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Moment arms of the digital flexor tendons at the wrist: Role of differential loading in stability of carpal tunnel tendons
Moment Arms of the Digital Flexor Tendons at the Wrist: Role of Differential Loading in Stability of Carpal Tunnel Tendons John M. Agee, MD, Timothy R. Maher, MS, Matthew S. Thompson, BS, Sacramento, CA When a flexor digitorum superficialis tendon crossing a flexed or extended wrist has a load applied to it in excess of that applied to adjacent tendons, that tendon may translate across the carpal tunnel. In 6 cadaver specimens, each of the 9 carpal tunnel tendons was loaded with a baseline tension of 85 g and the moment arms of the flexor pollicis Iongus and the 4 flexor digitorum superficialis tendons were determined. Applying a higher 540-g load to individual flexor digitorum superficialis tendons and the flexor pollicis Iongus while loading the remaining tendons with the baseline 85-g tension significantly changed the moment arms from those measured under baseline load. The results demonstrated that tendons with applied differential loads in the carpal tunnel shift their positions, as revealed by their changing moment arms. (J Hand Surg 1998;23A:998-1003. Copyright 9 1998 by the American Society for Surgery of the Hand.)
The hand undergoes m a n y complex m o v e m e n t s in activities that range from playing the piano to unscrewing the lid from a jar. Numerous muscles are used to produce these movements, including the extrinsic flexor muscles. The 9 digital extrinsic flexor muscle tendons cross the wrist through the carpal tunnel. As they cross the wrist, each digital flexor tendon has a m o m e n t arm for the plane of motion of the wrist. The m o m e n t arm is defined as the distance from the axis of joint rotation to the tendon (Fig. 1). When a muscle-tendon unit is tensioned, a rotational force is generated that is the product of the m o m e n t arm and the tensional force of the tendon. Discrete pulleys, like the 6 wrist extensor compartments, conFrom the Hand BiomechanicsLab, Inc, Sacramento, CA. Received for publication June 25, 1996; accepted in revised form June 9, 1998. The author or one or more of the authors have received or will receive benefits for personal or professional use from a commerical party related directly or indirectly to the subject of this article. Reprint requests: John M. Agee, MD, Hand BiomechanicsLab, Inc, 77 Scripps Dr, Suite 104, Sacramento, CA 95825. Copyright 9 1998 by the AmericanSociety for Surgery of the Hand 0363-5023/98/23A06-002053.00/0 998
The Journal of Hand Surgery
trol the tendon m o m e n t arms at all joints except the carpal tunnel at the wrist. 1 Kang et al 2 suggested that the transverse carpal ligament serves as a pulley to resist palmar tendon displacement. Dorsally, a bony arch defines the wall of the carpal tunnel. Despite these constraints on tendon position in the wrist, considerable space remains within the carpal tunnel in which the tendons can translate. To date, there have been no reports of the presence or absence of tendon translation that occurs perpendicular to longitudinal tendon excursion within the carpal tunnel. During complex hand use patterns, the extrinsic flexor tendons m a y be loaded differentially, ie, some tendons m a y experience higher loads while others exhibit lower tension. When applied to tendons that change direction as they cross the wrist, differential loading could cause those tendons to shift their positions. I f a tendon shifts palmar-dorsal position relative to adjacent tendons in the carpal tunnel, the m o m e n t arm of that tendon at the wrist will also change. By calculating the m o m e n t arms of the tendons, it is possible to determine whether the palmar-
The Journal of Hand Surgery / Vol. 23A No. 6 November 1998 999
Loading Conditions
Figure 1. A simplified cross-section of the wrist. The dashed horizontal line is the axis of rotation of flexionextension of the wrist. Also represented are a carpal tunnel tendon (long thin arrow) and the corresponding moment arm (thick double arrow).
dorsal position of the tendon within the carpal tunnel has changed. The objective of the present study was to demonstrate whether either the flexor digitorum superficialis or flexor pollicis longus (FPL) tendons in the carpal tunnel shift in position as a function of differential loading.
