Surface Size, Curvature Analysis, and Assessment of Knee Joint Incongruity With MRI In Vivo

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1 Magnetic Resonance in Medicine 47: (2002) DOI /mrm Surface Size, Curvature Analysis, and Assessment of Knee Joint Incongruity With MRI In Vivo Jan Hohe, 1,2 Gerard Ateshian, 3 Maximilian Reiser, 4 Karl-Hans Englmeier, 2 and Felix Eckstein 1 * The purpose of this study was to develop an MR-based technique for quantitative analysis of joint surface size, surface curvature, and joint incongruity and to assess its reproducibility under in vivo imaging conditions. The surface areas were determined after 3D reconstruction of the joint by triangulation and the incongruity by Gaussian curvature analysis. The precision was tested by analyzing four replicated MRI datasets of human knees in 14 individuals. The algorithms were shown to produce accurate data in geometric test objects. The interscan precision was <4% (CV%) for surface area, m -1 (SD) for the mean principal curvature, and m -1 for congruence indices. Incongruity was highest in the femoropatellar joint (79.7 m -1 ) and lowest in the medial femorotibial joint (28.6 m -1 ). This technique will permit identification of the specific role of surface size, curvature, and incongruity as potential risk factors for osteoarthritis. Magn Reson Med 47: , Wiley-Liss, Inc. Key words: diarthridial joints; MR imaging; curvature analysis; joint congruence; osteoarthritis Osteoarthritis (OA) affects more than half of the population above the age of 65 (1,2), with substantial effects on the quality of life of elderly individuals (3). The direct and indirect costs involved have been estimated to currently amount to 1% of the gross national product of the United States (4). However, it remains unknown why some individuals develop OA early in life, whereas others maintain normal cartilage morphology and function up to advanced age (5). Animal models (e.g., 6,7) and epidemiological studies (e.g., 8,9) have established that mechanical factors play an important role in the initiation and progression of OA. Clinical experience suggests that high degrees of joint incongruity leads to high peak stress, and thus to early cartilage degeneration (10 14). Theoretical computations have demonstrated that joint incongruity does not only involve higher peak stresses at the articular surface (due to smaller contact areas), but also negatively affects the mechanism of hydrostatic pressurization of the interstitial cartilage fluid (15). A lack of hydrostatic pressurization increases the shear stress encountered by the proteoglycan collagen network at the site of articular contact and has been suggested to promote matrix failure (15). Yet there exists no method for noninvasive assessment of the size of the joint surfaces and joint incongruity in vivo, as a surrogate of the peak pressure encountered by articular cartilage. Effective postprocessing tools have recently been developed for determining cartilage volume and thickness from high-resolution fat-suppressed gradient-echo MRI (16 20). In the present work we will 1) implement a technique for quantitative determination of the size, curvature, and incongruity of articular surfaces from MRIs; 2) determine the interscan precision (reproducibility) of these parameters in the human knee under in vivo imaging conditions (four replicated acquisitions); and 3) assess differences in these parameters between different compartments of the human knee as well as between different individuals. Analysis of joint surface size, curvature, and incongruity should be particularly useful in epidemiological studies on OA. By measuring the surface size and incongruity in individuals before the onset of cartilage degeneration (e.g., in the contralateral knee of patients with unilateral joint disease), these studies will make it possible to determine whether individuals with small joint surfaces (in relation to body weight and height) and with high degrees of joint incongruity have a higher risk/susceptibility of OA. A noninvasive in vivo method is therefore required for reliably measuring these parameters in cross-sectional and longitudinal population-based studies. MATERIALS AND METHODS Study