J. Bmmechcm~cs.
1911.
Vol.
IO.
pp
701-705.
PergamonPress. Pnnted w Great Br~tam
IN VIV0 AND ANALYTICAL STUDIES OF FORCES AND MOMENTS E. F.
IN EQUINE
LONG
BONES*
and E. J. MrLLst
RYBICKI
Applied Solid Mechanics Section, Battelle, Columbus Laboratories. Columbus. OH 43201.
U.S.A.
A. S. TURNER Department
of Veterinary Clinical Sciences, University of Saskatchewan, Saskatoon, Saskatchewan. Canada S7N OWO and F. A. SIMONEN Battelle. Pacific Northwest Laboratories. Richland. WA 99352. U.S.A.
study to evaluate the in uiuo forces acting on equine long bones is described. Results for the maximum axial forces and bending moments are presented for the radius, metacarpus. tibia. and metatarsus. The forces and bending moments are obtained by combining in uiuo strain gage readings and a mathematical model for the mechanics of the bones. Comparisons of equine activities including standing, walking, trotting, and getting up after the anesthetic indicate that one activity does not always produce the highest loads in all of the bones examined. However, for the cases considered here, recovery from the anesthetic produced the largest compressive forces in the metacarpus and the tibia. Also, large tensile forces were found during the foot-up positions during standing and trotting.
Abstract-A
INTRODUCI’ION
Equine long bones are an example of a weight bearing structure in nature with a demanding loading environment. Indeed, the forces and bending moments
imposed on equine long bones would represent a challenging load spectrum for any engineering structure. Such loadings make the task of maintaining fractured equine long bone segments in the proximity required for healing a formidable one. This becomes increasingly evident when one recognizes the problems involved in designing, fabricating, and implanting a device that will adequately secure the fractured bone while surviving the mechanical loadmg environment that the intact bone was capable of meeting. Currently, one approach to the treatment of equine fractures is through the adaptation of fixation plates used for human subjects. While these plates and attachment techniques are sophisticated, their application to equine bones is not well understood In addition to the difference in bone size and forces for human and equine bones, there seems to be some question about the proper location for implantation of bone plates in horses. Thus, it becomes important to understand the loading environment experienced by equine long bones as well as that experienced by plated fractured bones. One noticeable trend of past studies has been the lack of a stress analysis model to aid in understanding mechanics of the experimental studies The study described here is an integration of the authors’ previous
*Received 3 Ma.v 1977 t Currently with American Sterilizer Company, Erie, PA 16415. U.S.A.
experimental measurements and analytical modeling methods to obtain a better understanding of the in viuo mechanics of equine long bones. In viva strain data provide a local description of the strains experienced by the bones of interest. An analytic model is applied which relates these strains to forces and bending moments. Resulting forces and bending moments are calculated for typical equine activities. Also. forces developed during the process of attaching a bone plate are calculated. While the research presented here is not intended to solve the problem of designing an equine bone plate, it does provide information about the mechanics of equine long bones which can be useful for designing an equine bone plate. RELATED
STUDIES
The concept of placing strain gages on bones to study deformations or forces is not new. While many in vitro and in viva tests have been reported, the focus here is on irl rim results. More than thirty-five years ago. Gurdjian and Lissner (1944) reported a study on cranial concussions in canine using strain gages. Almost a decade later. Evans (1953) reported the use of strain gages to measure in vivo strains in canine tibia. Roberts (1966) conducted a review of in vi00 strain gage techniques describing previous work on this subject. Lanyon and Smith (1969) studied in viva strains on sheep tibia. Perron et al. (1969) considered the effects of an osteotomy and bone plate on the in viva strains on sheep tibia. Studies of the strains on the vertebrae of sheep during respiration and walking were reported by Lanyon (1972). Strains in canine tibia and ulna were measured during walking by Cochran (1974). Lanyon (1974) reported the use 701
702
E. F. RYBICKI.E. J. MILLS,A. S. TURNERand F. A. SIMONE~‘