Materials and Methods Specimens
Six fresh-frozen above-elbow cadaver specimens were instrumented to determine the excursions of the carpal tunnel tendons as they cross the wrist. Specimens were thawed and examined, and radiographs of the anteroposterior, lateral, oblique, and carpal tunnel views were taken to assure normalcy. Each specimen was refrozen with the elbow in midflexion and the wrist in a neutral position with the fingers in midflexion. The forearm was transected 5.5 to 10.0 cm proximal to the wrist flexion crease. Threaded bolts were placed in the intramedullary canals of the radius and ulna for mounting into a tendon-angular joint tracking device designed to measure the excursions of the carpal tunnel tendons. Braided stainless steel wires, 0.3 mm in diameter, were sutured to the extensor carpi radialis longus, extensor carpi radialis brevis, abductor pollicis longus, extensor carpi ulnaris, flexor carpi radialis, and flexor carpi ulnaris tendons and weighted with 454 g each to pull the carpus into a stable position. Additional wires were sutured to each of the 9 carpal tunnel tendons proximal to the carpal tunnel.
Excursion data were collected from each specimen with the fingers splinted in midflexion. Fingers were taped to plastic forms to assure reproducible finger positions and to ensure that the excursions measured were not affected by concomitant digital motion. Six different loading conditions were used. First, a baseline loading of 85 g was placed on each of the 9 carpal tunnel tendons. The 5 remaining conditions were differential loading conditions. A differentially loaded tendon was tensioned with a 540-g weight, while the remaining tendons remained tensioned with 85-g weights. Differentially loaded tendons included the FPL, the index flexor digitorum superficialis (FDS2), the long flexor digitorum superficialis (FDS3), the ring flexor digitorum superficialis (FDS4), and the little flexor digitorum superficialis (FDS5). The baseline loading of 85 g was chosen as the minimum load that stabilized the tendons. The greater 540-g differential load was chosen to simulate tension in a tendon as experienced during light hand u s e . 3'4 Measurement of Tendon Excursion
The following procedure was used to measure the excursions of carpal tunnel tendons under symmetric baseline and differential loading conditions. Individual specimens were mounted into a tendon-loading/ excursion device specifically designed for this study (Fig. 2). Each braided stainless steel wire, attached distally to a tendon, extended proximally through a guide plate, around a 12.7-mm diameter pulley, and attached to a calibrated weight. Each pulley was coupled to an optical encoder (HP HEDS-5500 C03; Hewlett-Packard Co, Palo Alto, CA). The output of each optical encoder was processed through a counter chip (HP HCTL-2020; Hewlett-Packard Co) that supplied an angular resolution of 0.9 ~. The calculated excursion resolution was 0.102 ram. Data from the counter chips were sampled by an Apple Power PC computer using a data acquisition card and LabView software (National Instruments, Austin, TX). Tendon excursion was calculated from the geometry and angular position of the pulley using the following equation: E=
r07r 180'
1000 Agee, Maher, and Thompson / Stability of Carpal Tunnel Tendons
Figure 2. A tendon-loading/excursion device.
where E is tendon.excursion (cm), r is the radius of the pulley and wire (cm), 7r is in radians, and 0 is the angular change of the pulley in degrees. The guide plate was fabricated with polytetrafluoroethylene-lined (Teflon; DuPont, Wilmington, DE) holes in a pattern such that the tension was applied to the tendons in an anatomically correct direction of pull for measurement of tendon excursion. As the wrist was manually moved from full flexion to full extension, excursion data were collected as a function of wrist angle. Time data were not collected.
perfect end point-fit boundary condition. 5 The equations used are shown below. 5 1 Xi(u ) = ~(l
1 -- u ) 3 X i _ l -[- ~ ( 3 u 3 1
Wrist angular joint motion was tracked by linking an additional optical encoder (HP HEDS-5500 C03) to the index finger metacarpal using a double-jointed linkage that avoided imposition of mechanical constraint on the wrist joint. Error of the wrist angle optical encoder was 0.9 ~ which was the resolution of the optical encoder. Cubic B-Spline Data Smoothing To minimize digital noise inherent in using optical encoders, data were fit with a cubic B-spline using a
1
+ ~ ( - 3 u 3 + 3u2 + 3u + 1)Xi+j + ~u3Xi+2 1
1
Yi(u) = ~(1 - u)3yi 1 -~- ~ ( 3u3 -- 6u2 + 4)Yi 1
Measurement of Wrist Angulation
6u2 + 4 ) X i
3
+~(--3u + 3 u 2 + 3 u +
1 3
1)Yi+~+~uYi+2
where X i is the ith wrist angle data point (~ Yi is the ith excursion data point (cm), and u is a varied parameter.
