On intrinsic equivalences of the finite helical axis, the instantaneous helical axis, and the SARA approach. A mathematical perspective.

Accurate determination of joint axes is essential for understanding musculoskeletal function. Whilst numerous algorithms to compute such axes exist, the conditions under which each of the methods performs best remain largely unknown. Typically, algorithms are evaluated for specific conditions only limiting the external validity of conclusions regarding their performance. We derive exact mathematical relationships between three commonly used algorithms for computing joint axes from motion data: finite helical axes (FHA), instantaneous helical axes (IHA) and SARA (symmetrical axis of rotation approach), including relationships for an extension to the mean helical axes methods that facilitate determining joint centres and axes. Through the derivation of a sound mathematical framework to objectively compare the algorithms we demonstrate that the FHA and SARA approach are equivalent for the analysis of two time frames. Moreover, we show that the position of a helical axis derived from the IHA using positional data is affected by a systematic error perpendicular to the true axis direction, whereas the axis direction is identical to those computed with either the FHA or SARA approach (true direction). Finally, with an appropriate choice of weighting factors the mean FHA (MFHA) method is equivalent to the Symmetrical Centre of Rotation Estimation (SCoRE) algorithm for determination of a Centre of Rotation (CoR), and similarly, equivalent to the SARA algorithm for determination of an Axis of Rotation (AoR). The deep understanding of the equivalences between methods presented here enables readers to choose numerically efficient, robust methods for determining AoRs and CoRs with confidence.

Towards understanding knee joint laxity: errors in non-invasive assessment of joint rotation can be corrected.

The in vivo quantification of rotational laxity of the knee joint is of importance for monitoring changes in joint stability or the outcome of therapies. While invasive assessments have been used to study rotational laxity, non-invasive methods are attractive particularly for assessing young cohorts. This study aimed to determine the conditions under which tibio-femoral rotational laxity can be assessed reliably and accurately in a non-invasive manner. The reliability and error of non-invasive examinations of rotational joint laxity were determined by comparing the artefact associated with surface mounted markers against simultaneous measurements using fluoroscopy in five knees including healthy and ACL deficient joints. The knees were examined at 0°, 30°, 60° and 90° flexion using a device that allows manual axial rotation of the joint. With a mean RMS error of 9.6°, the largest inaccuracy using non-invasive assessment was present at 0° knee flexion, whereas at 90° knee flexion, a smaller RMS error of 5.7° was found. A Bland and Altman assessment indicated that a proportional bias exists between the non-invasive and fluoroscopic approaches, with limits of agreement that exceeded 20°. Correction using average linear regression functions resulted in a reduction of the RMS error to below 1° and limits of agreement to less than ±1° across all knees and flexion angles. Given the excellent reliability and the fact that a correction of the surface mounted marker based rotation values can be achieved, non-invasive evaluation of tibio-femoral rotation could offer opportunities for simplified devices for use in clinical settings in cases where invasive assessments are not justified. Although surface mounted marker based measurements tend to overestimate joint rotation, and therefore joint laxity, our results indicate that it is possible to correct for this error.

Effective marker placement for functional identification of the centre of rotation at the hip.

The accuracy and precision of quantifying musculoskeletal kinematics, and particularly determining the centre of rotation (CoR) at the hip joint, using skin marker based motion analysis is limited by soft tissue artefact (STA). We posed the question of whether the contribution of individual markers towards improving the precision of the functional joint centre using marker based methods could be assessed, and then utilised to allow effective marker placement for determination of the CoR at the hip. Sixty-three retro-reflective skin markers were placed to encompass the thighs of seven healthy subjects, together with a set of sixteen markers on the pelvis. The weighted optimal common shape technique (wOCST) was then applied to determine the weighting, or importance, of each marker for identifying the centre of rotation at the hip. The markers with the highest weightings over all subjects and measurements were determined that identified the HJC with the highest precision. The use of six markers in selected regions (two anterior, two lateral and two posterior) allowed the HJC to be determined with a similar precision to the complete set of 63 markers, with the determined regions predominantly distant from the hip joint, excluding areas associated with the bellies of large muscles and therefore large motion artefact from muscle activity. The novel approach presented here allows an understanding of each marker's contribution towards a precise joint determination, and therefore enables the targeted placement of markers for reliable assessment of musculoskeletal kinematics.

Repeatability and reproducibility of OSSCA, a functional approach for assessing the kinematics of the lower limb.

Marker-based gait analysis of the lower limb that uses assumptions of generic anatomical morphology can be susceptible to errors, particularly in subjects with high levels of soft tissue coverage. We hypothesize that a functional approach for assessing skeletal kinematics, based on the application of techniques to reduce soft tissue artefact and functionally identify joint centres and axes, can more reliably (repeatably and reproducibly) assess the skeletal kinematics than a standard generic regression approach. Six healthy adults each performed 100 repetitions of a standardized motion, measured on four different days and by five different observers. Using OSSCA, a combination of functional approaches to reduce soft tissue artefact and identify joint centres and axes, the lengths of the femora and tibiae were determined to assess the inter-day and inter-observer reliability, and compared against a standard generic regression approach. The results indicate that the OSSCA was repeatable and reproducible (ICC lowest bound 0.87), but also provided an improvement over the regression approach (ICC lowest bound 0.69). Furthermore, the analysis of variance revealed a statistically significant variance for the factor "observers" (p<0.01; low-reproducibility) when using the regression approach for determining the femoral lengths. Here, this non-invasive, rapid and robust approach has been demonstrated to allow the repeatable and reproducible identification of skeletal landmarks, which is insensitive to marker placement and measurement session. The reliability of the OSSCA thus allows its application in clinical studies for reducing the uncertainty of approach-induced systematic errors.

A new model to predict in vivo human knee kinematics under physiological-like muscle activation.

Although a number of approaches have attempted to model knee kinematics, rarely have they been validated against in vivo data in a larger subject cohort. Here, we assess the feasibility of four-bar linkage mechanisms in addressing knee kinematics and propose a new approach that is capable of accounting for lengthening characteristics of the ligaments, including possible laxity, as well as the internal/external rotation of the joint. MR scans of the knee joints of 12 healthy volunteers were taken at flexion angles of 0 degrees , 30 degrees and 90 degrees under both passive and active muscle conditions. By reconstructing the surfaces at each position, the accuracy of the four-bar linkage mechanism was assessed for every possible combination of points within each cruciate ligament attachment area. The specific set of parameters that minimized the deviation between the predictions and the in vivo pose was derived, producing a mean error of 1.8 and 2.5 on the medial and 1.7 and 2.4mm on the lateral side at 30 degrees and 90 degrees flexion, respectively, for passive motion, significantly improving on the models that did not consider internal/external rotation. For active flexion, mean medial errors were 3.3 and 4.7 mm and lateral errors 3.4 and 4.8 mm. Using this best parameter set, a generic predictive model was created and assessed against the known in vivo positions, producing a maximum average error of 4.9 mm at 90 degrees flexion. The accuracy achieved shows that kinematics may be accurately reconstructed for subject specific musculoskeletal models to allow a better understanding of the load distribution within the knee.