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A new concept for a metacarpophalangeal prosthesis: consequence on joint biomechanics
ELSEVIER
Clinical Biomechanics14 (1999)166-176
A new concept for a metacarpophalangeal prosthesis: consequence on joint biomechanics David J. Beevers”, Bahaa B. Seedhom Rheumatology and Rehabilitation ResearchUnit, University of Leeds, Leeds LS2 9NZ, UK
Received3 November1997;accepted7 July 1998
Abstract Objective. The purpose of this work was to establish whether surface replacement non-constrained prostheses can duplicate the normal biomechanics of the metacarpophalangeal joint. Design. A series of mathematical models. Background. A non-constrained prostheses has been designed for the replacement of the metacarpophalangeal joint. It uses the concept of surface replacement in that it attempts to replicate the anatomy of the original cartilage surfaces. The centre of rotation of the prosthesis is also sited at the same position as in the natural joint to maintain the balance between the flexor and extensor tendon forces, such that the prosthesis duplicates the biomechanics of the normal joint. Due to the unique dimensions of each joint that may present for surgery, the four sizes of prosthesis that are available for implantation may not always produce an exact replication of the joint kinematics. These situations were examined to establish whether the biomechanics of the joint can indeed be restored. Methods. Mathematical models for each size of prosthesis implanted into a range of different sized metacarpophalangeal joints were developed. The prosthetic and cartilage surface profiles were compared and the balance between the tendon forces was examined. Results. Differences in size that may occur between the surface profiles of the normal joint and prosthesis, together with any relocation of the centre of rotation, would have negligible effects on the normal joint biomechanics. Conclusions. All four sizes of the non-constrained prosthesis can duplicate the normal biomechanics of the joint and hence provide normal function.
Relevance A non-constrained metacarpophalangeal prosthesis that was designed to replace the surfaces of the joint can duplicate the normal biomechanics of the joint and hence provide normal function, provided that they are implanted with the correct surgical technique. 0 1999 Elsevier Science Ltd. All rights reserved. Keywords: Prosthesis;Metacarpophalangeal joint; Biomechanics
1. Nomenclature
A, B, C, D, E, F
a, b, c, 4 e,f g1
g2
included angles (degrees) variables (mm) maximum overlap of the cartilage and prosthetic bearing surface profiles in the sagittal plane at 20” extension (mm) maximum
and
overlap
prosthetic
g3
g4
of the cartilage
bearing
surface h
*Correspondingauthor. 0268-0033/99/$ - seefront matter 0 1999ElsevierScienceLtd. AI1 rights reserved. PII: SO268-0033(98)00064-3
profiles in the sagittal plane at 45” flexion (mm) maximum overlap of the cartilage and prosthetic bearing surface profiles in the coronal plane at 20” abduction-adduction (mm) maximum overlap of the cartilage and prosthetic bearing surface profiles in the coronal plane at 20” abduction-adduction (mm) perpendicular distance from the centre of rotation to the line of action of a force produced by a
D.J. Beevers, B.B. SeedhomlClinical
hs h* P
RP R,S R,, s COR
tendon; the tendon moment arm (mm) tendon moment arm before the prosthesis is implanted (mm) tendon moment arm after the prosthesis is implanted (mm) force produced by a tendon (N) radius of spherical prosthetic bearing surface (mm) radius of metacarpal cartilage surface in sagittal plane (mm) radius of metacarpal cartilage surface in coronal plane (mm) distance the centre of rotation is shifted in a palmar or dorsal direction from that of the normal location by implanting the prosthesis (mm)
2. Introduction Over the last 30 years numerous prostheses have been used to treat rheumatoid arthritis (RA) of the metacarpophalangeal (MCP) joint of the fingers, commonly known as the knuckle joint [1,2]. Currently, the Swanson prosthesis (Wright Medical Technology, USA), which is most widely used, is a single component implant manufactured from flexible silicone rubber. It does not restore the biomechanics of the joint, but acts as a “dynamic” spacer to separate the metacarpal and proximal phalanx. The term dynamic has been used to indicate that while the prosthesis keeps the bone ends apart, it can also bend to allow joint movement. A fibrous capsule develops around the prosthesis after implantation which provides it with some stability; a process known as encapsulation. Swanson prostheses are still in wide current use
Metacarpal
Biomechanics 14 (1999) 166-176
because of their ease of implantation, ease of removal if reoperation is necessary and low cost. Also, patient satisfaction is generally good, due to pain relief and cosmetic improvement. However, high incident rates of fracture and recurrent deformity, together with a low range of motion (ROM), have been reported in longterm follow-up studies [3-71. Moreover, these flexible prostheses cannot be used to adequately treat MCP joints damaged by traumatic injuries or post-traumatic osteoarthrosis (OA). This is because silicone rubber does not possess sufficient strength to transmit the large joint forces that act in the hands of these patients during gripping activities. Thus, although MCP joint replacement is now a routine surgical procedure, it still has severe limitations. In order to overcome the problems associated with the Swanson prosthesis, the next generation of prostheses that are being currently designed for MCP joint replacement employ the concept of surface replacement. This concept relies on the prosthesis replicating the anatomy of the original metacarpal cartilage surface. In order to duplicate the biomechanics of the normal joint, the centre of rotation of the prosthesis must also be sited at the same position as in the natural joint, hence maintaining the balance between the flexor and extensor tendon forces. Such a surface replacement, non-constrained prostheses was therefore designed by the first author (DB) to replace the surfaces of joints affected by trauma, post-traumatic OA and RA in the early stages of the disease [8] (Fig. 1). Four sizes of this prosthesis are available, with spherical bearing surface radii of 5, 6, 7 or 8 mm respectively. These sizes were chosen and based on published data on the dimensions of the MCP joint [9]. Ideally, the prosthesis should replicate the metacarpal cartilage surface when implanted, so that
Centre of rotation
Proximal phalanx
Dorsal
c-#-
Sagittal plane
/
1 :
,
, Palmar
Fig. 1. The modular non-constrained,
surface metacarpophalangeal
167
(MCP) prosthesis consists of three components; a sleeve, head and base,
168
D.J. Beevers, B.B. SeedhomlClinical
of activities performed by the hand require the MCP joint to move in an arc of motion from 0” to 90” flexion in the sagittal plane [ll]. When the prosthesis is implanted it is therefore aligned with the distal and palmar cartilage surfaces in the sagittal plane to provide the optimum fit over this critical arc of motion. However, despite the attempt to optimise the fit, the radius of the prosthesis may not always match the radius of the cartilage surface over the full arc of motion. This can be seen in Fig. 2a, where in a position of joint flexion in the sagittal plane, the prosthetic bearing surface would not extend as far as the cartilage surface it replaces. Also, the position where the centre of rotation occurred in the natural joint may be relocated in a different position in the reconstructed joint. Although the concept of a surface replacement prosthesis is to restore the anatomical surfaces and the biomechanics of the MCP joint, the question arises as to whether it can do this with sufficient accuracy in order to restore normal function. This paper investigates whether the biomechanics of the replaced MCP joint are similar to those of a normal joint after implanting a surface prosthesis. It then discusses whether surface replacement prostheses can in fact restore the biomechanics and hence normal function of the MCP joint.
the biomechanics of the normal joint will be duplicated. This can only be achieved if the metacarpal cartilage surface is spherical with an identical radius to that of the prosthesis, i.e. corresponds to one of the four sizes manufactured, 5, 6, 7 or 8 mm. However, an exact match between the cartilage surface and the prosthetic bearing surface will not always be achieved due to the unique dimensions of the metacarpal cartilage surface:
(a) if
the radius of the metacarpal head’s spherical cartilage surface does not correspond in size to the bearing surface radii of one of the four head components (Fig. 2a), or (b) if the radius of the cartilage surface varies in either the sagittal or coronal planes so that it does not have an exact circular profile (Fig. 2b), or (cl if the cartilage surface has circular profiles in the sagittal and coronal planes, but the radii are not similar in those two planes (Fig. 2~). Previous studies have shown that the profile of the cartilage surface in the sagittal and coronal planes can be accurately described by a single radius [9, lo]. Any slight differences that may occur between the cartilage surface profile and the circle that is used to describe this shape are so small that condition (b) would have negligible effect on the joint biomechanics. However, since conditions (a) or (c) are likely to occur, one of the four available sizes of prosthetic head component which most accurately matches the cartilage surface of the metacarpal head should be implanted. The majority
3. Methods The following sections describe the mathematical models developed to examine the effect that a differ-
R*
R, =5:0 mm R,= 4.7 mm
Condition (a)
R, =5.Omm R,,= 4.9 mm
R, = 5.0 mm Rcc= variable
& = 5.0 mm R,,= 4.7 mm
Sagittal plane
Biomechanics 14 (1999) 166-I 76
*
*
R, =5.0 mm R,, = variable
Condition (b)
R, =5.Omm R,,= 4.7 mm
Condition (c)
Fig. 2. If the prosthesis does not duplicate the metacarpal cartilage surface due to one or more of the three conditions biomechanics of the joint may be changed (the radii are not drawn to scale).