of rosette strain gages to determine the principal strain directions and compare them with the bone structure. Lanyon, Hampson and Goodship (1974) reported the in viva strain recordings for a human tibia. In viva studies of equine long bones have not received as much attention as those for sheep and canine. Rooney (1969) has combined information concerning the anatomy of the horse and kinematics of motion to arrive at an estimate of the forces and stresses on certain equine long bones. Barnes and Pinder (1974) and Mills (1973) have examined strains on the medial and lateral aspects of the equine third metacarpus bone and compared these values with the related tendon loads. These studies have emphasized strain measurements where a relatively easy access to the bone surfact was available. In a recent study. however. by Turner, Mills and Gabel (1975), in uivo strains were recorded from the mid-diaphyseal region of the equine third metacarpus, metatarsus, radius, and tibia. These in vivo strain measurements are the basis for the present study which involves the calculation of forces and bending moments. MATHEMATICAL. MODEL FOR EXPERIMENTS
Strain data alone are not sufficient to determine forces and bending moments acting on bones. A geometric description of the bone and the mechanical properties of the bone are also needed In addition, a mathematical model for the deformation behavior of the bone is also required to relate forces and bending moments to the strain measurements, the geometric description of the bone and its mechanical properties. Owing to the location of the gages at the mid-dinphyseal section of the bones. a beam bending theory of deformation was selected. A detailed de scription of the beam bending model and its applications to bones is given for example by Rybicki, Simonen and Weis (1972) and by Rybicki, et al. (1974). Basically, beam bending theory assumes that any set of points located in a plane passing through the hody. hcforc loading is applied, will remain in
Fig. 1. Location of the bones investigated.
n plane after bending. Each cross sectional plane can tramlaw and rotate to ;I new location due to loading. The relative translation and rotation of one plane of the body with respect to a neighboring plane are inferred from the strain gage readings. The strain gage readings are used to calculate an average axial strain (e,-,)and curvatures (K, and K,,)of the deformed bone. Thus, the deformation is described in terms of three parameters (e,. tix, and K,,),which requires strain data from a minimum of three points on each cross section. In the present study, four gages were used at each cross section. , In equation form, the force, F, and the bending moments, M, and M, are given by the following expressions: F = E [AC, + lx K, + I, Q].
(1)
M, = E CI,E, + I,, K, + Ixpq,
(2)
My = ECI#, + fx,v~, + I,,h.,,-j,
(3)
where A is the area, I, and I, are the first moments of the area about the x and y axes and I,, I,, and I, are the moments of inertia about the x and y axes. The specific bones considered in this study are indicated in Fig. 1. Figure 2 shows a cross section of an equine third metacarpal with a coordinate system for the bone. The convention used in this study is that a positive bending moment will produce a tensile stress on the anterior side of the bone. The values for bone cross sectional properties were calculated from the geometries obtained by cross sectioning equine bones. The bones were sectioned at the gage locations after the studies were completed. Their cross sections were accurately traced and magnified 3 x before calculating the section properties. A small computer program was used to determine the section moduli, neutral axis locations, and area of the cross sections. FORCESAND BENDING MOMENTS ACTING ON INTACI- EQUINE BONES In vivo strain gages were attached to the middiaphyseal region of the metacarpus, radius, metatarsus and tibia. A different horse was used for each bone investigated. Foil strain gages were used in this study. A description of the technique to attach these gages is described by Turner, Mills and Gabel (1975). Four gages were positioned around the circumference of the bone. These gages were located on the anterior, medial, posterior, and lateral quadrants of the bones. Multichannel dynamic recording equipment gave a continuous record of all strain gage readings. Figure 2 shows an example cross section of a metacarpus and the locations of the gages around the circumference. A typical set of strain readings for all four quadrants of a metacarpus during walking are shown in Fig. 3. The geometric properties used in equations (l-3) to determine the resulting forces and moments are
Forces
and moments
in equine long bones
70.3
x 0.6 -
lIIIIIlIII 0.2 y Coordinate,
0.4
0.6
0.6
I.0
inch
