Cartilage contact stress elevation accompanying residual incongruity is high on the list of concerns in orthopaedic treatment of intraarticular fractures. Although this is only one among several factors seemingly predisposing to secondary osteoarthritis (OA), it is a factor that usually is at least somewhat amenable to surgical intervention, and which therefore merits systematic assessment as to its pathophysiologic role. Much remains to be learned as to what levels of contact stress elevation prevail for the wide range of incongruity situations encountered clinically, and as to the levels of contact stress elevation that can be tolerated successfully in specific situations.
A key requirement for making progress in this important area is to have means by which these cartilage contact stress elevations can be quantified reliably. This historically has been a challenging technical problem in the field of orthopaedic biomechanics, and one that has constituted a focus of intensive effort in numerous research centers. We highlight milestone developments in assessing contact stress aberrations attributable to articular incongruities, and review several promising directions of ongoing methodologic improvement.
Established Techniques for Quantifying Cartilage Pressures
Most of the early attacks on the problem of cartilage contact stress assessment involved estimates of spatial mean contact stress, based on known (or estimated) resultant loads distributed over measured contact areas. The contact area measurements were done using techniques such as dye exclusion,17 radiographic assessment,27 or solid castings.40 Early improvements on these nominal average stress estimates were provided by discrete local samplings, first by means of (diaphragmatic) fluid pressure transducers mounted either intraarticularly39 or subchondrally.33 Additional refinements of this approach involved groups or arrays of sensors, such as compliant miniature load cells embedded in the cartilage on one side of the articular surface,8 or discrete conductive rubber transducers,23 or piezoresistive polymer sheets.22 A conceptually related approach, especially noteworthy for having provided the first, and still only, human in vivo data (albeit for cartilage-on-metal rather than cartilage-on-cartilage articulation), was the telemetered hip hemiprosthesis system developed by Carlson et al.10
Discrete multichannel systems, although permitting transient recording, have major inherent limitations in their spatial resolution. Early continuous transducer sheets, conversely, permitted collection of stress data throughout the contact region, albeit at the expense of producing only one snapshot of the “high-water-mark” of the distribution. Modalities of this class include pressure-sensitive paper,14 viscoplastic indentation sheets,1 and Fuji Prescale film.15 Currently, Fuji film (Valhalla, NY) remains the technique of choice in most laboratories, because of its low expense, ease of use, and reasonable accuracy (approximately ±10%)20 for most purposes. In 1987, a technique was developed using sensor sheets involving multiplexed piezoresistive conductor arrays for dental occlusal measurements.32 This multiplexed sensor concept subsequently was extended to foot pressure measurements.42 Similarly conceived sensors for a wide range of contact interface geometries currently are marketed by Tekscan (Boston, MA). Although purchase price remains an obstacle in many settings, these multiplexed sensors are even easier to use than Fuji film, and if appropriately signal-conditioned,35 they offer comparable or better accuracy.
The other broad avenue of approach to determining articular joint contact stress has been mathematical. Closed-form analytical solutions for axisymmetric-layer compression problems13,17,18 date from the early 1970s, and subsequently were improved on by (iterative) integral equation solutions4 and by quasi-three-dimensional closed-form elasticity solutions.29 The main thrust of mathematical analysis, however, has been with numerics. For certain limited purposes, rigid body spring element formulations have proven effective,16,30 although the main thrust of computational approximation work has been with finite element techniques. This began with two-dimensional6 and axisymmetric26 materially linearly elastic contact formulations, followed in due course by three-dimensional linearly elastic formulations,24 and by incorporation of fluid or solid matrix constitutive behavior for two-dimensional11 and now three-dimensional12,41 geometries. Making contact stress computations on a patient-specific basis has not been tractable with traditional approaches to finite element mesh generation (preprocessing). In linearly elastic stress analysis problems—which involve prescribed loading(s) applied to simply behaved materials for which stress is proportional to strain (metals, and for most purposes, bone), and in which all material interfaces are contiguously bonded—there is ample precedent for using finite element meshes comprised of rectilinear block elements converted directly from the rectilinear voxel elements comprising the CT scans of patients.28 The stair-step jaggedness present at the margins of such voxel-based finite element meshes has precluded those meshes’ usage for representing the engagement of articular surfaces. With the recent introduction of automated techniques for smoothing those boundaries, however, it has now become possible to adapt voxel-based meshing to contact problems.19
The majority of past work with articular joint contact stress assessment has dealt with intact articular surfaces. Situations involving a local incongruity, such as from an imprecisely reduced intraarticular fracture, introduce yet additional technical hurdles. Most biomechanical studies of incongruities have necessarily worked with geometrically idealized configurations, primarily step-offs and gaps, which lend themselves to orderly parametric variation. Fuji film has been by far the preferred measurement vehicle for such work, because of its potential for high spatial resolution, approaching 10 MPa/mm for medium-range sensitivity film.20 The manufacturer’s original means for calibrating film staining intensity versus pressure involved the use of an analog densitometer, for which readings for the stain of interest needed to be compared with a set of presupplied stain samples. Unfortunately, the densitometer averaged staining intensity over its 3-mm diameter field of view, a level of resolution coarseness obviously unsuitable for studying local articular incongruities. Fortunately, when digital image analysis was introduced in 1987 as an alternative means for calibration,37 the film’s available spatial resolution became limited only by the intrinsic graininess of the microstains from rupture of the individual liquid-containing microcapsules dispersed in the film acetate.
