Jennifer S. Wayne1 Fellow ASME Orthopaedic Research Laboratory, Departments of Biomedical Engineering and Orthopaedic Surgery, Virginia Commonwealth University, P.O. Box 843067, Richmond, VA 23284-3067 e-mail: [email protected]
Afsarul Q. Mir Orthopaedic Research Laboratory, Departments of Biomedical Engineering and Orthopaedic Surgery, Virginia Commonwealth University, P.O. Box 843067, Richmond, VA 23284-3067 e-mail: [email protected]
Application of a Three-Dimensional Computational Wrist Model to Proximal Row Carpectomy A three-dimensional (3D) computational model of the wrist examined the biomechanical effects of the proximal row carpectomy (PRC), a surgical treatment of certain wrist degenerative conditions but with functional consequences. Model simulations, replicating the 3D bony anatomy, soft tissue restraints, muscle loading, and applied perturbations, demonstrated quantitatively accurate responses for the decreased motions subsequent to the surgical procedure. It also yielded some knowledge of alterations in radiocarpal contact force which likely increase contact pressure as well as additional insight into the importance of the triangular fibrocartilage complex and retinacular/capsular structures for stabilizing the deficient wrist. As better understanding of the wrist joint is achieved, this model could serve as a useful clinical tool. [DOI: 10.1115/1.4029902]
Introduction The wrist is one of the most complex and dexterous joints of the human body that can be prone to injury or degeneration. To restore stability and relieve pain associated with injuries or arthritis, various surgical procedures have been developed. These procedures often change function however, such as range of motion or load transmission, where insight into the altered behavior would be constructive to tailor treatment. The proximal row carpectomy (PRC) procedure, for example, has been found to be a clinically useful treatment for conditions such as scapho(lunate)collapse and Kienbock’s disease [1–4] where one of the proximal carpal bones have incurred extensive damage leading to fragmentation or collapse. With the PRC, the entire proximal row of carpal bones consisting of the scaphoid, lunate, and triquetrum is excised from the wrist which converts a multiarticulated wrist joint to a loose hinge with new articulation between the capitate and the radius. However, clinical studies have shown that the wrist demonstrates a decreased range of motion following PRC [1,5,6]. The change to articulating surfaces was found to alter not only range of motion but also load transmission in cadaveric studies [7,8]. While clinical studies have shown the functional outcomes of such corrective procedures, understanding the structural effects have been difficult especially due to the complex nature of joints. Computational models are useful to understand joint biomechanical function and can simulate injured and/or surgical states to predict behavior of these altered states in advance of their clinical usage. For the wrist, early studies developed simplified twodimensional models (2D) [9–11] to examine force transmission through different joints and changes with certain surgical procedures. Extension of the models into 3D continued the exploration of force transmission in different wrist positions, with different loadings, or in different wrist states (normal or surgically altered) [12–15]. Fischli et al. developed a first 3D rigid body model (RBM) to predict carpal bone motion and wrist kinematics [16]. These models have contributed to an improved understanding of wrist biomechanical function, but each has made various simplifications, including restriction to 2D, static wrist posture, and/or linking bones together as one functional unit to reduce 1 Corresponding author. Manuscript received August 13, 2014; final manuscript received January 13, 2015; published online March 18, 2015. Assoc. Editor: Zong-Ming Li.
Journal of Biomechanical Engineering
computational time and permit convergence. These simplifications, while may have been necessary for the computational model, do not accurately represent the physiological state and may have resulted in less accurate replication of wrist function. A recent 3D RBM [17] alleviated many of these simplifications by not constraining the wrist’s degrees-of-freedom nor restricting the model to static positions or fusing bones together. This then permitted the model to more accurately replicate the normal behavior of the wrist. Changes to biomechanical function were examined for the surgical procedure of limited wrist arthrodesis used to relieve the pain associated with radiocarpal arthritis. The model however did not incorporate some essential soft tissue structures that are part of this complex joint system. The triangular fibrocartilage complex (TFCC) is a structure that contributes to ulnar side stability and force transmission [18,19]. The retinacular structures that encompass the entire joint also play an important role in stabilization [20]. Since these structures influence normal wrist function, their incorporation may be important in replicating wrist function. The objective of this study was to build on and apply further the 3D computational model of the human wrist developed previously [17] whereby the bony anatomy is reconstituted and biomechanical function governed by 3D articular surface anatomy, ligamentous and soft tissue restraints, muscle loading, and external perturbations. Predictive behavior is explored for ranges of motion and load transmission and compared to existing studies in the literature for wrist surgical procedures, particularly the PRC and radioscapholunate (RSL) fusion.
Methods Model Creation. The 3D anatomy of the wrist model was obtained from a fresh frozen left upper extremity of a 52 year old male donor. The specimen was inspected for any obvious pathology, deformities and proper biomechanical range of motion. No obvious abnormalities were identified. The limb was scanned at submillimeter resolution (512 512 pixels at 0.4 mm increments) with a SOMATOM Sensation 64 helical scanner (Siemens AG, Forcheim, Germany) in a neutral position, with the long axis of the third metacarpal parallel to the long axis of the radius. As elaborated previously [17], CT scanned images were imported into the commercially available MIMICS (Materialise’s Interactive Medical Imaging Control System, Version 13, Materialise,
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Table 1 model
Ligament stiffness values defined for the 3D wrist
Ligament
Total stiffness (N/mm)
EXTRINSIC LIGAMENTS Radioscaphoid ligament (RS) Radiocapitate ligament (RC) Dorsal radiocarpal ligament (DRC) Long radiolunate ligament (LRL) Short radiolunate ligament (SRL) Ulnocapitate ligament (UC) Ulnolunate ligament (UL) Ulnotriquetrum ligament (UT) INTRINSIC LIGAMENTS Capitohamate interosseous ligament (CH) Capitotrapezoidal interosseous ligament (CT) Dorsal intercarpal ligament (DIC) Lunotriquetral interosseous ligament (LT) Pisohamate ligament (PH) Pisotriquetral interosseous ligament (PT) Scaphocapitate ligament (SC) Schapholunate interosseous ligament (SL) Scaphotrapeziotrapezoidal ligament (STT) Transverse carpal ligament (TCL) Trapeziotrapezoidal interosseous ligament (TT) Triquetrocapitate ligament (TC) Triquetrohamate ligament (TH) METACARPAL LIGAMENTS Carpometacarpal ligaments Intermetacarpal ligaments
50 [10,29] 50 [10,29,30] 75 [18,31] 37.5 [18,31] 37.5 [18,31] 50 [10] 40 [10,18] 40 [10] 325 [32] 300 [10,18,32] 50 [31] 350 [10,18,30] 50 100 40 [10,18] 230 [10] 150 [10,18] 130 [32] 150 [32] 40 [10,18,30] 50 [10] 100 100
Ann Arbor, MI) software for recreation of the 3D anatomy. Each of the 15 wrist bones (2 forearm bones, 8 carpal bones, and 5 metacarpal bones) and phalanges were individually identified. 2D masks were created to outline the osseous perimeter of interest on each slice, which were then used to create 3D solid bodies. The surface of each bone was represented as a network of triangulated surfaces and exported as STL (stereolithography) files. Each bone was imported into the assembly space of SOLIDWORKS (SolidWorks 2010, Dassault Syste`mes SolidWorks Corporation, Waltham, MA), a commercially available 3D CAD software, with their orientation and position defined by the initial CT scan. The radius and ulna were fixed in space in a neutral position as done experimentally. Then, within the SOLIDWORKS MOTION rigid-body software to solve the equations of motion in discrete time steps, function of soft tissue structures and additional boundary conditions were implemented as has been done previously for other joints [21–25]. Bones were defined as rigid bodies with surface contact interactions to prevent penetration. The 3D contact settings generated a contact force calculated from the overlap detected in each time step and the material stiffness of the
