Mini-symposium: the elbow (iv) biomechanic of the elbow

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Biomechanics Section, Mechanical Engineering Department, Imperial College, London SW72BX, UK cal capitellum laterally. If the elbow is positioned cor-rectly under an X-ray image intensi¢er, so that the view The upper limb is a complex mechanism with which we is exactly along the £exion ^ extension axis, it is seen that interact with the world around us. The joints act in con- these articulations have approximately circular cross- cert to position the hand, or to apply force on objects via sections and that these circles are nested concentrically the hand. It is the job of the shoulder to move the upper together. This means that the joint can act as a uniaxial limb around the body, so that the hand may reach in di- hinge during £exion ^ extension and that there will be rections that cover more than a hemisphere. At the no relative motion between the radius and ulna as this same time, the £exion ^ extension mobility of the elbow motion occurs. This has an important practical conse- allows the hand to reach out to objects, and then to quence, since it means that elbow prostheses can have a bring them back to the body.These activities usually also simple hinge design and do not require complex geome- require forearm rotation movements, the hand being try in order to maintain physiological kinematics. There pronated when picking up an object, and supinated when are, however, many papers in the literature that have it is brought close for examination or eating.
sought to complicate the situation, erroneously. They In addition to mobility, the upper limb must be strong have described phenomena such as closer contact be- enough for daily activities. It does not require any sophis- tween the radius and capitellum during a certain arc of ticated engineering analysis to realize that the upper limb elbow £exion, that does not really occur. The underlying is a relatively long and slender structure, which means reasons for this have been a lack of understanding of the that external forces acting on the hand have a long lever kinematics, relating to the orientation of the £exion ^ex- arm, while the internal muscles pass close to the joints tension axis, plus the use of lightly loaded cadaveric spe- and have short moment arms about their axes.The con- cimens that have not had their joint surfaces packed sequence of this mechanical disadvantage is that the in- ternal muscle forces will inevitably be much greater than Flexion ^ extension of the forearm does not occur in the external forces, and this will lead to large elbow joint the sagittal plane. This is because of the carrying angle forces. The force analysis later in this paper will show that causes the forearm to have a valgus angulation in re- that it is a mistake to consider the elbow to be ‘non- lation to the humerus when the elbow is extended. The load-bearing’: not only are the forces sometimes very carrying angle is larger in females than males, having va- large, but the bones are small when compared to the lues of 141 and 111, respectively. This di¡erence is pre- lower limb, and so the stresses on them are just as high.
sumed to relate to the di¡erent pelvic width and the The challenges faced by the surgeon dealing with the el- demands for carrying objects alongside the hips with bow are compounded by the e¡ects of rheumatoid dis- the elbow extendedThe characteristic shape given to ease. Not only are the relatively delicate bones of the the extended arm by the carrying angle can be lost inad- upper limb attenuated proportionately more by erosive vertently by malreduction of humeral supracondylar or changes, but the demands of weight-bearing through walk- condylar fractures, giving the unsightly ‘gunstock defor- ing aids such as elbow crutches must often be allowed for.
mity’ if the forearm moves into varus. This must beguarded against in children, in whom the carrying angleis smaller than in adults, being typically 61. The carrying angle is largest with the elbow extended and disappears in full £exion, so that the forearm overlays the upperarm. This carrying angle variation occurs because the The articular surfaces of the distal humerus consist of £exion ^ extension axis is inclined away from being med- the spool-shaped trochlea medially and the part-spheri- ial ^ lateral so that it is more proximal laterally, bya half of the carrying angleThus, if the carrying angle is Correspondence to: AAA [email protected]; Tel: 020 -7594 -7062 dir,7046 sec.
121, the £exion ^ extension axis will be 61 from the the coronoid process and of the rim of the radial headagainst the £oors of the anterior humeral fossae.