Fig. 2. Illustration of gage locations and bone cross section of equine third metacarpus. given in Table 1. Table 2 contains the calculated force values for several activities including recovery from anesthetic, standing, walking, trotting, and pacing. It can be seen from Table 2 that both tensile and compressive forces are supported by the bones In some cases, the largest forces occurred during recovery from the anesthetic. The weights of the animals were estimated to be between loo0 and 12oOlb. This weight range gives some feeling for how large the forces are in terms of the total body weight. Bending moments acting on these four bones were also calculated from the irk riw strains. Table 3 gives the maxi-
mum bending moments calculated during recovery from the anesthetic, standing, walking, and trotting. The results show that the bending moments acting on the bones are not negligible. Furthermore, the continuous record of strains showed that the force along the axis of the gaged bones can be tensile during hoof lift-off. The magnitudes of the forces ranged from 1120 lb tension on the tibia in foot-up position during trotting to 464Olb compression on the metacarpus while getting up during recovery from the anesthetic. In general, the most severe compressive loads occurred while getting up after the anesthetic. This
METACARPUS (Walking)
Loteral Tenwon
Posterior
Anterior
Compression
0
I ;....;
Foot Contact on Ground
Fig. 3. Strain recordings from equine metacarpus during walking.
704
E. F. RYBICKI,E. J. MILLS, A. S. TURNERand F. A. SIMONEN
Table 1. Geometric properties of equine long bones used in calculations of forces and bending moments Geometric property A (in.‘)
I, I, I, I, I,,
(in.“) (in.‘) (in.4) -in4) (in.4)
Metacarpus 0.96 0.023 0.037 0.08 0.003 0.16
Radius 1.42 0.056 0.005 0.37 o.ooo1 0.18
Metatarsus
Tibia
1.22 0.056 0.015 0.16 0.016 0.16
1.61 0.005 0.028 0.59 0.004 0.32
has been recognized as a critical time by veterinary surgeons who have attempted repair of these bones. The results of the study show thar forces on the metacarpus during recovery are about four times body weight for the animal studied This is considerably more than the force found for standing, which was calculated to be one-half body weight dr that calculated for walking, which was found to be one and one-half times body weight. IN WY0 mRAIN.3 DUE TO COMPRESSION PLATE The above data provides information on forces in particular long bones at locations where bone plates are commonly attached during fracture repair procedures. In a separate study in viuo measurements of strains were made on the mid-diaphyseal surface of an intact equine metatarsus during attachment of a bone plate.
* Association for the Study of Internal Fixation.
Strain patterns were recorded on the anterior. posterior. and lateral aspects before an A.S.I.F.*. I?-hole Dynamic Compression Plate (DCP) was attached to the lateral aspect of the same bone. While the plate was being attached, strains were recorded and the
forces in the bone were calculated using these strain values along with the cross sectional geometrical properties of the bone, a Young’s modulus value for the bone of 2.5 x IO6psi and a value of 30 x lo6 psi for the plate. When the first DCP screw was tightened, the strains recorded resulted in. a calculated force of 440 lb compression. A force of 689 lb compression was calculated when all of the screws were tightened While it is recognized that the metatarsus was intact, and possibly more compression could have been applied, the compression force of 689 lb applied by the Dcp was close to the tensile forces calculated for the foot-up walking conditions for the metacarpus and tibia in Table 2. Turner, Mills and Gabel (1975) pointed out that strain readings are helpful in selecting the locations for the bone plates. Since bone plates employ the tension band principle and produce compressive loads under the plate, they are best placed on the surface of the bone experiencing the most tensile strain. If, instead the plates were placed on the nominally compressive sides, the resulting forces from the plate would tend to further distract the bone fragments on the side normally experiencing tensile loads. In the past, equine bone plates were usually attached at the sites providing the best surgical access. If the assump tion is made that the entire bone cross section would experience compressive loads because of the weight of the animal, there would be no optimal plate
Table 2. Axial loads calculated from the in oiuo strains recorded during various modes of loading Loads (lb) Events Getting up following the anesthetic Standing Walking-foot down Walking-foot up Trotting or pacing-foot down Trotting or pacing-foot up l
Metacarpus
Radius
-4640’ -619 - 1690 +619 -2910 +940
- 1980 -1700 -2110 -182 - 2960 -204
\
Metatarsus
Tibia
-513 -837 -1180 -210 -1890 +317
-2640 +518 -107 f601 -630 +1120
The negative sign (-) signifies compressive loads and the plus sign (+) signifies tension load.
