CHAPTER 3 Biomechanics of the Elbow

Kai-Nan An, Mark E. Zobitz, Bernard F. Morrey

INTRODUCTION

Upper extremity use depends largely on a functional elbow joint. A complex joint, the elbow serves as a link in the lever arm system that positions the hand, as a fulcrum of the forearm lever, and as a load-carrying joint. Mobility and stability of the elbow joint are necessary for daily, recreational, and professional activities. Loss of function in the elbow, possibly more than that in any other joint, can jeopardize individual independence.

In our practice, a working knowledge of biomechanics has been extremely important and rewarding. Clinical relevance includes elbow joint design and technique, the rationale and execution of trauma management, and ligament reconstruction. In short, a clear understanding of biomechanics provides a scientific basis for clinical practice.⁵

From the clinician’s perspective, we have found the topic of elbow mechanics best discussed according to motion (kinematics), stability (constants), and strength (force transmission).

KINEMATICS

The elbow is described as a trochoginglymoid joint. That is, it possesses 2 degrees of freedom (motion): flexion-extension and supination-pronation. The articular components include the trochlea and capitellum on the medial and lateral aspects of the bifurcated distal humerus, and distally the upper end of the ulna and the head of the radius. Thus, the joint is composed of three articulations: the radiohumeral, the ulnohumeral, and the radioulnar.

FLEXION-EXTENSION

Because of the congruity at the ulnohumeral articulation and surrounding soft tissue constraint, elbow joint motion is considered primarily a hinge type. Yet, two separate three-dimensional studies of passive motion at the elbow revealed that the elbow does not function as a simple hinge joint.^51,⁶⁹ The position of the axis of elbow flexion, as measured from the intersection of the instantaneous axis with the sagittal plane, follows an irregular course. A type of helical motion of the flexion axis has been demonstrated.⁶⁹ This pattern was previously suggested^26,^50,⁶¹ and was attributed to the obliquity of the trochlear groove along which the ulna moves.⁵² An electromagnetic tracking device that allows a three-dimensional measurement of simulated active elbow joint motion reveals the amount of potential varus-valgus and axial laxity that occurs during elbow flexion to average about 3 to 4 degrees. This has been confirmed with more advanced electromagnetic tracking technology.¹⁰¹

CENTER OF ROTATION

The axis of motion in flexion and extension has been the subject of many investigations.⁶⁰ Fischer (1909), using Reuleaux’s technique, found the so-called locus of the instant center of rotation to be an area 2 to 3 mm in diameter at the center of the trochlea (Fig. 3-1).³⁴ Subsequent experiments with the same technique described a much larger locus.³² In a three-dimensional study of passive motion of the elbow joint, the observations of Fischer were confirmed by using the biplanar x-ray technique.⁶⁹ Based on direct experimental study as well as analytic investigation, Youm and associates¹⁰⁹ concluded that the axis does not change during flexion-extension. In our study, however, variations of up to 8 degrees in the position of the screw axis from individual to individual have been shown. As seen from below, the axis of rotation is internally rotated 3 to 8 degrees relative to the plane of the epicondyles. In the coronal plane, a line perpendicular to the axis of rotation forms a proximally and laterally opening angle of 4 to 8 degrees with the long axis of the humerus.¹⁰⁵ These data, coupled with the clinical information regarding implant loosening, have inspired the development of less constrained but coupled elbow joint replacement designs. It recently has been demonstrated that these designs do function as semiconstrained implants and allow for the normal out-of-plane rotations noted earlier (see Chapter 49).⁷⁵

FIGURE 3-1 Configuration and dimensions of the locus of the instant center of rotation of the elbow. This axis runs through the center of the articular surface, as viewed on both the anteroposterior (AP) and the lateral planes.