Population and Instrumentation The knee joints of 14 healthy volunteers (age years, 8 male, 6 female) were imaged four times, with repositioning of the joint between replicate acquisitions. Volunteers with a history of pain, trauma, or surgery at the knee were not included. The protocol was ratified by the local ethics committee. Imaging was performed with a 1.5 T scanner (Magnetom Vision, Siemens, Erlangen, Germany), a circularly polarized knee-coil, and with a fat-suppressed gradi- 2 Institut für Medizinische Informatik und Systemforschung, GSF Research ent echo sequence (fast low angle shot FLASH) with 1 Musculoskeletal Research Group, Institute of Anatomy, Ludwig-Maximilians Universität München, München, Germany. Center Neuherberg, Oberschlei heim, Germany. selective water excitation (21 24) (repetition time 3 Department of Mechanical Engineering, Columbia University, New York, 17.2 ms, echo time 6.6 ms, flip angle 20 ; NEX 1). New York. This sequence has been previously shown to produce consistent data on cartilage volume and thickness with those 4 Institute for Clinical Radiology, Klinikum der Ludwig- Maximilians Universität München, München, Germany. Grant sponsor: Deutsche Forschungsgemeinschaft. obtained from conventional fat-suppressed gradient-echo *Correspondence to: PD Dr. Felix Eckstein, Musculoskeletal Research Group, sequences with a prepulse (22) and with data obtained by Anatomische Anstalt, Pettenkoferstr. 11, D München, Germany. E- A-mode ultrasound, CT arthrography (23), and surgically mail: eckstein@anat.med.uni-muenchen.de Received 18 June 2001; revised 16 October 2001; accepted 5 November removed tissue in osteoarthritic patients (24). Sagittal datasets of the knee were acquired (Fig. 1) at a resolution of 2002 Wiley-Liss, Inc. 554

2 Joint Surface Size, Curvature, and Incongruity 555 femoral condyle, and the lateral condyle (Fig. 2). Curvature analysis was then applied to these subsections of the femoral surface. Since the tibial cartilages display highly convex peripheral rims that are partly covered by the menisci and that are not physiologically in direct contact with the femoral condyles, the analysis was refined in a further step to the central aspects of the tibia (Fig. 1). Surface curvature values and congruence indices were thus computed 1) for the entire tibial plateau and entire femoral condyle, 2) the central aspects of the tibial plateau (Fig. 1) and the entire femoral condyle, and 3) for the central aspect of the tibial plateau and that part of the femoral condyle that is in contact with the central region of the tibia in a slightly flexed position of the knee (approx. 15 in the MR scanner). Theoretical Development and Validation in Test Objects In each slice the contours of the articular surface and bone cartilage interface were extracted. Triangulation between contiguous slices was performed based on a Euclidean distance measure. Each contour point and its neighbor were connected to the closest point in the next slice to form a triangle. The sizes of the total surfaces were then calculated by numerically integrating the size of all trian- FIG. 1. Sagittal, fat-suppressed gradient-echo images of the medial (a) and lateral (b) femorotibial compartments. The black lines indicate the central regions of interest of the joint surface areas used for a secondary analysis of femorotibial incongruity. At this step the analysis was confined to the region between the posterior rim of the anterior horn and the posterior rim of the posterior horn of the menisci mm 0.31 mm 1.5 mm (field of view mm, matrix) and with an acquisition time of 9 min, 15 sec. All datasets were transferred to a high-end graphics computer (Octane Duo, Silicon Graphics, Mountain View, CA). Segmentation was performed on a sectionby-section basis using a semiautomatic B-Spline Snake algorithm (18). The articular surface and bone cartilage interface were reconstructed as described below and their size computed. The curvature values (see below) were only computed for the articular surface. The femoral cartilage plate was divided interactively into the facies patellaris femoris (the trochlea), the medial FIG. 2. Anatomical drawing showing the various joint surfaces in the human knee.