(a), (b) or (c), the
D.J. Beevers, B.B. SeedhomlClinical
ence between the prosthetic and cartilage surface radii, together with a repositioning of the centre of rotation, may have on the joint biomechanics. 3.I. Su$aceprofiles The difference between the cartilage and prosthetic bearing surfaces can be mathematically modelled in the sagittal and coronal planes as shown in Figs 3 and 4 respectively. In the sagittal plane the prosthesis provides a range of motion from 20” extension to 90” flexion in order to duplicate that of the natural joint. It can be seen in Fig. 3 that the overlap which occurs between the surface profiles expands during increasing joint extension. Thus, the maximum overlap between the surface profiles that would occur during finger extension, g,, would occur when the proximal phalanx is at the limit of normal motion with respect to the metacarpal head. This occurs when the finger is at a position of 20” extension and is represented by “LINE 1” on Fig. 3. The maximum overlap between the surface profiles that would occur during finger flexion, gz, would occur when the proximal phalanx is at a position of 45” flexion as shown on Fig. 3. This finger position is represented by “LINE 2” on Fig. 3. The terms g, and g, are positive when the prosthetic bearing surface profile extends beyond the cartilage surface profile (e.g. g, in Fig. 3a and g2 in Fig. 3b). This
Prosthetic bearing surface ,
Metacarpal cartilage surface Distal surface
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Biomechanics 14 (1999) 166-l 76
indicates that the proximal phalanx would be pushed further away from the metacarpal, when the finger is in this position after implantation of the prosthesis. Thus, the collateral ligaments would become tighter than normal. The terms gl and g2 are negative when the prosthetic profile is smaller than the cartilage profile (e.g. g, in Fig. 3b and g, in Fig. 3a). This indicates that the proximal phalanx would be closer to the metacarpal and the ligaments would be looser than normal when the finger is in this position. In order to calculate gl and gZ, the following angles and dimensions are defined: Angle A,, is formed by the line of zero flexiomextension that passes through the centre of the prosthetic bearing surface and the centre line of the proximal phalanx at 20” extension (LINE 1) at the position of maximum overlap between the surface profiles during joint extension. Angle A, is therefore constant at 20” throughout the calculations. Angle A2, is formed by the line of zero flexion/extension that passes through the centre of the prosthetic bearing surface and the centre line of the proximal phalanx at 45” flexion (LINE 2) at the position of maximum overlap between the surface profiles during joint flexion. Angle .A2 is therefore constant at 45” throughout the calculations. The included angle A is given by the addition of angles A, and A2 and is therefore constant af 65” throughout the calculations. Angle B is formed by LINE 2 and line a.
Prosthetic bearingsurface .~~~@---j-‘~~.~
Metacarpal cartilage surface Distalwrface
Centre of rotati
Centre of rotation of metacarpal cartilage surface
(a) Metacarpal smaller than prosthesis
(b) Metacarpal larger than prosthesis
Fig. 3. Mathematical model describing the maximum distances between the surface profiles of the prosthesis and cartilage that may occur over the arc of motion in the sagittal plane.
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D.J. Beevers, B.B. SeedhomlClinical
Prosthetic bearing surface I
Metacarpal ’ cart)lage ‘FEZ
Biomechanics 14 (1999) 166-l 76
Combining eqns (l)-(5), the maximum distance between the surface profiles in the sagittal plane at 20 extension, g,, is given by:
surface
R
2 sin 180-A-sin-’ sin A
g, =R,-
[(R, - R&os X
A21sin A 1
Rc,s
1I
Combining eqns (1) and (6) the maximum distance between the surface profiles in the sagittal plane at 45” flexion, g,, is given by: g,=R,-R,,-
Fig. 4. Mathematical model describing the maximum distances between the surface profiles of the prosthesis and cartilage that may occur over the arc of motion in the coronal plane.
R, - R,,
~ cos A2
In the coronal plane each prosthesis has to 20” arc of abduction and adduction from the in both the ulnar and radial directions. The difference between the surface profiles occurs at 20”, denoted as g3 and g4. Since e=R,,-Rcc
Line a is the line joining the centre of rotation of the metacarpal cartilage surface to the point where LINE 1 intersects the cartilage surface (this is equal to the radius of the cartilage surface in the sagittal plane, I?,,). Angle C is formed by LINE 2 and line a. Line c is the distance between the centre of rotation of the prosthetic bearing surface and the point where LINE 1 intersects the cartilage surface. The distance between the centre of rotation of the metacarpal surface and the centre of rotation of the prosthetic surface is given by length b. Since
b= -R, - 4s cos A2 b sin A
sin B= -
a
C= 180-(A+B)
(2)
(3)
a sin C
c= -
sin A
(4)
provide a centreline maximum t herefore (9)
.a=a=Rp-f
(10) Combining similar eqn (2)-(4) (11) and (12), the maximum distance between the surface profi le:s in the coronal plane at 20” abduction or adduction, g3, which is equal in magnitude to g4 due to the symmetrical nature of the prosthesis, is given by: R
g3=g4=Rp-
--? sin 180-D-sin’ sin D
Since the cartilage surfaces of the metacarpal head are often not true spheres (condition “c”), radius R,, is dependent on which finger the prosthesis is implanted in. The radius of the cartilage surface in the sagittal plane is approximately 12.0% larger than the radius in the coronal plane for an index finger [9]. The radius of the cartilage surface in the coronal plane is approximately 9.0, 1.6 and 1.6% larger than the radius in the sagittal plane for a middle, ring and little finger respectively [9], hence for an index finger:
hence: g,=R,-c
RC,C = R,,/I .12 (5)
and gz= R, - UL+b)
(6)
(12)
for a middle finger: Rc,c= 1.09Rw
for a ring or little finger: Rc,c= I .o16R,,5
(13) (14)
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Biomechanics 14 (1999) 166-176
3.2. Centre of rotation If the position of the natural centre of rotation of the joint is altered as a result of implanting a prosthesis, this can also affect the biomechanics. A simple model of the MCP joint is described in Fig. 5. The intrinsic muscles of the finger consist of the lumbrical, dorsal interosseous and palmar interosseous. Although the tendons of two intrinsic muscles act on the radial side of each MCP joint, they are represented by a single tendon for simplicity. The moment arms of the extensor (h3) and those of both flexors (h4, and h5) vary throughout the range of motion and these values measured from 30” extension Centre of rotation for metacarpal head
to 90” flexion are listed in Table 1 [12]. Youm et al. [12] found that the extensor tendon moment arm remained approximately constant throughout the flexion-extension arc of motion, while the moment arms of the flexor tendons increased by up to 50%. Similar results for the moment arms at a joint angle of 45” flexion have also been measured by Spoor [13]. Neither of these studies stated the dimensions of metacarpal head radius of the cadaveric specimens used in the experiments. However, we found that the moment arms measured matched those of a joint with a metacarpal radius of 7 mm, cross-sections of which were obtained from a set of published data [14]. These cross-sections were of joints at 0” flexion. Hence, the
Ulnar
Intrinsics
I-\ -,-,-I
Coronal plane
,/ I
\ -A
//-------+ 0
Radial Extensor digitorum
Sagittal plane
c----M--/ i I’ /\ \H 0’
Distal
Flexor digitorum profundus Flexor digitorum su Fig. 5. Movement of the joint in the coronal plane is caused by the intrinsic muscles. Movement flexor and extensor tendons.
Table 1 The extensor digitorum (ED), h3, flexor digitorum measured from 30” extension to 90” flexion Angle of MCP joint
ED, h
profundus
(FDP), h, and flexor digitorum
FDP, h,
FD
in the sagittal plane is caused by the pull of the
superficialis
(FDS), h,, tendon moment arms
FDS, k
30” extension 0” flexion 45” flexion 90” flexion
10 9 9 9
-10 -11 -13 -15
(1.00) (1.20) (1.44) (1.67)
FD c-1FDP
(-1FDP -12 -14 -16 -18
(1.20) (1.56) (1.78) (2.00)
All values are given in millimetres. The moment arms measured in a dorsal direction are given as positive values and those measured in a palmar direction as negative values. The values in parentheses are the moment arm ratios.
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D.J. Beevers,B.B. SeedhomlClinical Biomechanics 14 (1999) 166-176
values of the moment arms stated in Table 1 were assumed to belong to a metacarpal head of 7 mm radius and the tendon moment arms (h,) for all the other theoretical sizes of metacarpal head used in the analysis were calculated by scaling up or down these values using eqn (15).