Forearm rotation normally yields 801 pronation and 901 supination.If the motion is assessed using a rodgrasped in the hand, then a greater arc of motion will befound, due to movements of the ¢ngers, plus £exion ofthe ¢fth metacarpal in supination. Forearm rotation mo-tion can be described in both anatomical and functionalways.The classic anatomical description is that the radiusswings around the stationary ulna, in the manner of thehandle on a bucket. The anatomical axis of rotationpasses from the centre of the capitellum proximally tothe centre of the ulnar head distally, then on towardsthe little ¢nger. If the forearm is rotated while holdingthe little ¢nger in one place, the position of the hand isseen to move, and this is not the normal situation. Nor-mally, the hand remains in one place as the forearm ro-tates, and this corresponds to the rotation axis passingalong the long ¢nger. When observing this motion it isclear that pronation then entails ulnar abduction, and su-pination causes ulnar adduction. If the other hand iswrapped around the wrist, the motion of the distal ulnacan be felt: it seems to be following a rotary path.This isnot caused by the ulna rotating at the elbow, however, itis circumduction: the curved path in space is accom-plished by combinations of ulnar abduction and £exionduring pronation, and adduction and £exion during supi-nation. This description has been controversial, because Figure 1 The carrying angle, between the centrelines of the anatomists have noted the congruence of the humero-ul- forearm and upper arm, disappears as the elbow £exes, due to nar joint and clinical examination shows that the elbow the inclination of the £exion axis, that bisects the angle between appears to be stable against varus ^ valgus loads, so it was suggested that there must be complementarymovements of the humerus. This was disproven,however, by experiments in which the humerus wasimmobilized by pins, then double-exposure radiographs transverse direction. This mechanism can be demon- taken in pronation and supination: the humero- strated easily by copying the diagram and folding the ulnar varus ^ valgus motion of approximately 91 was paper along the axis. As well as remembering this orientation when reducing and imaging the reduction of Forearm rotation clearly involves rotational sliding fractures, it should be built into the design and placement motion between the concave endface of the radial head of elbow prostheses. An incorrect carrying angle will not and the capitellum; it also causes sliding of the proximal only look wrong, it will displace the paths of the muscles radio-ulnar joint. An end view shows that the radial head across the elbow, altering the balance of joint forces.
is not circular F it is approximately elliptical.This devia- Elbow £exion ^ extension is normally quoted as from tion from a circle is caused largely by there being extra 01 to 1451, but females sometimes have slightly greater material to create the bearing surface that bears against extension mobility, reaching up to 201 of hyperexten- the ulna. In the anatomical position, with the elbow supi- sion.Elbow hyperextension is also more common in nated, this articulation is seen as a part-cylindrical sur- some racial groups and this is sometimes in association face, that is anterior. As the forearm pronates, it passes with the presence of a supra-trochlear foramen that medially and then posteriorly. The proximal radio-ulnar links the olecranon and coronoid fossae.The range of ac- joint is stabilized by the surrounding annular ligament tive motion is limited by apposition of the anterior mus- that attaches strongly to the antero-lateral corner of cle bulk in £exion, and by impingement of the olecranon the coronoid and to the supinator ridge of the ulna. In- process into the £oor of the olecranon fossa, plus tigh- tegrity of this structure is important in preventing sub- tening of the anterior joint capsule, in extension. Passive luxation of the radial head: it resists the anteriorly movement usually obtains greater elbow £exion, which is directed tension of the biceps tendon during elbow then limited by simultaneous impingement of the tip of The simpli¢ed example was misleading because it con- centrated solely on a ‘muscle’ that was parallel to the hu-merus, and this is a natural way to think of the situation, It was noted in the introduction that the elbow muscles given that the elbow is £exed by muscles such as biceps work at a large mechanical disadvantage when compar- and brachialis. It suggests that the joint forces act onto ing their small moment arms about the joint axis to the the end of the humerus. However, considering the hand, large moment arms of loads exerted on the hand. It fol- it is clear that there are other muscle actions inherent in lows that the joint forces will be much greater than the elbow £exion, to grasp the object being lifted, and to sta- external forces, and also that they will depend almost en- bilize the wrist. If the ¢st is clenched, even without the tirely on the muscle tensions. Therefore, a good under- hand supporting a load, then the tensions in the ¢nger standing of which muscles act, and of their paths and £exor muscles compress the humero-ulnar joint, due to points of attachment, is central to appreciation of the £exor digitorum super¢cialis originating from the medial forces on the elbow. The joint forces in£uence many as- epicondyle. At the same time, the wrist must be held pects of clinical treatment, providing insight into why against the £exion moments exerted by the ¢nger £exor prostheses loosen or why bone fragments may tend not tensions, and so there is co-contraction of the extensor to remain in a reduced con¢guration, for example.