3 556 Hohe et al. gles attributed to the cartilage surface or bone cartilage interface. The calculation of the surface size was eventually validated on geometric test objects (sphere, cylinder, plane). To determine the curvature of the triangulated surface model of the cartilage, continuous B-spline surfaces were calculated through the discrete original (segmented) surface points (25). Because B-spline surfaces are continuous in the first and second derivative, analytic curvature calculation can be performed, which is problematic on discrete surface representations. Bicubic B-spline surfaces P (, ) were defined using: N P, i 0 M A i,j B N i B M j. [1] j 0 A i, j are the control points required to represent the 3D cartilage surface, N is the number of control points in horizontal, and M is the number in vertical direction. P (, ) is the spatial position of a surface point at the parametric coordinates, (0 1, 0 1). B represents the cubic blending-function, which is used to weight the geometric points and is defined by: 2 3 / /6 1 0 B / [2] 2 3 / other This cubic blending function (Eq. [2]) is derived from the general recursive description of B-spline blending functions and produces good results for cartilage surfaces. For the calculation of the B-spline surface it is assumed that the x-, y-, and z-coordinates of all control points A i, j are distributed at equal intervals of the parameter. The bicubic B-splines used in this work are a special case of the general B-spline formulation. The knot sequence is uniformly distributed and the spacing between the knots is unity. If and exactly meet a control point ( k/n, l/m; 0 k N; 0 l M), Eq. [1] reduces to: P k/n, l/m A k 1,l 1 A k 1,l 1 A k 1,l 1 A k 1,l 1 /36 A k 1,l A k 1,l A k,l 1 A k,l 1 /9 4A i,j /9. [3] Although it is possible to calculate surface representations of arbitrarily sized (N 1) (M 1) control point matrices, the B-spline surface was only derived for a 5 5 matrix for the curvature determination of the central matrix point ( 0.5, 0.5). To determine the 25 unknown control points A k,l,a square matrix of data points (P k,l ) was employed, which were extracted from the previously segmented contours with the surrounding two rows and two columns of the control points (around the central point) being determined with a Euclidean distance measure, in order to produce a rectangular surface area. To obtain a B-spline surface interpolation of these data points, 25 equations of type Eq. [3] were used, with P (k/n, l/m) P k,l to calculate the 25 control points A k,l. For a description of the resulting matrix equations, see Chung and Yan (26). A special treatment is required at the edges of the point grid because control points outside the defined area (e.g., A 0, 1 ) are used. The additional equations that are required for defining these points are introduced by the double endpoint feature, by repeating the edge points of the grid to define the points outside of the grid. The procedure of interpolating the surface points is independent of the grid size. The size of the matrix that has to be inverted for calculating the control points increases with larger grid sizes. The 5 5 matrix guarantees the most accurate representation of the interpolating bicubic B-spline surface, since control points more distant to the central matrix position do not contribute to the surface representation. Another advantage is that the interpolation of a 5 5 grid also ensures an accurate representation of the surface in an area around the central point. The general procedure can be summarized as follows: 1) For each surface point a 5 5 matrix of surrounding geometric surface data points was determined (based on a Euclidean distance measure) with the current point in the central position; b) The surface data points were used for calculating control points in order to produce an interpolating B-spline surface through the original surface points; c) The central position (the middle of the 5 5 matrix) of the interpolating B-spline surface was used to calculate the curvature of the current point. The principal curvatures [ 1 (, ), 2 (, )] at each surface point were calculated from the Weingarten-Transformation of the interpolated B-spline surface and are identical to the eigenvalues of the Weingarten-matrix. The components of the matrix are defined by the derivatives of the B-Spline