body as elaborated previously [17]. Joint articulations were considered frictionless and direction of gravity was defined according to the experimental study being simulated. The first metacarpal was fused to the trapezium bone since it does not influence wrist motion in the studies examined. The third metacarpal was fixed relative to the capitate since the two bones have been defined to move as one unit [16]. All other bones were free to move relative to one another. For ligaments, insertion sites of each structure were identified from anatomic texts [26–28] and bony anatomy and connected by tension-only force vectors incorporating tissue length and linear stiffness values from the literature (Table 1). Each ligament was modeled by at least two such linear elements depending on the width of the structure, distinct bands crossing between different bones, and/or dorsal/palmar bands. The TFCC was modeled as two distinct structures (proximal and distal) to replicate its functional behavior as an extension of the ulnar head, an articulating surface for the carpal bones, and attachment points for other wrist soft tissue structures such as the flexor and extensor retinaculum/capsules, pisiform, and extensor carpi ulnaris sheath. These structures were formulated into two rigid bodies, the geometry of which was generated from the cryoslice images within the U.S. National Library of Medicine’s (NIH, Bethesda MD) Visible Human Project (VHP), descriptions in the literature, and renditions in anatomical texts [26–28]. The proximal structure was rigidly connected to the ulna, due to this region of the TFCC anatomically encapsulating the distal ulnar head and the assumption that the relative motions between these bodies was minimal for the motions simulated in this study (Fig. 1). The distal structure was connected to the proximal structure with three tension only vectors with stiffness of 70 N/mm, which permitted the bodies to interact with the carpal bones while prohibiting penetration. The flexor and extensor retinacular/capsular structures were incorporated similarly to the TFCC as rigid bodies spanning the wrist as well as ligament-like structures (Fig. 2). The distal portion of the flexor retinaculum (FR), often referred to as the transverse carpal ligament, has attachment points laterally spanning the scaphoid tuberosity to the ridge of the trapezium. Medially, the structure attaches to the pisiform and hook of hamate. These were incorporated as tension only vectors with stiffness of 32.5 N/mm. The proximal portions of the retinaculum/capsule surrounding the proximal carpal row was simulated as two bodies each on the palmar and dorsal aspects connected by tension only vectors with stiffness of 40 N/mm. The force generated by six main muscles was incorporated within the model for the extensor carpi radialis longus (ECRL), extensor carpi radialis brevis (ECRB), extensor carpi ulnaris (ECU), flexor carpi radialis (FCR), and flexor carpi ulnaris (FCU). The tendon of each muscle body was simulated by two force vectors representing the lateral and medial borders of the tendon.
Fig. 1 Palmar (left) and dorsal (right) aspect of model illustrating the TFCC as a two part structure and the force vectors (interbody arrows) as their connection
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Fig. 2 Distal FR/capsule on the palmar aspect (left) incorporated as tension only structures (vectors). Flexor (right/top) and extensor (right/bottom) retinacular/capsular structures incorporated as rigid bodies connected with tension only vectors. Phalanges excluded for clarity.
Simulations. Before evaluating the effects of a PRC, behavior of the model with the additions of the TFCC and retinacular/ capsular structures was reconfirmed for the wrist fusion study performed previously [17] which simulated a cadaveric experimental study [33]. Here, the hand was held vertically while wrist movement was examined under flexion (FCR, FCU) or extension (ECRL, ECU) muscle action as well as radial (FCR, ECRL) or ulnar (ECU) deviation muscle actions (5 lb each). Range of motion in the respective plane was determined by measuring the angle between the long axis of the radius and the long axis of the third metacarpal. Intact, normal motion was evaluated followed by motion after a RSL fusion. Gravity was replicated in the direction appropriate to the experimental setup. Subsequently, the model was used to analyze the effects of a different surgical procedure, the PRC, simulating the experimental study performed by Blankenhorn et al. [7]. The wrist was positioned horizontally with the palm facing ground, in comparison to the vertical orientation of the prior fusion study. Range of motion was again examined in flexion, extension and radial/ulnar deviations with muscle loadings to achieve each wrist motion (experimentally between 5 and 50 N per muscle) (Table 2). Effects of the PRC were simulated by removal of the scaphoid, lunate, and triquetrum. The remaining carpal and metacarpal bones were temporarily locked to create one unit as the carpus was moved proximally toward the radius, such that the proximal capitate head rested on the lunate fossa of the radial articulating surface. The bones were then unlocked to move freely in response to applied perturbations, restrained only by the articulating surfaces and soft tissue structures. All ligaments with insertions on the excised bones were suppressed. The model then tested the four wrist motions with the same tendon loads used with the intact normal state, as described experimentally. A companion cadaveric study from the same group [8] was subsequently simulated in which the changes in force transmission at the radiocarpal joint occurring after PRC were examined. Here, only flexion–extension motions were examined, at the specific positions of 45 deg flexion, neutral, and 45 deg extension. Experimentally, this was achieved by manually altering the tendon loads (to 200 N total applied tendon force) until the desired position was Journal of Biomechanical Engineering
obtained; out of plane motions were manually prevented. Contact pressure and area were determined through insertion of Fujifilm. Computationally, the desired positions were obtained by replicating the bony positions of the wrist from the prior computational simulation, at 45 deg flexion and 45 deg extension. The long axis of the third metacarpal was then fixed in these two desired positions while still allowing the carpus to move along the proximal/ distal and dorsal/palmar directions. For the neutral position, the long axis of the third metacarpal was fixed to allow motion only in the proximal/distal direction. A radial styloidectomy was performed as done experimentally to eliminate carpal bone abutment against the radial styloid process during the contact tests. Tendon loads were applied for each position for a combined total of 200 N in the same ratios as used in the prior simulation. The retinacular bodies were suppressed in these simulations as their stabilizing role was unnecessary while the angular position was maintained.
Results Behavior of the model for the wrist fusion study exhibited very similar behavior to both the prior wrist model as well as the experimental study (Table 3). The main improvement seen was for ulnar deviation in which the addition of the TFCC with the current model brought motion to within the standard deviation of experimental findings, particularly for intact motion where the presence
Table 2 Muscle loads applied in the computational model for the intact normal wrist to achieve the wrist position designated by the experimental study.
Muscle name
Flexion (N)
Extension (N)
Radial deviation (N)
Ulnar deviation (N)
FCU FCR ECRL/ECRB ECU
24 24 12 12
12 12 30 30
20 40 50 12
4 5 5 25
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of the TFCC would be more pronounced. Flexion motion of the intact normal wrist also improved. Simulation of the PRC demonstrated excellent agreement between the experimental study and computational model predictions, both for the individual motion as well as the motion arc (Figs. 3–5). Motion was substantially reduced following a PRC, with 23% decrease in the flexion/extension arc computationally and 32% experimentally. A 29% decrease was predicted computationally in radial/ulnar deviation arc compared to 27% experimentally. When comparing the percent decrease in individual motions between the intact and PRC wrist, it was found to be accurate for flexion (Model 32% versus Experimental 29%62%) and for both radial (Model 40% versus Experimental 45%68%) and ulnar deviation (Model 22% versus Experimental 15%65%). In extension, the model underpredicted the percent change showing a 9% decrease in extension following PRC, while the cadaveric study reported a total 36%612% decrease. This difference most likely arose from the method of representation of the soft tissues and the assumptions made during the model’s development. A qualitative inspection of the PRC wrist during the range of motion testing demonstrated that wrist angular motion was isolated between the capitate and the radiocarpal articulating surface. In addition to the angular motion, some translational motion of the capitate head was observed. Some minor translational motion was observed in flexion, extension and radial deviation. However, in the case of ulnar deviation, a larger amount of translation was seen in the lateral direction of the wrist. This greater additional translation led the wrist to achieve the larger angular position in ulnar deviation as compared to radial deviation in the PRC state. In investigating force transmission at the radiocarpal joint, the experimental study presented average contact pressure and area, which were multiplied to calculate contact force, a parameter provided in the computational simulations. Measures were provided between the scaphoid and radius, scaphoid and lunate in the intact wrist, and between the capitate and radius in the PRC wrist (Fig. 6). Agreement in trends between the intact and PRC states was noted for the three positions although the computational model over-estimate contact force in extension and tended to under-estimate in flexion. While the contact force in the radiocarpal joint decreased with PRC, this was only the capitate contacting the radius with a contact area that averaged 26% of the intact wrist [8]. The model continued to predict a decrease in force with PRC while the experimental study predicted an increase in the flexed state.