carpi muscles.These all cross the lateral aspect of the el- Most of the elementary introductions to biomecha- bow and so compress the humero-radial joint.This is gra- nics (e.g. Nordin and Frankel) use elbow £exion as an phically demonstrated if the ¢st is clenched after a example with which to teach the basic fundamentals of Monteggia lesion, and the wrist imaged by an X-ray im- joint force calculation, by equilibrium analysis. In this sim- age intensi¢er: the radius migrates proximally in relation pli¢ed situation the tensionT in‘the £exor muscle’ to the ulna. The consequence of the forearm muscle ac- is estimated by considering equilibrium of the moments tions, for the situation seen in is that they tending to extend and to £ex the elbow.Thus, the exten- will now impose an AP force component onto the distal sion moment exerted by the load in the hand is 20 N humerus, in addition to the distal ^ proximal action of times 0.35 m, or 7N m.This must be opposed by an equal and opposite £exion moment from the muscle. So, if the Since the muscle forces are dominant, it is clear that a muscle exerts a moment of 7N m at a moment arm of joint force analysis depends critically on due allowance 35 mm (0.035 m), the muscle tensionT must equal 7N m for all of the co-operating muscles. There have been divided by 0.035 m, or 200 N. In order to predict the joint many papers on electromyography, aiming to under- force we use an analysis called resolution of forces, in this stand the actions of individual muscles, and how the elec- case in the vertical direction. Summing the forces must trical signals relate to force output. Much of the early lead to zero resultant, if the situation is in equilibrium.
work was brought together by Basmajian;in addition, Thus, the forces acting upwards must be equal and oppo- Long et showed how the forearm muscles contribute site to those acting downwards: T equals 20 N plus JF, so to the function of the hand. In summary, actions that re- JF is 180 N. Although this is a gross simpli¢cation (be- quire a large force to be exerted cause all of the available cause it is rather misleading), this example has been su⁄- muscles to contract, not just to produce a movement, cient both to demonstrate the basic fundamentals of but also to stabilize the joints.Thus, if the ¢st is clenched, equilibrium analysis, and also to show that most of the the biceps and triceps also contract, for example. It is joint force results from the muscle tension, and not di- clear that, if there are many active muscles crossing the rectly from the external force itself.
elbow, then the moment equilibrium equations will becomplex. The principal problem is to decide how muchis contributed by each muscle. It can be argued that thelower limb muscles are stimulated in a way that mini-mizes energy expended when walking, which is an activ-ity that does not impose high (fatigue inducing) stresses.
In the arm, however, we need to account for maximal ac-tions, such as lifting a heavy weight, or struggling to undoa container. Then it is appropriate to assign tensions inproportion to the sizes of the muscles via the physiologi-cal cross-sectional area, a measure of the number ofmuscle ¢bres.
The size of the joint forces obviously relates to the ex- ternal load. There was much ergonomics research done In this simpli¢ed analysis of elbow £exion, the mus- cle tensionT is 200 N, and so the joint force JF is180 N.The lackof in the 1950s and 1960s investigating strength when oper- any muscle actions modelled along the forearm means that JF is ating machines.This is useful here (e.g. Hunsicker), as an predicted to act axially onto the distal humerus.
input to the moment equilibrium equations.