The distance that the centre of rotation is shifted in a palmar or dorsal direction from that of the normal location in the natural joint by implanting the prosthesis is given by &OR= R, - R,, (16) The length of each tendon moment arm after the prosthesis is implanted is given by
prosthesis remain in the same position over this arc of motion. 4. Results
The radius of the bearing surfaces of the MCP prosthesis increase in steps of 1.0 mm. It is therefore possible to implant each size of prosthesis into an MCP joint that has a radius which is up to 0.5 mm larger or smaller than that of the prosthetic bearing surface. The discrepancies that may occur between the prosthetic and cartilage surface radii, together with any relocation of the centre of rotation, when implanting a prosthesis into a larger or smaller metacarpal head is described hereafter. 4.1. Maximum overlap between the su$ace profiles
h* = h, - RCoR
(17)
The percentage change between the normal tendon moment arm before implanting the prosthesis and the tendon moment arm after implanting the prosthesis is given by h* -h,
Percentage change in moment arm = 100 ( hs > (18) Hence, the difference between the tendon moment arms before and after implanting each size of prostheses can be calculated for any size of metacarpal head over the arc of flexion-extension, assuming that the centre of rotation of the normal MCP joint and
The distances between the cartilage and prosthetic bearing surface profiles at 20” extension dpr) and at 4.5” flexion (&) for each size of prosthesis in the sagittal plane are given in Fig. 6. If the radius of the prosthetic bearing surface is equal to the radius of the cartilage surface, distances g, and g2will be zero and a perfect fit will be obtained. However, as a prosthesis replaces cartilage surfaces with increasingly smaller radii, distances gl and g, will become increasingly positive and negative respectively (Fig. 6 and as represented in Fig. 3). When the joint is at 20” extension the proximal phalanx bone will therefore be further away from the natural position it should occupy next to the original cartilage surface. Thus, the collateral ligaments will be
85
-0.25
. +&6 - a. d-c - l -
I
J Metacarpal cartilage surface radius in sagittal plane, k,, (mm)
Fig. 6. Maximum distances between the surface profiles in the sagittal plane for each of the four sizes of prosthesis.
5 mm Prosthesis,g , 5 mm Prosthesis,g, mm Prosthesis,g , 6 mm Prosthesis,g, 7 mm Prosthesis,g , 7 mm Prosthesis,g, 8 mm Prosthesis,g 1 8 mm Prosthesis,gz
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cartilage surface it replaces. Hence, in the coronal plane the collateral ligaments in the reconstructed joint will be more lax in abduction and adduction than the natural joint. For each size of prosthesis the laxity of the collateral ligaments would be greatest, and therefore the worst fit would be obtained, when a prosthesis has to replace the largest radius cartilage surface in the range of metacarpal head sizes it has to cater for (Fig. 7); for example, when a prosthesis with a 7 mm radius is implanted in a joint with a 7.5 mm radius. If a prosthesis is implanted in a ring or little finger which has a smaller radius of cartilage surface in comparison to the radius of the prosthetic bearing surface, the collateral ligaments of the reconstructed joint would generally be more taut in abduction and adduction than in the natural joint (Fig. 7). Conversely, if the radius of the cartilage surface is larger than the prosthetic bearing surface, the collateral ligaments would generally be lax. The overlap between the surface profiles under this condition, however, is only half those for the index and middle. This is because the metacarpal head cartilage surfaces of the ring and little fingers are closer to a spherical shape.
stretched. When the joint is in a position of 45” flexion the prosthetic bearing surface will be effectively smaller than the cartilage surface and the collateral ligaments will therefore be lax. As a prosthesis replaces cartilage surfaces with increasingly larger radii, distances gl and g2 will be negative and positive respectively (Fig. 6). Hence, when the joint is at 20” extension the collateral ligaments will be lax and when the joint is in a position of 45” flexion the collateral ligaments will be taut. Since the prosthesis is chosen to match the metacarpal from the cartilage dimensions in the sagittal plane, a head with a different radius in the coronal plane may affect the biomechanics in the coronal plane. If a prosthesis is implanted into an index finger, the radius of the prosthetic bearing surface in the coronal plane would be larger than the radius of the cartilage surface it replaces (Fig. 4). Hence, in the coronal plane the collateral ligaments in the reconstructed joint will be more taut in abduction and adduction than in comparison to the natural joint. The collateral ligaments would be tightest and therefore the worst fit would be obtained, when a prosthesis has to replace the smallest radius cartilage surface in the range of metacarpal head sizes it has to cater for (Fig. 7). For example, a 7 mm radius prosthesis could be implanted into joints ranging in size from 6.5 to 7.5 mm in radius. Over this range of sizes the worst fit would be obtained when it was implanted in a joint with a 6.5 mm radius. If a prosthesis is implanted into a middle finger, the radius of the prosthetic bearing surface in the coronal plane would be generally smaller than the radius of the
4.2. Position of the centre of rotation after implantation When the prosthesis is implanted into the MCP joint, it is aligned with the centreline of the metacarpal in the coronal plane and with the distal and palmar cartilage surfaces in the sagittal plane. When considering alignment in the coronal plane, if the bearing surface of the prosthesis is larger or smaller in
4 A II
‘4 ‘4
h
\ ‘4
h
- -+ - RS - index
‘b l
‘4 T
‘4
‘A ‘4
l ‘8
- + - R6 - index
‘a
a
\
- + - R7 - index \
‘4
9.
- -* - R8 - index l *
-**+*-
R5
- middle
mm*****R6 - middle --**A-- K7 _ middle *****.’ R8 - middle
Y fs” .2 n
-0.04
+
R5 - ring / little
-
R6 - ring / little
+
R7 - ring / little
-C
R8 - ring / little
-0.06 -0.08
’ Metacarpal cartilage surface radius in sag&al plane, qS (mm)
Fig. 7. Maximum distances between the surface profiles in the coronal plane for each of the four sizes of prosthesis, when implanted into an index, middle, ring or little finger.
114
D.J. Beevers, B.B. SeedhomiClinical
radius in comparison to the cartilage surface, the centre of rotation may be shifted in a proximal or distal direction. However, it will still lie on the centreline of the bone and consequently the values of P,, Pz, h, and h2 (Fig. 5) will remain unchanged. The biomechanics of the joint in the coronal plane (abduction and adduction of the joint) cannot be significantly altered by a change in the position of the centre of rotation. Similarly, a proximal or distal shift in the centre of rotation in the sagittal plane would not significantly alter flexion or extension of the joint. However, a
Biomechanics 14 (1999) 166-176
palmar or dorsal shift in the centre of rotation will cause changes in h3, h4 and h5, the tendon moment arms. If the metacarpal head is smaller than the implanted prosthesis, the centre of rotation of the reconstructed joint would be positioned in a dorsal direction from that of the natural joint. The extensor moment arm (h3) is decreased, whereas those of the flexors (h, and h5) are increased (Fig. 8). Similarly, if the metacarpal head is larger than the implanted prosthesis, the centre of rotation would be placed in a palmar direction. The extensor moment arm (h3)
8 ,
-IOJ
1
Metacarpalcartilage surfaceradiusin sag&al plane, %,%(mm)
I
(a) Extensordigitorum 8 ‘;: G
6
--+--R5-45F -+.R6-30E
k
J -8
--B--R6-45F R6- 90F R7- 30E ~815 I-+-R7-OF .R7- 45F R7- 90F -+--R8-3OE --•--R8-45F
Metacarpalcartilage surfaceradiusin sag&al plane, RiJ (mm) (b) Flexor digitorum profundus
Metacarpalcartilage surfaceradiusin sag&al plane, &,S (mm) (c) Flexor digitorum superkiahs Fig. 8. Changes in the moment arm due to relocation of the centre of rotation. The analysis was performed on all four sizes of prosthesis represented by R5, R6, R7 and R8, at joint angles of 30” extension, 0”, 45” and 90” flexion (represented by 30E, OF,45F and 90F respectively).