Table 3. Maximum bending moments calculated from the in vivu strains recorded during various modes of loading Maximum bending moment, MY* (in.-lb) Event Getting up following the anesthetic Standing Walking-foot down Walking-foot up down Trotting or pacing-foot up Trotting or pacing-foot
Metacarpus
Radius
Metatarsus
Tibia
337 89 104 66 308 606
1560 1150 1480 45 1940 112
1160 37 776 212 860 301
927 858 381 379 2450 2950
* The moment, M, produces tension on the anterior side and compression on the posterior side of the bone.
Forces and moments in equine long bones
location. In fact. however. as reported (1975). tensile
REFERENCES
by Turner.
do occur on some aspects of equine long bones during normal walking and trotting. and hence, it was recommended that bone plates be placed on those surfaces for optimal internal fixation. Mills and Gabel
strains
705
Barnes. G. R. G. and Pinder. D. N. (19741 111riro tendon tension and bone strain measurement and correlation. J. Biomec/innics 7. 35-42. Cochran. G. V. B. (1974) A method for direct recording of electromechanical data from skeletal bone in living
animals. J. Biomechauics 7, 563-565. Evans. F. G. (1953) Methods of studying the biomechanical significance of bone form. .4m J. Phys. .Irlrhrop. Il.
SUMMARY AND CONCLUSIONS In uiuo strain gages were attached to equine metatarsus, metacarpus. radius, and tibia. Continuous readings were taken to give a record of the strains at discrete locations during walking, standing and trotting. These strain readings save valuable indicators of the local deformation of the bones. Subsequent transformation of these strains to forces and moments was made using known mechanical properties of the bone. the cross sectional shapes of the bones, and the locations of the gages. This information was coupled through beam bending theory to evaluate the forces and moments. The results indicate that one activity does not always produce the highest loads in the four bones studied. It is of interest to note that recovery from the anesthetic produced the largest compressive forces in the metacarpus and the tibia. Also, large tensile forces were found during the foot-up positions for standing and trotting. The study described here provides information on the loadings acting on equine long bones, and places this information in proper perspective as an important factor to be included in the design of equine fixation plates.
Acknowledgements-The authors acknowledge the Battelle Institute Engineering Science Program and the Ohio State University School of Veterinary Medicine for their support during this study.