Moment Arm Calculation Instantaneous moment arm was calculated from excursion data using the following equation.l MA-
dE dO
The Journal of Hand Surgery / Vol. 23A No. 6 November 1998
1.6 T 1.44
1.2+ > 4 I
1.6 ]-
Loaded ~ 72~
~
1
~ -
Loaded
1001
.__ !
X
r
....B elin
Baseline 1
0.8 Flexion
~ Z
Extension
~
,
.
-
t
......
Flexion
I
~ Z
-+-
I
Extension
Wrist Angle [degrees]
Wrist Angle [degrees] Figure 3. The FPL baseline and loaded moment arms. Data are averaged across all cadavers. Error bars indicate variability among cadavers.
Figure 4. The FDS2 baseline and loaded moment arms. Data are averaged across all cadavers. Error bars indicate variability among cadavers.
where MA is the instantaneous moment arm (cm), dE is the change in excursion (cm), and dO is the change in wrist angle (radians). The derivative of excursion with respect to wrist angle (moment arm) was determined analytically using the derivative of the cubic B-spline fit of the data.
wrist neutral. All minimum differences in moment arms occurred at 40 ~ extension from wrist neutral.
Statistical M e t h o d The moment arm of the differentially loaded tendon was evaluated using a 3-factor repeated measures ANOVA. The 3 factors used in the analysis were load, tendon, and wrist angle. The load factor had 2 levels: 85 g and 540 g. Levels for the tendon factor were FPL, FDS2, FDS3, FDS4, and FDS5. For the wrist angle factor, the 9 levels were data points taken at 10 ~ increments in an 80 ~ window centered about wrist neutral. Wrist neutral is defined as the midpoint between full flexion, the first wrist angle measured, and full extension, which was the last wrist angle measured.
Discussion The purpose of this study was to determine whether the moment arms of the FPL and each of the 4 FDS tendons change at the level o f the carpal tunnel as the wrist is passively extended from a flexed position with a differential load applied. The results confirmed that a differential load does change the moment arms, and therefore palmar-dorsal positions, of the FPL and each of the 4 FDS tendons. The increase in moment arm when an increased load was applied to the tendon indicates that the compliant synovial tissue that envelops the flexor tendons is
1.6 -i-
Loaded
I
Results A differential load of 540 g increased the moment arm from that calculated for 85-g baseline loading (p = .004) (Figs. 3-7). Maximum mean differences between loaded and baseline moment arms ranged from 1.1 _+ 1.3 m m in FDS5 to 2.3 _+ 1.5 m m in FDS3. Minimum mean differences ranged from 0.2 + 0.9 m m in FDS4 to 0.8 -+ 0.7 mm in the FPL. Changes in moment arm due to loading were dependent on angle (p = .046 for the load angle interaction). The maximum increases in moment arms occurred between 20 ~ of flexion from wrist neutral and
o.8
Flexion
......_. ~
Extension
Wrist Angle [degrees] Figure 5. The FDS3 baseline and loaded moment arms. Data are averaged across all cadavers. Error bars indicate variability among cadavers.
1002 Agee, Maher, and Thompson / Stability of Carpal Tunnel Tendons 1.6
Loaded ......... 5
1.4 1.2
Baseline
I
0.8
J --r
~
Flexion
~,
Extension
Wrist Angle [degrees] Figure 6. The FDS4 baseline and loaded moment arms. Data are averaged across all cadavers. Error bars indicate variability among cadavers.
inadequate to define reproducible moment arms. The differentially loaded tendons were loosely constrained within the carpal tunnel and were displaced in the palmar direction during both flexion and extension relative to wrist neutral. Because of the lack of separate pulleys for each tendon, the differentially loaded carpal tunnel tendons were expected to bowstring, resulting in a palmar shift from wrist flexion to wrist neutral and a dorsal shift from wrist neutral to wrist extension. Moment arm analysis revealed a palmar shift through the full arc of wrist flexionextension. At present, understanding of this phenomenon is incomplete. However, tendons loaded with higher tension exhibited moment arms that differed from those produced under baseline loading.
1,6
-
Loaded
Z 1.2
0.8
Baseline
---~-
Flexion
.....
+
-
-
-
~
-
~
-
-
~
Z
...........
