CANINE HIP DYSPLASIA

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BIOMECHANICS OF THE NORMAL AND ABNORMAL HIP JOINT Joseph P. Weigel, DVM, and Jack F. Wasserman, PhD

The mechanical considerations of motion and weight bearing of the canine hip joint is dependent on the anatomic relationships of the bony components as well as the structural integrity of the ligaments, tendons, and muscle. Resiliency and wear characteristics of the joint are dependent on the surface integrity of the articular cartilage, the distribution and magnitude of the forces acting on the joint, and the joint's inherent stability. An initial description of the mechanics of the canine hip joint can be based on a two-dimensional analysis of a motionless, statically loaded model. In addition to this approach, dynamic analysis represents an important contribution to the understanding of the mechanics of the joint. The use of a force plate will provide some raw dynamic data. Also important in the understanding of joint mechanics is analysis of force and motion in all three dimensions. Quantitative analysis of force involves magnitude and direction. These quantities can be visualized as vectors in three- or two-dimensional space. To identify a vector, a system of coordinates must be established. Three coordinate axes x, y, and z define three-dimensional space. Pairs of these coordinate axes also define two-dimensional planes. In anatomic terms, these two-dimensional planes are designated as transverse, sagittal, and frontal. In mathematical terms, these respective planes are referred to as the zy plane, zx plane, and the xy plane (Fig. 1). From the Department of Urban Practice, College of Veterinary Medicine (JPW), and the Department of Engineering Science and Mechanics, College of Engineering (JFW), UniverSity of Tennessee, Knoxville, Tennessee

VETERINARY CLINICS OF NORTH AMERICA: SMALL ANIMAL PRACTICE VOLUME 22 • NUMBER 3 • MAY 1992

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Figure 1. Reference planes for visualization of the direction of force and acceleration are based on the three·dimensional coordinate axes z, x, and y.

5T ATIC ANAL Y515

Evaluation under static load implies a condition of equilibrium where the sum of all forces equal zero. From this concept, forces, moments, and their directions can be analyzed. Recently, a static analysis of the forces and moments acting about the coxofemoral joint were analyzed from the perspective of the transverse or zy plane. l The static load was assumed to be the result of a dog in a three-legged stance with one rear leg raised off the ground. To maintain a level pelvis, the animal must create a moment about the spine. This moment facilitates the analysis of the hip joint forces. Using sketches traced from radiographs, force diagrams were drawn to describe the location, direction, and magnitude of forces acting on the hip joint (Fig. 2). There were four basic forces and one

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z

Figure 2. The basic forces acting on the hip joint in the zy or trans· verse plane are the abductor force (Fa). body weight (Fo). ground reaction force (Fk). and the total force on the hip joint (Fh) ' Mo represents the moment created about the spine to keep the pelvis level. The important angles to consider are the angie of the hip force (8 n). the angle of inclination 8n> and the angle of abduction-adduction (8,). (Adapted from Arnoczky SP. Torzilli PA: Biomechanical analysis of forces acting about the canine hip. Am J Vet Res 42:1581. 1981; with permission .)

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af

moment described from the transverse or zy plane: the force due to gravity, "Fo"; an abductor force, "Fa"; a ground reaction force, "Fk"; a resultant force, "Fh" (sum of the effects of Fa' Fo' and Fk on the femoral head); and the stabilizing moment, "Mo". Angles and distances were measured from the tracing. Also, Fo was assumed to be one third of the dog's weight. Through trigonometric analysis and a set of equilibrium equations, values for the resultant hip force Fh and abductor force Fa were calculated. The relevance of this analysis was not to produce absolute values but to demonstrate trends in the magnitude and direction of forces as certain anatomic relationships changed and as the stability of the hip joint changed. In the zy plane, the angle formed by the central axis of the femoral neck and axis of the shaft of the femur is called the head-and-neck angle or inclination angle. It has been implicated in creating an unfavorable mechanical state for the hip joint in certain breeds afflicted by canine hip dysplasia (CHD). Depending on the method of measure-