Discussion
Fig. 3 Flexion and extension wrist motions in the intact normal wrist and after the PRC for the 3D wrist model and the cadaveric study [7]
structures, replicating bony contact, and applying constraints via ligamentous and other soft tissue structures. Kinematic motion was achieved by applying forces to relevant muscle units. Comparison of model predictions to experimental evidence showed excellent agreement. The model also provided some insight into the functions of the various structures that form the overall joint. The TFCC is a not a fully understood tissue structure. Comparing the motions predicted by the current 3D wrist model and its predecessor [17] indicated that the TFCC plays a major stabilizing role on the ulnar aspect of the wrist. Additionally, when a PRC procedure was replicated without the TFCC, convergence was not obtained. This was caused by a lack of ulnar side support and a rapid and an unnatural motion response of the carpus during this motion. Removal of the proximal row disturbed the entire ligamentous attachments between the radius and ulna to the proximal row (scaphoid, lunate, and triquetrum) as well as the proximal row to the distal row (hamate, capitate, trapezium, and trapezoid). The distal row then articulated with the radius and ulna but without extensive ligamentous connections. Surgically, the soft tissues are sutured after the bony excision yet postoperative immobilization is necessary to avoid instability until scarring occurs. Since the TFCC was a critical aspect in stabilizing the surgically altered wrist, this may indicate that this soft tissue structure plays a more critical role than currently appreciated. A similar observation was made of the retinacular/capsular structures. As with the TFCC, the stabilizing role of the
The 3D wrist model developed in this study was able to replicate and predict the biomechanical response of the joint following two different surgical procedures, the PRC and RSL fusion. The model was created from accurately rendering the 3D bony Table 3 Range of motions (degrees) obtained from the current wrist model, the prior wrist model [17], and the cadaveric study [33] for the intact normal wrist and subsequent to RSL fusion
Flexion Extension Radial deviation Ulnar deviation
Current wrist model Prior wrist model Cadaveric study Current wrist model Prior wrist model Cadaveric study Current wrist model Prior wrist model Cadaveric study Current wrist model Prior wrist model Cadaveric study
Intact normal
RSL fusion
73 84 7067 55 58 5668 30 30 3068 32 39 3165
34 36 2768 22 23 2569 17 19 2067 18 20 2266
Fig. 4 Radial and ulnar deviation wrist motions in the intact normal wrist and after the PRC for the 3D wrist model and the cadaveric study [7]
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Fig. 5 Total wrist motion arc in the intact normal wrist and after the PRC in flexion/extension (F/E) and radial/ulnar (R/U) deviation for the 3D wrist model and the cadaveric study [7]
retinacular/capsular structures in the wrist is not well understood. In the computational model, these structures were essential in stabilizing the surgically altered PRC wrist by preventing unnatural wrist joint motion. Experimental studies have demonstrated decreased carpal arch stiffness [33] and increased carpal arch length [31] with sectioning of the transverse carpal ligament for carpal tunnel release. Additionally, significant bowstringing and tendon excursions to non-anatomically correct lines of action were observed following sectioning of the FR [34] and the extensor retinaculum [33]. While these studies did not investigate effects on carpal kinematics, they do indicate an overall stabilizing role of these structures. Its stabilizing role may be further enhanced in a deficient wrist that has undergone trauma or surgery. In this deficient state, the primary stabilizers may not be as effective as originally intended and thus these capsular structures may in fact passively stabilize the weakened joint. In similar cadaveric experimental studies reported within the literature for range of motion of the intact normal wrist, the work conducted by Berkhout et al. [35] reported a total flexion–extension arc of 149 6 19 deg and radioulnar motion arc of 54 6 14 deg while McCombe et al. [36] reported motion arcs of 141 6 9 deg and 49 6 9 deg, respectively. While the flexion–extension arcs are larger than those predicted by the model, the radioulnar motion arc was much more comparable to the predicted results. The greater difference in the flexion–extension arc may be explained by the various experimental testing
Fig. 6 Force transmission in the intact normal wrist and after the PRC in 45 deg flexion, neutral and 45 deg extension for the 3D wrist model and the cadaveric study [8]. Experimental standard deviations estimated at 25%.
Journal of Biomechanical Engineering
methodologies. In the study by Berkhout et al. [35], the wrist specimens were secured and tested in a vertical upward orientation and thus the force of gravity would promote further flexion/ extension. Additionally, the study utilized an electromagnetic tracking system which requires the attachment of hardware and can increase the total weight of the specimen. In the work conducted by McCombe et al. [36], instead of applying fixed specified loads, each specimen was manually moved through the two motion arcs to the approximate end-point of the range of motion. Finally, if the anatomical structure of the radiocarpal joint is analyzed, the bony articular surface limits motions in the radial and ulnar aspect of the joint. On the other hand, motions in the palmar and dorsal aspect of the wrist are controlled more by soft tissue structures. Thus, the flexion–extension arc is more likely dependent on the testing methodology, and thus greater differences are observed between studies. This could also explain the consistency observed in radioulnar motion arc between studies, even with different test methodologies. PRC is a motion preserving surgical procedure often employed to treat various degenerative diseases of the wrist proximal carpal bones. It is favored by many practitioners due to its ease of performance, lack of nonunion formation and early patient recovery [1,37]. In the short term, the procedure has demonstrated positive results in preservation of wrist motion and grip strength within functional ranges as well as providing pain relief. In a clinical study, an average 62610% preservation of the flexion–extension arc and 51618% of the radial-ulnar motion arc were reported after a PRC procedure [1]. Another study measured the average motion in 11 wrists after PRC to be 85 deg for the flexion– extension arc and 31 deg for radial-ulnar motion arc [37], a 64% retention average for all four motion arcs relative to the contralateral healthy wrist. In long-term follow-up studies, 61–63% average range of motion of the contralateral wrist is preserved [5,38]. With respect to the computationally predicted results, the 3D wrist model demonstrated an average 74% retention of the intact healthy wrist motion arc postoperatively, slightly higher than the clinically reported values. The difference is likely due to the in vivo response after a surgical procedure with healing and scar tissue formation, which would most likely provide additional restrictions and support to the carpal bones. This would lead to a reduced motion arc experienced by the joint. Additionally, clinical studies reported very small postoperative radial deviation angles such as 4 deg [37], 7 deg [1], and 9 deg [5]. These small angles were most likely caused by radial styloid impingement with the trapezium. No significant impingement was observed in the 3D wrist model which resulted in a 15 deg radial deviation prediction and would also account for the greater motion arc preservation predicted by the 3D wrist model. The in vitro cadaveric study