-q
Extension
Wrist Angle [degrees] 7. The FDS5 baseline and loaded moment arms. Data are averaged across all cadavers. Error bars indicate variability among cadavers. Figure
Figure 8. A simplified wrist cross-section depicting the theoretical dynamic soft tissue pulley in action. A differentially loaded carpal tunnel tendon (long thin arrow) fixed dorsally by 2 other carpal tunnel tendons (short thick arrows) under tension by synergistic firing of related muscle units.
In anatomic areas other than the carpal tunnel, the biomechanical effect of each tendon is defined by discrete fibro-osseous tunnels that effectively form pulleys. These pulleys dictate the precise offset and location of the tendon as it crosses the joint to generate the rotational forces or moments needed to effect controlled angulation and stability. However, discrete fibro-osseous tunnels are not present in the carpal tunnel to provide this function. In our opinion, some mechanism other than discrete pulleys must exist in vivo that more accurately defines the moment arm for each digital flexor tendon as it passes through the carpal tunnel. Without some mechanism for moment arm control, fine motor control of the digits would be difficult. The tension generated by each muscle would require continual adjustment as a function of the changing moment arms to deliver the required tension, and therefore torque, at each digital joint. We hypothesize that the stability of single or multiple carpal tunnel tendons can be achieved by a synergistic contraction of adjacent muscle tendon units to form dynamic soft tissue pulleys for each tendon. This mechanism would stabilize the moment arm of each digital flexor tendon as it traverses the carpal tunnel, creating a biomechanical effect functionally similar to that obtained by the fibro-osseous tunnels on the extensor side of the wrist. Contraction of the flexor digitomm profundus would provide a mechanical support deep in the carpal tunnel to stabilize differentially loaded FDS tendons (Fig. 8). In a similar manner, tensioned
The Journal of Hand Surgery / Vo]. 23A No. 6 November 1998
FDS tendons would resist palmar translation by a differentially loaded profundus tendon. An understanding of the dynamic nature of the tendons within the carpal tunnel may be clinically relevant. Without the dynamic action described above, the increased tension of a given m u s c l e tendon unit may cause the associated tendon to translate around the lower tensioned tendons until it stabilizes closer to the more rigid wall of the carpal tunnel. These translations might place altered mechanical loads, in the form of shear stress, on the tendons and interposed synovial membranes. Transverse tendon translation has been suggested as a mechanism of injury to the tissues surrounding the carpal tunnel tendons in both normal and carpal tunnel syndrome wrists. 6'7 Frictional forces associated with longitudinal tendon excursion also have been investigated as a possible cause of injury to the contents of the carpal tunnel, s It is unknown whether the translations observed in this study occur in vivo or are sufficient to cause damage to soft tissue. Further study is required to identify tendon translation in vivo and its potential role in the etiology of idiopathic carpal tunnel syndrome. Whether a dynamic soft tissue pulley occurs in vivo remains unknown. This study was limited to quasistatic wrist motion and differential loading of a single FDS or FPL tendon. Determination of the validity of the synergistic contraction theory would require either a more extensive dynamic experiment or differential loading of 2 or more tendons at once. Information about the effect of a differential load on
1003
the flexor digitorum profundus tendons may also provide further insight regarding the synergistic behavior of the tendons within the carpal tunnel. Dynamic experimentation would also provide data that would increase the understanding of changes in moment arm that occur as a function of time. The authorsthankBen Gossand CoraMorganfor theirtechnicaland editorial contributionsto the developmentof this report.
References 1. Brand PW, Hollister A. Clinical mechanics of the hand. 2rid ed. St Louis: Mosby Year Book, 1993:67-378. 2. Kang H-J, Lee S-G, Phillips CS, Mass DP. Biomechanical changes of cadaveric finger flexion: the effect of wrist position and of the transverse carpal ligament and palmar and forearm fasciae. J Hand Surg 1996;21A:963-968. 3. Chao EY, Opgrande JD, Axmear FE. Three-dimensional force analysis of finger joints in selected isometric hand functions. J Biomech 1976;9:387-396. 4. Goldstein SA, Armstrong TJ, Chaffin DB, Matthews LS. Analysis of cumulative strain in tendons and tendon sheaths. J Biomech 1987;20:1-6. 5. Gerald CF, Wheatley PO. Applied numerical analysis. 5th ed. Reading, MA: Addison-Wesley, 1994:244-253. 6. Armstrong TJ, Castelli WA, Evans FG, Diaz-Perez R. Some histological changes in carpal tunnel contents and their biomechanical implications. J Occup Med 1984;26:197200. 7. Schuind F, Ventura M, Pasteels JL. Idiopathic carpal tunnel syndrome: histologic study of flexor tendon synovium. J Hand Surg 1990;15A:497-503. 8. Bay BK, Sharkey NA, Szabo RM. Displacement and strain of the median nerve at the wrist. J Hand Surg 1997;22A: 621-627.