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ment, normal values for this angle range from approximately 1300 to 1450.5, 10, 14, 16 Measurement of inclination from the radiograph has been the subject of several reports. The early methods of Hauptman5 were followed by the biplanar method of Montavon lO and most recently by the symmetric axis or symax method advanced by Rumph. 15 The weakest link in the measurement of the anglEt is determining the correct central longitudinal axis of the femoral neck and femur. The object of the symax method is to reduce the complex biologic structure to a series of circles drawn within the boundaries of the structure with each circle touching the boundary in at least two places. The central axis of the structure falls in line with the centers of the circles. The symax method was found to be the simplest and most accurate when used by inexperienced operators. 15 The effect a widened inclination angle (coxa valga) has on the femoral head force can be explained by using the concept of moment (Fig. 3). A moment is produced by applying a force to an object not in line with its geometric center, causing it to rotate. The value or magnitude of the moment is determined by the product of the moment and the perpendicular distance from the force vector and the center of rotation (moment arm): Moment = force x length of moment arm As the inclination angle widens, the distance from the abductor force vector and femoral head decreases. Therefore, the magnitude of the moment produced by the same abductor force is less (Fig. 3). Abduction rotates the femoral head deeper into the acetabulum. In the presence of a widened inclination angle, the abductor muscles must exert a greater force to produce the same moment as is produced in the hip with a normal angle. This results in a greater force on the femoral head. In the analytical model, I an increasing inclination angle liOn" was shown to result in an increase in the abductor muscle force Fa and therefore an increased total force on the femoral head Fh (Fig. 4). To compensate and maintain an equilibrium state in an unstable

Figure 3. Moment is equal to the product of the force and moment arm. When comparing A and B, there is no change in the magnitude or direction of the abductor force Fa' but the moment arm I decreases to I' as the angle of inclination widens. The reduction in moment arm reduces the moment acting on the hip joint.

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FH FA FH FA FH FA

1.0 0.0 80

90

100 110 120 130 140 8No

150 160 170

180

Figure 4. Both the abductor force (Fa) and the total hip force (F h ) magnitude and rate of change dramatically increase as the angle of inclination (en) increases. Note that abduction (e, = 75°) decreases the rate of change in the magnitude of the forces. (From Arnoczky SP, Torzilli PA: Biomechanical analysis of forces acting about the canine hip. Am J Vet Res 42:1581 , 1981 ; with permission.)

hip, the muscles must maintain greater tone and strength. Dogs with well-conditioned muscles and good strength tend to clinically compensate for CHD better than those with weak muscle support. These analytical results also support the application of the varus osteotomy of the femur to reduce the inclination angle and thereby reduce the force on the femoral head in dogs afflicted with wide femoral head and neck angles and CHD. 16 The postural attitude of the rear leg also influences the rate of change in the magnitude of the femoral head force due to widening inclination angles . Adduction of the limb was found in the static model to reduce this rate of change (Fig. 4).1 Dogs with CHD often stand with adduction of the rear legs. This postural attitude may reduce the femoral head force and the subsequent strain on the periarticular soft tissues. The femoral head force must be viewed not only with respect to its magnitude but also to its direction of action. In mechanical terms, the musculoskeletal system functions most efficiently and exhibits the most strength when subjected to pure compression. Pure compression implies that the resultant force acts down the central axis of the structure orthogonally (perpendicularly) to the ground. When force acts eccentrically, bending occurs, which creates tension and compression surfaces along with shear forces. Bone as a structural material is stronger in compression than in tension. Ideally, a resultant force acting through a joint should act through the center of the joint and orthogonal to the ground. In the static model mentioned previously, with no adduction or abduction, the angle 8 h of the femoral head force was calculated to be approximately 69° from the horizontal. Using the same specimen