observed 69%617% total motion arc preservation with PRC, which is comparable to that predicted by the 3D wrist model. While there have been concerns over the degenerative effects caused by the significant reduction of joint articulation area, long term results have been satisfactory [5,38]. A minimum 20-year follow-up study [39] found that PRC provided a survival rate of 65%. Of these, degenerative radiographic changes at the radiocapitate joint were noted in 72% although patient satisfaction level did not correlate with the degeneration. The computational and experimental results of force transmission would support the clinical findings of the degenerative changes. While contact force decreases with PRC, contact area decreases substantially more depending on the articulating surface of the capitate. For some patients, early failure of PRC typically manifests as nonresolution of pain and additional procedures must be performed. For those in whom PRC is considered a success, the level of degeneration at 20 years, while not translating directly to patient dissatisfaction, is of enough concern to consider carefully its use in young patients [39]. A sensitivity analysis on the effect of model parameter variations such as ligament stiffness was not performed with this particular study. Previous computational simulations, however, JUNE 2015, Vol. 137 / 061001-5
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for the foot/ankle complex and the elbow created from the same modeling methodology as presented here have evaluated the effects of a range of parameter values [21–23]. Certainly, the biomechanical results change magnitude when the stiffnesses increase or decrease as these properties are expected to influence model behavior. However, the conclusions drawn between states remain consistent. Ligament stiffnesses in this wrist model were selected from the literature and were not manipulated in order to achieve specific results. During model development, certain assumptions and simplifications were made. The material properties of the ligaments and soft tissues incorporated within the model were based on experimentally measured values reported in the literature. These soft tissues were represented by linearly elastic passive tissue elements. A thorough characterization of their nonlinear behavior is not available. The TFCC was modeled as a two part structure, each of which was represented as a solid body. Anatomically, the TFCC is a soft tissue structure which could experience deformation during wrist motion. Flexibility was afforded to the TFCC by its inclusion as two separate bodies connected by springs. Additionally, the TFCC has soft tissue attachment points to the ulnar head and the radius which could permit relative movement. Minimal movement in flexion/extension and radial/ulnar deviation of the carpus was assumed, and thus the proximal TFCC body and the ulnar head were taken to function as one unit. To recreate the stabilizing effect of the retinacular/capsular structures, a similar assumption as for the TFCC was required. Finally, the computational model was characteristic of a single wrist. Future studies should reflect multiple wrists to provide the range of biomechanical parameters and more generalized conclusions to be made. In the comparison of force transmission, the overestimation in extension but underestimation in flexion between experimental findings and computational predictions may be due to multiple factors. Specific information on the methodology of the cadaveric study was not provided to be implemented in the wrist model, particularly for the magnitude of the tendon forces. The effect of manually controlling out-of-plane motions in the cadaver wrist is unknown as is whether the means to do so computationally adequately reflected experimental setup. In the neutral position, however, the computational predictions are well aligned. In conclusion, this 3D computational wrist model demonstrated the ability to predict biomechanical function and provided some insight into biomechanical function of tissue structures that are not well understood but whose role may be important not only in the normal wrist but also in injured or surgically altered states. In particular, the TFCC and the retinacular/capsular structures provided ulnar side support, influenced wrist motion, and helped stabilize the joints. Future refinement of the model will allow for continued investigation in other states as well as provide predictions of relevant physiologic parameters that are difficult or impossible to measure experimentally or clinically. This information may be useful to understand the biomechanical effects of injuries or corrective procedures.
Acknowledgment The U.S. National Library of Medicine’s Visible Human Project for the cryoslice sections was used to assist in recreating the triangular fibrocartilage complex.
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[4] Steenwerckx, A., De Smet, L., Zachee, B., and Fabry, G., 1997, “Proximal Row Carpectomy: An Alternative to Wrist Fusion?,” Acta Orthop. Belg., 63(1), pp. 1–7. [5] DiDonna, M. L., Kiefhaber, T. R., and Stern, P. J., 2004, “Proximal Row Carpectomy: Study With a Minimum of Ten Years of Follow-Up,” J. Bone Joint Surg., 86A(11), pp. 2359–2365. [6] Imbriglia, J. E., Broudy, A. S., Hagberg, W. C., and McKernan, D., 1990, “Proximal Row Carpectomy: Clinical Evaluation,” J. Hand Surg. Am., 15(3), pp. 426–430. [7] Blankenhorn, B. D., Pfaeffle, H. J., Tang, P., Robertson, D., Imbriglia, J., and Goitz, R. J., 2007, “Carpal Kinematics After Proximal Row Carpectomy,” J. Hand Surg. Am., 32(1), pp. 37–46. [8] Tang, P., Gauvin, J., Muriuki, M., Pfaeffle, H. J., Imbriglia, J. E., and Goitz, R. J., 2009, “Comparison of the ‘Contact Biomechanics’ of the Intact and Proximal Row Carpectomy Wrist,” J. Hand Surg. Am., 34(4), pp. 660–670. [9] Horii, E., Garcia-Elias, M., Bishop, A. T., Cooney, W. P., Linscheid, R. L., and Chao, E. Y., 1990, “Effect on Force Transmission Across the Carpus in Procedures Used to Treat Kienb€ ock’s Disease,” J. Hand Surg. Am., 15(3), pp. 393–400. [10] Schuind, F., Cooney, W. P., Linscheid, R. L., An, K. N., and Chao, E. Y., 1995, “Force and Pressure Transmission Through the Normal Wrist. A Theoretical Two-Dimensional Study in the Posteroanterior Plane,” J. Biomech., 28(5), pp. 587–601. [11] Manal, K., Lu, X., Nieuwenhuis, M. K., Helders, P. J. M., and Buchanan, T. S., 2002, “Force Transmission Through the Juvenile Idiopathic Arthritic Wrist: A Novel Approach Using a Sliding Rigid Body Spring Model,” J. Biomech., 35(1), pp. 125–133. [12] Iwasaki, N., Genda, E., Barrance, P. J., Minami, A., Kaneda, K., and Chao, E. Y., 1998, “Biomechanical Analysis of Limited Intercarpal Fusion for the Treatment of Kienb€ ock’s Disease: A Three-Dimensional Theoretical Study,” J. Orthop. Res., 16(2), pp. 256–263. [13] Genda, E., and Horii, E., 2000, “Theoretical Stress Analysis in Wrist Joint— Neutral Position and Functional Position,” J. Hand Surg. Br. Eur. Vol., 25(3), pp. 292–295. [14] Majima, M., Horii, E., Matsuki, H., Hirata, H., and Genda, E., 2008, “Load Transmission Through the Wrist in the Extended Position,” J. Hand Surg. Am., 33(2), pp. 182–188. [15] Matsuki, H., Horii, E., Majima, M., Genda, E., Koh, S., and Hirata, H., 2009, “Scaphoid Nonunion and Distal Fragment Resection: Analysis With ThreeDimensional Rigid Body Spring Model,” J. Orthop. Sci., 14(2), pp. 144–149. [16] Fischli, S., Sellens, R., Beek, M., and Pichora, D., 2009, “Simulation of Extension, Radial and Ulnar Deviation of the Wrist With a Rigid Body Spring Model,” J. Biomech., 42(9), pp. 1363–1366. [17] Majors, B. J., and Wayne, J. S., 2011, “Development and Validation of a Computational Model for Investigation of Wrist Biomechanics,” Ann. Biomed. Eng., 39(11), pp. 2807–2815. [18] An, K. N., Berger, R. A., and Cooney, W. P., 1991, Biomechanics of the Wrist Joint, Springer-Verlag, New