The hand undergoes m a n y complex m o v e m e n t s in activities that range from playing the piano to unscrewing the lid from a jar. Numerous muscles are used to produce these movements, including the extrinsic flexor muscles. The 9 digital extrinsic flexor muscle tendons cross the wrist through the carpal tunnel. As they cross the wrist, each digital flexor tendon has a m o m e n t arm for the plane of motion of the wrist. The m o m e n t arm is defined as the distance from the axis of joint rotation to the tendon (Fig. 1). When a muscle-tendon unit is tensioned, a rotational force is generated that is the product of the m o m e n t arm and the tensional force of the tendon. Discrete pulleys, like the 6 wrist extensor compartments, conFrom the Hand BiomechanicsLab, Inc, Sacramento, CA. Received for publication June 25, 1996; accepted in revised form June 9, 1998. The author or one or more of the authors have received or will receive benefits for personal or professional use from a commerical party related directly or indirectly to the subject of this article. Reprint requests: John M. Agee, MD, Hand BiomechanicsLab, Inc, 77 Scripps Dr, Suite 104, Sacramento, CA 95825. Copyright 9 1998 by the AmericanSociety for Surgery of the Hand 0363-5023/98/23A06-002053.00/0 998
The Journal of Hand Surgery
trol the tendon m o m e n t arms at all joints except the carpal tunnel at the wrist. 1 Kang et al 2 suggested that the transverse carpal ligament serves as a pulley to resist palmar tendon displacement. Dorsally, a bony arch defines the wall of the carpal tunnel. Despite these constraints on tendon position in the wrist, considerable space remains within the carpal tunnel in which the tendons can translate. To date, there have been no reports of the presence or absence of tendon translation that occurs perpendicular to longitudinal tendon excursion within the carpal tunnel. During complex hand use patterns, the extrinsic flexor tendons m a y be loaded differentially, ie, some tendons m a y experience higher loads while others exhibit lower tension. When applied to tendons that change direction as they cross the wrist, differential loading could cause those tendons to shift their positions. I f a tendon shifts palmar-dorsal position relative to adjacent tendons in the carpal tunnel, the m o m e n t arm of that tendon at the wrist will also change. By calculating the m o m e n t arms of the tendons, it is possible to determine whether the palmar-
The Journal of Hand Surgery / Vol. 23A No. 6 November 1998 999
Loading Conditions
Figure 1. A simplified cross-section of the wrist. The dashed horizontal line is the axis of rotation of flexionextension of the wrist. Also represented are a carpal tunnel tendon (long thin arrow) and the corresponding moment arm (thick double arrow).
dorsal position of the tendon within the carpal tunnel has changed. The objective of the present study was to demonstrate whether either the flexor digitorum superficialis or flexor pollicis longus (FPL) tendons in the carpal tunnel shift in position as a function of differential loading.
Materials and Methods Specimens
Six fresh-frozen above-elbow cadaver specimens were instrumented to determine the excursions of the carpal tunnel tendons as they cross the wrist. Specimens were thawed and examined, and radiographs of the anteroposterior, lateral, oblique, and carpal tunnel views were taken to assure normalcy. Each specimen was refrozen with the elbow in midflexion and the wrist in a neutral position with the fingers in midflexion. The forearm was transected 5.5 to 10.0 cm proximal to the wrist flexion crease. Threaded bolts were placed in the intramedullary canals of the radius and ulna for mounting into a tendon-angular joint tracking device designed to measure the excursions of the carpal tunnel tendons. Braided stainless steel wires, 0.3 mm in diameter, were sutured to the extensor carpi radialis longus, extensor carpi radialis brevis, abductor pollicis longus, extensor carpi ulnaris, flexor carpi radialis, and flexor carpi ulnaris tendons and weighted with 454 g each to pull the carpus into a stable position. Additional wires were sutured to each of the 9 carpal tunnel tendons proximal to the carpal tunnel.