D.J. Beevers, B.B. SeedhomlClinical
increases, while those of the flexors (hq and h5) decrease (Fig. 8). For any specific prosthesis implanted in any size of joint, the percentage change in the moment arm varies over the arc of motion (Fig. 8). The maximum change in the extensor tendon moment arm occurs in flexion and remains constant as the flexion angle increases from 0” to 90”. The maximum deviation of the flexor tendons moment arms occurs in extension, and as flexion of the joint increases, the deviation decreases (Fig. 8). The centre of rotation could be moved by a maximum distance of 0.5 mm in a dorsal or palmar direction for each size of prosthesis. The maximum change in the moment arms of the flexor and extensor tendons occurs when implanting a prosthesis with a 5 mm radius bearing surface into metacarpal heads that have cartilage surface radii of 4.5 or 5.5 mm. Under these conditions the tendon moment arm of extensor digitorum would be altered by a maximum of -8.6% and +7.1%. The tendon moment arm of flexor digitorum profundus would be altered by a maximum of +7.7% and -6.4%. The tendon moment arm of flexor digitorum superficialis would be altered by a maximum of +6.5% and -5.3%. 5. Discussion The profile of the cartilage surface may be larger or smaller than that of the prosthetic bearing surface and the centre of rotation of the reconstructed joint may be located in a palmar or dorsal direction in relation to its former position in that of the natural joint. Consequently, the various factors affecting the kinematics of the joint were investigated and are discussed in the following sections. 5.1. Differences in the radii of the natural and prosthetic joints
The worst fit between the radii of the natural and prosthetic joints for each size of prosthesis would be obtained when the prosthesis is implanted in joints which have a cartilage radius at the extreme of the range it has to cater for, i.e. a radius 0.5 mm larger or smaller than the radius of the prosthetic head (Fig. 6). These maximum discrepancies under similar conditions for each size of prosthesis are approximately equal. For example, a prosthesis with a 5 mm radius when implanted in a joint with a 4.5 mm radius, or a prosthesis with a 6 mm radius when implanted in a joint with a 5.5 mm radius, will have discrepancies of approximately 0.24 mm at 20” extension (gl), and -0.21 mm at 45” flexion (g2) (Fig. 6). However, these discrepancies become more significant in relation to
Biomechanics 14 (1999) 166-l 76
175
the prosthetic radius as the size of prosthetic head decreases (the ratio between the discrepancy and size of head becomes larger). Thus, the smallest size of prosthesis (5 mm) would provide the least accurate fit and the larger size (8 mm) the most accurate fit. How significant are these discrepancies between the radii of the natural and prosthetic joints? The maximum difference that would occur between the profiles of any size of prosthesis and natural joints in flexion-extension is 0.25 mm and in abduction-adduction is 0.09 mm. Minami et al. [15] have shown that during flexion from 0” to 80” the dorsal portions of both the radial and ulnar collateral ligaments of the normal MCP joint increased in length by 3.0 to 4.0 mm. The middle portions of each ligament were elongated by 0.4 to 1.0 mm and the palmar portions of each ligament were shortened by 1.0 to 2.0 mm. In extension, the dorsal portions of each ligament shortened by 2.0 to 3.0 mm, the middle third of the ligaments slightly shortened and the palmar thirds of the ligaments lengthened. The discrepancies that the theory predicts are therefore insignificant in relation to the amount by which the ligaments can extend. The full range of motion of the reconstructed joint would therefore be possible before the ligaments would become sufficiently stretched to prevent further motion, or sufficiently lax to allow deformation in the form of ulnar drift or subluxation. The slight differences that may occur between the surface profiles would have a negligible effect and the prosthesis would duplicate the normal biomechanics. 5.2. Dorsal or palmar shift in the centre of rotation
Since the centre of rotation can be moved a maximum distance of 0.5 mm in either a dorsal or palmar direction for each size of prosthesis, this has the most significant effect on the tendon moment arms when the prosthesis which has the smallest bearing surface radius is implanted. The maximum dorsal shift in the centre of rotation for the smallest prosthesis (5 mm radius) would be created when replacing a metacarpal head with a 4.5 mm cartilage radius. Under this condition the maximum change in the tendon moment arms of extensor digitorum, flexor digitorum profundus and flexor digitorum superficialis would be -8.6, 7.7 and 6.5% respectively. Although the distance between each tendon will remain the same in the reconstructed joint, the shift in the centre of rotation will change the ratio between the tendon moment arms. The original moment arm ratio of 1.22 for extensor digitorum and flexor digitorum profundus at 0” flexion would therefore be increased to 1.43 in the reconstructed joint, giving an increase of 17.4%. Similarly, the original moment arm ratio of 1.56 for extensor digitorum and
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D.J. Beevers, B.B. SeedhomJClinical Biomechanics 14 (1999) 166-I 76
flexor digitorum superficialis at 0” flexion would be increased to 1.80, giving an increase of 15.6%. These changes in the moment arm ratios would make flexion of the joint easier and extension more difficult. The slight increase in grip strength and difficulty of finger extension which would occur under this condition should not be sufficient to have a detrimental effect on the biomechanics and hence hand function. Similarly, if the centre of rotation is shifted in a palmar direction, by replacing a 5.5 mm radius cartilage surface with a 5 mm radius prosthesis, the maximum change in the tendon moment arms of extensor digitorum, flexor digitorum profundus and flexor digitorum superficialis would be 7.1, -6.4 and -5.3% respectively. The original moment arm ratio of 1.22 for extensor digitorum and flexor digitorum profundus at 0” flexion would therefore be decreased to 1.08 in the reconstructed joint, giving an decrease of 12.0%. Similarly, the original moment arm ratio of 1.56 for extensor digitorum and flexor digitorum superficialis at 0” flexion would be decreased to 1.39, giving an decrease of 10.8%. Thus, flexion of the joint would be more difficult and extension easier. Again, under this condition the slight ease of MCP joint extension and reduction in grip strength would not be sufficient to have a detrimental effect on the biomechanics and hence hand function. The surgical procedure required to implant a prosthesis in the stated position has highlighted the inadequacy of standard surgical instruments. Therefore, specialised surgical instruments have been developed and validated for accurate and reproducible positioning of the non-constrained MCP prosthesis described in this text. These instruments are the subject of a separate clinical paper. 6. Conclusions The MCP prosthesis was designed to be aligned with the distal and palmar cartilage surfaces in the sagittal plane to provide the optimum fit over the most commonly used arc of flexion. Each size of prosthesis may not duplicate the metacarpal cartilage surface and the centre of rotation may be relocated when it is implanted in this manner due to a mismatch between the dimensions of the cartilage surfaces and one of the four standard sizes of prosthesis that would be implanted. The prosthesis with the largest radius (8 mm) would provide the most accurate duplication of the normal joint biomechanics over the range of MCP joint sizes into which it can be implanted. The prosthesis with the 5 mm radius bearing surface would provide the least accurate duplication of the joint biomechanics. However, each size of prosthesis would
not produce a significant alteration in the biomechanics of the MCP joint. Consequently, all four sizes of the non-constrained prosthesis would provide normal joint function. Acknowledgements This research was supported by grants from The Arthritis and Rheumatism Council and from the Special Trustees of the Leeds Teaching Hospitals. The authors would like to thank M Pullan and B Whitham for their technical expertise and help with the experiments. References [l] Beevers DJ, Seedhom BB. Metacarpophalangeal joint prostheses: a review of past and current designs. Proc Instn Mech Engrs Part H 1993;207:195-206. PI Beevers DJ, Seedhom BB. Metacarpophalangeal joint prostheses. A review of the clinical results of past and current designs. J Hand Surg 1995;20B:125-136. [31 Beckenbaugh RD, Dobyns JH, Linscheid RL, Bryan RS. Review and analysis of silicone-rubber metacarpophalangeal implants. J Bone Jt Surg 1976;58A:483-487. [41 Bieber EJ, Weiland AJ, Volenec-Dowling S. Silicone-rubber implant arthroplasty of the metacarpophalangeal joints for rheumatoid arthritis. J Bone Jt Surg 1986;68A:206-209. Kay AGL, Jeffs JV, Scott JT. Experience with silastic prostheses in the rheumatoid hand: a 5-year follow-up. Ann Rheum Dis 1978;37:255-258. WI Kirschenbaum D, Schneider LH, Adams DC, Cody RP. Arthroplasty of the metacarpophalangeal joints with use of siliconerubber implants in patients who have rheumatoid arthritis. J Bone Jt Surg 1993;75A:3-12. 171 Wilson YG, Sykes PJ, Niranjan NS. Long-term follow-up of Swanson’s silastic arthroplasty of the metacarpophalangeal joints in rheumatoid arthritis. J Hand Surg 1993;18B:81-91. PI Beevers DJ, Seedhom BB. Laboratory development of a nonconstrained, noncemented, modular, metacarpophalangeal prosthesis. Proc Instn Mech Engrs Part H 1995;209:185-195. [91 Unsworth A, Alexander WJ. Dimensions of the metacarpophalangeal joint with particular reference to joint prostheses. Engng in Medicine 1979;8:75-80. WI Unsworth A, Dowson D, Wright V. Cracking joints: a bioengineering study of cavitation in the metacarpophalangeal joint. Ann Rheum Dis 1971;30:348-358. IllI Badley EM, Wagstaff S, Wood PHN. Measures of functional ability (disability) in arthritis in relation to impairment of joint movement. Ann Rheum Dis 1984;43:563-569. [121Youm Y, Gillespie TE, Flatt AE, Sprague BL. Kinematic investigation of normal MCP joint. J Biomechanics 1978;11:109-118. P31 Spoor CW. Balancing a force on the fingertip of a two-dimensional finger model without intrinsic muscles. J Biomechanics 1983;16:497-504. P41 Meals RA, Seeger LL, An atlas of forearm and hand crosssectional anatomy. Martin Dunitz, London, 1991. USI Minami A, An KN, Cooney WP, Linscheid RL, Chao EY. Ligamentous structures of the metacarpophalangeal joint: a quantitative anatomic study. J Orthop Res 1984;1:361-368.