York. [19] Palmer, A. K., and Werner, F. W., 1981, “The Triangular Fibrocartilage Complex of the Wrist—Anatomy and Function,” J. Hand Surg. Am., 6(2), pp. 153–162. [20] Palmer, A. K., Skahen, J. R., Werner, F. W., and Glisson, R. R., 1985, “The Extensor Retinaculum of the Wrist: An Anatomical and Biomechanical Study,” J. Hand Surg. Br. Eur. Vol., 10(1), pp. 11–16. [21] Liacouras, P. C., and Wayne, J. S., 2007, “Computational Modeling to Predict Mechanical Function of Joints—Application to the Lower Leg With Simulation of Two Cadaver Studies,” ASME J. Biomech. Eng., 129(6), pp. 811–817. [22] Fisk, J. P., and Wayne, J. S., 2009, “Development and Validation of a Computational Musculoskeletal Model of the Elbow and Forearm,” Ann. Biomed. Eng., 37(4), pp. 803–812. [23] Iaquinto, J. M., and Wayne, J. S., 2010, “Computational Model of the Lower Leg and Foot/Ankle Complex: Application to Arch Stability,” ASME J. Biomech. Eng., 132(2), p. 021009. [24] Spratley, E. M., and Wayne, J. S., 2011, “Computational Model of the Human Elbow and Forearm—Application to Complex Varus Instability,” Ann. Biomed. Eng., 39(3), pp. 1084–1091. [25] Spratley, E. M., Matheis, E. A., Hayes, C. W., Adelaar, R. S., and Wayne, J. S., 2014, “A Population of Patient-Specific Adult Acquired Flatfoot Deformity Models Before and After Surgery,” Ann. Biomed. Eng., 42(9), pp. 1913–1922. [26] Netter, F. H., 2010, Atlas of Human Anatomy, Professional Edition, 5th ed., W.B. Saunders Co., St. Louis MO. [27] Agur, A. M., and Dalley, A. F., 2008, Grant’s Atlas of Anatomy, 12th ed., Lippincott Williams & Wilkins, Philadelphia, PA. [28] Rohen, J. W., Lutjen-Drecoll, E., and Yokochi, C., 2006, Color Atlas of Anatomy: A Photographic Study of the Human Body, Sixth ed., Lippincott Williams & Wilkins, Philadelphia, PA. [29] Mayfield, J. K., and Williams, W. J., 1979, “Biomechanical Properties of Human Carpal Ligaments,” Orthop. Trans., 3, pp. 143–144. [30] Nowalk, M. D., and Logan, S. E., 1991, “Distinguishing Biomechanical Properties of Intrinsic and Extrinsic Human Wrist Ligaments,” ASME J. Biomech. Eng., 113(1), pp. 85–93. [31] Schuind, R., An, K. N., Berglund, L., Rey, R., Cooney, W. P., Linscheid, R. L., and Chao, E. Y., 1991, “The Distal Radioulnar Ligaments: A Biomechanical Study,” J. Hand Surg. Am., 16(6), pp. 1106–1114. [32] Garcia-Elias, M., An, K. N., Cooney, W. P., Linscheid, R. L., and Chao, E. Y., 1989, “Stability of the Transverse Carpal Arch: An Experimental Study,” J. Hand Surg. Am., 14(2 Part 1), pp. 277–282.
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[33] Pervaiz, K., Bowers, W. H., Isaacs, J. E., Owen, J. R., and Wayne, J. S., 2009, “Range of Motion Effects of Distal Pole Scaphoid Excision and Triquetral Excision After Radioscapholunate Fusion: A Cadaver Study,” J. Hand Surg. Am., 34(5), pp. 832–837. [34] Fuss, F. K., and Wagner, T. F., 1996, “Biomechanical Alterations in the Carpal Arch and Hand Muscles After Carpal Tunnel Release: A Further Approach Toward Understanding the Function of the Flexor Retinaculum and the Cause of Postoperative Grip Weakness,” Clin. Anat., 9(2), pp. 100–108. [35] Berkhout, M. J., Shaw, M. N., Berglund, L. J., An, K. N., Berger, R. A., and Ritt, M. J. P. F., 2010, “The Effect of Radioscapholunate Fusion on Wrist Movement and the Subsequent Effects of Distal Scaphoidectomy and Triquetrectomy,” J. Hand Surg. Eur., 35(9), pp. 740–745.
Journal of Biomechanical Engineering
[36] McCombe, D., Ireland, D. C., and McNab, I., 2001, “Distal Scaphoid Excision After Radioscaphoid Arthrodesis,” J. Hand Surg. Am., 26(5), pp. 877–882. [37] Wyrick, J. D., Stern, P. J., and Kiefhaber, T. R., 1995, “Motion-Preserving Procedures in the Treatment of Scapholunate Advanced Collapse Wrist: Proximal Row Carpectomy Versus Four-Corner Arthrodesis,” J. Hand Surg. Am., 20(6), pp. 965–970. [38] Jebson, P. J., Hayes, E. P., and Engber, W. D., 2003, “Proximal Row Carpectomy: A Minimum 10-Year Follow-Up Study,” J. Hand Surg. Am., 28(4), pp. 561–569. [39] Wall, L. B., DiDonna, M. L., Kiefhaber, T. R., and Stern, P. J., 2013, “Proximal Row Carpectomy: Minimum 20-Year Follow-Up,” J. Hand Surg. Am., 38(8), pp. 1498–1504.
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Afsarul Q. Mir Orthopaedic Research Laboratory, Departments of Biomedical Engineering and Orthopaedic Surgery, Virginia Commonwealth University, P.O. Box 843067, Richmond, VA 23284-3067 e-mail: [email protected]
Application of a Three-Dimensional Computational Wrist Model to Proximal Row Carpectomy A three-dimensional (3D) computational model of the wrist examined the biomechanical effects of the proximal row carpectomy (PRC), a surgical treatment of certain wrist degenerative conditions but with functional consequences. Model simulations, replicating the 3D bony anatomy, soft tissue restraints, muscle loading, and applied perturbations, demonstrated quantitatively accurate responses for the decreased motions subsequent to the surgical procedure. It also yielded some knowledge of alterations in radiocarpal contact force which likely increase contact pressure as well as additional insight into the importance of the triangular fibrocartilage complex and retinacular/capsular structures for stabilizing the deficient wrist. As better understanding of the wrist joint is achieved, this model could serve as a useful clinical tool. [DOI: 10.1115/1.4029902]
Introduction The wrist is one of the most complex and dexterous joints of the human body that can be prone to injury or degeneration. To restore stability and relieve pain associated with injuries or arthritis, various surgical procedures have been developed. These procedures often change function however, such as range of motion or load transmission, where insight into the altered behavior would be constructive to tailor treatment. The proximal row carpectomy (PRC) procedure, for example, has been found to be a clinically useful treatment for conditions such as scapho(lunate)collapse and Kienbock’s disease [1–4] where one of the proximal carpal bones have incurred extensive damage leading to fragmentation or collapse. With the PRC, the entire proximal row of carpal bones consisting of the scaphoid, lunate, and triquetrum is excised from the wrist which converts a multiarticulated wrist joint to a loose hinge with new articulation between the capitate and the radius. However, clinical studies have shown that the wrist demonstrates a decreased range of motion following PRC [1,5,6]. The change to articulating surfaces was found to alter not only range of motion but also load transmission in cadaveric studies [7,8]. While clinical studies have shown the functional outcomes of such corrective procedures, understanding the structural effects have been difficult especially due to the complex nature of joints. Computational models are useful to understand joint biomechanical function and can simulate injured and/or surgical states to predict behavior of these altered states in advance of their clinical usage. For the wrist, early studies developed simplified twodimensional models (2D) [9–11] to examine force transmission through different joints and changes with certain surgical procedures. Extension of the models into 3D continued the exploration of force transmission in different wrist positions, with different loadings, or in different wrist states (normal or surgically altered) [12–15]. Fischli et al. developed a first 3D rigid body model (RBM) to predict carpal bone motion and wrist kinematics [16]. These models have contributed to an improved understanding of wrist biomechanical function, but each has made various simplifications, including restriction to 2D, static wrist posture, and/or linking bones together as one functional unit to reduce 1 Corresponding author. Manuscript received August 13, 2014; final manuscript received January 13, 2015; published online March 18, 2015. Assoc. Editor: Zong-Ming Li.