Excursion data were collected from each specimen with the fingers splinted in midflexion. Fingers were taped to plastic forms to assure reproducible finger positions and to ensure that the excursions measured were not affected by concomitant digital motion. Six different loading conditions were used. First, a baseline loading of 85 g was placed on each of the 9 carpal tunnel tendons. The 5 remaining conditions were differential loading conditions. A differentially loaded tendon was tensioned with a 540-g weight, while the remaining tendons remained tensioned with 85-g weights. Differentially loaded tendons included the FPL, the index flexor digitorum superficialis (FDS2), the long flexor digitorum superficialis (FDS3), the ring flexor digitorum superficialis (FDS4), and the little flexor digitorum superficialis (FDS5). The baseline loading of 85 g was chosen as the minimum load that stabilized the tendons. The greater 540-g differential load was chosen to simulate tension in a tendon as experienced during light hand u s e . 3'4 Measurement of Tendon Excursion
The following procedure was used to measure the excursions of carpal tunnel tendons under symmetric baseline and differential loading conditions. Individual specimens were mounted into a tendon-loading/ excursion device specifically designed for this study (Fig. 2). Each braided stainless steel wire, attached distally to a tendon, extended proximally through a guide plate, around a 12.7-mm diameter pulley, and attached to a calibrated weight. Each pulley was coupled to an optical encoder (HP HEDS-5500 C03; Hewlett-Packard Co, Palo Alto, CA). The output of each optical encoder was processed through a counter chip (HP HCTL-2020; Hewlett-Packard Co) that supplied an angular resolution of 0.9 ~. The calculated excursion resolution was 0.102 ram. Data from the counter chips were sampled by an Apple Power PC computer using a data acquisition card and LabView software (National Instruments, Austin, TX). Tendon excursion was calculated from the geometry and angular position of the pulley using the following equation: E=
r07r 180'
1000 Agee, Maher, and Thompson / Stability of Carpal Tunnel Tendons
Figure 2. A tendon-loading/excursion device.
where E is tendon.excursion (cm), r is the radius of the pulley and wire (cm), 7r is in radians, and 0 is the angular change of the pulley in degrees. The guide plate was fabricated with polytetrafluoroethylene-lined (Teflon; DuPont, Wilmington, DE) holes in a pattern such that the tension was applied to the tendons in an anatomically correct direction of pull for measurement of tendon excursion. As the wrist was manually moved from full flexion to full extension, excursion data were collected as a function of wrist angle. Time data were not collected.
perfect end point-fit boundary condition. 5 The equations used are shown below. 5 1 Xi(u ) = ~(l
1 -- u ) 3 X i _ l -[- ~ ( 3 u 3 1
Wrist angular joint motion was tracked by linking an additional optical encoder (HP HEDS-5500 C03) to the index finger metacarpal using a double-jointed linkage that avoided imposition of mechanical constraint on the wrist joint. Error of the wrist angle optical encoder was 0.9 ~ which was the resolution of the optical encoder. Cubic B-Spline Data Smoothing To minimize digital noise inherent in using optical encoders, data were fit with a cubic B-spline using a
1
+ ~ ( - 3 u 3 + 3u2 + 3u + 1)Xi+j + ~u3Xi+2 1
1
Yi(u) = ~(1 - u)3yi 1 -~- ~ ( 3u3 -- 6u2 + 4)Yi 1
Measurement of Wrist Angulation
6u2 + 4 ) X i
3
+~(--3u + 3 u 2 + 3 u +
1 3
1)Yi+~+~uYi+2
where X i is the ith wrist angle data point (~ Yi is the ith excursion data point (cm), and u is a varied parameter.
Moment Arm Calculation Instantaneous moment arm was calculated from excursion data using the following equation.l MA-
dE dO
The Journal of Hand Surgery / Vol. 23A No. 6 November 1998
1.6 T 1.44
1.2+ > 4 I
1.6 ]-
Loaded ~ 72~
~
1
~ -
Loaded
1001
.__ !
X
r
....B elin
Baseline 1
0.8 Flexion
~ Z
Extension
~
,
.
-
t
......