Clinical Biomechanics14 (1999)166-176
A new concept for a metacarpophalangeal prosthesis: consequence on joint biomechanics David J. Beevers”, Bahaa B. Seedhom Rheumatology and Rehabilitation ResearchUnit, University of Leeds, Leeds LS2 9NZ, UK
Received3 November1997;accepted7 July 1998
Abstract Objective. The purpose of this work was to establish whether surface replacement non-constrained prostheses can duplicate the normal biomechanics of the metacarpophalangeal joint. Design. A series of mathematical models. Background. A non-constrained prostheses has been designed for the replacement of the metacarpophalangeal joint. It uses the concept of surface replacement in that it attempts to replicate the anatomy of the original cartilage surfaces. The centre of rotation of the prosthesis is also sited at the same position as in the natural joint to maintain the balance between the flexor and extensor tendon forces, such that the prosthesis duplicates the biomechanics of the normal joint. Due to the unique dimensions of each joint that may present for surgery, the four sizes of prosthesis that are available for implantation may not always produce an exact replication of the joint kinematics. These situations were examined to establish whether the biomechanics of the joint can indeed be restored. Methods. Mathematical models for each size of prosthesis implanted into a range of different sized metacarpophalangeal joints were developed. The prosthetic and cartilage surface profiles were compared and the balance between the tendon forces was examined. Results. Differences in size that may occur between the surface profiles of the normal joint and prosthesis, together with any relocation of the centre of rotation, would have negligible effects on the normal joint biomechanics. Conclusions. All four sizes of the non-constrained prosthesis can duplicate the normal biomechanics of the joint and hence provide normal function.
Relevance A non-constrained metacarpophalangeal prosthesis that was designed to replace the surfaces of the joint can duplicate the normal biomechanics of the joint and hence provide normal function, provided that they are implanted with the correct surgical technique. 0 1999 Elsevier Science Ltd. All rights reserved. Keywords: Prosthesis;Metacarpophalangeal joint; Biomechanics
1. Nomenclature
A, B, C, D, E, F
a, b, c, 4 e,f g1
g2
included angles (degrees) variables (mm) maximum overlap of the cartilage and prosthetic bearing surface profiles in the sagittal plane at 20” extension (mm) maximum
and
overlap
prosthetic
g3
g4
of the cartilage
bearing
surface h
*Correspondingauthor. 0268-0033/99/$ - seefront matter 0 1999ElsevierScienceLtd. AI1 rights reserved. PII: SO268-0033(98)00064-3
profiles in the sagittal plane at 45” flexion (mm) maximum overlap of the cartilage and prosthetic bearing surface profiles in the coronal plane at 20” abduction-adduction (mm) maximum overlap of the cartilage and prosthetic bearing surface profiles in the coronal plane at 20” abduction-adduction (mm) perpendicular distance from the centre of rotation to the line of action of a force produced by a
D.J. Beevers, B.B. SeedhomlClinical
hs h* P
RP R,S R,, s COR
tendon; the tendon moment arm (mm) tendon moment arm before the prosthesis is implanted (mm) tendon moment arm after the prosthesis is implanted (mm) force produced by a tendon (N) radius of spherical prosthetic bearing surface (mm) radius of metacarpal cartilage surface in sagittal plane (mm) radius of metacarpal cartilage surface in coronal plane (mm) distance the centre of rotation is shifted in a palmar or dorsal direction from that of the normal location by implanting the prosthesis (mm)
2. Introduction Over the last 30 years numerous prostheses have been used to treat rheumatoid arthritis (RA) of the metacarpophalangeal (MCP) joint of the fingers, commonly known as the knuckle joint [1,2]. Currently, the Swanson prosthesis (Wright Medical Technology, USA), which is most widely used, is a single component implant manufactured from flexible silicone rubber. It does not restore the biomechanics of the joint, but acts as a “dynamic” spacer to separate the metacarpal and proximal phalanx. The term dynamic has been used to indicate that while the prosthesis keeps the bone ends apart, it can also bend to allow joint movement. A fibrous capsule develops around the prosthesis after implantation which provides it with some stability; a process known as encapsulation. Swanson prostheses are still in wide current use
Metacarpal
Biomechanics 14 (1999) 166-176
because of their ease of implantation, ease of removal if reoperation is necessary and low cost. Also, patient satisfaction is generally good, due to pain relief and cosmetic improvement. However, high incident rates of fracture and recurrent deformity, together with a low range of motion (ROM), have been reported in longterm follow-up studies [3-71. Moreover, these flexible prostheses cannot be used to adequately treat MCP joints damaged by traumatic injuries or post-traumatic osteoarthrosis (OA). This is because silicone rubber does not possess sufficient strength to transmit the large joint forces that act in the hands of these patients during gripping activities. Thus, although MCP joint replacement is now a routine surgical procedure, it still has severe limitations. In order to overcome the problems associated with the Swanson prosthesis, the next generation of prostheses that are being currently designed for MCP joint replacement employ the concept of surface replacement. This concept relies on the prosthesis replicating the anatomy of the original metacarpal cartilage surface. In order to duplicate the biomechanics of the normal joint, the centre of rotation of the prosthesis must also be sited at the same position as in the natural joint, hence maintaining the balance between the flexor and extensor tendon forces. Such a surface replacement, non-constrained prostheses was therefore designed by the first author (DB) to replace the surfaces of joints affected by trauma, post-traumatic OA and RA in the early stages of the disease [8] (Fig. 1). Four sizes of this prosthesis are available, with spherical bearing surface radii of 5, 6, 7 or 8 mm respectively. These sizes were chosen and based on published data on the dimensions of the MCP joint [9]. Ideally, the prosthesis should replicate the metacarpal cartilage surface when implanted, so that
Centre of rotation
Proximal phalanx
Dorsal
c-#-
Sagittal plane
/
1 :
,
, Palmar
Fig. 1. The modular non-constrained,
surface metacarpophalangeal
167
(MCP) prosthesis consists of three components; a sleeve, head and base,
168
D.J. Beevers, B.B. SeedhomlClinical
of activities performed by the hand require the MCP joint to move in an arc of motion from 0” to 90” flexion in the sagittal plane [ll]. When the prosthesis is implanted it is therefore aligned with the distal and palmar cartilage surfaces in the sagittal plane to provide the optimum fit over this critical arc of motion. However, despite the attempt to optimise the fit, the radius of the prosthesis may not always match the radius of the cartilage surface over the full arc of motion. This can be seen in Fig. 2a, where in a position of joint flexion in the sagittal plane, the prosthetic bearing surface would not extend as far as the cartilage surface it replaces. Also, the position where the centre of rotation occurred in the natural joint may be relocated in a different position in the reconstructed joint. Although the concept of a surface replacement prosthesis is to restore the anatomical surfaces and the biomechanics of the MCP joint, the question arises as to whether it can do this with sufficient accuracy in order to restore normal function. This paper investigates whether the biomechanics of the replaced MCP joint are similar to those of a normal joint after implanting a surface prosthesis. It then discusses whether surface replacement prostheses can in fact restore the biomechanics and hence normal function of the MCP joint.
the biomechanics of the normal joint will be duplicated. This can only be achieved if the metacarpal cartilage surface is spherical with an identical radius to that of the prosthesis, i.e. corresponds to one of the four sizes manufactured, 5, 6, 7 or 8 mm. However, an exact match between the cartilage surface and the prosthetic bearing surface will not always be achieved due to the unique dimensions of the metacarpal cartilage surface:
(a) if
the radius of the metacarpal head’s spherical cartilage surface does not correspond in size to the bearing surface radii of one of the four head components (Fig. 2a), or (b) if the radius of the cartilage surface varies in either the sagittal or coronal planes so that it does not have an exact circular profile (Fig. 2b), or (cl if the cartilage surface has circular profiles in the sagittal and coronal planes, but the radii are not similar in those two planes (Fig. 2~). Previous studies have shown that the profile of the cartilage surface in the sagittal and coronal planes can be accurately described by a single radius [9, lo]. Any slight differences that may occur between the cartilage surface profile and the circle that is used to describe this shape are so small that condition (b) would have negligible effect on the joint biomechanics. However, since conditions (a) or (c) are likely to occur, one of the four available sizes of prosthetic head component which most accurately matches the cartilage surface of the metacarpal head should be implanted. The majority
3. Methods The following sections describe the mathematical models developed to examine the effect that a differ-
R*
R, =5:0 mm R,= 4.7 mm
Condition (a)
R, =5.Omm R,,= 4.9 mm
R, = 5.0 mm Rcc= variable
& = 5.0 mm R,,= 4.7 mm
Sagittal plane
Biomechanics 14 (1999) 166-I 76
*
*
R, =5.0 mm R,, = variable
Condition (b)
R, =5.Omm R,,= 4.7 mm
Condition (c)
Fig. 2. If the prosthesis does not duplicate the metacarpal cartilage surface due to one or more of the three conditions biomechanics of the joint may be changed (the radii are not drawn to scale).