When triceps tension resists the £exing moment The force on the distal humerus, during elbow £ex- from an external load, tensile stresses are caused in the olecra- ion, is greatest near extension, because the forearm and elbow non, causing it to be vulnerable to fracture.
£exor muscles act in nearly the same directions. As £exion pro-gresses, the elbow joint force reduces and swings onto the ante- tends to sublux the radial head anteriorly during elbow rior aspect of the humeral joint surfaces. It acts onto the base ofthe coronoid and the posterior lip of the radial head at all angles £exion the joint is stabilized by the axial forces in the forearm muscles that keep the capitellum engaged inthe concave endface of the radial head.
Elbow extension results primarily from triceps ten- The variation of forces acting onto the distal humerus sion; the triceps is by far the strongest muscle in the during elbow £exion is shown in When the elbow is upper limb. It follows that elbow extension causes large near full extension both the forearm muscles and the el- humero-ulnar joint forces and that the triceps tension bow £exors (principally biceps, brachialis, brachioradialis causes large tensile stresses in the olecranon and pronator teres) are pulling in similar directions.Their The joint force varies from 1.5 kN acting onto the distal tensile forces are then additive, resulting in very large aspect of the humerus at full extension, to 3.5 kN acting forces acting onto the end of the humerus. This reaches onto the antero-distal aspect at 1201 £exion. This is im- a maximum of 5 kN at 301 £exion, for maximal isometric portant when placing an elbow prosthesis, since the ole- strength of a normal young male adultIn the middle of cranon may be eroded by rheumatoid disease, and the arc of £exion the force vectors are AP for the fore- further excavation for the ¢xation stem or keel of an im- arm muscles and proximal for the elbow £exors, giving plant should be minimized.There is also some force on intermediate force values (2.5 kN) acting posteriorly the humero-radial joint as the elbow extends, partly due and proximally onto the distal humerus In the to the wrist stabilizing muscles and partly from the lat- £exed elbow the elbow £exors tend to distract the joint, eral head of the triceps, which does not insert into the in opposition to the forearm muscles that are always act- tip of the olecranon but passes alongside it laterally and ing along the forearm.Thus, the elbow forces fall to their dissipates into the fascia over the anconeus.
lowest values,1kN maximum. In addition to the e¡ect of Forearm pronation is driven primarily by the pronator the directions of the force vectors the joint forces fall as teres and pronator quadratus, while supination results the elbow £exes because of the increasing muscle mo- primarily from actions in biceps and supinator.Although ment arms and falling muscle tensions. In extension the these muscles tend to cause forces acting transversely to elbow £exors rest against the anterior aspect of the the axis of the forearm, they normally act in concert joint so they have small moment arms about the axis.
with hand gripping and wrist stabilising actions that pull This entails large tensions in order to produce a given the bones axially.The result is that the humero-radial and £exion e¡ect. As £exion proceeds, so the moment arms humero-ulnar joints are loaded, while the proximal of the muscles increase and the joint force can decrease.
radio-ulnar joint is subjected to only small forces.
At the same time, the muscle length-tension e¡ect Actions in which the hand is pushing towards the cen- comes into play: as the muscle shorten, so their maxi- treline of the body with the elbow £exed, such as when mum active tension producing capability decreases, pulling a door open or holding a large box, tend to cause also causing the joint force to decrease.
torsion load on the humerus. This is in response to ten- Because of the combination of forearm muscles and sions in the anterior pectoral muscles causing internal elbow £exors acting, the forces acting on the distal hu- rotation at the shoulder. This situation shows why the merus correspond to equal and opposite reactive forces distal humerus is so wide: this gives a base to resist the onto the radius and ulna, and these are mostly acting dis- abduction action of the forearm. The load is resisted by tally and slightly posteriorly, that is towards the base of a force couple: tension in the medial collateral ligament, the coronoid process and towards the posterior rim of and compression in the humero-radial joint If the radial head Although the biceps tension the radial head is missing, it is clear that the forces will tions have shown that, if the force is directed along thecentreline of the forearm, then approximately 70% of theload is transmitted by the radius directly to the capitel-lum.If the force vector passes towards the lateral sideof the elbow, then all of the load passes directly to theradius and this is a stable situation. If the force passesmedially, the tenuous lateral collateral ligament struc-tures do not maintain stability, but this situation is notnormally encountered due to the carrying angle biasingthe loads to the radial side of the elbow.