Flexion
I
~ Z
-+-
I
Extension
Wrist Angle [degrees]
Wrist Angle [degrees] Figure 3. The FPL baseline and loaded moment arms. Data are averaged across all cadavers. Error bars indicate variability among cadavers.
Figure 4. The FDS2 baseline and loaded moment arms. Data are averaged across all cadavers. Error bars indicate variability among cadavers.
where MA is the instantaneous moment arm (cm), dE is the change in excursion (cm), and dO is the change in wrist angle (radians). The derivative of excursion with respect to wrist angle (moment arm) was determined analytically using the derivative of the cubic B-spline fit of the data.
wrist neutral. All minimum differences in moment arms occurred at 40 ~ extension from wrist neutral.
Statistical M e t h o d The moment arm of the differentially loaded tendon was evaluated using a 3-factor repeated measures ANOVA. The 3 factors used in the analysis were load, tendon, and wrist angle. The load factor had 2 levels: 85 g and 540 g. Levels for the tendon factor were FPL, FDS2, FDS3, FDS4, and FDS5. For the wrist angle factor, the 9 levels were data points taken at 10 ~ increments in an 80 ~ window centered about wrist neutral. Wrist neutral is defined as the midpoint between full flexion, the first wrist angle measured, and full extension, which was the last wrist angle measured.
Discussion The purpose of this study was to determine whether the moment arms of the FPL and each of the 4 FDS tendons change at the level o f the carpal tunnel as the wrist is passively extended from a flexed position with a differential load applied. The results confirmed that a differential load does change the moment arms, and therefore palmar-dorsal positions, of the FPL and each of the 4 FDS tendons. The increase in moment arm when an increased load was applied to the tendon indicates that the compliant synovial tissue that envelops the flexor tendons is
1.6 -i-
Loaded
I
Results A differential load of 540 g increased the moment arm from that calculated for 85-g baseline loading (p = .004) (Figs. 3-7). Maximum mean differences between loaded and baseline moment arms ranged from 1.1 _+ 1.3 m m in FDS5 to 2.3 _+ 1.5 m m in FDS3. Minimum mean differences ranged from 0.2 + 0.9 m m in FDS4 to 0.8 -+ 0.7 mm in the FPL. Changes in moment arm due to loading were dependent on angle (p = .046 for the load angle interaction). The maximum increases in moment arms occurred between 20 ~ of flexion from wrist neutral and
o.8
Flexion
......_. ~
Extension
Wrist Angle [degrees] Figure 5. The FDS3 baseline and loaded moment arms. Data are averaged across all cadavers. Error bars indicate variability among cadavers.
1002 Agee, Maher, and Thompson / Stability of Carpal Tunnel Tendons 1.6
Loaded ......... 5
1.4 1.2
Baseline
I
0.8
J --r
~
Flexion
~,
Extension
Wrist Angle [degrees] Figure 6. The FDS4 baseline and loaded moment arms. Data are averaged across all cadavers. Error bars indicate variability among cadavers.
inadequate to define reproducible moment arms. The differentially loaded tendons were loosely constrained within the carpal tunnel and were displaced in the palmar direction during both flexion and extension relative to wrist neutral. Because of the lack of separate pulleys for each tendon, the differentially loaded carpal tunnel tendons were expected to bowstring, resulting in a palmar shift from wrist flexion to wrist neutral and a dorsal shift from wrist neutral to wrist extension. Moment arm analysis revealed a palmar shift through the full arc of wrist flexionextension. At present, understanding of this phenomenon is incomplete. However, tendons loaded with higher tension exhibited moment arms that differed from those produced under baseline loading.
1,6
-
Loaded
Z 1.2
0.8
Baseline
---~-
Flexion
.....
+
-
-
-
~
-
~
-
-
~
Z
...........
-q
Extension
Wrist Angle [degrees] 7. The FDS5 baseline and loaded moment arms. Data are averaged across all cadavers. Error bars indicate variability among cadavers. Figure
Figure 8. A simplified wrist cross-section depicting the theoretical dynamic soft tissue pulley in action. A differentially loaded carpal tunnel tendon (long thin arrow) fixed dorsally by 2 other carpal tunnel tendons (short thick arrows) under tension by synergistic firing of related muscle units.