(a), (b) or (c), the
D.J. Beevers, B.B. SeedhomlClinical
ence between the prosthetic and cartilage surface radii, together with a repositioning of the centre of rotation, may have on the joint biomechanics. 3.I. Su$aceprofiles The difference between the cartilage and prosthetic bearing surfaces can be mathematically modelled in the sagittal and coronal planes as shown in Figs 3 and 4 respectively. In the sagittal plane the prosthesis provides a range of motion from 20” extension to 90” flexion in order to duplicate that of the natural joint. It can be seen in Fig. 3 that the overlap which occurs between the surface profiles expands during increasing joint extension. Thus, the maximum overlap between the surface profiles that would occur during finger extension, g,, would occur when the proximal phalanx is at the limit of normal motion with respect to the metacarpal head. This occurs when the finger is at a position of 20” extension and is represented by “LINE 1” on Fig. 3. The maximum overlap between the surface profiles that would occur during finger flexion, gz, would occur when the proximal phalanx is at a position of 45” flexion as shown on Fig. 3. This finger position is represented by “LINE 2” on Fig. 3. The terms g, and g, are positive when the prosthetic bearing surface profile extends beyond the cartilage surface profile (e.g. g, in Fig. 3a and g2 in Fig. 3b). This
Prosthetic bearing surface ,
Metacarpal cartilage surface Distal surface
169
Biomechanics 14 (1999) 166-l 76
indicates that the proximal phalanx would be pushed further away from the metacarpal, when the finger is in this position after implantation of the prosthesis. Thus, the collateral ligaments would become tighter than normal. The terms gl and g2 are negative when the prosthetic profile is smaller than the cartilage profile (e.g. g, in Fig. 3b and g, in Fig. 3a). This indicates that the proximal phalanx would be closer to the metacarpal and the ligaments would be looser than normal when the finger is in this position. In order to calculate gl and gZ, the following angles and dimensions are defined: Angle A,, is formed by the line of zero flexiomextension that passes through the centre of the prosthetic bearing surface and the centre line of the proximal phalanx at 20” extension (LINE 1) at the position of maximum overlap between the surface profiles during joint extension. Angle A, is therefore constant at 20” throughout the calculations. Angle A2, is formed by the line of zero flexion/extension that passes through the centre of the prosthetic bearing surface and the centre line of the proximal phalanx at 45” flexion (LINE 2) at the position of maximum overlap between the surface profiles during joint flexion. Angle .A2 is therefore constant at 45” throughout the calculations. The included angle A is given by the addition of angles A, and A2 and is therefore constant af 65” throughout the calculations. Angle B is formed by LINE 2 and line a.
Prosthetic bearingsurface .~~~@---j-‘~~.~
Metacarpal cartilage surface Distalwrface
Centre of rotati
Centre of rotation of metacarpal cartilage surface
(a) Metacarpal smaller than prosthesis
(b) Metacarpal larger than prosthesis
Fig. 3. Mathematical model describing the maximum distances between the surface profiles of the prosthesis and cartilage that may occur over the arc of motion in the sagittal plane.
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D.J. Beevers, B.B. SeedhomlClinical
Prosthetic bearing surface I
Metacarpal ’ cart)lage ‘FEZ
Biomechanics 14 (1999) 166-l 76
Combining eqns (l)-(5), the maximum distance between the surface profiles in the sagittal plane at 20 extension, g,, is given by:
surface
R
2 sin 180-A-sin-’ sin A
g, =R,-
[(R, - R&os X
A21sin A 1
Rc,s
1I
Combining eqns (1) and (6) the maximum distance between the surface profiles in the sagittal plane at 45” flexion, g,, is given by: g,=R,-R,,-
Fig. 4. Mathematical model describing the maximum distances between the surface profiles of the prosthesis and cartilage that may occur over the arc of motion in the coronal plane.
R, - R,,
~ cos A2
In the coronal plane each prosthesis has to 20” arc of abduction and adduction from the in both the ulnar and radial directions. The difference between the surface profiles occurs at 20”, denoted as g3 and g4. Since e=R,,-Rcc
Line a is the line joining the centre of rotation of the metacarpal cartilage surface to the point where LINE 1 intersects the cartilage surface (this is equal to the radius of the cartilage surface in the sagittal plane, I?,,). Angle C is formed by LINE 2 and line a. Line c is the distance between the centre of rotation of the prosthetic bearing surface and the point where LINE 1 intersects the cartilage surface. The distance between the centre of rotation of the metacarpal surface and the centre of rotation of the prosthetic surface is given by length b. Since
b= -R, - 4s cos A2 b sin A
sin B= -
a
C= 180-(A+B)
(2)
(3)
a sin C
c= -
sin A
(4)
provide a centreline maximum t herefore (9)
.a=a=Rp-f
(10) Combining similar eqn (2)-(4) (11) and (12), the maximum distance between the surface profi le:s in the coronal plane at 20” abduction or adduction, g3, which is equal in magnitude to g4 due to the symmetrical nature of the prosthesis, is given by: R
g3=g4=Rp-
--? sin 180-D-sin’ sin D
Since the cartilage surfaces of the metacarpal head are often not true spheres (condition “c”), radius R,, is dependent on which finger the prosthesis is implanted in. The radius of the cartilage surface in the sagittal plane is approximately 12.0% larger than the radius in the coronal plane for an index finger [9]. The radius of the cartilage surface in the coronal plane is approximately 9.0, 1.6 and 1.6% larger than the radius in the sagittal plane for a middle, ring and little finger respectively [9], hence for an index finger:
hence: g,=R,-c
RC,C = R,,/I .12 (5)
and gz= R, - UL+b)
(6)
(12)
for a middle finger: Rc,c= 1.09Rw
for a ring or little finger: Rc,c= I .o16R,,5
(13) (14)
D.J. Beevers, B.B. SeedhomlClinical
171
Biomechanics 14 (1999) 166-176
3.2. Centre of rotation If the position of the natural centre of rotation of the joint is altered as a result of implanting a prosthesis, this can also affect the biomechanics. A simple model of the MCP joint is described in Fig. 5. The intrinsic muscles of the finger consist of the lumbrical, dorsal interosseous and palmar interosseous. Although the tendons of two intrinsic muscles act on the radial side of each MCP joint, they are represented by a single tendon for simplicity. The moment arms of the extensor (h3) and those of both flexors (h4, and h5) vary throughout the range of motion and these values measured from 30” extension Centre of rotation for metacarpal head
to 90” flexion are listed in Table 1 [12]. Youm et al. [12] found that the extensor tendon moment arm remained approximately constant throughout the flexion-extension arc of motion, while the moment arms of the flexor tendons increased by up to 50%. Similar results for the moment arms at a joint angle of 45” flexion have also been measured by Spoor [13]. Neither of these studies stated the dimensions of metacarpal head radius of the cadaveric specimens used in the experiments. However, we found that the moment arms measured matched those of a joint with a metacarpal radius of 7 mm, cross-sections of which were obtained from a set of published data [14]. These cross-sections were of joints at 0” flexion. Hence, the
Ulnar
Intrinsics
I-\ -,-,-I
Coronal plane
,/ I
\ -A
//-------+ 0
Radial Extensor digitorum
Sagittal plane
c----M--/ i I’ /\ \H 0’
Distal
Flexor digitorum profundus Flexor digitorum su Fig. 5. Movement of the joint in the coronal plane is caused by the intrinsic muscles. Movement flexor and extensor tendons.
Table 1 The extensor digitorum (ED), h3, flexor digitorum measured from 30” extension to 90” flexion Angle of MCP joint
ED, h
profundus
(FDP), h, and flexor digitorum
FDP, h,
FD
in the sagittal plane is caused by the pull of the
superficialis
(FDS), h,, tendon moment arms
FDS, k
30” extension 0” flexion 45” flexion 90” flexion
10 9 9 9
-10 -11 -13 -15
(1.00) (1.20) (1.44) (1.67)
FD c-1FDP
(-1FDP -12 -14 -16 -18
(1.20) (1.56) (1.78) (2.00)
All values are given in millimetres. The moment arms measured in a dorsal direction are given as positive values and those measured in a palmar direction as negative values. The values in parentheses are the moment arm ratios.
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D.J. Beevers,B.B. SeedhomlClinical Biomechanics 14 (1999) 166-176
values of the moment arms stated in Table 1 were assumed to belong to a metacarpal head of 7 mm radius and the tendon moment arms (h,) for all the other theoretical sizes of metacarpal head used in the analysis were calculated by scaling up or down these values using eqn (15).
