4/2/2023 0 Comments Kinematics input to postview![]() ![]() To our knowledge, Elliot was the #worldfirst #digitalorthopaedics #fellow. Sadly, for me, Elliot Sappey-Marinier recently returned to #lyon, #france to start his career in private practice with several esteemed colleagues, having spent a year with me in both the clinic and the operating room, as well as shadowing my work in the #digitalorthopaedics space. You arre right in principle that curvature is attached to a point.All good things sooner or later come to a close. However, both in classcial differential geometry and in Riemannian geometry, a "curvature" is not necessarily a number. One often reduces to numbers in the end (since these are easy to compare), but intially, one has more general objects. In the setting of surfaces, I would say that the basic curvature object is the Weingarten map, which, in a point, is a symmetric endomorphism of the tangent plane at that point. The principal curvatures (which are indeed numbers) are the eigenvalues of this linear map. Using the inner product, the Weingarten map can be converted to a symmetric bilinear form (the second fundamental form) on the tangent space. The usual interpretation of the normal cuvature is as the restriction of the quadratic form defined by this symmetric bilinear form to the unit sphere in the tangent space. As such, it is a smooth function on the unit circle, which (if non-constant) has a unique minumum and a unique maximum. These are easily seen to coincide with the two eigenvalues of the Weingarten map and thus with the principal cuvatures. ![]() ![]() The Riemann cuvature in general is a much more complicated object (a trilinear map from three copies of the tangent space to the tangent space with certain symmetries). However, in two dimensions, the space of such maps is one-dimensional, so again you can reduce it to one number. In an appropriate identification that number coincides with the determinant of the Weingarten map, i.e. Things look very different in higher dimensions.Predictions from biomechanical models of gait may be sensitive to joint center locations. Most often, the hip joint center (HJC) is derived from locations of reflective markers adhered to the skin. Here, predictive techniques use regression equations of pelvic anatomy to estimate the HJC, whereas functional methods track motion of markers placed at the pelvis and femur during a coordinated motion. Skin motion artifact may introduce errors in the estimate of HJC for both techniques. Quantifying the accuracy of these methods is an area of open investigation. In this study, we used dual fluoroscopy (DF) (a dynamic X-ray imaging technique) and three-dimensional reconstructions from computed tomography images, to measure HJC locations in vivo. Using dual fluoroscopy as the reference standard, we then assessed the accuracy of three predictive and two functional methods. Eleven non-pathologic subjects were imaged with DF and reflective skin marker motion capture. ![]() Additionally, DF-based solutions generated virtual markers placed on bony landmarks, which were input to the predictive and functional methods to determine if estimates of the HJC improved. Using skin markers, functional methods had better mean agreement with the HJC measured by DF (11.0 ± 3.3 mm) than predictive methods (18.1 ± 9.5 mm) estimates from functional and predictive methods improved when using the DF-based solutions (1.3 ± 0.9 and 17.5 ± 8.6 mm, respectively). The Harrington method was the best predictive technique using both skin markers (13.2 ± 6.5 mm) and DF-based solutions (10.6 ± 2.5 mm). Overall, functional methods were superior to predictive methods for HJC estimation. However, the improvements observed when using the DF-based solutions suggest that skin motion artifact is a large source of error for the functional methods.īegon, M., T. Effects of movement for estimating the hip joint centre. A comparison of the accuracy of several hip center location prediction methods. Validation of a new model-based tracking technique for measuring three-dimensional, in vivo glenohumeral joint kinematics. ![]()
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