One troublesome problem with local incongruities, however, is that they exacerbate Fuji film’s well-known tendency to crinkle in situations that call for it to conform to bidirectional surface curvatures, as usually is the case in articular joint pressure measurements. This leaves pronounced streak-like artifacts in the staining distribution, which interfere with quantifying the local pressure levels. Strategically placed relief cuts31 can help reduce crinkle artifact, and when combined with compensatory digital image analysis procedures,9 the problem can be controlled reasonably. Incongruity step-off studies with Fuji film date from the late 1980s, and have focused especially on the acetabulum3,36 and the tibial plateau.5 Similar methodology subsequently has been extended to various idealized pressure measurements for specialized incongruity situations, including at the ankle,38 elbow,34 and wrist.2 Related measurement techniques have been applied to osteochondral defects, where defect severity can be modulated readily simply by changing the diameter of a circular defect milled or drilled in the weightbearing area of the articular surface.7
Finite element techniques have been used occasionally to study stress aberrations near local incongruities. The first contact formulation reported for such problems involved linear elastic characterization of cartilage for step-off defects in the tibial plateau, where it was shown that global joint congruency and local incongruity interact to determine local cartilage stress elevations.25 Additional developments addressed incongruities with additional geometric complexity, such as osteochondral defects, and have adopted more complex constitutive models for cartilage, particularly biphasic formulations,21 that allow study of fluid-flow-dependent load transmission.
New Assessment Modalities
Existing techniques for voxel-based finite element mesh generation for and Tekscan piezoresistive contact stress measurement have provided points of departure for recent advances particularly applicable to local articular incongruities. Regarding finite element analysis, geometrically simplified incongruity models have provided valuable insights into how stresses vary in response to individual parameters. However, work of that type has been difficult to extrapolate to the clinical arena, where fractures always have complicated, idiosyncratic geometry. Intraoperatively, a key challenge is to decide whether a given candidate reduction is suitably precise to avoid deleteriously high cartilage stresses. Any biomechanical tools used to aid in that assessment must be patient-specific and incongruity specific. Moreover, regarding finite element analysis, even if the model captures the full geometric fidelity of the fracture site, conventional mesh assembly procedures requiring hours or even days of analyst time are far too unwieldy to be of potential benefit in the fast-moving clinical setting. For that reason, voxel-based contact models hold enormous attraction because they incorporate idiosyncratic fracture geometry reported from CT scans and because the element creation process (zoning) can be expedited greatly by using the source voxel data set as the finite element mesh. Of course, because cartilage contact stresses are the mechanical variable of primary interest, the voxel “stair-step” irregularities at the surface must be smoothed appropriately.
