Elements of the Physics of Pulley Injury (draft)

Transcription

1 Elements of the Physics of Pulley Injury (draft) I. Introduction. Rock climbers have long been plagued with finger injuries due to various climbing activities, almost all of which include crimping at some time. These injuries have been vaguely referred to as tendon pulls or the like, but the possibility of explicit pulley injuries and their mechanism was not advanced until the early 1990s [1]. The A2 and A4 pulleys are often singled out as being particularly or commonly injury- prone due to crimping, especially in the middle finger (because it is relied upon so heavily) and the ring or pinky fingers (weaker), but there is disagreement on both the mechanism and relative likelihood of injury; to some degree, this disagreement extends to the use of taping to prevent or alleviate injury. II. Anatomy. There are a wide variety of diagrams to be found in textbooks and on the internet that identify the ligament/tendon/pulley anatomy of the finger. Two such diagrams are shown in Fig. 1. Figure 1. Finger Anatomy Tension in the flexor tendons causes the pulleys to create constraint forces that could lead to injury of the pulleys. Differences between the flexor tendons (FDP and FDS) are not distinguished except to note that both tendons pass through the A2 and A3, while only the FDP tendon passes through the A4. These tendons, and the constraints created by the pulleys and the bone/joint structures, dictate the baseline physics of the crimp hold. The tendons are designed to incur larger forces during normal usage and are less likely to incur a traumatic injury. The focus of this article is the A2/A3/A4 pulleys, which can be injured when sudden loads are placed on them by the tendons, often due to sudden events such a falling or extreme climbing moves. III. Physics. The standard crimp hold is shown in Fig. 2, which includes some of the forces required to understand the physics of this hold under static load. The

2 force of the rock surface on the fingers is shown in yellow, the flexor tendon(s) are shown in blue (under tension), and the constraint forces created by tension in the pulleys are shown in magenta. No bone or joint forces are included, and none of the forces are drawn to scale. The so- called PIP and DIP joints are denoted by white dots. A3 PIP A2 A4 DIP Figure 2. Standard crimp (adapted from [2]) The relationship between the force due to the tension in the tendon in the direction along the tendon s length, and the constraint force due to the tension in an orthogonal support structure (the pulley) is non- linear. Figure 3 shows the relevant physics in the very simplest approximation: Pulley Constraint Force (T) θ Flexor Tendon Force Tr β Flexor Tendon Force Tf Figure 3. Vector relationship of forces near a constraint pulley.

3 The constraint force that the pulley must exert is T = (Tr sinθ + Tf sinβ). Under the assumption that the tensions in the flexor tendon on either side of the pulley are equal and that the angles are approximately the same, the constraint force T is a relatively small fraction of the longitudinal force exerted by the tendon (about 3.5% of the longitudinal force, per degree, for angles that are smaller than about 10 ). A version of Fig. 3 applies to all three pulleys; therefore, the full analysis is a rather complicated geometry and trigonometry problem that is compounded by the effects of friction and viscoelasticity in the pulleys. A future version of this application note will explore this in more detail; for now the take- home message is that for a given tendon tension, the pulley constraint force is low for small angles and high for large angles. IV. Predictions. Applying this geometry to Fig. 2 suggests that the A3 pulley provides the largest force (largest angles), then the A4, and finally the A2 with the lowest force; however, these conclusions are highly dependent on the actual angles, which are in turn dependent on the pulley extension. Cadaver measurements show that all three pulleys provide a similar strength based on their sheath length [3]. The A3 has a smaller sheath length and therefore can withstand the smallest load (by a factor of 4 to 9 compared to the A4 and A2, respectively). At the same time, the A3 pulley is more compliant (by a factor of 6 to 8 than the A2 or A4, respectively). These complementary observations make an engineering prediction of what happens under stress quite difficult. Regardless, the behavior of the weaker A3 can substantially effect what happens to the stronger A2 or the A4. It is commonly (and apparently correctly) assumed that micro- traumas to, or the outright partial or complete ruptures of one or more pulleys, lead to the pain that rock climbers experience as a result of a large and often sudden load in the crimp grip. For example, a popular depiction of partial and total ruptures of the A2 are shown in Fig. 4. Figure 4. Popular representation of A2 damage.

