal of the product of plate length, plate width, and fastener minor diameter, a failure envelope for all tests could be obtained (Fig 9). In general, Fig 9 suggests that for a particular combination of plate and fastener a capacity of not less than the value denoted by the curve may be expected. It is quite possible that the value will be greater than is indicated by the curve, but not likely to be less. Of the 27 tests conducted, test 202 (3 in. by 1 in., No. 12) appeared to be considerably lower than the failure envelope would indicate. It was decided to test the reliability of this data point, and four additional tests of this plate fastener combination were conducted. Values of C for all five tests ranged between 156 and 33.2 per cent (Table 4). Tests 296, 298. and 299 exhibited close agreement among test results but test 297 appears quite low. It was noted during the testing of specimen 297 that 3 of the 4 screws failed, two breaking simultaneously and the third shortly there-
0
I
2
3 I ~Wki’.
4
5
IN.-’
Fig. 9. Failure envelope for ail tests.
6
A
parametricanalysis
after. Fracture of the bone was not observed, and hence, it is believed that this test is the least characteristic since bone fracture was observed in each of the other tests. Such a spread of data does serve to illustrate the variation in results that may occur. It also suggests that to achieve results possessing a high degree of statistical reliability would require a large number of tests. Since only two specimens can be obtained from one animal, the presence of differences in health and nutrition among animals also dictates that the number of tests be large. Hence, the discussion presented here must be regarded as observations of only the general trends that occur as a result of varying plate length, plate width, and fastener size. Insuficient replication was obtained to determine reliability. In addition, this discussion concerns results obtained for one condition of loading, specifically Aexure with the fixation plate on the side of the bone opposite the applied load. In all probability, this configuration wifl offer the greatest resistance to loading Thus, the values presented here represent the best performance that can normally be expected where singular tiation plates are employed. In the general case, combined loading conditions on a single plate wiIl probably produce a more critical situation. Thus. it is tentatively conduded that. except for extraordinary cases, it is doubtful that the use of a single fixation ‘plate would provide adequate structural sup port during the period when osteogenesis is occurring in large animals, such as the horse. This conclusion is supported by clinical results obtained at the College of Veterinary Medicine. Texas A&M University. where within the past two years fracture fixation has been attempted in 15 horses using the largest commercial plates and screws available, with only one success. In most cases, failure has occurred within a matter of hours after implantation when the anesthetic wore off and the animal attempted to stand. The use of dual plates has been suggested (Lindahl, 1967) and tried (Peterson and
of bone fixation plates
173
Reeder, 1963; Murray ef al. 1964) in a few selected cases in human medicine. However, the problem of infection is compounded ,with this method, and hence the results of its use are diicult to evaluate despite the apparent gain in mechanical advantage. No mention could be found within the literature of attempts at fracture fixation in the horse using two plates. It is hypothesized, however, that two small plates placed medially and laterally on the anterior surface of the bone may provide more efficient support in the combined loading condition than can be achieved with a single plate. Another factor aggravating the structural aspects of the problem is the presence of gross mis-match in the elastic moduli of bone and steel. This factor may contribute to the failure of the composite structure, resulting in the low to moderate capacities. Thus it is believed that a fiber reinforced polymer (e.g. fiberglass) possessing an elastic modulus more closely matched with bone would enhance the integrity of the composite structure. Several such materials have been developed by the aerospace industry within recent years that possess tensile strengths in excess of stainless steel. Polymers are used as implant materials in many situations in human and veterinary medicine but have been rarely regarded as structural materials. It is conceivable that a highly * inert polymer, reinforced with high strength fibers. could serve as a better material for fixation devices than conventional stainless steel. provided adverse tissue reactions do not occur. 6. CONCLUSIONS (.1) For a particular size of fixation plate. increasing the screw from No. 8 to No. 14 produced no substantial increase in the capacity of the composite structure. (2) Increasing the plate width (lateral hole pitch) from O-5in. to 1 in. produced no significant increase in the overall capacity of the composite structure. (3) For the loading condition described. in-
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D. R. RAY et al.