surface (P,P,P,P,P ) and can be reduced to the first and second derivation of the blendingfunction B( ), B ( ), and B ( ). From the local principal curvatures, the average mean [( 1 (, ) 2 (, ))/2] and average Gaussian [ 1 (, ) * 2 (, )] curvature can be derived (25,27). The curvature analysis was validated on geometric test surfaces (sphere, cylinder, plane, paraboloid, hyperbolic paraboloid) with varying sizes and radii (Fig. 3). Points were defined on the respective geometric surfaces and a B-spline surface was interpolated through them. The results of the curvature analysis were compared to the theoretical curvature values. The curvature calculation is dependent on the resolution of the triangulated object, or on the error that is allowed between the B-spline and original surface (25). If the error is kept at zero (highest resolution), the curvature analysis picks up noise of the articular surface and will not demonstrate the curvatures of interest (25). If the error is allowed to be very large, relevant local information is lost. For this reason the local curvature values were plotted onto 3D-reconstructions of cartilage surfaces of the human knee (Fig. 4). It was found that a resolution of 20:4 (every 20th point on the contour, and every 4th contour in the MR dataset) was adequately suited for delineating the local curvatures. This means that the B-spline surface is forced through original surface points at 6-mm intervals, whereas the surface between these points follows the continuous B-spline progression, to reduce noise. This represents an

4 Joint Surface Size, Curvature, and Incongruity 557 consistent underestimation of 1.4% for cylinders of different radii (10 mm, 20 mm, and 40 mm). For spheres, the differences were 3.2%, 1.6%, and 4.1% for radii of 10 mm, 20 mm, and 40 mm, respectively. The minimal and maximal curvatures were accurately computed for the plane and were consistently underestimated by 0.2% in cylinders of various sizes. In a quarter sphere, the differences were 1%, and in a semisphere 2%. For the paraboloid and the hyperbolic paraboloid, the deviations were 0.2%, both for the minimal and maximal principal curvatures. FIG. 3. Geometric test objects used for validating computations of surface size and surface curvature: hemisphere (a); cylinder (b); paraboloid (c); hyperbolic paraboloid (d). alternative way of smoothing the surfaces to other techniques described in the literature. The average minimal and mean maximal principal curvatures were subsequently used to derive an approximate, quantitative measure of joint incongruity (28). Conceptually, the curvatures of two contacting surfaces are transformed into an equivalent surface, and the incongruity is defined by the curvatures of this surface at the point of initial contact with a plane. The minimal (Ke min) and maximal (Ke max) principal curvatures of the equivalent surface were derived from the minimal and maximal principal curvatures of the contacting surfaces and the angle between them. These values represent the incongruity along the least and most congruent directions (28). An overall congruence index (Ke rms) was finally computed from these two indices (28). In Vivo Precision Analysis The precision of the surface size calculations, curvature values, and congruence indices was assessed by determining the standard deviation (SD) of the four repeated measurements in each of the 14 volunteers. The mean value was then determined as the root means square (RMS) SD (29). For the size of the surface areas, the coefficient of variation (CV% SD / mean of four repeated measurements 100) was derived. Statistical comparisons for curvature and congruence values in the different compartments of the knee were made with the paired t-test (Statview 4.5, Abacus Concepts, Berkeley, CA), setting the accepted error to 5%. RESULTS Validation in Geometric Test Objects The computation of the size of the surface areas displayed no difference with the expected value for a plane and a FIG. 4. Spatial distribution of the minimal principal curvature throughout the human knee joint. White areas indicate regions of positive minimal curvature (convex / 80 m-1) and dark areas regions of negative minimal curvature (concave / 80 m-1). The mean minimal and mean maximal curvature values are used to compute congruence indices between contacting surfaces.