4 These depictions are both ordinary and unusual for several reasons. They do correctly depict damage to the A2 pulley, and they suggest that a complete rupture leads to the phenomenon of bowstringing, in which the tendon pulls away from its normal proximity to the bone. In contrast, these representations are unusual from a physics standpoint because there is little reason to believe that this geometry could lead to either A4 or A2 trauma, or significant bowstringing, because of the largely non- extended depiction of the A3 pulley. In contrast, Fig. 5 is a more believable depiction of the partial rupture of the A2, with the attendant bowstringing. Figure 5. Partial rupture of the A2, resulting in tendon bowstringing [4] Note that in order for bowstringing to be palpable in this depiction, the A3 is virtually required to be totally ruptured. V. Experiment. Comprehensive experiments on cadaver fingers were performed in both the early and late 1990s [2, 3]; the latter found that isolated ruptures of the A2 are rare, and that the A3 rarely if ever ruptures except after rupture of A2 and A4. There were discrepancies between the measured failure loads ([2] found that the failure load of the A2 and A4 pulleys is roughly the same; in contrast, [3] found that the failure load differed by a factor of two). However, by far the most important observation is that the A4 is predisposed to fail first, then the A2, then the A3. This

5 strongly suggests that despite the low load limit of the A3, its large compliance allows the transfer of tendon load to the A2 and the A4, putting each of them in position for injury. It also directly contradicts the typically reported result that A2 injuries are more common. Radiographs [5] showed significant variation in the geometry of the entire pulley system (including the cruciate pulleys); therefore, a wide variability of pulley response to loads between different people is not surprising. Taken together, there are few predictions that can be made about the injury mechanism that can occur in an actual climbing situation, save for one: measurements of bowstringing contradicts its use as a clinical sign of rupture of the A2 or A4: generally, both the A3 and either the A2 or A4 must be ruptured to see subtle bowstringing; significant bowstringing occurs after all three pulleys are ruptured; and, no bowstringing is observed with rupture of just the A2 or A4. With these difficulties, the efficacy of bowstringing to diagnose any trauma less than multiple ruptures is very small. VI. Effect of Taping. There is a belief that taping the A2 pulley will alleviate pain, assist in the repair, or help prevent injury by supporting the A2 pulley; however, experiments on volunteers, in which both bowstringing and pulley load in vivo for the crimp grip was externally measured, indicated that such taping was of minimal biomechanical effectiveness [6, 7]. The main findings were: Taping made only a small difference in the palpable bowstringing Taping provided only about 10% of the constraint provided by the A2 itself These results were not significantly different, regardless of whether the taping was performed mid- phalanx or closer to the PIP joint. The bowstringing result is not surprising, given the obvious geometry of the pulleys described here and in the literature. The inefficacy of taping from a force perspective is a less intuitive result, and is controversial not only in the climbing community but also in the literature. For example, taping has been reported to provide good functional outcomes as part of a conservative treatment regimen that includes immobilization and physical therapy in the case of minor injury, and splinting or surgery in cases of major injury [8]. In particular, the use of a special geometry referred to as H- taping shows an improved biomechanical effectiveness; however, it is emphasized that such taping a) results in no apparent change to finger strength in uninjured fingers, b) the results may be linked strongly to psychology, and c) efficacy may be highly dependent on repeated taping (i.e., retaping after every route) [9]. A future draft of this note will explore the effect of taping in more detail.

6 VII. References. 1. S.R. Bollen, Injury to the A2 Pulley in Rock Climbers, J Hand Surgery 15B: (1990). 2. R.A.W. Marco et al., Pathomechanics of Closed Rupture of the Flexor Tendon Pulleys in Rock Climbers, J Bone and Joint Surgery 80- A: (1998). 3. G- T. Lin et al., Mechanical Properties of Human Pulleys, J Hand Surgery 15B: (1990). 4. D.A. Neumann, Kinesiology of the Musculoskeletal System. St. Louis: Mosby, G- T. Lin et al., Functional Anatomy of the Human Digital Flexor Pulley System, J Hand Surgery 14A: (1989). 6. A. Schweizer, Biomechanical Effectiveness Of Taping The A2 Pulley In Rock Climbers, J Hand Surgery 25B: (2000). 7. W.J. Warme et al., The Effect of Circumferential Taping on Flexor Tendon Pulley Failure in Rock Climbers, Amer. J Sports Medicine 5: (2000). 8. V.R. Schöffl et al., Injuries to the Finger Flexor Pulley System in Rock Climbers: Current Concepts, J Hand Surgery 31A: (2006). 9. I. Schöffl et al., Impact of Taping After Finger Flexor Tendon Pulley Ruptures in Rock Climbers, J Appl Biomechanics 23:52-62 (2007).