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from which the analytical diagrams were made, the trabeculae of the femoral neck were measured to be approximately 69 with the horizontal. 1 Because these trabeculae were oriented in line with the resultant femoral head force, these trabeculae were subjected to primarily compression. With a changing inclination angle, the angle 8 h of the resultant femoral head force shifts from 690 toward 800 with the horizontal (Fig. 5). This shift in the direction-of the femoral head force loads the trabeculae eccentrically, producing bending and shearing of the bone. An eccentrically loaded joint will also have shear forces across the articular cartilage. Excessive shearing will prematurely wear articular cartilage. Shifting the direction of the resultant femoral head force by subluxation of the femoral head or widened inclination angles can exacerbate the loss of articular cartilage on the dorsum of the femoral head, which is a common pathologic change in CHD. Subluxation of the femoral head is the essential biomechanical alteration in the hip joint that identifies CHD. Subluxation of the femoral head does have an affect on the magnitude and direction of the resultant femoral head force. The static model had also been used to evaluate the changes in the femoral head force under varying amounts of subluxation. As the degree of subluxation increases, the magnitude of the resultant femoral head force also increases (Fig. 6). Without subluxation, the femoral head force Fh was calculated to be 4.4 times the force due to gravity Fo and with 1 cm of subluxation the femoral head force Fh increased to 5.2 times Fo. The angle of the femoral head force 8 h is also altered by subluxation. 1 With a subluxation of 1 cm, the angle of the femoral head force 0

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Figure 5. The position of the femur as abducted or adducted represented by the angle 6, has a significant effect on the direction of the total hip force (Fh ), which is represented by the angle 6h • (From Arnoczky SP, Torzilli PA: Biomechanical analysis of forces acting about the canine hip. Am J Vet Res 42:1581 , 1981 ; with permission.)

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Figure 6. Subluxation of the hip increases both the magnitude and direction of the total hip force (Fh) ' In the vector diagram, Fy represents a lateral component of Fh, which increases in magnitude as the direction of Fh changes.

was reduced from 69 degrees to 61 degrees. This change in direction of force will lead to eccentric loading of the trabeculae and articular cartilage with bending and shearing as the result. Using the trigonometry of right triangles, the components of the femoral head force were diagramed, demonstrating that by simply changing the angle of Fh , the lateral component Fy becomes larger (Fig. 6). Since the direction of Fy is lateral, there would be a greater shear component and a greater tendency toward subluxation with a larger Fy. Anteversion is the angle e a made by the central axis of the femoral neck and the y axis in the frontal plane or xy plane (Fig. 7) . Normal anteversion angles range from approximately 12° to 48° with a mean of around 30°. 2, 10, 11 For all practical purposes, femoral anteversion is an expression of femoral torsion that has been implicated in CHDY Like the situation with the inclination angle, the method of measurement of the anteversion angle is varied. The flouroscopic method involves direct measurement of the angle,l1 whereas the right angle triangle biplanar

Figure 7. The angle of anteversion (6 a ) is made by the central axis of the femoral neck and the y coordinate axis.

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method of Bardee is an indirect method. In the xy plane, excessive femoral anteversion reduces the moment arm acting about the hip joint just as in the case with a widened inclination angle. Anteversion acts similarly in creating abnormal magnitude and direction of force acting on the femoral head. Femoral anteversion tends to rotate the femoral head out of the acetabulum, thus contributing to the effects of subluxation. Stress as a function of the strength of material is determined by the magnitude of force per unit area over which the force is acting on. High degrees of stress are observed where forces are concentrated over a small area. Subluxation will increase the stress especially in the articular cartilage by reducing the area of contact between opposing weight-bearing surfaces, thus allowing a greater concentration of force. In the previously described model, increasing inclination angles and lateral subluxation demonstrated the increased magnitude of force within the joint. The additional affect of these abnormalities is the increase in the stress of the articular cartilage. The resultant femoral head force Fh can also be viewed as the summation of an infinite series of force vectors distributed over the surface of the joint. The ideal mechanical circumstance is a wide distribution of these vectors. In the dysplastic hip with subluxation, these vectors are concentrated over a small area of contact. This results in unacceptably high stress, which leads to the premature erosion and loss of articular cartilage commonly seen in dysplastic hips (Fig. 8) .14

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Figure 8. Left, The distribution of force is wide, resulting in a low stress value; Right, a concentration of force over a small area, with stress values considerably higher. (Stress value data from Prieur WO: Coxarthrosis in the dog: Part I. Normal and abnormal biomechanics of the hip joint. Vet Surg 9:145, 1980.)