In the past, anatomical texts noted how the shaft of the ulna increases in cross-section proximally, which isthe opposite of the tendency of the radius. It seemed lo-gical to suggest that this re£ected load transfer from ra-dius to ulna via the ¢bres of the interosseous membrane,since the main ¢bres are oriented from proximal on theradius to distal on the ulna. Although an attractive con-cept, this mechanism does not hold up to an engineeringstress analysis. This is because the membrane has muchlower sti¡ness than the radius, so it cannot transmit asigni¢cant load until it is stretched by a proximal migra-tion of its radial attachment; this can only occur after ra-dial head fracture. The intact radius does not deformsu⁄ciently for a signi¢cant tension to build up in the in-terosseous membrane.
A further factor that limits the ability of the inteross- eous membrane to transmit force is that it is slack whenthe forearm is pronated, the functional position whenpushing or falling onto the outstretched hand.This is be-cause the anatomical axis of forearm rotation passesanterior to the crest of the ulnar diaphysis to which themembrane is attached. The result is that the membraneis tightest with the forearm in mid rotation, when the During an adduction action, the external load radius is beyond the axis from the ulna, and slackens in pressinginto the palm causes an abduction moment atthe elbow.
pronation, when the radius is alongside the axis. An al- This is resisted by coupled actions of tension in the medial collat- ternative hypothesis for the function of the interosseous eral ligament and compression in the humeroradial joint. Similar membrane is that it is an extensive area for muscle at- forces apply during a fall onto the outstretched hand.
tachment, and so it acts to transmit tensile force fromthe deep muscles to the radius, in equilibrium with thecompressive force of the carpus loading the end of the be concentrated onto the lateral edge of the coronoid radius. A side-e¡ect of the muscle attachments is that process. Since the base is narrower, this load will be the muscles will tend to pull the ¢bres distally, away from greater than that which had acted on the radial head, the radius after an injury that has ruptured the mem- and so too will be the tension in the ligament. It is these brane, and so it often will not heal.
forces that cause torsional ¢xation failure of prostheses In a fall forwards onto the outstretched hand, the and which require the ¢xation to spread widely into or posture taken up automatically has the shoulder partly internally rotated, the elbow slightly £exed (approxi-mately 151), and the forearm semi-pronated, so that thepalm faces the £oor.The £exed posture is important because this allows the elbow to £ex and the shoulder to extend, after impact, thus absorbing energy bystretching their surrounding muscles rather than frac- Pushing actions cause compressive forces to pass turing a rigid column of bone.The landing posture places through the hand and wrist, then along the forearm to the lateral aspect of the elbow uppermost on impact.
the elbow. This situation is magni¢ed in a fall, when the Consideration of the dorsi£exing tendency of the force hand is extended to break the fall. A number of investiga- from the £oor onto the hand reveals that the radius will be compressed and the medial collateral ligament tensed (similar to .Thus,100% of the impact force passes tothe radial head and so it is the most common site of bone 1. Amis A A, Miller J H. The elbow. In: Measurement of Joint fracture at the elbowThe trabecular architecture of Movement. Clin Rheum Dis 1982; 8: 571–593.
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The elbow is a complex mechanism and the articular 12. Amis A A, Miller J H, Dowson D, Wright V. Axial forces in the geometry, kinematics, muscle actions and joint forces forearm. Their relationship to excision of the head of the radius.
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