From a practical point of view, despite the different findings of various investigators, the deviation of the center of joint rotation is minimal and the reported variation is probably due to limitations in the experimental design. Thus, the ulnohumeral joint could be assumed to move as a uniaxial articulation except at the extremes of flexion and extension. The axis of rotation passes through the center of the arcs formed by the trochlear sulcus and capitellum.⁵⁶

The center of rotation can be identified from external landmarks. In the sagittal plane, the axis lies anterior to the midline of the humerus ⁹² and lies on a line that is colinear with the anterior cortex of the distal humerus.⁶⁹ The coronal orientation is defined by the plane of the posterior cortex of the distal humerus.¹⁹ This axis emerges from the center of the projected center of the capitellum and from the anteroinferior aspect of the medial epicondyle (see Fig. 3-1).

Similarly, the effect of altering the center of rotation on the kinematics of the forearm has been recently studied. Alterations of as much as 5 mm proximally, distally, anteriorly, or posteriorly have been shown to have only a slight effect on elbow kinematics (Fig. 3-2). This observation has great clinical relevance regarding the design and insertion of prosthetic replacement and articulating external fixation devices.

FIGURE 3-2 Experimental data using the electromagnetic tracking system reveals 5-mm changes in the elbow axis site (A) and causes relatively small effects in the kinematics of the forearm (B).

FOREARM ROTATION

The radiohumeral joint, which forms the lateral half of the elbow joint, has a common transverse axis with the elbow joint, which coincides with the ulnohumeral axis during flexion-extension motion. In addition, the radius rotates around the ulna, allowing for forearm rotation or supination-pronation. In general, the longitudinal axis of the forearm is considered to pass through the convex head of the radius in the proximal radioulnar joint and through the convex articular surface of the ulna at the distal radioulnar joint.^34,⁹⁷ The axis therefore is oblique to the longitudinal axes of both the radius and the ulna (Fig. 3-3), and rotation is independent of elbow position.⁴⁵

FIGURE 3-3 The longitudinal axis of pronation-supination runs proximally from the distal end of the ulna to the center of the radial head. The axis is at the ulnar cortex in the distal one third of the forearm.

Mori has characterized the axis of forearm rotation as passing through the attachment of the interosseous membrane at the ulna in the distal fourth of the forearm (see Fig. 3-32).⁶² This may have particular applications with regard to the sensitivity of forearm rotation to angular deformity in this particular portion of the bone. Clinically and experimentally, less than 10% angulation of either the radius or the ulna causes no functionally significant loss of forearm rotation.⁹¹

FIGURE 3-32 A, Pressure distribution on elbow joint surface as external load P is applied at the distal end of the ulna. Distribution of muscle force, F_e and F_f, influences the magnitude, R, and the direction, F, of resultant force on the elbow joint. F represents the “attempted displacement,” U, of the humerus relative to the direction of the ulna. B, For the given loading condition, resultant joint force increased with increasing involvement of extensor muscle, as represented by the ratio of extension force F_e to flexor force F_f (top). Peak articular pressure and the direction of the attempted displacement of the humerus also are affected by the level of involvement of extensor muscle (bottom).

(From An, K. N., Himeno, S., Tsumura, H., Kawai, T., and Chao, E. Y.: Pressure distribution on articular surfaces: Application to joint stability evaluation. J. Biomech. 23:1013, 1990.)

In the past, ulnar rotation was described as being coupled with forearm rotation.¹⁰⁶ This observation could not be reproduced in a subsequent study by Youm and associates.¹⁰⁸ By using a metal rod introduced transversely into the ulna, extension, lateral rotation, and then flexion of the ulna was described with rotation from pronation to supination. The axial rotational movements of the ulna were also observed by others.^14,^22,^30,^43,^69,^88,¹⁰⁸

Ray and associates ⁸⁸ also suggested that varus-valgus movement of the ulna occurs if the forearm rotates on an axis extending from the head of the radius to the index finger. Experiments from our laboratory⁷⁶ have demonstrated external axial rotation of the ulna with forearm supination. Internal rotation or closure of the lateral ulnohumeral joint occurs with pronation.

