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К 185-летию великого русского российского ученого и гражданина России -Дмитрия Ивановича Менделеева и 150-летию его наследия -«Периодического закона для химических элементов». К 170-летию Ивана Петровича Павлова - выдающегося русского российского исследователя в области физиологии, первого нобелевского лауреата России.
UDK 372.2; 514; 539.13; 611.7; 616.072; 616.7; 617.3; 617.9
K. J. van Zwieten a, K. P. Schmidta, P. Adriaensens a, O. E. Piskun b, S. A. Varzin b c
ANATOMICAL OBSERVATIONS ON THE INCONGRUENCES OF THE ARTICULAR SURFACES OF THE PROXIMAL INTERPHALANGEAL (P.I.P.) JOINT IN THE
NORMAL HUMAN FINGER
a) Functional Morphology, Department of Anatomy, University of Hasselt, Diepenbeek, Belgium, b) Department of Physical Culture and Adaptation, Peter-the-Great St. Petersburg Polytechnic University, St. Petersburg, Russia, c) Department of Intermediate Level Surgery, Faculty of Medicine, St. Petersburg State University, St. Petersburg, Russia. koosjaap.vanzwieten@uhasselt.be
Summary.
By plane geometry graphical constructions, applied on a two-dimensional High Resolution MRI sagittal slice of the proximal interphalangeal (P.I.P.-) joint of an anatomical specimen of the normal human finger, the incongruences of the mating joint surfaces were quantified. Our outcome data offer better insights and may be useful for novel PIP prostheses development.
Keywords PIP-joint; articular surfaces; graphical analysis; PIP-arthroplasty Introduction
In the past decade, various reports were published containing qualitative and quantitative data on osteoarthritis (OA) and rheumatoid arthritis (RA) in Russian communities [1] as well as in the Russian Federation [2-3]. These chronic diseases can be characterised as follows. "Osteoarthritis is a degenerative joint disease, that changes the tissue homeostasis of articular cartilage and subchondral bone. ... The common features of osteoarthritis are loss of cartilage, joint space narrowing, hypertrophic bone changes, osteophyte formation, osteophytes defined as outgrowth of the bone and cartilage occurring at the joint margins" [4]. "Rheumatoid arthritis is a chronic, destructive, inflammatory disease of the synovial membrane that lines . the surface of joints, where it produces lubricating and nourishing synovial fluid" [5]. In the Russian Federation, not only the physical health problems, but also the social burden and the discomfort of OA and RA have been
К 185-летию великого русского российского ученого и гражданина России -Дмитрия Ивановича Менделеева и 150-летию его наследия -«Периодического закона для химических элементов».
К 170-летию Ивана Петровича Павлова - выдающегося русского российского исследователя в области физиологии, первого нобелевского лауреата России.
reported [6], [7]. State of the art
To overcome the debilitating effects caused by OA and RA, such as pain, loss of function, and deformations of the interphalangeal joints, during the past decades prostheses of these joints were developed and applied, especially Proximal Inter Phalangeal (PIP) prostheses, also known as PIP-implant arthroplasties. In the wake of this, a wealth of clinical and epidemiological reports on their higher or lower success rates followed, e.g. [8], [9], [10], [11]. Anatomically, the PIP-joint of the human finger is composed by the convex caput (or head) of the proximal phalanx articulating with the concave basis (or base) of the middle phalanx (Fig. 1a, Fig. 1b). Meanwhile, the development of any novel PIP-prosthesis (or implant arthroplasty) greatly depends on in situ measurements in anatomical specimens of the normal human finger. In general, with the only exception of [12] and [13], measurement data on PIP-arthroplasty design remain remarkably scarce. In [13], an alternative concept of a rolling-without-sliding PIP-arthroplasty is presented, in a certain way foreshadowed by [14], while the concept of [12] is mainly based on circle-like shapes, which in fact are not so realistic anatomically. In view of all this, is is justified to provide some more data on the morphology of the proximal convex part, as well as of the distal concave part, of the PIP-joint of the normal human finger in situ. Therefore, the plane geometrical properties of the curvatures of both parts, also in relation to each other, are subject of this study.
