MECHANICAL
PROPERTIES
G.-T. LIN, W. P. COONEY,
OF HUMAN P. C. AMADIO
PULLEYS
and K.-N. AN
From the Biomechanics Laboratory, Department of Orthopedics, Mayo Clinic and Foundation, U.S.A.
In order to determine the mechanical properties of the fibro-osseous pulleys in the hand, the diaphyseal annular pulleys, the volar plate annular pulleys and the cruciate or condensable portions were tested. A custom-made loading device provided proper fit of the soft tissues for a uniform distribution of the pulley load during testing. The A2 pulley was found to be the strongest of the pulleys; the Al and A4 were the next strongest. The A3 pulley was nearly equal in mean breaking strength to the other annular pulleys, but in absolute breaking load was considerably weaker because of its shortness. The A4 was the least compliant of the pulleys. We concluded that the fibro-osseous A2 and A4 were mechanically stronger and stiffer pulleys than the Al, A3, A5 (volar plate) pulleys. In testing one type of pulley reconstruction, we found that the “belt loop” technique of Karev nearly matched the annular pulleys in strength and energy absorption. Journal of Hand Surgery (British Volume, 1990) 15B: 429-434
Doyle and Blythe (1975) defined four annular and three cruciate pulleys in the flexor tendon sheath of human digits and determined the optimum placement of the pulleys for effective flexor function. The critical pulleys were the second annular (A2) and the fourth annular (A4) at the mid-portion of the proximal and middle phalanges. Manske and ILesker (1977, 1983) concluded that the Al and A4 pulleys were the strongest and that the A2 was the weakest. It is our impression that the A2 is the longest and strongest of the annular pulleys. This pulley must resist the force of not one but two flexor tendons during pinch and grasp (Fig. 1). Two annular pulleys (A2, A4) are true fibro-osseous pulleys attached to bone over the proximal and middle phalanges, while the other annular pulleys attach to the volar plate and may be considered as joint pulleys rather than fibro-osseous pulleys. The purpose of this study is to define the mechanical properties of the annular pulleys (Al-A5) and the condensable (cruciate) pulleys (Cl-C3). One type of pulley reconstruction, the “belt loop” pulley (Karev, et al., 1987) was tested to determine if it had significant mechanical characteristics to be of value for pulley function. Several important parameters have been derived from the mechanical test which should be useful for establishing (criteria for reconstruction of the pulley system. Material and methods Five fresh cadaveric hands obtained within 24 hours of death were frozen and preserved at -30°C until ready for dissection. The finger rays were disarticulated at the carpo-metacarpal joint. The flexor sheath of each finger was carefully dissected from surrounding soft tissue but left attached to bone. The flexor tendons were divided at their insertions by an incision through the tendon sheath distal to the A5 pulley and between the A4 and C2 pulleys VOL. 15B No. 4 NO\‘EMBER 1990
Fig. 1 Anatomy of human pulleys: fibro-osseous annular pulleys (A2, A4), volar plate annular pulleys (Al, A3, A5), cruciate or condensable pulleys (Cl, C2, and C3).
for flexor profundus and superficialis respectively, then pulled out from the tendon sheath proximally. The five annular pulleys and the condensable portions of the tendon sheath (which include the cruciate pulleys) were tested by inserting a rigid tendon hook into the pulley canal (Fig. 2). With the tendon hook placed beneath the annular pulley, the fingers were firmly held in place and prevented from sliding by a set of wedged pins (Fig. 2). A distraction force was applied directly by an Instron materials testing machine (Instron Corporation, Canton, MA) until the pulley ruptured. The deformation of the test apparatus, including fixation and tendon hook, under the load range tested was found to be much less than the deformation of the pulley system. The displacement of the cross head was then recorded as the deformation of the pulley along with the tension as measured by load transducer on the machine. The Instron Series IX automated materials testing system was integrated with a VAXmate computer (Digital Equipment Corporation, Marlboro, MA) to operate the testing machine and collect the data. 429
G.-T. LIN,
W. P. COONEY,
P. C. AMADIO
AND
K.-N.
AN
In addition to the tests of the annular pulley and condensable portions of the tendon sheath, the volar plate pulley reconstruction which creates a new pulley from the fibrous central portion of the volar plate (Karev, 1987; Lin et al., 1989b) was also tested under identical conditions to the testing of normal pulleys. Before each test, the length of the pulley attachment on bone along the line of the tendon hook was measured by a digital caliper for data normalisation. The maximum breaking strength (Newtons/mm.) of the pulley system was only determined as a function of pulley length. From the results of the load-deformation curve (Fig. 3), the maximum breaking load (in Newtons), maximum breaking strength (Newtons/mm. measured by dividing the maximum load by the pulley length), the stiffness (Newtons/mm. : calculated by measuring the slope of the load-deformation curve) and the deformation at maximum breaking load (mm of displacement at maximum load) were derived. The energy absorption to complete failure (joules) was also documented by the area under the load-deformation curve. Results Fig. 2
The set-up for mechanical testing of the pulley system. Metal rods of different diameter and curvature were used to fit different pulleys for more uniform stress distribution during testing.