A sequence showing a voxel-based contact finite element analysis at the ankle (Fig 1A) begins with a conventional CT scan. Voxels delimiting the bony members are identified by a search algorithm that detects all volume occupied by material for which density (CT Hounsfield number) lies above a specific threshold. Based on the local densities thus identified for discrete voxels near the periphery of each bony member, a continuous three-dimensional surface then is interpolated. This surface, termed an iso-surface, has the property of being the best estimate (least-squares error) of a continuous surface on which the density would be uniformly equal to the prescribed density threshold value. From this iso-surface, a set of planar contours is generated smoothly outlining the bone surface at successive cross sections. The operator then designates a juxtaarticular region of each bony member for high-resolution finite element meshing, allowing the remainder of the structure (of lesser interest for contact stress analysis) to be represented with relatively coarse meshing. This designation is important, because contact problems are nonlinear and require computationally burdensome iterative solution techniques, and would be intractable if the entire structure were to be analyzed at a resolution appropriate for the contact regions. After this meshing procedure is repeated for both sides of the joint, the two members are brought geometrically into incipient contact, and then physiologic loading is applied. The resulting contact stress distribution (Fig 1B) then is fully patient-specific. The contact model can be formulated either with rigid or deformable representation of bone (the former offering appreciable computational economy). Output data include the full surface traction vector (normal plus shear) at the contact interface, and the full continuum stress tensor within all deformable continuum regions, such as the articular cartilage. The computational procedure operates equivalently for intact articular surfaces and for those with imprecisely reduced intraarticular fractures (Fig 2). For the latter instance, there is no need to invoke simplified geometric descriptors such as step-offs or gaps. Rather, the full complexity of the fracture surface is incorporated automatically in the contact model. This therefore provides a new paradigm for measuring severity of incongruity. Rather than relying on geometric measures that are effectively only surrogate indices of contact abnormality, it becomes possible to assess cartilage contact stress aberration, the parameter of direct physiologic consequence.
Besides geometric idiosyncracy, another major attraction of voxel-based contact stress analysis is that it facilitates making cartilage stress estimates for various candidate fracture reductions. Once the individual bony fragments are identified initially, the corresponding voxel subsets can be maneuvered spatially for virtual reduction of the fracture (Fig 3), and the corresponding contact problem can be solved for any given candidate reduction. Computationally, this requires that fragment motion be prescribed in terms of a sequence of small incremental translations and rotations, which allows construction of a corresponding virtual CT scan at each repositioned increment, based on the new position occupied by any given translated or rotated voxel from the original fragment CT scan. The computational algorithm developed to implement this fragment manipulation procedure also includes penetration detection logic, to preclude physically overlapping multiple bony fragments. Because all the fragment motions are conducted with voxel arrays, the bony density distribution (Hounsfield numbers) remains fully registered throughout the analysis, allowing complete incorporation of the anatomic elastic modulus distribution. Currently, this type of virtual reduction is purely in the research domain, pending development of means to physically implement the corresponding fragment motions. However, because of the rapid ongoing advances in computer-guided surgery and robotics, the development of capabilities for computer-controlled manipulation of fracture fragments seems a very plausible near-term possibility. Even with manual control of fragment positioning, however, voxel-based contact analysis provides a previously unavailable basis for objective preoperative planning.
Another attractive direction for methodologic advance lies in developing improved means for experimental measurement of contact stress transients. Local cartilage response to incongruity depends on the stresses experienced throughout pertinent physiologic loading events, such as the stance phase of the gait cycle for lower extremity joints. Because cartilage exhibits time-dependent load uptake because of rate-dependent interaction of the fluid and solid components of its matrix, physical measurements of cartilage stress seemingly should be done transiently, and for realistic histories of joint loading.
Improving on the early generation of Tekscan pressure sensors, which had been developed for studying contact stresses in total knee implants, seemed an inviting direction to pursue. Manipulable design parameters in that regard included the physical density of sampling sites (sensels), the sensing range of the piezoresistive element at each sampling site, and the geometric layout of the sensor grid and its associated families of connector leads. A new-generation sensor developed specifically for studying contact stress anomalies accompanying articular incongruities in the ankle (Fig 4) achieves spatial resolution of 0.693 mm2 per sensel (versus 1.61 mm2 for the earlier-generation knee implant sensor), offers sensitivity of 10 data bits per MPa (versus 3 bits per MPa for the knee sensor), and captures pressure distributions at 132 frames per second. Illustrative data captured during stance phase ankle loading in a cadaveric preparation (Fig 5) document the capability to achieve high-resolution transient pressure histories. When positioned over a local incongruity such as a step-off, Tekscan sensors sometimes undergo gradual degradation of response over the course of an experiment, in addition to exhibiting quasi-static drift.35 Frequent recalibration therefore is highly desirable. Ongoing work with this new instrument includes improved techniques for in situ calibration, tuning band-pass digital filtering to optimize signal-to-noise ratio, and postprocessing the raw pressure output to automate the reporting of physically consequential parameters such as pressure gradients, time-derivatives of contact stress, and site-specific cumulative loading. Although technically capable of collecting intraoperative pressure data, the use of these new sensors lies primarily in parametric cadaveric studies. Geometrically, the sensors conform best to surfaces that have only modest curvature (tibial plateaus) or for which curvature is appreciable in only one plane (cylinder-like surfaces such as the talar dome). These sensors also provide previously unavailable capabilities for physical validation of patient-specific finite element contact stress computations.