5 558 Hohe et al. Table 1 Size of the Articular Surface and Bone Cartilage Interface in the Knee Articular surface (cm 2 ) Precision SD*/CV%* mean SD Bone interface (cm 2 ) mean SD Precision SD*/CV%* Patella /3.6% /3.6% Femur /2.0% /2.1% Tibia med /2.5% /2.5% Tibia lat /2.8% /2.7% Total knee /2.0% /2.1% *Root mean square (RMS) of the 14 volunteers according to Glüer et al. (29), not mean or median SD/CV%. Mean values in 14 healthy volunteers and precision for four repeated measurements with repositioning. Application to High-Resolution MRI of the Human Knee Table 1 lists the SD and CV% of repeated measurements of the size of the surface areas as well as the mean values for the 14 volunteers. The precision error (RMS average CV%) ranged from 2.0% for the total knee to 3.6% for the patella. On all surfaces of the knee the precision error was substantially lower than the intersubject variability (13 25%), the ratio between the latter and the former ranging from 5.1:1 (articular surface medial tibia) to 8.5:1 (bone interface total knee). Figure 4 displays the distribution of the minimal principal curvature values throughout the knee joint surfaces in one healthy volunteer at a resolution of 20:4 (for explanations on resolution, see above). Table 2 lists the RMS SD of repeated measurements for the average mean and Gaussian curvature as well as for the average minimal and maximal principal curvatures. The RMS SD ranged from 2.9 m -1 to 10.5 m -1 for the average mean, minimal, and maximal principal curvatures, and from 0.22 m -2 to 0.88 m -2 for the average Gaussian curvature. The intersubject variability ranged from 2.6 m -1 to 19.1 m -1, and from 0.2 m -2 to 0.8 m -2, respectively. The mean values and the intersubject variability in the 14 volunteers are shown in Table 3. All surfaces displayed predominantly convex ovoid shapes (positive Gaussian curvature and positive mean curvature), except for the central aspect of the medial tibia ( m -1 ). The highest values for average mean curvature were found for the patella ( m -1 ). None of the surfaces displayed saddle-like properties (negative Gaussian curvature), with the highest values for the patella ( 2.8 m -2 ) and the smallest for the central aspect of the medial tibia ( 0.1 m -2 ). Note that values for the femoral trochlea do not indicate a saddle-shaped topography ( m -2 ), as these were derived for the entire trochlear surface and not only in the central aspect of the surface (the trochlear groove). The average minimal curvature displayed negative values (concavity) in most surfaces except for the femoral condyles, which were found to be predominantly convex in all planes. When confining the analysis to the central aspects of the tibia (excluding convexly formed peripheral rims), the curvature parameters became smaller, with the most negative values (the highest degree of concavity) for the central aspect of the medial tibia ( m -1 ). The effect was not statistically significant for the average minimal but for the average maximal curvature (P 0.001). Comparison between the normal values and the precision showed that the precision errors were considerably smaller than the differences between different surfaces in the knee, but they were only marginally smaller than the intersubject variability within young, healthy volunteers. Table 4 displays the precision of the congruence indices for the femoropatellar joint and the femorotibial joints, respectively. The precision (RMS SD) for Ke rms ranged from 4.1 m -1 to 7.4 m -1. The precision for analyses of the central aspects of the tibia and femoral condyles was higher than that for the total joint surface. Table 5 displays the mean values and intersubject variability of the congruence indices. The femoropatellar joint displayed the high- Table 2 Precision of Gaussian Curvature Analysis of Human Knee Joint Surfaces Average mean Average Gaussian curvature (m 2 ) Average minimum Average maximum Patella Trochlea Tib. med. tot Tib med. centr MFC tot MFC centr Tib. lat. tot Tib. lat. centr LFC tot LFC centr Tib. tibia, med. medial, tot. total joint surface, centr. central (contacting) joint surface, MFC medial femorla condyle, lat. lateral, LFC lateral femoral condyle. Root mean square (RMS) of standard deviation.