41: 415. Gud_iun. k. S. and Lissner. H. R. (19441 Mechanism
of head injury as studied by the cathode ray oscilloscope -A preliminary report. J. Neurosurg. 1, 393. Lanyon. L. E. (1972) 11: c&o bone strain recorded from the thoracic vertebrae of sheep. J. Biormxharrics 5. 277-281. Lanyon, L. E. (1974) Experimental support for the trajectoral theory of bone structure. J. Bone Jnr Surg. 56B. 160. Lanyon, L. E.. Hampson. W. G.. Goodship. A. E. and Shah. J. S. (1974) Bone deformation recorded ij, r*iro from strain gauges attached to the human tibia1 shaft. J. Borne Jut Surg. 56B. 565. Lanyon. L. E. and Smith. R. N. (1969) Measurements of bone stram in the walkmg animal. Res. Vet. SC;. IO, 9394. Mills, E. J. (1973) A new high-elongation strain gage. Society for Experimental Stress Analysis Winter Meeting, Indianapolis, IN. 19 October. Perren. S. M., Hugger. A., Russenberger. M.. Straumann. F., Mtiller, M. E. and Allgower, M. (1969) A method of measuring the change in compression applied to living cortical bone. Acta orthop. stand. 125, suppl. 3. Roberts, V. L. (1966) Strain gauge techniques in biomechanics. Exp. Me& 6, 14. Rooney, J. R. (1969) Biomecharlics q/ Lameness iu Horses. pp. 30-34. Williams 8; Wilkins. Baltimore. Rybicki. E. F., Simonen. F. A.. Mills. E. J.. Hassler. C. R., Stoles. P.. Milne. D. and Weis. E. B.. Jr. (1974) Mathematical and experimental studies on the mechanics of plated transverse fractures. J. Biomechauics 7, 377-384. Rybicki, E. F., Simonen. F. A. and Weis. E. B.. Jr. (1972) On the mathematical analysis of stress in the human femur. J. Biomechaitics 4. 203-215. Turner, A. S.. Mills. E. J. and Gabel. A. A. (1975) Iri uiw measurement of bone strain in the horse. .4m. J. C’et. Res. 36. 1573-l 579.
1911.
Vol.
IO.
pp
701-705.
PergamonPress. Pnnted w Great Br~tam
IN VIV0 AND ANALYTICAL STUDIES OF FORCES AND MOMENTS E. F.
IN EQUINE
LONG
BONES*
and E. J. MrLLst
RYBICKI
Applied Solid Mechanics Section, Battelle, Columbus Laboratories. Columbus. OH 43201.
U.S.A.
A. S. TURNER Department
of Veterinary Clinical Sciences, University of Saskatchewan, Saskatoon, Saskatchewan. Canada S7N OWO and F. A. SIMONEN Battelle. Pacific Northwest Laboratories. Richland. WA 99352. U.S.A.
study to evaluate the in uiuo forces acting on equine long bones is described. Results for the maximum axial forces and bending moments are presented for the radius, metacarpus. tibia. and metatarsus. The forces and bending moments are obtained by combining in uiuo strain gage readings and a mathematical model for the mechanics of the bones. Comparisons of equine activities including standing, walking, trotting, and getting up after the anesthetic indicate that one activity does not always produce the highest loads in all of the bones examined. However, for the cases considered here, recovery from the anesthetic produced the largest compressive forces in the metacarpus and the tibia. Also, large tensile forces were found during the foot-up positions during standing and trotting.
Abstract-A
INTRODUCI’ION
Equine long bones are an example of a weight bearing structure in nature with a demanding loading environment. Indeed, the forces and bending moments
imposed on equine long bones would represent a challenging load spectrum for any engineering structure. Such loadings make the task of maintaining fractured equine long bone segments in the proximity required for healing a formidable one. This becomes increasingly evident when one recognizes the problems involved in designing, fabricating, and implanting a device that will adequately secure the fractured bone while surviving the mechanical loadmg environment that the intact bone was capable of meeting. Currently, one approach to the treatment of equine fractures is through the adaptation of fixation plates used for human subjects. While these plates and attachment techniques are sophisticated, their application to equine bones is not well understood In addition to the difference in bone size and forces for human and equine bones, there seems to be some question about the proper location for implantation of bone plates in horses. Thus, it becomes important to understand the loading environment experienced by equine long bones as well as that experienced by plated fractured bones. One noticeable trend of past studies has been the lack of a stress analysis model to aid in understanding mechanics of the experimental studies The study described here is an integration of the authors’ previous
*Received 3 Ma.v 1977 t Currently with American Sterilizer Company, Erie, PA 16415. U.S.A.