creasing the plate length from 3 in. to 6 in. approximately doubled the capacity of the composite structure. (4) Where the largest feasible plate was employed (i.e. 6 in. by 0.75 in., No. 14), the maximum capacity that can normally be expected under loading conditions similar to that described is approximately 60 per cent. (5) In general, the use of a single fixation plate for fracture fixation of equine third metacarpal will not provide sufiicient strength for weight bearing during osteogenesis. 7. RBcoMMplDATlONS
(1) The possibility of using two small tixation plates placed medially and laterally on the anterior bone surface should be investigated. (2) The possibie use of a fiber reinforced polym~ as a fixation plate material should be investigated for strength and modulus compatibility, as well as tissue tolerance in the host. (3) In conjunction with the use of polymeric fixation plates, a more efficient method of fastening the plate to the bone should be investigated (e.g. biind rivets, bolts with lock nuts, nylon or other polymeric fasteners). (4) An analytical method of structurally analyzing the compositive under various loading conditions should be devised to facilitate the proper design of fixation plates. (5) Standards for testing and acceptance protocol are needed to help prevent structural failures due to inadequate designs of current fixation plates and other devices. Acknowledgement-The
metcrial for this paper was excerpted from a thesis by D. R. Ray submitted to the Graduate College of Texas A&M University in partial fuhlllment of the requitements for a Master of Science in CiviI Engineering degree.
NOMBNCLATURB Symbol L ti f i
Typical Variable Imits notmakedload ksi in.-hips appliedmoment distance from bone cross-section cenin. troid to extreme bone fiber moment of inertia of bone crosssection about its ccntroidal axis in.’ (perpendicular to applied load)
half majordiameter of outer ellipse in. half minor diameter of outer ellipse in. half major diameter of inner ellipse half minor diameter of inner elliose . vertkatoffset ofinner ellipse with respect to outer ellipse in. hotizontai offset of inner ellipse with respect to outer ellipse in. centroid coordinate of bone crossin. section centroid coordinate of bone cross-
section modulus of rupturefor whole bone ultimate norm&& load capacity, reconstructed bone longitudinai hole pitch lateral hoie pitch ;a$e major screw diameter
minor screw diameter. boaedrilidbmeter
ei ksi per ant m. m. in. in. in. in. in.
REFERENCES
Bynum. D., Jr., Ledbeuer, W. 9.. Boyd C. L. and Ray, D. R ( 1969) Flexural proputk of equine metacarpus. Paper submitted to 1. Biotncd. Mark Res. Evans, F. G. and Lebow, M. (1951) Regionaldilkence in some of the physical properties ofthe human femur. 1. appl. Phyriol. 3.563-572. Evans, F. G. (1964) Signikant ditTerencein the tensile strength of adult human compact bone. Proc. Firs? Europa~ Bone and Tooth Symposium. pp. 3 19-33 1. Evans, F. G. and Vhtcent&, R. (1969) R&ion of cdlagen fiber orientation to some mschankaJ propettks of human cortical bone. J. Biomcchanics 2.63-7 1. Guthrie, G. W. (1%3),Direct hxation in fractures. Am. Med. 5,376-379.
Hodgkinson. R. (l%l) Internal fixation of fktures of long bones with metallic devices. Med. J. Aust. 46, 691-693.
Jacobs. P. A. and Guten, G. N. (1967) Compression furationofbone. Wk. med.J. 66.412417. Lindahl, 0. (1962) Rigidity of immobiion of tmnsverse bXures.Acta orthop. scand.32 237-246. Lii, 0. (1961) Rigidity of immobilization of oblique fmctures. Rcta orrhop. stand. 35.39-50. Lindahl, 0. (1967) The rigidity offrectum immobihzation withpiates.Actaorrhop.rcund.38,101-141. Lundvall. R. L. (1960) Observations on the treatment of &actures of the long bones in large animals. J. Am. vet. med. Ass. l37,308-3 12. Mart& C. D. (1956) Stress tolerance in bone and metal. 1. BoneJ. Surg. 3% 827-834. Munay, W. R., Lucas. D. B., and Inman. V. T. (1964)
Treatment of non-union of fractures of the long bones by the two-pkate method. J. Bone Jt Surg. 46.4. 1027Peizn. L. T. and Reeder. 0. S. (1963) Dual Slotted plates in fixation of fractums of the femoral Shaft J. Bone Jt Sutlr. 4W 430-43 1. Weisman, S. (I%@ Metals for implantation in the human body.dnn. N. Y.Acad. Sci.146,80-85.