Despite the recent improvements in sensel size, the spatial resolution available with Tekscan remains approximately an order of magnitude below that available with Fuji film. Both modalities therefore have a place in studying local articular incongruities: Tekscan when transient recordings are of primary interest, and Fuji film when the focus is on local detail. These modalities fortunately lend themselves to interchangeable use, in immediately sequential data captures, to provide complementary information drawing on the strength of each.
Because of the lack of appropriate measurement or modeling modalities, opportunities historically have been limited for studying the cartilage contact stress aberrations caused by displaced intraarticular fractures. The presence of local articular incongruity compounds the already appreciable technical difficulties associated with studying contact in an intact joint. An appreciation of these difficulties is helpful for drawing reliable clinical inferences from the laboratory literature in this area. The recent availability of high-resolution transient contact stress distribution sensors, and the development of capability for patient-specific contact finite element analysis using meshes created directly from clinical CT scans, open exciting possibilities for systematic study of this clinically important but underinvestigated class of contact problems.
We thank Dr. Douglas R. Pedersen, Daniel C. Koos, Yang Dai, Dr. Yuki Tochigi, Hannah Lundbergh, Dr. Anneliese Heiner, and Thomas E. Baer for technical support. Drs. Todd O. McKinley, Charles L. Saltzman, J. Lawrence Marsh, and Joseph A. Buckwalter provided helpful advice and clinical perspective.
1. Ahmed AH: A pressure distribution transducer for in-vitro static measurements in synovial joints. J Biomech Eng 105:309–314, 1983.
2. Anderson DD, Bell AL, Gaffney MB, Imbriglia JE: Contact stress distributions in malreduced intraarticular fistal radius fractures. J Orthop Trauma 10:331–337, 1996.
3. Bay BK, Hamel AJ, Olson SA, Sharkey NA: Statically equivalent load and support conditions produce different hip joint contact pressures and periacetabular strains. J Biomech 10:193–196, 1997.
4. Brinckmann P, Frobin W, Hierholzer E: Stress on the articular surface of the hip joint in healthy adults and in persons with idiopathic osteoarthritis of the hip joint. J Biomech 14:149–156, 1981.
5. Brown TD, Anderson DD, Nepola JV, et al: Contact stress aberrations following imprecise reduction of simple tibial plateau fractures. J Orthop Res 6:851–862, 1988.
6. Brown TD, DiGioia AM: A contact-coupled finite element analysis of the natural adult hip. J Biomech 17:437–448, 1984.
7. Brown TD, Pope DF, Hale JE, Buckwalter JA, Brand RA: Effects of osteochondral defect size on cartilage contact stress. J Orthopaedic Res 9:559–567, 1991.
8. Brown TD, Shaw DT: A technique for measuring instantaneous in vitro contact stress distributions in articular joints. J Biomech 15:329–334, 1982.
9. Caldwell NJ, Hale JE, Rudert MJ, Brown TD: An algorithm for approximate crinkle artifact compensation in pressure-sensitive film recordings. J Biomech 26:1001–1010, 1993.
10. Carlson CE, Mann RW, Harris WH: A radio telemetry device for monitoring cartilage surface pressures in the human hip. IEEE Trans Biomed Eng 21:257–264, 1974.
11. Donzelli PS, Spilker RL: A contact finite element formulation for biological soft hydrated tissues. Comput Methods Appl Mech Eng 153:63–79, 1998.
12. Dunbar Jr WL, Un K, Donzelli PS, Spilker RL: An evaluation of three-dimensional diarthrodial joint contact using penetration data and the finite element method. J Biomech Eng 123:333–340, 2001.
13. Eberhardt AW, Keer LM, Lewis JL, Vithoontien V: An analytical model of joint contact. J Biomech Eng 112:407–413, 1990.
14. Frisina W, Lehneis HR: Pressure mapping: A preliminary report. J Biomech 3:526, 1970.
15. Fukubayashi T, Kurosawa H: The contact area and pressure distribution pattern of the knee: A study of normal and osteoarthritic knee joints. Acta Orthop Scand 51:871–879, 1980.
16. Genda E, Iwasaki N, Li G, et al: Normal hip joint contact pressure distribution in single-leg standing effect of gender and anatomic parameters. J Biomech 34:895–905, 2001.