experimental measurements and analytical modeling methods to obtain a better understanding of the in viuo mechanics of equine long bones. In viva strain data provide a local description of the strains experienced by the bones of interest. An analytic model is applied which relates these strains to forces and bending moments. Resulting forces and bending moments are calculated for typical equine activities. Also. forces developed during the process of attaching a bone plate are calculated. While the research presented here is not intended to solve the problem of designing an equine bone plate, it does provide information about the mechanics of equine long bones which can be useful for designing an equine bone plate. RELATED
STUDIES
The concept of placing strain gages on bones to study deformations or forces is not new. While many in vitro and in viva tests have been reported, the focus here is on irl rim results. More than thirty-five years ago. Gurdjian and Lissner (1944) reported a study on cranial concussions in canine using strain gages. Almost a decade later. Evans (1953) reported the use of strain gages to measure in vivo strains in canine tibia. Roberts (1966) conducted a review of in vi00 strain gage techniques describing previous work on this subject. Lanyon and Smith (1969) studied in viva strains on sheep tibia. Perron et al. (1969) considered the effects of an osteotomy and bone plate on the in viva strains on sheep tibia. Studies of the strains on the vertebrae of sheep during respiration and walking were reported by Lanyon (1972). Strains in canine tibia and ulna were measured during walking by Cochran (1974). Lanyon (1974) reported the use 701
702
E. F. RYBICKI.E. J. MILLS,A. S. TURNERand F. A. SIMONE~‘
of rosette strain gages to determine the principal strain directions and compare them with the bone structure. Lanyon, Hampson and Goodship (1974) reported the in viva strain recordings for a human tibia. In viva studies of equine long bones have not received as much attention as those for sheep and canine. Rooney (1969) has combined information concerning the anatomy of the horse and kinematics of motion to arrive at an estimate of the forces and stresses on certain equine long bones. Barnes and Pinder (1974) and Mills (1973) have examined strains on the medial and lateral aspects of the equine third metacarpus bone and compared these values with the related tendon loads. These studies have emphasized strain measurements where a relatively easy access to the bone surfact was available. In a recent study. however. by Turner, Mills and Gabel (1975), in uivo strains were recorded from the mid-diaphyseal region of the equine third metacarpus, metatarsus, radius, and tibia. These in vivo strain measurements are the basis for the present study which involves the calculation of forces and bending moments. MATHEMATICAL. MODEL FOR EXPERIMENTS
Strain data alone are not sufficient to determine forces and bending moments acting on bones. A geometric description of the bone and the mechanical properties of the bone are also needed In addition, a mathematical model for the deformation behavior of the bone is also required to relate forces and bending moments to the strain measurements, the geometric description of the bone and its mechanical properties. Owing to the location of the gages at the mid-dinphyseal section of the bones. a beam bending theory of deformation was selected. A detailed de scription of the beam bending model and its applications to bones is given for example by Rybicki, Simonen and Weis (1972) and by Rybicki, et al. (1974). Basically, beam bending theory assumes that any set of points located in a plane passing through the hody. hcforc loading is applied, will remain in
Fig. 1. Location of the bones investigated.
n plane after bending. Each cross sectional plane can tramlaw and rotate to ;I new location due to loading. The relative translation and rotation of one plane of the body with respect to a neighboring plane are inferred from the strain gage readings. The strain gage readings are used to calculate an average axial strain (e,-,)and curvatures (K, and K,,)of the deformed bone. Thus, the deformation is described in terms of three parameters (e,. tix, and K,,),which requires strain data from a minimum of three points on each cross section. In the present study, four gages were used at each cross section. , In equation form, the force, F, and the bending moments, M, and M, are given by the following expressions: F = E [AC, + lx K, + I, Q].