6 Joint Surface Size, Curvature, and Incongruity 559 Table 3 Results of Gaussian Curvature Analysis of Human Knee Joint Surfaces Average mean Average Gaussian curvature (m 2 ) Average minimum Average maximum Patella Trochlea Tib. med. tot Tib med. centr MFC tot MFC centr Tib. lat. tot Tib. lat. centr LFC tot LFC centr Tib. tibia, med. medial, tot. total joint surface, centr. central (contacting) joint surface, MFC medial femorla condyle, lat. lateral, LFC lateral femoral condyle. Mean values standard deviation. est degree of incongruity, the Ke rms value being significantly higher than in the femorotibial compartments (P 0.05 vs. the medial, and P vs. the lateral). The Ke rms was not significantly different between the medial and lateral femorotibial compartment when accounting for the total surface of the tibia and femur (including peripheral areas), but the values became significantly different (P 0.001) when only accounting of the central areas, with lower values on the medial side. DISCUSSION AND CONCLUSIONS The objective of this study was 1) to develop a noninvasive MR based technique for quantitative analysis of joint surface size, curvature, and incongruity; 2) to assess its reproducibility under in vivo imaging conditions; and 3) to analyze the differences between knee joint surfaces as well as those between individuals. The application of the algorithm to test objects confirms the accuracy of surface size and curvature computations vs. objects of defined geometry. Although no direct comparison was made between the curvature analyses in the MRI datasets of human knees vs. other experimental methods, a previous study by Cohen et al. (19) has shown that the cartilage surface topography is Table 4 Precision of the Congruence Indices of Human Knee Joint Surfaces (m 1 ) Ke min Ke max Ke rms FPJ MFTJ a MFTJ b MFTJ c LFTJ a LFTJ b LFTJ c FPJ femoro-patellar joint; MFTJ medial femoro-tibial joint; LFTJ lateral femoro-tibial joint. a Total tibia/total femoral condyle. b Central tibia/total femoral condyle. c Central tibia/central femoral condyle. *Root mean square (RMS) of the 14 volunteers according to Glüer et al. (29), not mean or median SD. virtually identical between MRI and stereophotogrammetry (SPG). SPG is a known standard for the ex situ surface analysis of anatomical specimens and the average accuracy error for MRI was found to be only 0.22 mm for the cartilage surface (19). As these authors have used a similar pulse sequence (fat suppressed gradient echo) and resolution, we assume that applying the current surface curvature algorithm to MRI and SPG datasets would result in very similar curvature values and congruence indices for both techniques. Moreover, our data are qualitatively consistent with a subjective evaluation of the anatomic features of the human knee and they agree with a previous SPG analysis of the human patella (27). The particular strength of the present technique vs. SPG is, however, that it can be applied in vivo. As recommended by Glüer et al. (29), our in vivo precision analysis involved repositioning of the joints and contained 42 degrees of freedom (14 volunteers, four repeated measurements). This implies that the true precision error upon repositioning in the population is not underestimated by more than 25% at a 95% confidence level (29). It should also be noted that the computation of the RMS of the individual CV% represents a conservative estimate of precision error compared with the mean or median CV% (29). The reason for this is that high values contribute more strongly to the RMS as compared with the latter variables. Table 5 Mean Values SD for Congruence Indices of Human Knee Joint Surfaces (m 1 ) Ke min Ke max Ke rms FPJ MFTJ a MFTJ b MFTJ c LFTJ a LFTJ b LFTJ c FPJ femoro-patellar joint; MFTJ medial femoro-tibial joint; LFTJ lateral femoro-tibial joint. a Total tibia/total femoral condyle. b Central tibia/total femoral condyle. c Central tibia/central femoral condyle.