I
I
I
I
I
I
I
I
I
Load-deformation curves (Fig. 3) demonstrated that the diaphyseal annular pulleys, A2 and A4, are relatively stiffer or less deformable and have a higher breaking
I
A2 :IMUM
BREAKING
ENERGY
LOAD
(N
ABSORPTION TO
FAILURE
( Joules
Al
I.
I
Dicplocement Fig. 3 Typical force-displacement 430
Cmm)
curves for Al-A5 pulleys. THE JOURNAL
OF HAND
SURGERY
MECHANICAL
PROPERTIES
2.5
OF HUMAN
7.5
5.0
Dioplacoment
Fig. 4
Typical force-displacement
PULLEYS
10.0
(mm)
curves for Cl-C3 pulley and volar plate “belt loop” pulley, Vl-V3.
strength than the Al, A3, and A5 pulleys. The loaddeformation curve at the Al pulley showed several small peaks associated with the early failure of fibres connected to the volar plate at the base of the M.P. joint (Fig. 3). The reconstructed belt loop pulleys (Vl-V3) and condensable portion which included cruciate pulleys (ClC3) had similar characteristics (Fig. 4).
the cruciate pulleys had much less strength, with a range of 5.4 to 10.4 Newtons/mm. The volar plate reconstructed pulleys, with a mean breaking strength of 21.5 to 39.6 Newtons/mm., were as strong as the annular pulleys. StifSness The stiffness measurements of the pulley system are summarised in Table 2 and Figure 6. The A4 pulley was
Maximum breaking load The results of average maximum breaking load of each pulley for each finger are shown in Table 1 and graphically represented in Figure 5 as a mean for all of the digits. The A2 pulley had the greatest breaking load, 407.49 Newtons, followed by the Al and A4 pulleys with 324.28 and 209.57 Newtons, respectively. The breaking load of the A3, A5, and cruciate pulleys was quite low (less than 100 Newtons). The reconstructed belt loop pulleys (Vl and V2) had breaking loads comparable to those of normal pulleys.
1
Maximum breaking strength The breaking strengths (Newtons/mm.) of the different annular pulleys were similar (Table 3) and ranged from 22.2 to 34.2 Newtons/mm. The condensable portion of VOL.
15B No. 4 NOVEMBER
1990
PULLEYS Fig. 5 Maximum breaking load of the pulley.
431
G.-T. LIN,
Table l-Maximum
Table Z-Stiifness
Middle
AND
K.-N.
AN
Ring
Little
Total
Mean
S.D.
Mean
S.D.
Mean
S.D.
Mean
S.D.
Mean
S.D.
336.23 431.86 52.47 202.22 38.48 60.07 41.43 43.23 323.59 217.07 70.60
13.76 83.98 20.74 46.33 24.06 10.64 17.19 12.36 75.42 26.85 40.51
402.00 465.67 50.77 210.48 50.87 105.69 40.32 63.90 244.91 183.23 101.82
53.08 202.67 22.01 121.95 45.36 85.04 6.59 18.41 112.37 31.65 21.25
315.24 431.64 52.20 272.83 29.59 69.71 45.51 41.95 303.09 194.71 68.49
36.43 97.82 17.93 92.69 12.16 15.61 11.93 11.26 67.36 71.89 25.83
243.66 305.69 30.74 172.41 31.51 79.94 31.77 45.11 215.87 119.56 78.54
52.37 44.67 15.47 82.12 24.61 18.40 25.56 12.18 68.13 43.83 42.19
324.28 407.49 47.80 209.57 32.89 81.34 39.86 50.05 269.14 176.76 90.62
75.21 126.85 20.47 85.13 29.72 43.51 16.08 14.84 85.54 54.41 42.40
(Newtons/millimetre)*
Index
Al A2 A3 A4 A5 Cl c2 c3 Vl v2 v3
P. C. AMADIO
breaking load (Newtons)
Index
Al A2 A3 A4 A5 Cl c2 c3 Vl v2 v3
W. P. COONEY,
Middle
Ring
Total
Little
Mean
S.D.
Mean
S.D.
Mean
S.D.
Mean
S.D.
Mean
S.D.
82.48 129.59 32.72 129.39 33.35 26.49 15.01 27.51 7i.49 60.31 55.42
27.96 40.81 3.60 12.81 16.18 10.56 9.64 14.22 11.52 10.00 22.13
79.95 161.78 17.45 176.25 27.71 33.91 10.05 31.59 52.51 42.45 44.57
13.60 52.19 6.37 45.27 19.76 21.55 5.17 7.76 18.39 5.61 10.67
81.07 129.87 21.16 142.97 20.23 30.61 10.44 23.05 68.87 53.88 39.50
25.08 40.87 4.10 84.44 8.82 6.91 3.18 5.57 7.09 10.36 9.14
57.82 117.81 15.75 203.48 20.70 31.84 17.10 34.13 63.50 47.07 63.53
8.69 28.21 5.01 109.02 12.89 13.85 14.21 11.74 29.23 9.33 18.17
74.82 135.34 22.00 167.99 22.71 30.71 13.58 21.94 66.33 50.93 50.75
22.72 38.04 8.07 63.20 14.46 13.05 7.74 11.02 14.93 10.54 17.05
* Newtonsper millimetreof displacementas measuredby the slope of the load/deformationcurve.