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DYNAMIC ANALYSIS

In the previous model, all forces were summed to zero, which describes the static state of equilibrium. When forces become unbalanced and no longer sum to zero, motion occurs requiring dynamic analysis where the sum of the forces is equal to the product of the mass and acceleration. Although motion is present in all three planes, for the dog, the sagittal plane or zx plane is the most significant because the animal moves principally in this plane. Force plate analysis of quadrupedal locomotion has been reported for both normal and abnormal gaits. 3, 4, 7, 8, 13 With force plate analysis, joint forces are not directly measured; however, ground reaction fortes are measured and often are related to the animal's body weight (Fig. 9) .3 The force plate measures forces in the vertical direction (dorsoventral) or along the z axis, the horizontal direction (craniocaudal) or along the x axis, and the mediolateral direction or along the y axis. The vertical forces relate primarily to weight support, whereas the horizontal forces relate to propulsion and braking action and the mediolateral forces, which are very small and insignificant. From such analysis of normal quadruped animals, it has been confirmed that each rear limb bears approximately 20% of the body weight and that the rear limb is primarily responsible for propulsion and the front limb for braking. 3 Force plate data in animals can be difficult to interpret and control because the type of gait the animal uses during the test and its speed will influence the data. The performance of individual joints is not easy to ascertain; however, some impressions have been advanced based on force plate data. During walking, a quadruped's hip, stifle, and hock have a very similar pattern in the magnitude and distribution of the vertical forces. 13 When the joint moment is calculated from this data, some differences are noted. The joint moment about the hip is much greater than the hock and is in the opposite direction to the moment occurring about the stifle joint. 13 Joint power can be calculated and was found to be high in the hip joint, indicating major energy production in the hip. The joint power calculated for the stifle was substantial but opposite in direction, leading to the interpretation that the stifle is absorbing energy during walking and therefore acts as a damper in the system. 13 Force plate techniques also have been applied to the analysis of gaits associated with various pathologic states of the hip joint. For example, excision arthroplasty of the hip, total hip replacement, and unoperated dysplastic hip joints were compared dynamically with force plate data. From such analysis, it was concluded that a successful excision arthroplasty of the hip can perform as well or better than a total hip prosthesis. In this study, both walking and running were evaluated. 4 Analytic models similar to those proposed for the study of forces

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Figure 9, A representative example of force plate data demonstrating the distribution of force at the ground level as a percentage of body weight. (From Budsberg se, Vestraete Me, Soutas-Little RW: Force plate analysis of the walking gait in healthy dogs. Am J Vet Res 48 :915, 1987; with permission. )

under a static load condition are more difficult and complex for the dynamic state. Force plate analysis has shown that the most significant forces in terms of magnitude are the vertical forces. A model could be proposed to demonstrate the trend in the vertical forces and gain some insight into the magnitude of force present in the moving hip joint. The model proposed here is an oversimplification but does take into account the velocities and accelerations that playa role in the dynamic state,

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this mechanical model is a sliding collar pinned to a solid cylindrical rod (Fig. 10). This rod translates horizontally as well as rotating about the pinned joint. From the sagittal or zx plane, this model will be used to evaluate the joint by replacing the collar with the pelvis, the pinned joint for the hip, and the rod for the femur. The objective is to analyze the effect motion has on hip forces. The collar or pelvis moves horizontally along the x axis with an assumed acceleration of 1 mls squared. The rod or femur while moving horizontally along with the collar at the same acceleration is also rotating

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Figure 10. A sliding collar device can be used to model the canine hip joint. In this simplified model, the femur is simply rotated about the y axis, and the pelvis moves linearly along the x axis. In the free body diagram, Az represents the vertical force, A, the horizontal force, and W the weight of the femur. The kinetic diagram represents the dynamic side of the equation where m is the mass of the femur, a is the linear acceleration, a, is the tangential acceleration, an is the normal acceleration, I is the mass moment of inertia, and alpha is the angular acceleration . (Part A is from Meriam JL, Kraige LG : Plane kinetics of rigid bodies. In Engineering Mechanics Dynamics. New York, John Wiley and Sons, 1986, p 369; with permission.)