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computational time and permit convergence. These simplifications, while may have been necessary for the computational model, do not accurately represent the physiological state and may have resulted in less accurate replication of wrist function. A recent 3D RBM [17] alleviated many of these simplifications by not constraining the wrist’s degrees-of-freedom nor restricting the model to static positions or fusing bones together. This then permitted the model to more accurately replicate the normal behavior of the wrist. Changes to biomechanical function were examined for the surgical procedure of limited wrist arthrodesis used to relieve the pain associated with radiocarpal arthritis. The model however did not incorporate some essential soft tissue structures that are part of this complex joint system. The triangular fibrocartilage complex (TFCC) is a structure that contributes to ulnar side stability and force transmission [18,19]. The retinacular structures that encompass the entire joint also play an important role in stabilization [20]. Since these structures influence normal wrist function, their incorporation may be important in replicating wrist function. The objective of this study was to build on and apply further the 3D computational model of the human wrist developed previously [17] whereby the bony anatomy is reconstituted and biomechanical function governed by 3D articular surface anatomy, ligamentous and soft tissue restraints, muscle loading, and external perturbations. Predictive behavior is explored for ranges of motion and load transmission and compared to existing studies in the literature for wrist surgical procedures, particularly the PRC and radioscapholunate (RSL) fusion.
Methods Model Creation. The 3D anatomy of the wrist model was obtained from a fresh frozen left upper extremity of a 52 year old male donor. The specimen was inspected for any obvious pathology, deformities and proper biomechanical range of motion. No obvious abnormalities were identified. The limb was scanned at submillimeter resolution (512 512 pixels at 0.4 mm increments) with a SOMATOM Sensation 64 helical scanner (Siemens AG, Forcheim, Germany) in a neutral position, with the long axis of the third metacarpal parallel to the long axis of the radius. As elaborated previously [17], CT scanned images were imported into the commercially available MIMICS (Materialise’s Interactive Medical Imaging Control System, Version 13, Materialise,
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Table 1 model
Ligament stiffness values defined for the 3D wrist
Ligament
Total stiffness (N/mm)
EXTRINSIC LIGAMENTS Radioscaphoid ligament (RS) Radiocapitate ligament (RC) Dorsal radiocarpal ligament (DRC) Long radiolunate ligament (LRL) Short radiolunate ligament (SRL) Ulnocapitate ligament (UC) Ulnolunate ligament (UL) Ulnotriquetrum ligament (UT) INTRINSIC LIGAMENTS Capitohamate interosseous ligament (CH) Capitotrapezoidal interosseous ligament (CT) Dorsal intercarpal ligament (DIC) Lunotriquetral interosseous ligament (LT) Pisohamate ligament (PH) Pisotriquetral interosseous ligament (PT) Scaphocapitate ligament (SC) Schapholunate interosseous ligament (SL) Scaphotrapeziotrapezoidal ligament (STT) Transverse carpal ligament (TCL) Trapeziotrapezoidal interosseous ligament (TT) Triquetrocapitate ligament (TC) Triquetrohamate ligament (TH) METACARPAL LIGAMENTS Carpometacarpal ligaments Intermetacarpal ligaments
50 [10,29] 50 [10,29,30] 75 [18,31] 37.5 [18,31] 37.5 [18,31] 50 [10] 40 [10,18] 40 [10] 325 [32] 300 [10,18,32] 50 [31] 350 [10,18,30] 50 100 40 [10,18] 230 [10] 150 [10,18] 130 [32] 150 [32] 40 [10,18,30] 50 [10] 100 100
Ann Arbor, MI) software for recreation of the 3D anatomy. Each of the 15 wrist bones (2 forearm bones, 8 carpal bones, and 5 metacarpal bones) and phalanges were individually identified. 2D masks were created to outline the osseous perimeter of interest on each slice, which were then used to create 3D solid bodies. The surface of each bone was represented as a network of triangulated surfaces and exported as STL (stereolithography) files. Each bone was imported into the assembly space of SOLIDWORKS (SolidWorks 2010, Dassault Syste`mes SolidWorks Corporation, Waltham, MA), a commercially available 3D CAD software, with their orientation and position defined by the initial CT scan. The radius and ulna were fixed in space in a neutral position as done experimentally. Then, within the SOLIDWORKS MOTION rigid-body software to solve the equations of motion in discrete time steps, function of soft tissue structures and additional boundary conditions were implemented as has been done previously for other joints [21–25]. Bones were defined as rigid bodies with surface contact interactions to prevent penetration. The 3D contact settings generated a contact force calculated from the overlap detected in each time step and the material stiffness of the
body as elaborated previously [17]. Joint articulations were considered frictionless and direction of gravity was defined according to the experimental study being simulated. The first metacarpal was fused to the trapezium bone since it does not influence wrist motion in the studies examined. The third metacarpal was fixed relative to the capitate since the two bones have been defined to move as one unit [16]. All other bones were free to move relative to one another. For ligaments, insertion sites of each structure were identified from anatomic texts [26–28] and bony anatomy and connected by tension-only force vectors incorporating tissue length and linear stiffness values from the literature (Table 1). Each ligament was modeled by at least two such linear elements depending on the width of the structure, distinct bands crossing between different bones, and/or dorsal/palmar bands. The TFCC was modeled as two distinct structures (proximal and distal) to replicate its functional behavior as an extension of the ulnar head, an articulating surface for the carpal bones, and attachment points for other wrist soft tissue structures such as the flexor and extensor retinaculum/capsules, pisiform, and extensor carpi ulnaris sheath. These structures were formulated into two rigid bodies, the geometry of which was generated from the cryoslice images within the U.S. National Library of Medicine’s (NIH, Bethesda MD) Visible Human Project (VHP), descriptions in the literature, and renditions in anatomical texts [26–28]. The proximal structure was rigidly connected to the ulna, due to this region of the TFCC anatomically encapsulating the distal ulnar head and the assumption that the relative motions between these bodies was minimal for the motions simulated in this study (Fig. 1). The distal structure was connected to the proximal structure with three tension only vectors with stiffness of 70 N/mm, which permitted the bodies to interact with the carpal bones while prohibiting penetration. The flexor and extensor retinacular/capsular structures were incorporated similarly to the TFCC as rigid bodies spanning the wrist as well as ligament-like structures (Fig. 2). The distal portion of the flexor retinaculum (FR), often referred to as the transverse carpal ligament, has attachment points laterally spanning the scaphoid tuberosity to the ridge of the trapezium. Medially, the structure attaches to the pisiform and hook of hamate. These were incorporated as tension only vectors with stiffness of 32.5 N/mm. The proximal portions of the retinaculum/capsule surrounding the proximal carpal row was simulated as two bodies each on the palmar and dorsal aspects connected by tension only vectors with stiffness of 40 N/mm. The force generated by six main muscles was incorporated within the model for the extensor carpi radialis longus (ECRL), extensor carpi radialis brevis (ECRB), extensor carpi ulnaris (ECU), flexor carpi radialis (FCR), and flexor carpi ulnaris (FCU). The tendon of each muscle body was simulated by two force vectors representing the lateral and medial borders of the tendon.
Fig. 1 Palmar (left) and dorsal (right) aspect of model illustrating the TFCC as a two part structure and the force vectors (interbody arrows) as their connection
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Fig. 2 Distal FR/capsule on the palmar aspect (left) incorporated as tension only structures (vectors). Flexor (right/top) and extensor (right/bottom) retinacular/capsular structures incorporated as rigid bodies connected with tension only vectors. Phalanges excluded for clarity.