220
annular pulleys. The results indicated that the Al, A2, and A4 pulleys remained relatively unchanged in their location during tendon loading and joint flexion. In contrast, the location and constraint of A3, A5, and the cruciate pulleys were readily changed during loading and joint flexion. The stiffness of belt-loop reconstructed pulleys (Vl-V3) was found to be less than the osseous annular pulleys but more than the cruciate and volar plate annular pulleys.
1 7.99
Deformation at maximum load
A3
A4
A6
Cl
c2
c3
“1
VT2
“3
PULLEYS Fig. 6
Stiffness of the pulley.
the stiffest, followed by the A2 and Al pulleys. The volar plate annular pulleys (A3 and A5) and the cruciate pulleys (Cl, C2, C3) were relatively less stiff than the osseous 432
Deformation at maximum load is shown in Table 3. Deformation of the annular pulleys ranged from 5.39 mm for Al to 1.09 mm for A5 and appeared directly related to pulley length and maximum load. Deformation of cruciate and belt loop pulleys was similar and neither was significantly different from the annular pulleys. Deformation does not appear to be an important parameter of normal pulley performance and suggests that pulleys will fail before significant change in shape would produce clinically significant bow-stringing. THE JOURNAL
OF HAND
SURGERY
MECHANICAL Table 3-Maximum
PROPERTIES
OF HUMAN
PULLEYS
breaking strength, deformation and energy absorp-
tiOll
Maximum Breaking Strength (Nimm.l
Al A2 A3 A4 A5 Cl c2 c3 VI v2 v3
Deformation at Maximum Load (mm.)
Energy Absorption to Total Failure -(J)
Mean
S.D.
Mean
S.D.
Mean
S.D.
31.71 21.11 22.20 34.20 6.32 8.10 5.42 10.41 39.61 37.31 21.49
6.60 10.17 14.03 12.95 4.54 4.54 2.16 3.59 11.65 8.84 9.11
5.39 3.29 2.10 1.51 1.09 3.79 3.71 2.64 5.66 3.86 2.04
1.78 0.71 0.70 0.89 1.03 1.64 2.12 0.87 2.34 1.00 0.60
1.25 1.01 0.08 0.40 0.02 0.31 0.12 0.13 1.57 0.60 0.23
0.55 0.39 0.05 0.22 0.14 0.18 0.08 0.06 0.76 0.27 0.19 Fig. 7
Energy absorption to complete failure
The energy absorption to complete failure was greatest in the Al and A.2 annular pulleys, at 1.25 and 1.01 joules respectively. This confirms the importance of these pulleys in maintaining the tendon close to the phalanges and joints while resisting substantial loads of pinch and grasp. The A4 pulley absorbed 0.4 joules to failure, about a third of the energy absorption of the Al and A2 pulleys. The other pulleys had much lower values (Table 3). Importantly, the belt-loop pulleys had significant energy absorption prior to failure, the Vl pulley having a greater amount of energy absorption than did the annular pulleys (A 1, Al) before failure. Discussion
The fibro-osseous tendon sheath is essential to normal function of the human flexor tendon. Without a competent pulley system, bow-stringing of the tendon will occur with poor transfer of the forces required for pinch and grasp. From the biomechanical point of view, the pulley system provides the constraint of tendons as they cross the joint. The intact and any reconstructed pulley should be strong, as indicated by the maximum breaking load and the strength, to resist the interactive force from the tendon. In addition, the compliance and stiffness of the pulley system to the stretchability under load of the pulley are important to the function of the pulley. The amount of displacement or stretch of the pulley under load to prevent bow-stringing will influence the degree of constraint and bow-stringing of the tendon when crossing the joint. Manske and Lesker (1977) measured the length, breaking force, and tensile strength of the annular VOL. 15B No. 4 NOVEMBER
1990
Different loading conditions on the pulley system: A) The loading device is too straight, with one-point contact. B) Proper fit of the loading device. C) Too much curve of the loading device, with stress concentration at both edges. D) Loading with soft tissue also caused two-point contact.