Stating the problem
"The phalangeal condyles have the particularity of displaying a radius of curvature with an almost perfect regularity. This character clearly differentiates it from the femoral condyles (in the knee) that we always take as an example. In fact, the geometric location of the axis of flexion-extension movements of the second phalanx on the first phalanx...can be roughly considered as a single constant and fixed transverse axis" [15]. Indeed, comparing the proximal interphalangeal (PIP) joint (Fig. 1a) with the femoral condyles and the articulating surfaces of the tibia in the knee joint [16] makes clear such differences. Meanwhile, not only the knee joint, but also the PIP-joint of the finger have incongruent contact surfaces. Moreover, in anatomy, 'incongruent' is defined as "not agreeing in conformation; as, incongruent surfaces of a joint" [17]. One glance at the osseous outlines of the normal PIP-joint (Figs. 1a and 1b) is enough to note that the concavity of the distal segment, and the convexity of the proximal segment, do not match perfectly, in other words, they are incongruent. As a
К 185-летию великого русского российского ученого и гражданина России -Дмитрия Ивановича Менделеева и 150-летию его наследия -«Периодического закона для химических элементов». К 170-летию Ивана Петровича Павлова - выдающегося русского российского исследователя в области физиологии, первого нобелевского лауреата России.
consequence, dorsal and palmar gaps between their bony surfaces can be observed (Fig. 1b, red arrows).
In the in situ anatomical specimen of the human finger, however, wedge-shaped synovial folds - at least partly - compensate for such incongruences of the mating surfaces [18].
Fig. 1 a (top). Osteology of the proximal interphalangeal (PIP-) joint of an otherwise normal second finger, radial view. Left is distal; right is proximal. Fig. 1 b (bottom).
К 185-летию великого русского российского ученого и гражданина России -Дмитрия Ивановича Менделеева и 150-летию его наследия -«Периодического закона для химических элементов». К 170-летию Ивана Петровича Павлова - выдающегося русского российского исследователя в области физиологии, первого нобелевского лауреата России.
Line drawing of Fig. 1a. Arrows indicate "gaps" of joint. Material and methods
As the present study intends to assess the plane geometrical curvatures of the in situ articular surfaces of the concave distal segment, as well as of the "perfectly regular" [15] convex proximal segment, in one and the same PIP-joint of an anatomical specimen of the finger, we made use of archive pictural material, part of which had been already published [18], [19]. As a consequence, we are able to present real high resolution images, instead of the usual line diagrams of these curvatures [20]. Technical data are as follows. High Resolution-MRI (HR-MRI) of an otherwise normal human anatomical specimen of an extended right third finger was performed. Technical data of HR-MRI: Varian 400 spectrometer, 9,4 T superconducting magnet. Field of view FOV (mm) in transverse plane: 25 x 25; imaging data matrix of 350 x 350; pixel resolution (^m) 71 x 71. Further acquisition parameters: repetition time TR: 2500 ms; echo time TE: 18 ms; number of averages NA = 24; slice thickness 2 mm. One sagittal slice of the PIP-joint was used (Fig. 2a), meeting requirements normally posed by plane geometry.
Fig. 2 a (left). HR-MRI sagittal slice of PIP-joint (see text), showing curvatures (left to right) of the distal segment, and of the proximal segment. Arrows in green: bone cortex; - blue: hyaline cartilage; - white: synovial fluid
Fig. 2 b (right). Approximate radii of a curvature can be found through the perpendicular bisectors of inscribed open polygon formed by its successive chords
К 185-летию великого русского российского ученого и гражданина России -Дмитрия Ивановича Менделеева и 150-летию его наследия -«Периодического закона для химических элементов». К 170-летию Ивана Петровича Павлова - выдающегося русского российского исследователя в области физиологии, первого нобелевского лауреата России.
Fig. 2a shows one resulting sagittal slice of the PIP-joint, including the curvatures (from left to right) of the distal segment, and of the proximal segment. According to a classical method in plane geometry [21], approximate radii of a curvature can be found through the perpendicular bisectors of an inscribed open polygon formed by its successive chords (Fig. 2b, facsimile of original [21]).