The distance that the centre of rotation is shifted in a palmar or dorsal direction from that of the normal location in the natural joint by implanting the prosthesis is given by &OR= R, - R,, (16) The length of each tendon moment arm after the prosthesis is implanted is given by
prosthesis remain in the same position over this arc of motion. 4. Results
The radius of the bearing surfaces of the MCP prosthesis increase in steps of 1.0 mm. It is therefore possible to implant each size of prosthesis into an MCP joint that has a radius which is up to 0.5 mm larger or smaller than that of the prosthetic bearing surface. The discrepancies that may occur between the prosthetic and cartilage surface radii, together with any relocation of the centre of rotation, when implanting a prosthesis into a larger or smaller metacarpal head is described hereafter. 4.1. Maximum overlap between the su$ace profiles
h* = h, - RCoR
(17)
The percentage change between the normal tendon moment arm before implanting the prosthesis and the tendon moment arm after implanting the prosthesis is given by h* -h,
Percentage change in moment arm = 100 ( hs > (18) Hence, the difference between the tendon moment arms before and after implanting each size of prostheses can be calculated for any size of metacarpal head over the arc of flexion-extension, assuming that the centre of rotation of the normal MCP joint and
The distances between the cartilage and prosthetic bearing surface profiles at 20” extension dpr) and at 4.5” flexion (&) for each size of prosthesis in the sagittal plane are given in Fig. 6. If the radius of the prosthetic bearing surface is equal to the radius of the cartilage surface, distances g, and g2will be zero and a perfect fit will be obtained. However, as a prosthesis replaces cartilage surfaces with increasingly smaller radii, distances gl and g, will become increasingly positive and negative respectively (Fig. 6 and as represented in Fig. 3). When the joint is at 20” extension the proximal phalanx bone will therefore be further away from the natural position it should occupy next to the original cartilage surface. Thus, the collateral ligaments will be
85
-0.25
. +&6 - a. d-c - l -
I
J Metacarpal cartilage surface radius in sagittal plane, k,, (mm)
Fig. 6. Maximum distances between the surface profiles in the sagittal plane for each of the four sizes of prosthesis.
5 mm Prosthesis,g , 5 mm Prosthesis,g, mm Prosthesis,g , 6 mm Prosthesis,g, 7 mm Prosthesis,g , 7 mm Prosthesis,g, 8 mm Prosthesis,g 1 8 mm Prosthesis,gz
173
D.J. Beevers, B.B. Seedhom/Clinical Biomechanics 14 (1999) 166-176
cartilage surface it replaces. Hence, in the coronal plane the collateral ligaments in the reconstructed joint will be more lax in abduction and adduction than the natural joint. For each size of prosthesis the laxity of the collateral ligaments would be greatest, and therefore the worst fit would be obtained, when a prosthesis has to replace the largest radius cartilage surface in the range of metacarpal head sizes it has to cater for (Fig. 7); for example, when a prosthesis with a 7 mm radius is implanted in a joint with a 7.5 mm radius. If a prosthesis is implanted in a ring or little finger which has a smaller radius of cartilage surface in comparison to the radius of the prosthetic bearing surface, the collateral ligaments of the reconstructed joint would generally be more taut in abduction and adduction than in the natural joint (Fig. 7). Conversely, if the radius of the cartilage surface is larger than the prosthetic bearing surface, the collateral ligaments would generally be lax. The overlap between the surface profiles under this condition, however, is only half those for the index and middle. This is because the metacarpal head cartilage surfaces of the ring and little fingers are closer to a spherical shape.
stretched. When the joint is in a position of 45” flexion the prosthetic bearing surface will be effectively smaller than the cartilage surface and the collateral ligaments will therefore be lax. As a prosthesis replaces cartilage surfaces with increasingly larger radii, distances gl and g2 will be negative and positive respectively (Fig. 6). Hence, when the joint is at 20” extension the collateral ligaments will be lax and when the joint is in a position of 45” flexion the collateral ligaments will be taut. Since the prosthesis is chosen to match the metacarpal from the cartilage dimensions in the sagittal plane, a head with a different radius in the coronal plane may affect the biomechanics in the coronal plane. If a prosthesis is implanted into an index finger, the radius of the prosthetic bearing surface in the coronal plane would be larger than the radius of the cartilage surface it replaces (Fig. 4). Hence, in the coronal plane the collateral ligaments in the reconstructed joint will be more taut in abduction and adduction than in comparison to the natural joint. The collateral ligaments would be tightest and therefore the worst fit would be obtained, when a prosthesis has to replace the smallest radius cartilage surface in the range of metacarpal head sizes it has to cater for (Fig. 7). For example, a 7 mm radius prosthesis could be implanted into joints ranging in size from 6.5 to 7.5 mm in radius. Over this range of sizes the worst fit would be obtained when it was implanted in a joint with a 6.5 mm radius. If a prosthesis is implanted into a middle finger, the radius of the prosthetic bearing surface in the coronal plane would be generally smaller than the radius of the
4.2. Position of the centre of rotation after implantation When the prosthesis is implanted into the MCP joint, it is aligned with the centreline of the metacarpal in the coronal plane and with the distal and palmar cartilage surfaces in the sagittal plane. When considering alignment in the coronal plane, if the bearing surface of the prosthesis is larger or smaller in
4 A II
‘4 ‘4
h
\ ‘4
h
- -+ - RS - index
‘b l
‘4 T
‘4
‘A ‘4
l ‘8
- + - R6 - index
‘a
a
\
- + - R7 - index \
‘4
9.
- -* - R8 - index l *
-**+*-
R5
- middle
mm*****R6 - middle --**A-- K7 _ middle *****.’ R8 - middle
Y fs” .2 n
-0.04
+
R5 - ring / little
-
R6 - ring / little
+
R7 - ring / little
-C
R8 - ring / little
-0.06 -0.08
’ Metacarpal cartilage surface radius in sag&al plane, qS (mm)
Fig. 7. Maximum distances between the surface profiles in the coronal plane for each of the four sizes of prosthesis, when implanted into an index, middle, ring or little finger.
114
D.J. Beevers, B.B. SeedhomiClinical
radius in comparison to the cartilage surface, the centre of rotation may be shifted in a proximal or distal direction. However, it will still lie on the centreline of the bone and consequently the values of P,, Pz, h, and h2 (Fig. 5) will remain unchanged. The biomechanics of the joint in the coronal plane (abduction and adduction of the joint) cannot be significantly altered by a change in the position of the centre of rotation. Similarly, a proximal or distal shift in the centre of rotation in the sagittal plane would not significantly alter flexion or extension of the joint. However, a
Biomechanics 14 (1999) 166-176
palmar or dorsal shift in the centre of rotation will cause changes in h3, h4 and h5, the tendon moment arms. If the metacarpal head is smaller than the implanted prosthesis, the centre of rotation of the reconstructed joint would be positioned in a dorsal direction from that of the natural joint. The extensor moment arm (h3) is decreased, whereas those of the flexors (h, and h5) are increased (Fig. 8). Similarly, if the metacarpal head is larger than the implanted prosthesis, the centre of rotation would be placed in a palmar direction. The extensor moment arm (h3)
8 ,
-IOJ
1
Metacarpalcartilage surfaceradiusin sag&al plane, %,%(mm)
I
(a) Extensordigitorum 8 ‘;: G
6
--+--R5-45F -+.R6-30E
k
J -8
--B--R6-45F R6- 90F R7- 30E ~815 I-+-R7-OF .R7- 45F R7- 90F -+--R8-3OE --•--R8-45F
Metacarpalcartilage surfaceradiusin sag&al plane, RiJ (mm) (b) Flexor digitorum profundus
Metacarpalcartilage surfaceradiusin sag&al plane, &,S (mm) (c) Flexor digitorum superkiahs Fig. 8. Changes in the moment arm due to relocation of the centre of rotation. The analysis was performed on all four sizes of prosthesis represented by R5, R6, R7 and R8, at joint angles of 30” extension, 0”, 45” and 90” flexion (represented by 30E, OF,45F and 90F respectively).