pulleys. They concluded that the first and fourth annular pulleys were the strongest, while the second annular pulley was the weakest. Our results differ from theirs. The maximum breaking strength of all the pulleys in our study ranged from 6.3 to 31.7 Newtons/mm and was similar to that found by Manske and Lesker. The maximum breaking load in our experiment, however, was highest for the A2 pulley (409 Newtons), while the Al pulley (324 Newtons) was one-fourth as strong, and the A4 pulley (209 Newtons) was half as strong as the A2 pulley. In addition, the maximum breaking load recorded in our study was 668.3 Newtons for the middle finger A2 pulley, while Manske showed a breaking load range up to 808 Newtons for the same finger but for the A 1 pulley. One of the important elements of this study was the design of the special pulley testing device. Ideally, a test of breaking strength of the pulley system should result in rupture of the entire pulley structure at one time. Our results may differ from earlier studies because our tendon loading device provides better conformity to the soft tissues. This avoids stress concentration which would result from a non-uniform force applied to the pulley. We tested the tendon loop technique used by Manske and Lesker and found results similar to those reported by those authors, but it appeared that the stress was concentrated at both edges rather than distributed uniformily along the pulley (Fig. 7). As one might anticipate, pulleys attached to bone had greater breaking strength than pulleys attached to the volar plates. The osseous annular pulleys were stiffer (less elastic) and, in general, absorbed more energy than did volar plate pulleys prior to failure. The tensile strength of annular pulleys per unit length was quite similar. The 433
G.-T. LIN, W. P. COONEY,
annular pulleys were uniformly stronger than the cruciate pulleys, as one would expect; within themselves, however, no part of an annular pulley was stronger than any one part of another pulley. The length and width of a pulley along with its bone or soft tissue attachment appears to be the main determinant of its strength (Landsmeer, 1976). Because the diameter of the A4 pulley is less than that of the A2 pulley, its relative elongation per unit of displacement is greater than that of the A2 pulley. These differences in diameter and length make comparison of stiffness between pulleys of different sizes less meaningful: a difference in stiffness may not reflect a true difference in material property but a difference in structural properties. The A2 and A4 pulley were more stiff than the other pulleys and deformed little with applied loads until failure. The volar plate pulleys were more compliant, which reflects their change in position with finger flexion. In pulley reconstruction, the location of the pulley as well as its length and thickness will have an effect on the final tension. The length of 5 mm., recommended by Doyle for the A2 pulley, may not be enough to approximate normal pulley mechanical function. In this study, the A3, A5, and cruciate pulleys were weaker than those of the diaphyseal annular pulleys. Reconstruction of pulleys to bone should be mechanically stronger than reconstruction to soft tissue and such a reconstruction is recommended. Our experiment demonstrated that the pulley belt loop technique, which involves making a new pulley out of part of the volar plate, is also quite strong and should be considered in staged flexor tendon reconstruction (Table 1). The breaking strengths are nearly equal to those of normal annular pulleys. We conclude that the annular pulleys which attach to bone (the A2 and A4 pulleys) are mechanically the
434
P. C. AMADIO AND K.-N. AN
strongest. They are less compliant than the Al, A3, and A5 (volar plate pulleys) and deform the least. The volar plate pulleys, which change their position during flexion, are more compliant and, except for the Al pulley, have a maximal breaking strength considerably less than the bony pulleys. When pulley reconstruction is to be performed, the mechanical characteristics (strength, stiffness, and deformity) need to be considered to duplicate their natural counterparts. Acknowledgement This study was supported by grant number AR 17172 from the National Institute of Health.
References DOYLE, J. R. and BLYTHE, W. The finger flexor tendon sheath and pulleys: anatomy and reconstruction. American Academy of Orthopaedic Surgeons Symposium on Tendon Surgery in the Hand. St. Louis, C. V. Mosby, 1985: 8187. KAREV, A., STAHL, S. and TARAN, A. (1987). The mechanical efficiency of the pulley system in normal digits compared with a reconstructed system using the “belt loop” technique. Journal of Hand Surgery, 12A: 4: 596-601. LANDSMEER, J. M. F. Atlas of Anatomy of the Hand. Edinburgh, Churchill Livingstone, 1976: 179-226. LIN, G. T., AMADIO, P. C., AN, K. N. and COONEY, W. P. (1989a). Functional Anatomy of the Human Digital Flexor Pulley System. Journal of Hand Surgery, American Volume: in press. LIN, G. T., AMADIO, P. C., AN, K. N., COONEY, W. P. and CHAO, E. Y. S. (1989b). Biomechanical Analysis of Finger Flexor Pulley Reconstruction. Journal of Hand Surgery, 14-B : 3 : 278-283. MANSKE, P. R. and LESKER, P. A. (1977). Strength of human pulleys. The Hand, 9: 2: 147-152. MANSKE, P. R. and LESKER, P. A. (1983). Palmar aponeurosis pulley. Journal of Hand Surgery, 8: 3: 259-263.
Accepted: 18 July 1989 William P. Cooney, III, M.D., 55905, U.S.A. 0
1990 The British
Society
Biomechanics
for Surgery
Laboratory,
Mayo
Clinic,
Rochester,
Minnesota
of the Hand
0266-7681/90/~15W29/$10.00
THE JOURNAL
OF HAND SURGERY
PROPERTIES
G.-T. LIN, W. P. COONEY,
OF HUMAN P. C. AMADIO
PULLEYS
and K.-N. AN
From the Biomechanics Laboratory, Department of Orthopedics, Mayo Clinic and Foundation, U.S.A.