Simulations. Before evaluating the effects of a PRC, behavior of the model with the additions of the TFCC and retinacular/ capsular structures was reconfirmed for the wrist fusion study performed previously [17] which simulated a cadaveric experimental study [33]. Here, the hand was held vertically while wrist movement was examined under flexion (FCR, FCU) or extension (ECRL, ECU) muscle action as well as radial (FCR, ECRL) or ulnar (ECU) deviation muscle actions (5 lb each). Range of motion in the respective plane was determined by measuring the angle between the long axis of the radius and the long axis of the third metacarpal. Intact, normal motion was evaluated followed by motion after a RSL fusion. Gravity was replicated in the direction appropriate to the experimental setup. Subsequently, the model was used to analyze the effects of a different surgical procedure, the PRC, simulating the experimental study performed by Blankenhorn et al. [7]. The wrist was positioned horizontally with the palm facing ground, in comparison to the vertical orientation of the prior fusion study. Range of motion was again examined in flexion, extension and radial/ulnar deviations with muscle loadings to achieve each wrist motion (experimentally between 5 and 50 N per muscle) (Table 2). Effects of the PRC were simulated by removal of the scaphoid, lunate, and triquetrum. The remaining carpal and metacarpal bones were temporarily locked to create one unit as the carpus was moved proximally toward the radius, such that the proximal capitate head rested on the lunate fossa of the radial articulating surface. The bones were then unlocked to move freely in response to applied perturbations, restrained only by the articulating surfaces and soft tissue structures. All ligaments with insertions on the excised bones were suppressed. The model then tested the four wrist motions with the same tendon loads used with the intact normal state, as described experimentally. A companion cadaveric study from the same group [8] was subsequently simulated in which the changes in force transmission at the radiocarpal joint occurring after PRC were examined. Here, only flexion–extension motions were examined, at the specific positions of 45 deg flexion, neutral, and 45 deg extension. Experimentally, this was achieved by manually altering the tendon loads (to 200 N total applied tendon force) until the desired position was Journal of Biomechanical Engineering
obtained; out of plane motions were manually prevented. Contact pressure and area were determined through insertion of Fujifilm. Computationally, the desired positions were obtained by replicating the bony positions of the wrist from the prior computational simulation, at 45 deg flexion and 45 deg extension. The long axis of the third metacarpal was then fixed in these two desired positions while still allowing the carpus to move along the proximal/ distal and dorsal/palmar directions. For the neutral position, the long axis of the third metacarpal was fixed to allow motion only in the proximal/distal direction. A radial styloidectomy was performed as done experimentally to eliminate carpal bone abutment against the radial styloid process during the contact tests. Tendon loads were applied for each position for a combined total of 200 N in the same ratios as used in the prior simulation. The retinacular bodies were suppressed in these simulations as their stabilizing role was unnecessary while the angular position was maintained.
Results Behavior of the model for the wrist fusion study exhibited very similar behavior to both the prior wrist model as well as the experimental study (Table 3). The main improvement seen was for ulnar deviation in which the addition of the TFCC with the current model brought motion to within the standard deviation of experimental findings, particularly for intact motion where the presence
Table 2 Muscle loads applied in the computational model for the intact normal wrist to achieve the wrist position designated by the experimental study.
Muscle name
Flexion (N)
Extension (N)
Radial deviation (N)
Ulnar deviation (N)
FCU FCR ECRL/ECRB ECU
24 24 12 12
12 12 30 30
20 40 50 12
4 5 5 25
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of the TFCC would be more pronounced. Flexion motion of the intact normal wrist also improved. Simulation of the PRC demonstrated excellent agreement between the experimental study and computational model predictions, both for the individual motion as well as the motion arc (Figs. 3–5). Motion was substantially reduced following a PRC, with 23% decrease in the flexion/extension arc computationally and 32% experimentally. A 29% decrease was predicted computationally in radial/ulnar deviation arc compared to 27% experimentally. When comparing the percent decrease in individual motions between the intact and PRC wrist, it was found to be accurate for flexion (Model 32% versus Experimental 29%62%) and for both radial (Model 40% versus Experimental 45%68%) and ulnar deviation (Model 22% versus Experimental 15%65%). In extension, the model underpredicted the percent change showing a 9% decrease in extension following PRC, while the cadaveric study reported a total 36%612% decrease. This difference most likely arose from the method of representation of the soft tissues and the assumptions made during the model’s development. A qualitative inspection of the PRC wrist during the range of motion testing demonstrated that wrist angular motion was isolated between the capitate and the radiocarpal articulating surface. In addition to the angular motion, some translational motion of the capitate head was observed. Some minor translational motion was observed in flexion, extension and radial deviation. However, in the case of ulnar deviation, a larger amount of translation was seen in the lateral direction of the wrist. This greater additional translation led the wrist to achieve the larger angular position in ulnar deviation as compared to radial deviation in the PRC state. In investigating force transmission at the radiocarpal joint, the experimental study presented average contact pressure and area, which were multiplied to calculate contact force, a parameter provided in the computational simulations. Measures were provided between the scaphoid and radius, scaphoid and lunate in the intact wrist, and between the capitate and radius in the PRC wrist (Fig. 6). Agreement in trends between the intact and PRC states was noted for the three positions although the computational model over-estimate contact force in extension and tended to under-estimate in flexion. While the contact force in the radiocarpal joint decreased with PRC, this was only the capitate contacting the radius with a contact area that averaged 26% of the intact wrist [8]. The model continued to predict a decrease in force with PRC while the experimental study predicted an increase in the flexed state.
Discussion
Fig. 3 Flexion and extension wrist motions in the intact normal wrist and after the PRC for the 3D wrist model and the cadaveric study [7]
structures, replicating bony contact, and applying constraints via ligamentous and other soft tissue structures. Kinematic motion was achieved by applying forces to relevant muscle units. Comparison of model predictions to experimental evidence showed excellent agreement. The model also provided some insight into the functions of the various structures that form the overall joint. The TFCC is a not a fully understood tissue structure. Comparing the motions predicted by the current 3D wrist model and its predecessor [17] indicated that the TFCC plays a major stabilizing role on the ulnar aspect of the wrist. Additionally, when a PRC procedure was replicated without the TFCC, convergence was not obtained. This was caused by a lack of ulnar side support and a rapid and an unnatural motion response of the carpus during this motion. Removal of the proximal row disturbed the entire ligamentous attachments between the radius and ulna to the proximal row (scaphoid, lunate, and triquetrum) as well as the proximal row to the distal row (hamate, capitate, trapezium, and trapezoid). The distal row then articulated with the radius and ulna but without extensive ligamentous connections. Surgically, the soft tissues are sutured after the bony excision yet postoperative immobilization is necessary to avoid instability until scarring occurs. Since the TFCC was a critical aspect in stabilizing the surgically altered wrist, this may indicate that this soft tissue structure plays a more critical role than currently appreciated. A similar observation was made of the retinacular/capsular structures. As with the TFCC, the stabilizing role of the
The 3D wrist model developed in this study was able to replicate and predict the biomechanical response of the joint following two different surgical procedures, the PRC and RSL fusion. The model was created from accurately rendering the 3D bony Table 3 Range of motions (degrees) obtained from the current wrist model, the prior wrist model [17], and the cadaveric study [33] for the intact normal wrist and subsequent to RSL fusion
Flexion Extension Radial deviation Ulnar deviation
Current wrist model Prior wrist model Cadaveric study Current wrist model Prior wrist model Cadaveric study Current wrist model Prior wrist model Cadaveric study Current wrist model Prior wrist model Cadaveric study
Intact normal
RSL fusion
73 84 7067 55 58 5668 30 30 3068 32 39 3165
34 36 2768 22 23 2569 17 19 2067 18 20 2266
Fig. 4 Radial and ulnar deviation wrist motions in the intact normal wrist and after the PRC for the 3D wrist model and the cadaveric study [7]
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Fig. 5 Total wrist motion arc in the intact normal wrist and after the PRC in flexion/extension (F/E) and radial/ulnar (R/U) deviation for the 3D wrist model and the cadaveric study [7]
retinacular/capsular structures in the wrist is not well understood. In the computational model, these structures were essential in stabilizing the surgically altered PRC wrist by preventing unnatural wrist joint motion. Experimental studies have demonstrated decreased carpal arch stiffness [33] and increased carpal arch length [31] with sectioning of the transverse carpal ligament for carpal tunnel release. Additionally, significant bowstringing and tendon excursions to non-anatomically correct lines of action were observed following sectioning of the FR [34] and the extensor retinaculum [33]. While these studies did not investigate effects on carpal kinematics, they do indicate an overall stabilizing role of these structures. Its stabilizing role may be further enhanced in a deficient wrist that has undergone trauma or surgery. In this deficient state, the primary stabilizers may not be as effective as originally intended and thus these capsular structures may in fact passively stabilize the weakened joint. In similar cadaveric experimental studies reported within the literature for range of motion of the intact normal wrist, the work conducted by Berkhout et al. [35] reported a total flexion–extension arc of 149 6 19 deg and radioulnar motion arc of 54 6 14 deg while McCombe et al. [36] reported motion arcs of 141 6 9 deg and 49 6 9 deg, respectively. While the flexion–extension arcs are larger than those predicted by the model, the radioulnar motion arc was much more comparable to the predicted results. The greater difference in the flexion–extension arc may be explained by the various experimental testing
Fig. 6 Force transmission in the intact normal wrist and after the PRC in 45 deg flexion, neutral and 45 deg extension for the 3D wrist model and the cadaveric study [8]. Experimental standard deviations estimated at 25%.