D.J. Beevers, B.B. SeedhomlClinical
increases, while those of the flexors (hq and h5) decrease (Fig. 8). For any specific prosthesis implanted in any size of joint, the percentage change in the moment arm varies over the arc of motion (Fig. 8). The maximum change in the extensor tendon moment arm occurs in flexion and remains constant as the flexion angle increases from 0” to 90”. The maximum deviation of the flexor tendons moment arms occurs in extension, and as flexion of the joint increases, the deviation decreases (Fig. 8). The centre of rotation could be moved by a maximum distance of 0.5 mm in a dorsal or palmar direction for each size of prosthesis. The maximum change in the moment arms of the flexor and extensor tendons occurs when implanting a prosthesis with a 5 mm radius bearing surface into metacarpal heads that have cartilage surface radii of 4.5 or 5.5 mm. Under these conditions the tendon moment arm of extensor digitorum would be altered by a maximum of -8.6% and +7.1%. The tendon moment arm of flexor digitorum profundus would be altered by a maximum of +7.7% and -6.4%. The tendon moment arm of flexor digitorum superficialis would be altered by a maximum of +6.5% and -5.3%. 5. Discussion The profile of the cartilage surface may be larger or smaller than that of the prosthetic bearing surface and the centre of rotation of the reconstructed joint may be located in a palmar or dorsal direction in relation to its former position in that of the natural joint. Consequently, the various factors affecting the kinematics of the joint were investigated and are discussed in the following sections. 5.1. Differences in the radii of the natural and prosthetic joints
The worst fit between the radii of the natural and prosthetic joints for each size of prosthesis would be obtained when the prosthesis is implanted in joints which have a cartilage radius at the extreme of the range it has to cater for, i.e. a radius 0.5 mm larger or smaller than the radius of the prosthetic head (Fig. 6). These maximum discrepancies under similar conditions for each size of prosthesis are approximately equal. For example, a prosthesis with a 5 mm radius when implanted in a joint with a 4.5 mm radius, or a prosthesis with a 6 mm radius when implanted in a joint with a 5.5 mm radius, will have discrepancies of approximately 0.24 mm at 20” extension (gl), and -0.21 mm at 45” flexion (g2) (Fig. 6). However, these discrepancies become more significant in relation to
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the prosthetic radius as the size of prosthetic head decreases (the ratio between the discrepancy and size of head becomes larger). Thus, the smallest size of prosthesis (5 mm) would provide the least accurate fit and the larger size (8 mm) the most accurate fit. How significant are these discrepancies between the radii of the natural and prosthetic joints? The maximum difference that would occur between the profiles of any size of prosthesis and natural joints in flexion-extension is 0.25 mm and in abduction-adduction is 0.09 mm. Minami et al. [15] have shown that during flexion from 0” to 80” the dorsal portions of both the radial and ulnar collateral ligaments of the normal MCP joint increased in length by 3.0 to 4.0 mm. The middle portions of each ligament were elongated by 0.4 to 1.0 mm and the palmar portions of each ligament were shortened by 1.0 to 2.0 mm. In extension, the dorsal portions of each ligament shortened by 2.0 to 3.0 mm, the middle third of the ligaments slightly shortened and the palmar thirds of the ligaments lengthened. The discrepancies that the theory predicts are therefore insignificant in relation to the amount by which the ligaments can extend. The full range of motion of the reconstructed joint would therefore be possible before the ligaments would become sufficiently stretched to prevent further motion, or sufficiently lax to allow deformation in the form of ulnar drift or subluxation. The slight differences that may occur between the surface profiles would have a negligible effect and the prosthesis would duplicate the normal biomechanics. 5.2. Dorsal or palmar shift in the centre of rotation
Since the centre of rotation can be moved a maximum distance of 0.5 mm in either a dorsal or palmar direction for each size of prosthesis, this has the most significant effect on the tendon moment arms when the prosthesis which has the smallest bearing surface radius is implanted. The maximum dorsal shift in the centre of rotation for the smallest prosthesis (5 mm radius) would be created when replacing a metacarpal head with a 4.5 mm cartilage radius. Under this condition the maximum change in the tendon moment arms of extensor digitorum, flexor digitorum profundus and flexor digitorum superficialis would be -8.6, 7.7 and 6.5% respectively. Although the distance between each tendon will remain the same in the reconstructed joint, the shift in the centre of rotation will change the ratio between the tendon moment arms. The original moment arm ratio of 1.22 for extensor digitorum and flexor digitorum profundus at 0” flexion would therefore be increased to 1.43 in the reconstructed joint, giving an increase of 17.4%. Similarly, the original moment arm ratio of 1.56 for extensor digitorum and
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D.J. Beevers, B.B. SeedhomJClinical Biomechanics 14 (1999) 166-I 76
flexor digitorum superficialis at 0” flexion would be increased to 1.80, giving an increase of 15.6%. These changes in the moment arm ratios would make flexion of the joint easier and extension more difficult. The slight increase in grip strength and difficulty of finger extension which would occur under this condition should not be sufficient to have a detrimental effect on the biomechanics and hence hand function. Similarly, if the centre of rotation is shifted in a palmar direction, by replacing a 5.5 mm radius cartilage surface with a 5 mm radius prosthesis, the maximum change in the tendon moment arms of extensor digitorum, flexor digitorum profundus and flexor digitorum superficialis would be 7.1, -6.4 and -5.3% respectively. The original moment arm ratio of 1.22 for extensor digitorum and flexor digitorum profundus at 0” flexion would therefore be decreased to 1.08 in the reconstructed joint, giving an decrease of 12.0%. Similarly, the original moment arm ratio of 1.56 for extensor digitorum and flexor digitorum superficialis at 0” flexion would be decreased to 1.39, giving an decrease of 10.8%. Thus, flexion of the joint would be more difficult and extension easier. Again, under this condition the slight ease of MCP joint extension and reduction in grip strength would not be sufficient to have a detrimental effect on the biomechanics and hence hand function. The surgical procedure required to implant a prosthesis in the stated position has highlighted the inadequacy of standard surgical instruments. Therefore, specialised surgical instruments have been developed and validated for accurate and reproducible positioning of the non-constrained MCP prosthesis described in this text. These instruments are the subject of a separate clinical paper. 6. Conclusions The MCP prosthesis was designed to be aligned with the distal and palmar cartilage surfaces in the sagittal plane to provide the optimum fit over the most commonly used arc of flexion. Each size of prosthesis may not duplicate the metacarpal cartilage surface and the centre of rotation may be relocated when it is implanted in this manner due to a mismatch between the dimensions of the cartilage surfaces and one of the four standard sizes of prosthesis that would be implanted. The prosthesis with the largest radius (8 mm) would provide the most accurate duplication of the normal joint biomechanics over the range of MCP joint sizes into which it can be implanted. The prosthesis with the 5 mm radius bearing surface would provide the least accurate duplication of the joint biomechanics. However, each size of prosthesis would
not produce a significant alteration in the biomechanics of the MCP joint. Consequently, all four sizes of the non-constrained prosthesis would provide normal joint function. Acknowledgements This research was supported by grants from The Arthritis and Rheumatism Council and from the Special Trustees of the Leeds Teaching Hospitals. The authors would like to thank M Pullan and B Whitham for their technical expertise and help with the experiments. References [l] Beevers DJ, Seedhom BB. Metacarpophalangeal joint prostheses: a review of past and current designs. Proc Instn Mech Engrs Part H 1993;207:195-206. PI Beevers DJ, Seedhom BB. Metacarpophalangeal joint prostheses. A review of the clinical results of past and current designs. J Hand Surg 1995;20B:125-136. [31 Beckenbaugh RD, Dobyns JH, Linscheid RL, Bryan RS. Review and analysis of silicone-rubber metacarpophalangeal implants. J Bone Jt Surg 1976;58A:483-487. [41 Bieber EJ, Weiland AJ, Volenec-Dowling S. Silicone-rubber implant arthroplasty of the metacarpophalangeal joints for rheumatoid arthritis. J Bone Jt Surg 1986;68A:206-209. Kay AGL, Jeffs JV, Scott JT. Experience with silastic prostheses in the rheumatoid hand: a 5-year follow-up. Ann Rheum Dis 1978;37:255-258. WI Kirschenbaum D, Schneider LH, Adams DC, Cody RP. Arthroplasty of the metacarpophalangeal joints with use of siliconerubber implants in patients who have rheumatoid arthritis. J Bone Jt Surg 1993;75A:3-12. 171 Wilson YG, Sykes PJ, Niranjan NS. Long-term follow-up of Swanson’s silastic arthroplasty of the metacarpophalangeal joints in rheumatoid arthritis. J Hand Surg 1993;18B:81-91. PI Beevers DJ, Seedhom BB. Laboratory development of a nonconstrained, noncemented, modular, metacarpophalangeal prosthesis. Proc Instn Mech Engrs Part H 1995;209:185-195. [91 Unsworth A, Alexander WJ. Dimensions of the metacarpophalangeal joint with particular reference to joint prostheses. Engng in Medicine 1979;8:75-80. WI Unsworth A, Dowson D, Wright V. Cracking joints: a bioengineering study of cavitation in the metacarpophalangeal joint. Ann Rheum Dis 1971;30:348-358. IllI Badley EM, Wagstaff S, Wood PHN. Measures of functional ability (disability) in arthritis in relation to impairment of joint movement. Ann Rheum Dis 1984;43:563-569. [121Youm Y, Gillespie TE, Flatt AE, Sprague BL. Kinematic investigation of normal MCP joint. J Biomechanics 1978;11:109-118. P31 Spoor CW. Balancing a force on the fingertip of a two-dimensional finger model without intrinsic muscles. J Biomechanics 1983;16:497-504. P41 Meals RA, Seeger LL, An atlas of forearm and hand crosssectional anatomy. Martin Dunitz, London, 1991. USI Minami A, An KN, Cooney WP, Linscheid RL, Chao EY. Ligamentous structures of the metacarpophalangeal joint: a quantitative anatomic study. J Orthop Res 1984;1:361-368.