In order to determine the mechanical properties of the fibro-osseous pulleys in the hand, the diaphyseal annular pulleys, the volar plate annular pulleys and the cruciate or condensable portions were tested. A custom-made loading device provided proper fit of the soft tissues for a uniform distribution of the pulley load during testing. The A2 pulley was found to be the strongest of the pulleys; the Al and A4 were the next strongest. The A3 pulley was nearly equal in mean breaking strength to the other annular pulleys, but in absolute breaking load was considerably weaker because of its shortness. The A4 was the least compliant of the pulleys. We concluded that the fibro-osseous A2 and A4 were mechanically stronger and stiffer pulleys than the Al, A3, A5 (volar plate) pulleys. In testing one type of pulley reconstruction, we found that the “belt loop” technique of Karev nearly matched the annular pulleys in strength and energy absorption. Journal of Hand Surgery (British Volume, 1990) 15B: 429-434
Doyle and Blythe (1975) defined four annular and three cruciate pulleys in the flexor tendon sheath of human digits and determined the optimum placement of the pulleys for effective flexor function. The critical pulleys were the second annular (A2) and the fourth annular (A4) at the mid-portion of the proximal and middle phalanges. Manske and ILesker (1977, 1983) concluded that the Al and A4 pulleys were the strongest and that the A2 was the weakest. It is our impression that the A2 is the longest and strongest of the annular pulleys. This pulley must resist the force of not one but two flexor tendons during pinch and grasp (Fig. 1). Two annular pulleys (A2, A4) are true fibro-osseous pulleys attached to bone over the proximal and middle phalanges, while the other annular pulleys attach to the volar plate and may be considered as joint pulleys rather than fibro-osseous pulleys. The purpose of this study is to define the mechanical properties of the annular pulleys (Al-A5) and the condensable (cruciate) pulleys (Cl-C3). One type of pulley reconstruction, the “belt loop” pulley (Karev, et al., 1987) was tested to determine if it had significant mechanical characteristics to be of value for pulley function. Several important parameters have been derived from the mechanical test which should be useful for establishing (criteria for reconstruction of the pulley system. Material and methods Five fresh cadaveric hands obtained within 24 hours of death were frozen and preserved at -30°C until ready for dissection. The finger rays were disarticulated at the carpo-metacarpal joint. The flexor sheath of each finger was carefully dissected from surrounding soft tissue but left attached to bone. The flexor tendons were divided at their insertions by an incision through the tendon sheath distal to the A5 pulley and between the A4 and C2 pulleys VOL. 15B No. 4 NO\‘EMBER 1990
Fig. 1 Anatomy of human pulleys: fibro-osseous annular pulleys (A2, A4), volar plate annular pulleys (Al, A3, A5), cruciate or condensable pulleys (Cl, C2, and C3).
for flexor profundus and superficialis respectively, then pulled out from the tendon sheath proximally. The five annular pulleys and the condensable portions of the tendon sheath (which include the cruciate pulleys) were tested by inserting a rigid tendon hook into the pulley canal (Fig. 2). With the tendon hook placed beneath the annular pulley, the fingers were firmly held in place and prevented from sliding by a set of wedged pins (Fig. 2). A distraction force was applied directly by an Instron materials testing machine (Instron Corporation, Canton, MA) until the pulley ruptured. The deformation of the test apparatus, including fixation and tendon hook, under the load range tested was found to be much less than the deformation of the pulley system. The displacement of the cross head was then recorded as the deformation of the pulley along with the tension as measured by load transducer on the machine. The Instron Series IX automated materials testing system was integrated with a VAXmate computer (Digital Equipment Corporation, Marlboro, MA) to operate the testing machine and collect the data. 429
G.-T. LIN,
W. P. COONEY,
P. C. AMADIO
AND
K.-N.
AN
In addition to the tests of the annular pulley and condensable portions of the tendon sheath, the volar plate pulley reconstruction which creates a new pulley from the fibrous central portion of the volar plate (Karev, 1987; Lin et al., 1989b) was also tested under identical conditions to the testing of normal pulleys. Before each test, the length of the pulley attachment on bone along the line of the tendon hook was measured by a digital caliper for data normalisation. The maximum breaking strength (Newtons/mm.) of the pulley system was only determined as a function of pulley length. From the results of the load-deformation curve (Fig. 3), the maximum breaking load (in Newtons), maximum breaking strength (Newtons/mm. measured by dividing the maximum load by the pulley length), the stiffness (Newtons/mm. : calculated by measuring the slope of the load-deformation curve) and the deformation at maximum breaking load (mm of displacement at maximum load) were derived. The energy absorption to complete failure (joules) was also documented by the area under the load-deformation curve. Results Fig. 2
The set-up for mechanical testing of the pulley system. Metal rods of different diameter and curvature were used to fit different pulleys for more uniform stress distribution during testing.