Finally, the radius has been shown to migrate 1 to 2 mm proximally with pronation.⁶⁷ This observation had not been reported previously but has been confirmed by observations at the wrist.⁸²

CARRYING ANGLE

The carrying angle is defined as that formed by the long axis of the humerus and the long axis of the ulna. It averages 10 to 15 degrees in men and is about 5 degrees greater in women.^1,^18,^53,⁹⁷

However, uncertainty has arisen over the use of the term carrying angle in the dynamic setting. Dempster ²⁷ described an oscillatory pattern during elbow flexion, whereas Morrey and Chao⁶⁹ reported a linear change, with the valgus angle being the greatest at full extension and diminishing during flexion. The confusion arises because three descriptions based on different reference systems have been adopted for the measurement of carrying angle changes.

Definition 1

The carrying angle is the acute angle formed by the long axis of the humerus as the long axis of the ulna projects on the plane containing the humerus (Fig. 3-4A).

FIGURE 3-4 A, Carrying angle between the humerus and the ulna as measured by viewing from the direction perpendicular to the plane containing the humeral and the flexion axes. Conventionally, the acute angle instead of the obtuse angle shown is used as the carrying angle measurement. B, Carrying angle between humerus and ulna as measured by viewing from the direction perpendicular to the plane containing the ulnar and flexion axes. Conventionally, the acute angle instead of the obtuse angle shown is based as the carrying angle measurement.

(From An, K. N., Morrey, B. F., and Chao, E. Y. S.: Carrying angle of the human elbow joint. J. Orthop. Res. 1:369, 1984.)

Definition 2

The carrying angle is described as the acute angle formed by the long axis of the ulna and the projection of the long axis of the humerus onto the plane of the ulna (see Fig. 3-4B).

Definition 3

The carrying angle is defined analytically as the abduction-adduction angle of the ulna with respect to the humerus when eulerian angles are being used to describe arm motion.

From an anatomic point of view, it is not difficult to conclude that the existence of the carrying angle is due to the existence of obliquities, or cubital angles, between the proximal humeral shaft, the trochlea, and the distal ulnar shaft. By assuming that the ulnohumeral joint is a pure hinge joint and that the axis of rotation coincides with the axis of the trochlea, the change in the carrying angle during flexion can be defined as a function of anatomic variations of the obliquity of the articulations according to simple trigonometric calculations.⁸ If the first or second definition is accepted, the carrying angle changes minimally during flexion. The specific varus/valgus relationship of the forearm to the humerus during flexion therefore depends on the relative angular relationship of the humeral and ulnar articulations (Fig. 3-5).

FIGURE 3-5 The positional relationship of the forearm referable to the humerus in the frontal plane of the humerus (carrying angle) is dependent on the relative tilt of the humeral and ulnar articulations referable to their long axes.

RESTRICTION OF MOTION

In normal circumstances, elbow flexion ranges from 0 degrees or slightly hyperextended to about 150 degrees in flexion. Forearm rotation averages from about 75 degrees (pronation) to 85 degrees (supination) (see Chapter 2). The cartilage of the trochlea forms an arc of about 320 degrees, whereas the sigmoid notch creates an arc of about 180 degrees. Generally, the arc of the radial head depression is about 40 degrees,⁹⁷ which articulates with the capitellum, presenting an angle of 180 degrees.

The significance of the 30-degree anterior angulation of the trochlea with the 30-degree posterior orientation of the greater sigmoid notch to flexion and extension and stability of the elbow joint is discussed in detail in Chapter 1 (Fig. 3-6). Impact of the olecranon process on the olecranon fossa and the tension of the anterior ligament and the flexor muscles as well as tautness of the anterior bundle of the medial collateral ligament have been described as serving as a check to extension.^40,⁵² The anterior muscle bulk of the arm and forearm, along with contraction of the triceps, is also reported to prevent active flexion beyond 145 degrees.⁵² However, the factors limiting passive flexion include the impact of the head of the radius against the radial fossa, the impact of the coronoid process against the coronoid fossa, and tension from the capsule and triceps.