(1)
M, = E CI,E, + I,, K, + Ixpq,
(2)
My = ECI#, + fx,v~, + I,,h.,,-j,
(3)
where A is the area, I, and I, are the first moments of the area about the x and y axes and I,, I,, and I, are the moments of inertia about the x and y axes. The specific bones considered in this study are indicated in Fig. 1. Figure 2 shows a cross section of an equine third metacarpal with a coordinate system for the bone. The convention used in this study is that a positive bending moment will produce a tensile stress on the anterior side of the bone. The values for bone cross sectional properties were calculated from the geometries obtained by cross sectioning equine bones. The bones were sectioned at the gage locations after the studies were completed. Their cross sections were accurately traced and magnified 3 x before calculating the section properties. A small computer program was used to determine the section moduli, neutral axis locations, and area of the cross sections. FORCESAND BENDING MOMENTS ACTING ON INTACI- EQUINE BONES In vivo strain gages were attached to the middiaphyseal region of the metacarpus, radius, metatarsus and tibia. A different horse was used for each bone investigated. Foil strain gages were used in this study. A description of the technique to attach these gages is described by Turner, Mills and Gabel (1975). Four gages were positioned around the circumference of the bone. These gages were located on the anterior, medial, posterior, and lateral quadrants of the bones. Multichannel dynamic recording equipment gave a continuous record of all strain gage readings. Figure 2 shows an example cross section of a metacarpus and the locations of the gages around the circumference. A typical set of strain readings for all four quadrants of a metacarpus during walking are shown in Fig. 3. The geometric properties used in equations (l-3) to determine the resulting forces and moments are
Forces
and moments
in equine long bones
70.3
x 0.6 -
lIIIIIlIII 0.2 y Coordinate,
0.4
0.6
0.6
I.0
inch
Fig. 2. Illustration of gage locations and bone cross section of equine third metacarpus. given in Table 1. Table 2 contains the calculated force values for several activities including recovery from anesthetic, standing, walking, trotting, and pacing. It can be seen from Table 2 that both tensile and compressive forces are supported by the bones In some cases, the largest forces occurred during recovery from the anesthetic. The weights of the animals were estimated to be between loo0 and 12oOlb. This weight range gives some feeling for how large the forces are in terms of the total body weight. Bending moments acting on these four bones were also calculated from the irk riw strains. Table 3 gives the maxi-
mum bending moments calculated during recovery from the anesthetic, standing, walking, and trotting. The results show that the bending moments acting on the bones are not negligible. Furthermore, the continuous record of strains showed that the force along the axis of the gaged bones can be tensile during hoof lift-off. The magnitudes of the forces ranged from 1120 lb tension on the tibia in foot-up position during trotting to 464Olb compression on the metacarpus while getting up during recovery from the anesthetic. In general, the most severe compressive loads occurred while getting up after the anesthetic. This
METACARPUS (Walking)
Loteral Tenwon
Posterior
Anterior
Compression
0
I ;....;
Foot Contact on Ground
Fig. 3. Strain recordings from equine metacarpus during walking.
704
E. F. RYBICKI,E. J. MILLS, A. S. TURNERand F. A. SIMONEN
Table 1. Geometric properties of equine long bones used in calculations of forces and bending moments Geometric property A (in.‘)
I, I, I, I, I,,
(in.“) (in.‘) (in.4) -in4) (in.4)
Metacarpus 0.96 0.023 0.037 0.08 0.003 0.16
Radius 1.42 0.056 0.005 0.37 o.ooo1 0.18
Metatarsus
Tibia
1.22 0.056 0.015 0.16 0.016 0.16
1.61 0.005 0.028 0.59 0.004 0.32
has been recognized as a critical time by veterinary surgeons who have attempted repair of these bones. The results of the study show thar forces on the metacarpus during recovery are about four times body weight for the animal studied This is considerably more than the force found for standing, which was calculated to be one-half body weight dr that calculated for walking, which was found to be one and one-half times body weight. IN WY0 mRAIN.3 DUE TO COMPRESSION PLATE The above data provides information on forces in particular long bones at locations where bone plates are commonly attached during fracture repair procedures. In a separate study in viuo measurements of strains were made on the mid-diaphyseal surface of an intact equine metatarsus during attachment of a bone plate.
* Association for the Study of Internal Fixation.