I
I
I
I
I
I
I
I
I
Load-deformation curves (Fig. 3) demonstrated that the diaphyseal annular pulleys, A2 and A4, are relatively stiffer or less deformable and have a higher breaking
I
A2 :IMUM
BREAKING
ENERGY
LOAD
(N
ABSORPTION TO
FAILURE
( Joules
Al
I.
I
Dicplocement Fig. 3 Typical force-displacement 430
Cmm)
curves for Al-A5 pulleys. THE JOURNAL
OF HAND
SURGERY
MECHANICAL
PROPERTIES
2.5
OF HUMAN
7.5
5.0
Dioplacoment
Fig. 4
Typical force-displacement
PULLEYS
10.0
(mm)
curves for Cl-C3 pulley and volar plate “belt loop” pulley, Vl-V3.
strength than the Al, A3, and A5 pulleys. The loaddeformation curve at the Al pulley showed several small peaks associated with the early failure of fibres connected to the volar plate at the base of the M.P. joint (Fig. 3). The reconstructed belt loop pulleys (Vl-V3) and condensable portion which included cruciate pulleys (ClC3) had similar characteristics (Fig. 4).
the cruciate pulleys had much less strength, with a range of 5.4 to 10.4 Newtons/mm. The volar plate reconstructed pulleys, with a mean breaking strength of 21.5 to 39.6 Newtons/mm., were as strong as the annular pulleys. StifSness The stiffness measurements of the pulley system are summarised in Table 2 and Figure 6. The A4 pulley was
Maximum breaking load The results of average maximum breaking load of each pulley for each finger are shown in Table 1 and graphically represented in Figure 5 as a mean for all of the digits. The A2 pulley had the greatest breaking load, 407.49 Newtons, followed by the Al and A4 pulleys with 324.28 and 209.57 Newtons, respectively. The breaking load of the A3, A5, and cruciate pulleys was quite low (less than 100 Newtons). The reconstructed belt loop pulleys (Vl and V2) had breaking loads comparable to those of normal pulleys.
1
Maximum breaking strength The breaking strengths (Newtons/mm.) of the different annular pulleys were similar (Table 3) and ranged from 22.2 to 34.2 Newtons/mm. The condensable portion of VOL.
15B No. 4 NOVEMBER
1990
PULLEYS Fig. 5 Maximum breaking load of the pulley.
431
G.-T. LIN,
Table l-Maximum
Table Z-Stiifness
Middle
AND
K.-N.
AN
Ring
Little
Total
Mean
S.D.
Mean
S.D.
Mean
S.D.
Mean
S.D.
Mean
S.D.
336.23 431.86 52.47 202.22 38.48 60.07 41.43 43.23 323.59 217.07 70.60
13.76 83.98 20.74 46.33 24.06 10.64 17.19 12.36 75.42 26.85 40.51
402.00 465.67 50.77 210.48 50.87 105.69 40.32 63.90 244.91 183.23 101.82
53.08 202.67 22.01 121.95 45.36 85.04 6.59 18.41 112.37 31.65 21.25
315.24 431.64 52.20 272.83 29.59 69.71 45.51 41.95 303.09 194.71 68.49
36.43 97.82 17.93 92.69 12.16 15.61 11.93 11.26 67.36 71.89 25.83
243.66 305.69 30.74 172.41 31.51 79.94 31.77 45.11 215.87 119.56 78.54
52.37 44.67 15.47 82.12 24.61 18.40 25.56 12.18 68.13 43.83 42.19
324.28 407.49 47.80 209.57 32.89 81.34 39.86 50.05 269.14 176.76 90.62
75.21 126.85 20.47 85.13 29.72 43.51 16.08 14.84 85.54 54.41 42.40
(Newtons/millimetre)*
Index
Al A2 A3 A4 A5 Cl c2 c3 Vl v2 v3
P. C. AMADIO
breaking load (Newtons)
Index
Al A2 A3 A4 A5 Cl c2 c3 Vl v2 v3
W. P. COONEY,
Middle
Ring
Total
Little
Mean
S.D.
Mean
S.D.
Mean
S.D.
Mean
S.D.
Mean
S.D.
82.48 129.59 32.72 129.39 33.35 26.49 15.01 27.51 7i.49 60.31 55.42
27.96 40.81 3.60 12.81 16.18 10.56 9.64 14.22 11.52 10.00 22.13
79.95 161.78 17.45 176.25 27.71 33.91 10.05 31.59 52.51 42.45 44.57
13.60 52.19 6.37 45.27 19.76 21.55 5.17 7.76 18.39 5.61 10.67
81.07 129.87 21.16 142.97 20.23 30.61 10.44 23.05 68.87 53.88 39.50
25.08 40.87 4.10 84.44 8.82 6.91 3.18 5.57 7.09 10.36 9.14
57.82 117.81 15.75 203.48 20.70 31.84 17.10 34.13 63.50 47.07 63.53
8.69 28.21 5.01 109.02 12.89 13.85 14.21 11.74 29.23 9.33 18.17
74.82 135.34 22.00 167.99 22.71 30.71 13.58 21.94 66.33 50.93 50.75
22.72 38.04 8.07 63.20 14.46 13.05 7.74 11.02 14.93 10.54 17.05
* Newtonsper millimetreof displacementas measuredby the slope of the load/deformationcurve.