In anatomic areas other than the carpal tunnel, the biomechanical effect of each tendon is defined by discrete fibro-osseous tunnels that effectively form pulleys. These pulleys dictate the precise offset and location of the tendon as it crosses the joint to generate the rotational forces or moments needed to effect controlled angulation and stability. However, discrete fibro-osseous tunnels are not present in the carpal tunnel to provide this function. In our opinion, some mechanism other than discrete pulleys must exist in vivo that more accurately defines the moment arm for each digital flexor tendon as it passes through the carpal tunnel. Without some mechanism for moment arm control, fine motor control of the digits would be difficult. The tension generated by each muscle would require continual adjustment as a function of the changing moment arms to deliver the required tension, and therefore torque, at each digital joint. We hypothesize that the stability of single or multiple carpal tunnel tendons can be achieved by a synergistic contraction of adjacent muscle tendon units to form dynamic soft tissue pulleys for each tendon. This mechanism would stabilize the moment arm of each digital flexor tendon as it traverses the carpal tunnel, creating a biomechanical effect functionally similar to that obtained by the fibro-osseous tunnels on the extensor side of the wrist. Contraction of the flexor digitomm profundus would provide a mechanical support deep in the carpal tunnel to stabilize differentially loaded FDS tendons (Fig. 8). In a similar manner, tensioned
The Journal of Hand Surgery / Vo]. 23A No. 6 November 1998
FDS tendons would resist palmar translation by a differentially loaded profundus tendon. An understanding of the dynamic nature of the tendons within the carpal tunnel may be clinically relevant. Without the dynamic action described above, the increased tension of a given m u s c l e tendon unit may cause the associated tendon to translate around the lower tensioned tendons until it stabilizes closer to the more rigid wall of the carpal tunnel. These translations might place altered mechanical loads, in the form of shear stress, on the tendons and interposed synovial membranes. Transverse tendon translation has been suggested as a mechanism of injury to the tissues surrounding the carpal tunnel tendons in both normal and carpal tunnel syndrome wrists. 6'7 Frictional forces associated with longitudinal tendon excursion also have been investigated as a possible cause of injury to the contents of the carpal tunnel, s It is unknown whether the translations observed in this study occur in vivo or are sufficient to cause damage to soft tissue. Further study is required to identify tendon translation in vivo and its potential role in the etiology of idiopathic carpal tunnel syndrome. Whether a dynamic soft tissue pulley occurs in vivo remains unknown. This study was limited to quasistatic wrist motion and differential loading of a single FDS or FPL tendon. Determination of the validity of the synergistic contraction theory would require either a more extensive dynamic experiment or differential loading of 2 or more tendons at once. Information about the effect of a differential load on
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the flexor digitorum profundus tendons may also provide further insight regarding the synergistic behavior of the tendons within the carpal tunnel. Dynamic experimentation would also provide data that would increase the understanding of changes in moment arm that occur as a function of time. The authorsthankBen Gossand CoraMorganfor theirtechnicaland editorial contributionsto the developmentof this report.
References 1. Brand PW, Hollister A. Clinical mechanics of the hand. 2rid ed. St Louis: Mosby Year Book, 1993:67-378. 2. Kang H-J, Lee S-G, Phillips CS, Mass DP. Biomechanical changes of cadaveric finger flexion: the effect of wrist position and of the transverse carpal ligament and palmar and forearm fasciae. J Hand Surg 1996;21A:963-968. 3. Chao EY, Opgrande JD, Axmear FE. Three-dimensional force analysis of finger joints in selected isometric hand functions. J Biomech 1976;9:387-396. 4. Goldstein SA, Armstrong TJ, Chaffin DB, Matthews LS. Analysis of cumulative strain in tendons and tendon sheaths. J Biomech 1987;20:1-6. 5. Gerald CF, Wheatley PO. Applied numerical analysis. 5th ed. Reading, MA: Addison-Wesley, 1994:244-253. 6. Armstrong TJ, Castelli WA, Evans FG, Diaz-Perez R. Some histological changes in carpal tunnel contents and their biomechanical implications. J Occup Med 1984;26:197200. 7. Schuind F, Ventura M, Pasteels JL. Idiopathic carpal tunnel syndrome: histologic study of flexor tendon synovium. J Hand Surg 1990;15A:497-503. 8. Bay BK, Sharkey NA, Szabo RM. Displacement and strain of the median nerve at the wrist. J Hand Surg 1997;22A: 621-627.