FIGURE 3-6 The distal humeral forward flexion is complemented by a 30-degree posterior rotation of the opening of the greater sigmoid notch.

(With permission, Mayo Foundation.)

For pronation and supination, Braune and Flugel ²⁰ found that passive resistance of the stretched antagonistmuscle restricts the excursion range more than that of the ligamentous structures. Spinner and Kaplan,⁹⁶ however, have shown that the quadrate ligament does provide some static constraint to forearm rotation. Impingement of tissue restrains pronation, especially by the flexor pollicis longus, which is forced against the deep finger flexors. The entire range of active excursion in an intact arm is about 150 degrees, whereas when the muscles are removed from a cadaver specimen, the range increases to 185 to 190 degrees. With cutting the ligaments, the range increased up to 205 to 210 degrees.

CAPACITY AND CONTACT AREA OF THE ELBOW JOINT

The capacity of the elbow joint recently has been shown to average about 25 mL. The maximum capacity is observed to occur with the elbow at about 80 degrees of flexion.⁷⁸ This explains the clinical observation that stiff elbows tend to have fixed deformities at about 80 to 90 degrees of flexion.⁶³

Accurate measurement of the contact points of the elbow is extremely difficult, and several techniques have been applied to this highly congruous joint.⁹⁹ Silicone casting, Fuji Prescale film, and reversible cartilage staining are most commonly used. Each has advantages and disadvantages. The contact area of the articular surface during elbow joint motion has been investigated by Goodfellow and Bullough, using a staining technique.³⁹ They found that the central depression of the radial head articulates with the dome of the capitellum and that the medial triangular facet was always in contact with the ulna. The upper rim of the radial head made no contact at all. At the humeroulnar joint, the articular surfaces were always in contact during some phases of movement. Others have verified these observations.¹⁰⁷ The contact areas on the ulna occurred anteriorly and posteriorly and tended to move together and slightly inward from each side from 0 to 90 degrees of flexion and with increasing load.^31,⁷⁴ Using a wax casting technique, in full extension, the contact has been observed to be on the lower medial aspect of the ulna, whereas in other postures, the pressure areas described a strip extending from posterolateral to anteromedial.³⁷ The radiocapitellar joint also revealed contact during flexion without externally applied load. Investigations in our laboratory show that the contact areas of the elbow occur at four facets: two at the coronoid and two at the olecranon (Fig. 3-7). Only a slight increase in total surface area occurred with elbow flexion and with a sevenfold increase in load.⁹⁹ With a 10-N load, about 9% contact of the articular surfaces occurs, and with 1280 N, the area increased to about 73%.³¹

FIGURE 3-7 Contact in the sigmoid fossa moves toward the center of the fossa during elbow flexion.

(Redrawn from Walker, P. S.: Human Joints and Their Artificial Replacements. Springfield, IL, Charles C. Thomas, 1977.)

When varus and valgus loads are applied to the forearm, the contact changes medially and laterally. This implies a pivot point about which the radioulnar articulation rotates on the humerus in the anteroposterior (AP) plane in extension with varus and valgus stress. In vivo experiments have demonstrated the varus-valgus pivot point of the elbow to reside in the midpoint of the lateral face of the trochlea (Fig. 3-8).

FIGURE 3-8 The line of action in the muscles produces a compression force at the radial head when situated just lateral to the middle of the lateral face of the trochlea, and a tension force on the radial head is situated just medial to this point. This indicates that the varus-valgus pivot point in the elbow lies at that point on the AP plane.

(From Morrey, B. F., An, K. N., and Stormont, T. J.: Force transmission through the radial head. J. Bone Joint Surg. [Am.] 70:250-256, 1988.)