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WEIGEL & WASSERMAN

about the pinned joint or hip with an assumed angular velocity of 2 radians/so This model also assumes negligible friction in the hip joint, does not include the propulsive or braking effects of the muscles, and does not take into consideration the full weight of the dog. In this simplified model, the femur has a mass of 0.5 kg and a length of 0.3 meters. To clarify the problem, the femur ca.n be represented by two diagrams. The first is referred to as a "free body diagram" representing the force vectors as they act upon the femur. 9There are two components of the force acting at the hip joint, "Az", which is the vertical compo· nent, and "A/', the horizontal component. Weight "w" also acts on the femur, and this force is considered to act from the center of gravity, point G, of the femur. The second is the "kinetic diagram,"9 which takes into account the accelerations present in the model. There are several accelerations to consider: the linear acceleration in the x direction; the curvilinear accelerations: "normal acceleration" and "tangential acceleration"; and the rotational velocity "0." Using Newton's second law of motion, which states that the force is equal to the product of the mass and linear acceleration: F

=

rna

and the corresponding relationship for rotation, which states that the moment is equal to the product of the mass moment of inertia "I" and the angular acceleration a:

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=

I (a)

The summation of moment about point G: Ax(1/2)

=

I (a)

where I is the length of the femur, I is the mass moment of inertia of a slender, solid cylindrical rod, and a is the angular acceleration. Associated with the curvilinear motion of the center point "G" is the tangential acceleration "a,", which may be written as: a,

=

r (a)

where "r" is the radius of rotation. The forces in the x direction are related to both the linear and tangential acceleration: Ax=ma-ma, also: Ax = rna - mr (a) Solving simultaneous independent equations yields: a = 5 radians/s 2 Ax = 0.125 Newtons

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Associated with the rotation of the femur is the normal acceleration "an", which may be written as: an

=

r (W)2

The forces in the z direction are related to the weight and the normal acceleration:

also: mr (W)2 Solving for Az yields: Az

=

5.2 Newtons

Without motion and under equilibrium conditions, the vertical force Az is approximately 4.9 Newtons and is due solely to the weight of the femur while the horizontal force Ax is O. By simply swinging the femur back and forth and setting the pelvis in motion and without any additional external force, a change in the distribution of the forces acting on the hip joint occurs. A small horizontal force appears, and the vertical force tends to increase. Also note that these forces were calculated at the instant in time when the femur was orthogonal to the ground. This model can be further developed by adding the effects of body weight and muscle tension (Fig. 11). When body weight is added, the

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Figure 11 . A spring has been added to the sliding collar model, and the reaction forces Bz and B, have been added to the free body diagram. The kinetic diagram remains the same.

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WEIGEL & WASSERMAN

components of ground reaction forces must be represented in the free body diagram and in the equations of motion. Assuming that 20% of the body weight is delivered to one rear limb and that the total weight of the dog is 8.2 kg, the vertical force Bz is found by using Newton's second law and the acceleration of gravity:

Bz = W(g). If W is 20% of the total weight of the dog and g is the acceleration due to gravity, then

Bz = 16.09 Newtons To find the horizontal component of the reaction force, consider the fact that the linear acceleration of the dog is 1 mls 2 • Also consider that at the moment the femur is orthogonal to the ground, the foot is planted and not in motion. The horizontal force Ax is also found with Newton's second law of motion: Ax

=

W(a)

If W is 20% of the total weight of the dog and "a" is the linear acceleration of the dog, then

Ax = 8.2 Newtons Under equilibrium conditions, all the horizontal forces must sum to zero, so Bx must equal Ax in magnitude but is acting in the opposite direction. To include the additional force of the hamstring muscles, a spring can be added to the model (see Fig. 11). This spring is acting at a 45° angle, and the force exerted by the spring can be calculated from the equilibrium condition where the spring balances the moment created about the hip joint by Bx: Fs (sin 45) (r) = Bxr where r = moment arm and Fs is the spring force. Fs = 11.6 Newtons Because this force acts at a 45° angle, both its vertical and horizontal components are the same. This spring force is then added to the ground reaction forces to arrive at values for Bz and Bx when both body weight and muscle force are applied. Bz = 19.8 Newtons Bx = 27.69 Newtons Using the same equations of motion developed in the original sliding collar model but adding Bz and Bx' new values for the hip forces Az and Ax can be calculated. Under equilibrium conditions, Ax changes from 0 Newtons to 19.55 Newtons and Az changes from 4.9 Newtons to 27.69 Newtons. When an omega value of 2 radians/s is assumed as