Strain patterns were recorded on the anterior. posterior. and lateral aspects before an A.S.I.F.*. I?-hole Dynamic Compression Plate (DCP) was attached to the lateral aspect of the same bone. While the plate was being attached, strains were recorded and the
forces in the bone were calculated using these strain values along with the cross sectional geometrical properties of the bone, a Young’s modulus value for the bone of 2.5 x IO6psi and a value of 30 x lo6 psi for the plate. When the first DCP screw was tightened, the strains recorded resulted in. a calculated force of 440 lb compression. A force of 689 lb compression was calculated when all of the screws were tightened While it is recognized that the metatarsus was intact, and possibly more compression could have been applied, the compression force of 689 lb applied by the Dcp was close to the tensile forces calculated for the foot-up walking conditions for the metacarpus and tibia in Table 2. Turner, Mills and Gabel (1975) pointed out that strain readings are helpful in selecting the locations for the bone plates. Since bone plates employ the tension band principle and produce compressive loads under the plate, they are best placed on the surface of the bone experiencing the most tensile strain. If, instead the plates were placed on the nominally compressive sides, the resulting forces from the plate would tend to further distract the bone fragments on the side normally experiencing tensile loads. In the past, equine bone plates were usually attached at the sites providing the best surgical access. If the assump tion is made that the entire bone cross section would experience compressive loads because of the weight of the animal, there would be no optimal plate
Table 2. Axial loads calculated from the in oiuo strains recorded during various modes of loading Loads (lb) Events Getting up following the anesthetic Standing Walking-foot down Walking-foot up Trotting or pacing-foot down Trotting or pacing-foot up l
Metacarpus
Radius
-4640’ -619 - 1690 +619 -2910 +940
- 1980 -1700 -2110 -182 - 2960 -204
\
Metatarsus
Tibia
-513 -837 -1180 -210 -1890 +317
-2640 +518 -107 f601 -630 +1120
The negative sign (-) signifies compressive loads and the plus sign (+) signifies tension load.
Table 3. Maximum bending moments calculated from the in vivu strains recorded during various modes of loading Maximum bending moment, MY* (in.-lb) Event Getting up following the anesthetic Standing Walking-foot down Walking-foot up down Trotting or pacing-foot up Trotting or pacing-foot
Metacarpus
Radius
Metatarsus
Tibia
337 89 104 66 308 606
1560 1150 1480 45 1940 112
1160 37 776 212 860 301
927 858 381 379 2450 2950
* The moment, M, produces tension on the anterior side and compression on the posterior side of the bone.
Forces and moments in equine long bones
location. In fact. however. as reported (1975). tensile
REFERENCES
by Turner.
do occur on some aspects of equine long bones during normal walking and trotting. and hence, it was recommended that bone plates be placed on those surfaces for optimal internal fixation. Mills and Gabel
strains
705
Barnes. G. R. G. and Pinder. D. N. (19741 111riro tendon tension and bone strain measurement and correlation. J. Biomec/innics 7. 35-42. Cochran. G. V. B. (1974) A method for direct recording of electromechanical data from skeletal bone in living
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SUMMARY AND CONCLUSIONS In uiuo strain gages were attached to equine metatarsus, metacarpus. radius, and tibia. Continuous readings were taken to give a record of the strains at discrete locations during walking, standing and trotting. These strain readings save valuable indicators of the local deformation of the bones. Subsequent transformation of these strains to forces and moments was made using known mechanical properties of the bone. the cross sectional shapes of the bones, and the locations of the gages. This information was coupled through beam bending theory to evaluate the forces and moments. The results indicate that one activity does not always produce the highest loads in the four bones studied. It is of interest to note that recovery from the anesthetic produced the largest compressive forces in the metacarpus and the tibia. Also, large tensile forces were found during the foot-up positions for standing and trotting. The study described here provides information on the loadings acting on equine long bones, and places this information in proper perspective as an important factor to be included in the design of equine fixation plates.
Acknowledgements-The authors acknowledge the Battelle Institute Engineering Science Program and the Ohio State University School of Veterinary Medicine for their support during this study.
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