ELBOW STABILITY

The elbow is one of the most congruous joints of the musculoskeletal system and, as such, is one of the most stable. This feature is the result of an almost equal contribution from the soft tissue constraints and the articular surfaces.

The static soft tissue stabilizers include the collateral ligament complexes and the anterior capsule. Studies from our laboratory regarding the anatomy of the lateral collateral ligament ^68,⁷⁷ and others^36,^79,⁹⁵ have been discussed previously (see Chapter 2). The lateral collateral ligament and the anterior bundle of the medial collateral ligament originate from points through which the axis of rotation passes. Furthermore, the medial collateral ligament has two discrete components.^66,⁹³ The anterior bundle has been shown to be taut in extension; the converse is true for the posterior fibers of the anterior bundle. Because elbow joint motion occurs about a nearly perfect hinge axis through the center of the capitellum and trochlea, the posterior bundle of the medial collateral ligament complex will be taut at different positions of elbow flexion (Fig. 3-9). The lateral collateral ligament and the anterior bundle lying on the axis of rotation will assume a rather uniform tension, regardless of elbow position. Furthermore, the lateral ulnar collateral ligament has inserts on the ulna and, as such, helps to stabilize the lateral ulnohumeral joint (Fig. 3-10).^23,^66,^77,⁸¹ In experiments performed in our laboratory, O’Driscoll and associates have demonstrated that the lateral ulnar collateral ligament is essential to control the pivot shift maneuver (see Chapter 4). Further evidence of the contribution of the lateral ligament complex to elbow stability is offered by S∅︀jbjerg and associates.⁹⁴ These investigators also attributed a major role in varus and valgus stability to the annular ligament. Although our work suggests that the major component in the varus and rotatory stability is the structure termed the lateral ulnar collateral ligament, the parallel findings of these investigators suggest that the lateral complex is, in fact, a major valgus stabilizer of the elbow joint and functions with or without the radial head.⁸⁰

FIGURE 3-9 The anterior medial collateral ligament remains more taut during elbow flexion than does the posterior segment of the ligament. The radial collateral ligament originates at the axis of rotation for elbow flexion; hence, the ligament has little length variation during flexion and extension.

(With permission, Mayo Foundation.)

FIGURE 3-10 The orientation and attachment of the lateral collateral ligament stabilizes the ulna to resist varus and rotatory stresses just as the medial ligament resists valgus stress.

ARTICULAR AND LIGAMENTOUS INTERACTION

The influence of the ligamentous and articular components on joint stability are usually studied with the use of the materials testing machine by imparting a given and controlled displacement to the elbow.^47,^65,⁸⁷ The relative contribution of each stabilizing structure can be demonstrated by sequentially eliminating each element and observing the load recorded by the load cell for the constant displacement imparted, usually 2 to 5 degrees ⁹⁵ (Fig. 3-11).

FIGURE 3-11 Force displacement curves demonstrate relative contribution of elements to elbow stability in extension (A) and flexion (B).

(From Morrey, B. F., and An, K. N.: Articular and ligamentous contributions to the stability of the elbow joint. Am. J. Sports Med. 11:315, 1983.)

A simplified summary of the observations from such an experiment is shown in Table 3-1. In extension, the anterior capsule provides about 70% of the soft tissue restraint to distraction, whereas the medial collateral ligament assumes this function at 90 degrees of flexion. Varus stress is checked in extension equally by the joint articulation (55%) and the soft tissue, lateral collateral ligament, and capsule. In flexion, the articulation provides 75% of the varus stability. Valgus stress in extension is equally divided between the medial collateral ligament, the capsule, and the joint surface. With flexion, the capsular contribution is assumed by the medial collateral ligament, which is the primary stabilizer (54%) to valgus stress at this position. Furthermore, for all practical purposes, the anterior portion of the medial collateral ligament provides virtually all of the structure’s functional contribution.