Journal of Biomechanical Engineering
methodologies. In the study by Berkhout et al. [35], the wrist specimens were secured and tested in a vertical upward orientation and thus the force of gravity would promote further flexion/ extension. Additionally, the study utilized an electromagnetic tracking system which requires the attachment of hardware and can increase the total weight of the specimen. In the work conducted by McCombe et al. [36], instead of applying fixed specified loads, each specimen was manually moved through the two motion arcs to the approximate end-point of the range of motion. Finally, if the anatomical structure of the radiocarpal joint is analyzed, the bony articular surface limits motions in the radial and ulnar aspect of the joint. On the other hand, motions in the palmar and dorsal aspect of the wrist are controlled more by soft tissue structures. Thus, the flexion–extension arc is more likely dependent on the testing methodology, and thus greater differences are observed between studies. This could also explain the consistency observed in radioulnar motion arc between studies, even with different test methodologies. PRC is a motion preserving surgical procedure often employed to treat various degenerative diseases of the wrist proximal carpal bones. It is favored by many practitioners due to its ease of performance, lack of nonunion formation and early patient recovery [1,37]. In the short term, the procedure has demonstrated positive results in preservation of wrist motion and grip strength within functional ranges as well as providing pain relief. In a clinical study, an average 62610% preservation of the flexion–extension arc and 51618% of the radial-ulnar motion arc were reported after a PRC procedure [1]. Another study measured the average motion in 11 wrists after PRC to be 85 deg for the flexion– extension arc and 31 deg for radial-ulnar motion arc [37], a 64% retention average for all four motion arcs relative to the contralateral healthy wrist. In long-term follow-up studies, 61–63% average range of motion of the contralateral wrist is preserved [5,38]. With respect to the computationally predicted results, the 3D wrist model demonstrated an average 74% retention of the intact healthy wrist motion arc postoperatively, slightly higher than the clinically reported values. The difference is likely due to the in vivo response after a surgical procedure with healing and scar tissue formation, which would most likely provide additional restrictions and support to the carpal bones. This would lead to a reduced motion arc experienced by the joint. Additionally, clinical studies reported very small postoperative radial deviation angles such as 4 deg [37], 7 deg [1], and 9 deg [5]. These small angles were most likely caused by radial styloid impingement with the trapezium. No significant impingement was observed in the 3D wrist model which resulted in a 15 deg radial deviation prediction and would also account for the greater motion arc preservation predicted by the 3D wrist model. The in vitro cadaveric study observed 69%617% total motion arc preservation with PRC, which is comparable to that predicted by the 3D wrist model. While there have been concerns over the degenerative effects caused by the significant reduction of joint articulation area, long term results have been satisfactory [5,38]. A minimum 20-year follow-up study [39] found that PRC provided a survival rate of 65%. Of these, degenerative radiographic changes at the radiocapitate joint were noted in 72% although patient satisfaction level did not correlate with the degeneration. The computational and experimental results of force transmission would support the clinical findings of the degenerative changes. While contact force decreases with PRC, contact area decreases substantially more depending on the articulating surface of the capitate. For some patients, early failure of PRC typically manifests as nonresolution of pain and additional procedures must be performed. For those in whom PRC is considered a success, the level of degeneration at 20 years, while not translating directly to patient dissatisfaction, is of enough concern to consider carefully its use in young patients [39]. A sensitivity analysis on the effect of model parameter variations such as ligament stiffness was not performed with this particular study. Previous computational simulations, however, JUNE 2015, Vol. 137 / 061001-5
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for the foot/ankle complex and the elbow created from the same modeling methodology as presented here have evaluated the effects of a range of parameter values [21–23]. Certainly, the biomechanical results change magnitude when the stiffnesses increase or decrease as these properties are expected to influence model behavior. However, the conclusions drawn between states remain consistent. Ligament stiffnesses in this wrist model were selected from the literature and were not manipulated in order to achieve specific results. During model development, certain assumptions and simplifications were made. The material properties of the ligaments and soft tissues incorporated within the model were based on experimentally measured values reported in the literature. These soft tissues were represented by linearly elastic passive tissue elements. A thorough characterization of their nonlinear behavior is not available. The TFCC was modeled as a two part structure, each of which was represented as a solid body. Anatomically, the TFCC is a soft tissue structure which could experience deformation during wrist motion. Flexibility was afforded to the TFCC by its inclusion as two separate bodies connected by springs. Additionally, the TFCC has soft tissue attachment points to the ulnar head and the radius which could permit relative movement. Minimal movement in flexion/extension and radial/ulnar deviation of the carpus was assumed, and thus the proximal TFCC body and the ulnar head were taken to function as one unit. To recreate the stabilizing effect of the retinacular/capsular structures, a similar assumption as for the TFCC was required. Finally, the computational model was characteristic of a single wrist. Future studies should reflect multiple wrists to provide the range of biomechanical parameters and more generalized conclusions to be made. In the comparison of force transmission, the overestimation in extension but underestimation in flexion between experimental findings and computational predictions may be due to multiple factors. Specific information on the methodology of the cadaveric study was not provided to be implemented in the wrist model, particularly for the magnitude of the tendon forces. The effect of manually controlling out-of-plane motions in the cadaver wrist is unknown as is whether the means to do so computationally adequately reflected experimental setup. In the neutral position, however, the computational predictions are well aligned. In conclusion, this 3D computational wrist model demonstrated the ability to predict biomechanical function and provided some insight into biomechanical function of tissue structures that are not well understood but whose role may be important not only in the normal wrist but also in injured or surgically altered states. In particular, the TFCC and the retinacular/capsular structures provided ulnar side support, influenced wrist motion, and helped stabilize the joints. Future refinement of the model will allow for continued investigation in other states as well as provide predictions of relevant physiologic parameters that are difficult or impossible to measure experimentally or clinically. This information may be useful to understand the biomechanical effects of injuries or corrective procedures.
Acknowledgment The U.S. National Library of Medicine’s Visible Human Project for the cryoslice sections was used to assist in recreating the triangular fibrocartilage complex.
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