Fig. 3 a (left). Inscribed polygon A-L, plotted in order to approximate the concave curvature of the distal part of the PIP-joint, derived from Fig. 2a. Fig. 3 b (right). Inscribed polygon A-S, plotted in order to approximate the convex curvature of the proximal part of the PIP-joint, derived from Fig. 2a.
In Fig. 3, these chords are plotted on the HR-MRI-slice, resulting in the shorter open polygon A-L of the distal curvature (Fig. 3a) and the longer open polygon A-S of the proximal curvature (Fig. 3b). With the mathematical computer graphics method [22], we graphically constructed the perpendicular bisectors of the chords of both curvatures, with the exception of chords JK and KL of the distal curvature that are convex instead of concave, as already suggested by the upper red arrow in Fig. 1b.
Results
1. Distal curvature (concave)
The majority of points of intersection M through R of each pair of successive
К 185-летию великого русского российского ученого и гражданина России -Дмитрия Ивановича Менделеева и 150-летию его наследия -«Периодического закона для химических элементов». К 170-летию Ивана Петровича Павлова - выдающегося русского российского исследователя в области физиологии, первого нобелевского лауреата России.
perpendicular bisectors of the chords, namely the points M, N, O, Q, and R, appears to be clustered (Fig. 4a). Other such clusters are not observed.
Fig. 4 a (top). Open polygon A-J (Fig. 3a) approximating the concave curvature of the distal part of the PIP-joint, used to graphically construct (see text) perpendicular bisectors of its chords, resulting in intersection points K-R.
Fig. 4 b (bottom). Open polygon A-S (Fig. 3b) approximating the convex curvature of the proximal part of the PIP-joint, used to graphically construct (see text) perpendicular bisectors of its chords, resulting in intersection points T-A1.
Fig. 4a and Fig. 4b show the resulting geometrical constructions, by means of chord approximations of both original curves, as well as the intersection points of any pair of
К 185-летию великого русского российского ученого и гражданина России -Дмитрия Ивановича Менделеева и 150-летию его наследия -«Периодического закона для химических элементов». К 170-летию Ивана Петровича Павлова - выдающегося русского российского исследователя в области физиологии, первого нобелевского лауреата России. their successive perpendicular bisectors. As far as our computer program [22] allowed,
most points of intersection were consecutively marked by successive lettering, namely
K-R for the shorter concave distal curvature, and T-Z-A1 for the longer convex
proximal curvature (Fig. 4a and Fig. 4b).
2. Proximal curvature (convex)
Roughly, two clusters of points of intersection of each pair of successive perpendicular bisectors of the chords can be noted (Fig. 4b). One cluster is located in the vicinity of point T. As our computer program [22] did not allow to insert an even finer and denser lettering, "T" alone stands for this cluster that represents some 10 successive points of intersection. Of the remaining successive points of intersection, the points U, V, Z, and A1, located in more distal and more palmar positions than "T", represent the second cluster.
3. Comparing both curvatures
When both graphical constructions are compared with each other, by representing them in one image (Fig. 5) at the same scale (as indicated by bold vertical bars I in Fig. 5), obvious differences between the two curvatures become apparent. Most of the radii of the distal (concave) curvature, starting from the cluster "M, N, O, Q, and R" are shorter than most of the radii of the proximal (convex) curvature, starting from the cluster around point "T"
This difference is indicated schematically in Fig. 5 by comparing the shorter line segment GH (Fig. 5, above) with the longer line segment IJ (Fig. 5, below). Radii of the rest of the proximal (convex) curvature, however, departing from cluster "U, V, Z, and A1", are much shorter than the line segment GH. In other words, in the extended PIP joint (that is to say, in the situation from where our analysis started) most of the distal curvature is too concave in relation to the convexity of the proximal curvature. In 90° flexion of the PIP-joint, however, the remaining (palmar) part of the proximal curvature is too convex in relation to the concavity of the distal curvature. Fig. 6b gives a model-wise approximation of the latter remarkable situation.