7 560 Hohe et al. Our study shows that the in vivo precision (reproducibility) of the surface sizes is sufficient to reliably discriminate between individuals in the given sample. The precision of surface curvature analysis is less satisfactory in this respect, as it allows for reliable discrimination between different knee joint surfaces, but to a lesser degree between person to person. It should, however, be noted that the present sample included only young, healthy individuals, which may not display noticeable deviations among each other. Elderly individuals and, in particular, patients, may display larger deviations from these normal values and it may be that these can be reliably detected based on the technique described in this study. As surface curvature can vary substantially throughout a cartilage plate (e.g., Fig. 4), it may be necessary to exclude certain aspects of a surface (for instance, the anterior and posterior margins of the tibial plateau) in order to assess the incongruity in those parts of the joint surfaces that are likely in contact. Although the selection of certain aspects of the joint surfaces requires user interaction, our data show that at least for an experienced user the precision for this type of analysis is not less than that for the entire surface. Several previous studies have investigated the correlation of cartilage volume (as determined from MRI) with anthropometric variables (20,30,31), gender (31 33), and the level of physical exercise (33). However, the problem with these studies is that the cartilage volume represents an integral of cartilage thickness and size of the joint surface areas. To separate the two entities, reliable analysis of joint surface size is required. Faber et al. (34), for instance, reported that women display significantly smaller joint surface than men, but not significantly thinner cartilage. The same was observed for weight- and size-matched men and women (20). It may be interesting to investigate whether joint surface area is a relevant risk factor, since women have also been found to display a higher susceptibility for OA (1,2). Epidemiological studies may thus be directed at determining the role of joint surface size as a potential risk factor for degenerative joint disease using high-resolution MRI data and digital postprocessing. Quantitative assessment of the joint surface area can also be useful for retrospectively estimating cartilage loss in osteoarthritic joints. Burgkart et al. (24) have shown that cartilage volume is only a relatively poor discriminator between diseased and normal joints, given the large intersubject variability of cartilage volume and joint surface area in the normal population. However, when normalizing individual cartilage volumes in patients to the original (now partly denuded) cartilage surface size, discrimination between normals and patients can be enhanced substantially. Joint incongruity has for some time been suggested to represent a potential risk factor for OA, but few studies have so far attempted to quantitatively assess the degree of geometric mismatch between contacting joint surfaces. Ateshian et al. (28) used stereophotogrammetry and found women to display a significantly higher degree of incongruity in the thumb carpometacarpal joint. This was associated with a higher prevalence of women to OA in this joint, given the higher peak loads expected with smaller load-bearing surfaces and higher degrees of mismatch. To date, however, no in vivo technique is available for population-based epidemiologic studies and for following individuals longitudinally. Clinical assessment of joint incongruity has so far been based on conventional radiography (e.g., 35 37), but this technique only delineates the bone cartilage interface and not the cartilage surface. As the cartilage thickness is not uniform, the topography of the cartilage surface can show substantial deviations from that of the joint surface (38,39). Moreover, radiography only represents a projection of a curved surface onto a 2D film and only provides a relatively crude measurement in comparison to the noninvasive 3D imaging techniques currently available. The technique presented here may thus be used to determine whether incongruity changes physiologically with aging (40) and whether incongruity is a relevant epidemiologic risk factor for the initiation and progression of joint disease. In future studies we intend to determine whether the curvature characteristics in the human knee are systematically different between men and women and whether they are subject to change with increasing age. By determining the surface size and incongruity in individuals before the onset of cartilage degeneration (e.g., in the contralateral knee of patients with unilateral joint disease), population-based studies should also make it possible to determine whether individuals with small joint surfaces (in relation to body weight and height) and with high degrees of joint incongruity have a higher risk/susceptibility of OA. In conclusion, we find that 3D reconstruction by triangulation and Gaussian curvature analysis can be successfully employed to reliably determine surface size and surface curvature in high-resolution MR datasets of human knee joint surfaces. The in vivo precision error was less than 4% for determining the size of the joint surfaces in the human knee and was considerably smaller than the intersubject variability. The precision errors for analysis of principal curvatures were smaller than the differences between different knee joint surfaces, but only marginally smaller than the intersubject variability in young healthy volunteers. The femoropatellar joint was shown to display a higher degree of incongruity compared with the femorotibial compartments, and the (central) lateral femorotibial joint a higher degree of incongruity compared with the (central) medial one. The technique presented will permit determination of the size, curvature, and incongruity of human knee joint surfaces under physiological and pathological conditions in the living and to identification of their specific role as potential risk factors for OA. 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