TABLE 3-1 Percent Contribution of Restraining Varus-Valgus Displacement

Limitations of this experimental model have resulted in an overestimation of the role of the radial head inresisting valgus load.^47,^65,⁹⁰ This has prompted the development of an experimental technique that allows simultaneous and accurate measurement of three-dimensional angular and translational changes under given loading conditions (Fig. 3-12). Using the electromagnetic tracking device, an accurate technique for measuring the function of the articular and capsuloligamentous structures was developed.⁷⁰ More accurate and relevant data were generated.⁷⁰ Valgus stability is resisted primarily by the medial collateral ligament. With an intact medial collateral ligament, the radial head does not offer any significant additional valgus constraint. With a released or compromised medial collateral ligament, the radial head does resist valgus stress. This important experiment documents that the radial head is a secondary stabilizer for resisting valgus stress, whereas the medial collateral ligament is the primary stabilizer against valgus force (Fig. 3-13). In a laboratory investigation, the hyperextension trauma produces lesions of the anterior capsule, the avulsion of proximal insertions of both medial and lateral collateral ligaments.¹⁰³ The degree of extension increased by 17 degrees and induced significant joint laxity in forced valgus internal-external rotation, but not varus.¹⁰³

FIGURE 3-12 The arrangement of the electromagnetic tracking device allows varus-valgus stresses applied to the elbow during simulated motion with the flexor and extensor muscles. Real-time simultaneous three-dimensional motion of the forearm may be monitored with reference to the humerus.

FIGURE 3-13 The stabilizing role of the radial head to valgus stress with the collateral intact resection of the radial head has little effect on valgus stability (A). However, if the medial collateral ligament (MCL) has been sectioned, the absence of a radial head markedly increases valgus displacement (B). The fact that the radial head is important only when the medial collateral ligament is released defines the radial head as the secondary stabilizer against valgus stress.

It has been recently observed that the valgus and varus laxity of the elbow is dependent on forearm rotation.⁸⁶ Increased valgus/varus laxity with forearm pronation, particularly in medial collateral ligament deficient elbows, implies a possible additional factor in throwing kinematics that might put professional baseball pitchers at risk of medial collateral ligament injury due to chronic valgus overload. The forearm rotation should be considered during the clinical examination of elbow instability. The stabilizing effects of monoblock and bipolar designs of radial head replacements in cadaver elbows with a deficient medial collateral ligament were studied.⁸⁵ The constraint mechanism inherent in the implant design significantly affected the mean valgus laxity. The implants all performed similarly except in neutral forearm rotation, in which the elbow laxity associated with the Judet implant was significantly greater than that associated with the other two implants.

Comminuted radial head fractures associated with an injury of the medial collateral ligament can be treated with a radial head implant. However, lengthening and shortening of the radial neck by 2.5 mm significantly alters the kinematics and contact pressure through the radiocapitellar joint in the medial collateral ligament-deficient elbow ¹⁰⁴ (Fig. 3-14). Radial neck lengthening caused a significant decrease in varus-valgus laxity and ulnar rotation, with the ulna tracking in varus and external rotation. Shortening caused a significant increase in varus-valgus laxity and ulnar rotation, with the ulna tracking in valgus and internal rotation. Therefore, a radial head replacement should be performed with the same level of concern for accuracy and reproducibility of component position and orientation as is appropriate with any other prosthesis.

FIGURE 3-14 Average varus (-) or valgus (+) position of the ulna under different radial neck shortening and lengthening conditions, with the application of valgus (top line) or varus (bottom line) gravitational stress.

(From Van Glabbeek, F., Van Riet, R. P., Baumfeld, J. A., Neale, P. G., O’Driscoll, S. W., Morrey, B. F., and An, K. N.: Detrimental effects of overstuffing or understuffing with a radial head replacement in the medial collateral-ligament deficient elbow. J. Bone Joint Surg. [Am.] 86:2629, 2004.)

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