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in the original model, the vertical force Az changes from 5.2 Newtons to 28.29 Newtons. If the speed is increased to 20 radians/s, which corresponds to approximately 13 mph, then the vertical force Az triples to 87.69 Newtons. These forces under dynamic conditions are variable and quite significant. This model is an oversimplified method to demonstrate the potential interplay that motion, acceleration, body weight, and muscle pull have on the distribution of force acting on the hip joint. A more sophisticated model backed by experimental data would provide a more accurate and complete understanding of the mechanics of the canine hip joint. Consideration of all these biomechanical effects is necessary for designing corrective osteotomies, and hip prostheses for the dog. SUMMARY

Static analysis of the canine hip has given some insight to the nature and trend of the force and subsequent stress that is normally applied to the joint. Using the static model, the magnitude and direction of force and stress worsens in the hip with the anatomic and stability changes associated with CHD. More sophisticated dynamic models that take into account unbalanced forces and moments with the resultant motion are needed to better understand the mechanics of the hip joint. References 1. Arnoczky SP, Torzilli PA: Biomechanical analysis of forces acting about the canine hip. Am J Vet Res 42:1581, 1981 2. Bardet JF, Rudy RL, Hohn RB: Measurement of femoral torsion in dogs using a biplanar method. Vet Surg 12:1, 1983 3. Budsberg SC, Vestraete MC, Soutas-Little RW: Force plate analysis of the walking gait in healthy dogs. Am J Vet Res 48:915, 1987 4. Dueland R, Bartel DL, Antonson E: Force-plate technique for canine gait analysis of total hip and excision arthroplasty. J Am Anim Hosp Assoc 13:547, 1977 5. Hauptman J, Prieur WD, Butler HC, et al: The angle of inclination of the canine femoral head and neck. Vet Surg 8:74, 1979 6. Hutton We, Freeman MAR, Swanson SA V: The forces exerted by the pads of the walking dog. J Small Anim Pract 10:71, 1969 7. Hutton WC, England JPS: The femoral head prosthesis and the dog. J Small Anim Pract 10:79, 1969 8. Leach DH: Assissment of bipedal and quadrupedal locomotion: Part I. Veterinary Comparative Orthopeadics and Trauma 2:49, 1989 9. Meriam JL, Kraige LG: Plane kinetics of rigid bodies. In Engineering Mechanics Dynamics. New York, John Wiley and Sons, 1986, p 369 10. Motavon PM, Hohn RB, Olmstead ML, et al: Inclination and anteversion angles of the femoral head and neck in the dog: Evaluation of a standard method of measurement. Vet Surg 14:277, 1985 11. Nunamaker DM, Biery DN, Newton CD: Femoral neck anteversion in the dog: Its radiographic measurement. J Am Vet Radiol Soc 14:45, 1973 12. Nunamaker DM: Surgical correction of large femoral anteversion angles in the dog. J Am Vet Med Assoc 165:1061, 1974

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13. Pandy MG, Kumar V, Berme N, et al: The dynamics of quadrupedal locomotion. Transactions of the American Society of Mechanical Engineers 110:230, 1988 14. Prieur WD: Coxarthrosis in the dog part I: Normal and abnormal biomechanics of the hip jOint. Vet Surg 9:145, 1980 15. Rumph PF, Hathcock JT: A summetric axis-based method for measuring the projected femoral angle of inclination in dogs. Vet Surg 19:328, 1990 16. Walker TL, Prieur WD: Intertrochanteric femoral osteotomy. Semin Vet Med Surg (Small Anim) 2:117, 1987

Address reprint requests to Joseph P. Weigel, DVM Associate Professor of Surgery Department of Urban Practice University of Tennessee College of Veterinary Medicine Knoxville, TN 37901-1071