220
annular pulleys. The results indicated that the Al, A2, and A4 pulleys remained relatively unchanged in their location during tendon loading and joint flexion. In contrast, the location and constraint of A3, A5, and the cruciate pulleys were readily changed during loading and joint flexion. The stiffness of belt-loop reconstructed pulleys (Vl-V3) was found to be less than the osseous annular pulleys but more than the cruciate and volar plate annular pulleys.
1 7.99
Deformation at maximum load
A3
A4
A6
Cl
c2
c3
“1
VT2
“3
PULLEYS Fig. 6
Stiffness of the pulley.
the stiffest, followed by the A2 and Al pulleys. The volar plate annular pulleys (A3 and A5) and the cruciate pulleys (Cl, C2, C3) were relatively less stiff than the osseous 432
Deformation at maximum load is shown in Table 3. Deformation of the annular pulleys ranged from 5.39 mm for Al to 1.09 mm for A5 and appeared directly related to pulley length and maximum load. Deformation of cruciate and belt loop pulleys was similar and neither was significantly different from the annular pulleys. Deformation does not appear to be an important parameter of normal pulley performance and suggests that pulleys will fail before significant change in shape would produce clinically significant bow-stringing. THE JOURNAL
OF HAND
SURGERY
MECHANICAL Table 3-Maximum
PROPERTIES
OF HUMAN
PULLEYS
breaking strength, deformation and energy absorp-
tiOll
Maximum Breaking Strength (Nimm.l
Al A2 A3 A4 A5 Cl c2 c3 VI v2 v3
Deformation at Maximum Load (mm.)
Energy Absorption to Total Failure -(J)
Mean
S.D.
Mean
S.D.
Mean
S.D.
31.71 21.11 22.20 34.20 6.32 8.10 5.42 10.41 39.61 37.31 21.49
6.60 10.17 14.03 12.95 4.54 4.54 2.16 3.59 11.65 8.84 9.11
5.39 3.29 2.10 1.51 1.09 3.79 3.71 2.64 5.66 3.86 2.04
1.78 0.71 0.70 0.89 1.03 1.64 2.12 0.87 2.34 1.00 0.60
1.25 1.01 0.08 0.40 0.02 0.31 0.12 0.13 1.57 0.60 0.23
0.55 0.39 0.05 0.22 0.14 0.18 0.08 0.06 0.76 0.27 0.19 Fig. 7
Energy absorption to complete failure
The energy absorption to complete failure was greatest in the Al and A.2 annular pulleys, at 1.25 and 1.01 joules respectively. This confirms the importance of these pulleys in maintaining the tendon close to the phalanges and joints while resisting substantial loads of pinch and grasp. The A4 pulley absorbed 0.4 joules to failure, about a third of the energy absorption of the Al and A2 pulleys. The other pulleys had much lower values (Table 3). Importantly, the belt-loop pulleys had significant energy absorption prior to failure, the Vl pulley having a greater amount of energy absorption than did the annular pulleys (A 1, Al) before failure. Discussion
The fibro-osseous tendon sheath is essential to normal function of the human flexor tendon. Without a competent pulley system, bow-stringing of the tendon will occur with poor transfer of the forces required for pinch and grasp. From the biomechanical point of view, the pulley system provides the constraint of tendons as they cross the joint. The intact and any reconstructed pulley should be strong, as indicated by the maximum breaking load and the strength, to resist the interactive force from the tendon. In addition, the compliance and stiffness of the pulley system to the stretchability under load of the pulley are important to the function of the pulley. The amount of displacement or stretch of the pulley under load to prevent bow-stringing will influence the degree of constraint and bow-stringing of the tendon when crossing the joint. Manske and Lesker (1977) measured the length, breaking force, and tensile strength of the annular VOL. 15B No. 4 NOVEMBER
1990
Different loading conditions on the pulley system: A) The loading device is too straight, with one-point contact. B) Proper fit of the loading device. C) Too much curve of the loading device, with stress concentration at both edges. D) Loading with soft tissue also caused two-point contact.