17. Greenwald AS, Haynes DW: Weight-bearing areas in the human hip. J Bone Joint Surg 54B:157–163, 1972.
18. Greenwald AS, O’Connor JJ: The transmission of load through the human hip joint. J Biomech 4:507–528, 1971.
19. Grosland NM, Brown TD: A voxel-based formulation for contact finite element analysis. Comput Methods Biomech Biomed Eng 5:21–32, 2002.
20. Hale JE, Brown TD: Contact stress gradient detection limits of pressensor film. J Biomech Eng 114:352–357, 1992.
21. Hale JE, Rudert MJ, Brown TD: Indentation assessment of biphasic mechanical property deficits in size-dependent osteochondral defect repair. J Biomech 26:1319–1325, 1993.
22. Halls AA, Travill A: Transmission of pressure across the elbow joint. Anat Rec 150:243–247, 1964.
23. Hara T, Horii E, An KN, et al: Force distribution across the wrist joint: Application of pressure-sensitive conductive rubber. J Hand Surg 17A:339–347, 1992.
24. Heegaard J, Leyvraz PF, Cumier A, Rakotomanana L, Huiskes R: The biomechanics of the human patella during passive knee flexion. J Biomech 28:1265–1279, 1995.
25. Huber-Betzer H, Brown TD, Mattheck C: Some effects of global joint morphology on local stress aberrations near imprecisely reduced intra-articular fractures. J Biomech 23:811–822, 1990.
26. Huiskes R: Finite element analysis of acetabular reconstruction. Acta Orthop Scand 58:620–625, 1987.
27. Kettelkamp DB, Jacobs AW: Tibiofemoral contact area: Determination and implications. J Bone Joint Surg 54A:349–356, 1972.
28. Keyak JH, Meagher JM, Skinnet HB, Mote Jr CD: Automated three-dimensional finite element modeling of bone: A new method. J Biomed Eng 12:389–397, 1990.
29. Legal H: Introduction to the Biomechanics of the Hip. In Tonnis B (ed). Congenital Displasia and Dislocation of the Hip. Berlin, Springer-Verlag, 1987.
30. Li G, Genda E, Sakamoto M, Chao EYS: Surface Pressure Distribution in Articular Joints Under Static Load. In Askew M (ed). 1994 Advances in Bioengineering. Vol 28: New York. The American Society of Mechanical Engineers, 139–140, 1994.
31. MacKenzie JR, Callaghan JJ, Pedersen DR, Brown TD: Areas of contact and extent of gaps with implantation of oversized acetabular components in total hip arthroplasty. Clin Orthop 298:127–136, 1994.
32. Maness WL, Benjamin M, Podoloff R, Bobick A, Golden R: Computerized occlusal analysis: A new technology. Quintessence Int 18:287–292, 1987.
33. Mizrahi J, Solomon L, Kaufman B: A method for direct measurement of local pressures in the human cadaver hip joint. Phys Med Biol 25:1181, 1980.
34. Moed BR, Ede D, Brown TD: Fracture of the olecranon: An in vitro study of elbow joint stresses after tension band wire fixation vs. proximal fracture fragment excision. J Trauma 53:1088–1093, 2002.
35. Otto JK, Brown TD, Callaghan JJ: Static and dynamic response of a multiplexed-array piezoresistive contact sensor. Expt Mech 39:317–323, 1999.
36. Rennirt G, Helfet D, Brown TD, Pedersen DR: Increased peak contact stress following incongruent reduction of transverse acetabular fractures: A cadaveric model. J Trauma 15:704–709, 2001.
37. Singerman RJ, Pedersen DR, Brown TD: Quantitation of pressure-sensitive film using digital image scanning. Exp Mech 27:99–105, 1987.
38. Steffensmeier SJ, Saltzman CL, Berbaum KS, Brown TD: Effects of medial/lateral displacement calcaneal osteotomy on tibiotalar joint contact stresses. J Orthop Res 14:980–985, 1996.
39. Walker PS, Erkman M: The role of the menisci in force transmission across the knee. Clin Orthop 109:184–192, 1975.
40. Walker PS, Hajek JV: The load bearing area in the knee joint. J Biomech 5:581–592, 1972.
41. Wu JZ, Herzog W, Epstein M: Evaluation of the finite element software ABAQUS for biomechanical modeling of biphasic tissues. J Biomech 31:165–169, 1998.
© 2004 Lippincott Williams & Wilkins, Inc.
42. Young CR: The F-SCAN system of foot pressure analysis. Clin Podiatr Med Surg 10:455–461, 1993.