Our graphical plane geometry construction results (Fig.4) finally suggest that a) the distal curvature's cluster of points shows rather equal radii of curvature of the involved area, and thus approximates the center of one circle; b) the proximal cluster around point "T" represents in even better approximation the
К 185-летию великого русского российского ученого и гражданина России -Дмитрия Ивановича Менделеева и 150-летию его наследия -«Периодического закона для химических элементов». К 170-летию Ивана Петровича Павлова - выдающегося русского российского исследователя в области физиологии, первого нобелевского лауреата России.
center of another circle; and c) points "U, V, Z, and A1" lie by approximation on the evolute of their more palmar curvature.
E
?G H
I J
:r—•
Fig. 5. Presenting both constructions Fig. 4a (above, concave curvature of distal part of PIP-joint) and Fig 4b (below, convex curvature of proximal part of PIP-joint) at the same scale (see text), shows quantitative differences between the clusters of points of intersection of their respective perpendicular bisectors. Discussion
Our plane geometry graphic constructions, based on HR-imaging of a normal PIP-joint of the finger revealed - by approximation - separate clusters of centers of the curvatures of the distal concave part, as well as of the proximal convex part of this joint, and their radii. Starting with the convex curvature (Fig. 4b), correspondence of our cluster around "T" exists, with the gross general statement in [15] and with the refined findings of [23], produced much later than [15] and with the help of highly advanced technical methods. However, in [23] and also in [24], such methods are applied mainly to define kinematical axes of flexion and extension of the PIP-joint. Only [25] analyses the
К 185-летию великого русского российского ученого и гражданина России -Дмитрия Ивановича Менделеева и 150-летию его наследия -«Периодического закона для химических элементов». К 170-летию Ивана Петровича Павлова - выдающегося русского российского исследователя в области физиологии, первого нобелевского лауреата России. curvatures - be it in the distal inter phalangeal (DIP-) joint of the finger.
With respect to our Results (3), model-wise two-dimensional representations of the
PIP-joint in extension (Fig. 6a) show, that even with 'ideally matching' distal and
proximal curvatures, flexion of this joint (Fig. 6b) will result in the palmar proximal
curvature being too convex in relation to the distal curvature.
Fig. 6 a (left). Model of extended PIP-joint [18]; blue dots: proper collateral ligament attachments; red dots: accessory collateral ligament attachments. Fig. 6 b (right). In spite of these "ideal" congruencies in extension (Fig. 5a), PIP-flexion causes proximal curvature to be too convex for distal curvature.
Fig. 7 a (left). Osseous outline of extended interphalangeal joints, exploded view.
Arrow indicates impression of proximal curvature in distal curvature.
Fig. 7 b (right). PIP-joint, transverse HR-MRI [26]: impressions are visible.
К 185-летию великого русского российского ученого и гражданина России -Дмитрия Ивановича Менделеева и 150-летию его наследия -«Периодического закона для химических элементов». К 170-летию Ивана Петровича Павлова - выдающегося русского российского исследователя в области физиологии, первого нобелевского лауреата России.
Corresponding well with our Results (3.), [27] notes a certain "suction cup effect", thus stabilising the PIP-joint in full extension, also thanks to the synovial fluid layer squeezed between resilient hyaline cartilage layers, that cover the joint surfaces. This phenomenon leaves some 'impressions' in the concave curvature (Fig. 7). These layers display themselves as white and slightly grey crescents respectively, halfway the HR-MRI (Fig. 2a, arrows). Concerning the PIP-joint in flexion, [24] describes comparable phenomena, and also notes that the 'center of rotation' shifts in distal and palmar direction.
Conclusion
In the proximal interphalangeal (PIP-) joint of the human finger, the incongruences of articular surfaces of its distal part (base of middle phalanx), and proximal part (head of proximal phalanx), quantified by plane geometry, are based on different, separate centers of curvatures, and radii of curvatures.
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К 185-летию великого русского российского ученого и гражданина России -Дмитрия Ивановича Менделеева и 150-летию его наследия -«Периодического закона для химических элементов». К 170-летию Ивана Петровича Павлова - выдающегося русского российского исследователя в области физиологии, первого нобелевского лауреата России.
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