pulleys. They concluded that the first and fourth annular pulleys were the strongest, while the second annular pulley was the weakest. Our results differ from theirs. The maximum breaking strength of all the pulleys in our study ranged from 6.3 to 31.7 Newtons/mm and was similar to that found by Manske and Lesker. The maximum breaking load in our experiment, however, was highest for the A2 pulley (409 Newtons), while the Al pulley (324 Newtons) was one-fourth as strong, and the A4 pulley (209 Newtons) was half as strong as the A2 pulley. In addition, the maximum breaking load recorded in our study was 668.3 Newtons for the middle finger A2 pulley, while Manske showed a breaking load range up to 808 Newtons for the same finger but for the A 1 pulley. One of the important elements of this study was the design of the special pulley testing device. Ideally, a test of breaking strength of the pulley system should result in rupture of the entire pulley structure at one time. Our results may differ from earlier studies because our tendon loading device provides better conformity to the soft tissues. This avoids stress concentration which would result from a non-uniform force applied to the pulley. We tested the tendon loop technique used by Manske and Lesker and found results similar to those reported by those authors, but it appeared that the stress was concentrated at both edges rather than distributed uniformily along the pulley (Fig. 7). As one might anticipate, pulleys attached to bone had greater breaking strength than pulleys attached to the volar plates. The osseous annular pulleys were stiffer (less elastic) and, in general, absorbed more energy than did volar plate pulleys prior to failure. The tensile strength of annular pulleys per unit length was quite similar. The 433
G.-T. LIN, W. P. COONEY,
annular pulleys were uniformly stronger than the cruciate pulleys, as one would expect; within themselves, however, no part of an annular pulley was stronger than any one part of another pulley. The length and width of a pulley along with its bone or soft tissue attachment appears to be the main determinant of its strength (Landsmeer, 1976). Because the diameter of the A4 pulley is less than that of the A2 pulley, its relative elongation per unit of displacement is greater than that of the A2 pulley. These differences in diameter and length make comparison of stiffness between pulleys of different sizes less meaningful: a difference in stiffness may not reflect a true difference in material property but a difference in structural properties. The A2 and A4 pulley were more stiff than the other pulleys and deformed little with applied loads until failure. The volar plate pulleys were more compliant, which reflects their change in position with finger flexion. In pulley reconstruction, the location of the pulley as well as its length and thickness will have an effect on the final tension. The length of 5 mm., recommended by Doyle for the A2 pulley, may not be enough to approximate normal pulley mechanical function. In this study, the A3, A5, and cruciate pulleys were weaker than those of the diaphyseal annular pulleys. Reconstruction of pulleys to bone should be mechanically stronger than reconstruction to soft tissue and such a reconstruction is recommended. Our experiment demonstrated that the pulley belt loop technique, which involves making a new pulley out of part of the volar plate, is also quite strong and should be considered in staged flexor tendon reconstruction (Table 1). The breaking strengths are nearly equal to those of normal annular pulleys. We conclude that the annular pulleys which attach to bone (the A2 and A4 pulleys) are mechanically the
434
P. C. AMADIO AND K.-N. AN
strongest. They are less compliant than the Al, A3, and A5 (volar plate pulleys) and deform the least. The volar plate pulleys, which change their position during flexion, are more compliant and, except for the Al pulley, have a maximal breaking strength considerably less than the bony pulleys. When pulley reconstruction is to be performed, the mechanical characteristics (strength, stiffness, and deformity) need to be considered to duplicate their natural counterparts. Acknowledgement This study was supported by grant number AR 17172 from the National Institute of Health.
References DOYLE, J. R. and BLYTHE, W. The finger flexor tendon sheath and pulleys: anatomy and reconstruction. American Academy of Orthopaedic Surgeons Symposium on Tendon Surgery in the Hand. St. Louis, C. V. Mosby, 1985: 8187. KAREV, A., STAHL, S. and TARAN, A. (1987). The mechanical efficiency of the pulley system in normal digits compared with a reconstructed system using the “belt loop” technique. Journal of Hand Surgery, 12A: 4: 596-601. LANDSMEER, J. M. F. Atlas of Anatomy of the Hand. Edinburgh, Churchill Livingstone, 1976: 179-226. LIN, G. T., AMADIO, P. C., AN, K. N. and COONEY, W. P. (1989a). Functional Anatomy of the Human Digital Flexor Pulley System. Journal of Hand Surgery, American Volume: in press. LIN, G. T., AMADIO, P. C., AN, K. N., COONEY, W. P. and CHAO, E. Y. S. (1989b). Biomechanical Analysis of Finger Flexor Pulley Reconstruction. Journal of Hand Surgery, 14-B : 3 : 278-283. MANSKE, P. R. and LESKER, P. A. (1977). Strength of human pulleys. The Hand, 9: 2: 147-152. MANSKE, P. R. and LESKER, P. A. (1983). Palmar aponeurosis pulley. Journal of Hand Surgery, 8: 3: 259-263.
Accepted: 18 July 1989 William P. Cooney, III, M.D., 55905, U.S.A. 0
1990 The British
Society
Biomechanics
for Surgery
Laboratory,
Mayo
Clinic,
Rochester,
Minnesota
of the Hand
0266-7681/90/~15W29/$10.00
THE JOURNAL
OF HAND SURGERY
