Constrained least-squares optimization for robust estimation of center of rotation.

This paper presents a new direct method for estimating the average center of rotation (CoR). An existing least-squares (LS) solution has been shown by previous works to have reduced accuracy for data with small range of motion (RoM). Alternative methods proposed to improve the CoR estimation use iterative algorithms. However, in this paper we show that with a carefully chosen normalization scheme, constrained least-squares solutions can perform as well as iterative approaches, even for challenging problems with significant noise and small RoM. In particular, enforcing the normalization constraint avoids poor fits near plane singularities that can affect the existing LS method. Our formulation has an exact solution, accounts for multiple markers simultaneously, and does not depend on manually-adjusted parameters. Simulation tests compare the method to four published CoR estimation techniques. The results show that the new approach has the accuracy of the iterative methods as well as the short computation time and repeatability of a least-squares solution. In addition, application of the new method to experimental motion capture data of the thumb carpometacarpal (CMC) joint yielded a more plausible CoR location compared to the previously reported LS solution and required less time than all four alternative techniques.

Robust estimation of dominant axis of rotation.

A simple method is developed for robustly estimating a fixed dominant axis of rotation (AoR) of anatomical joints from surface marker data. Previous approaches which assume a model of circular marker trajectories use plane fitting to estimate the direction of the AoR. However, when there is limited joint range of motion and rotation due to a second degree of freedom, minimizing only the planar error can give poor estimates of the AoR direction. Optimizing a cost function which includes the error component within a plane, instead of only the component orthogonal to a plane, leads to improved estimates of the AoR direction for joints which exhibit additional rotational motion from a second degree of freedom. Results from synthetic data validation show the ranges of motion where the new method has lower estimation error compared to plane-fitting techniques. Estimates of the flexion-extension AoR from empirical motion capture data of the knee and index finger joints were also more anatomically plausible.

Age-dependent properties and quasi-static strain in the rat sagittal suture.

We measured the morphology of and performed tensile tests on sagittal sutures from rats of postnatal age 2 to 60 days. Using the properties measured ex vivo and a pressure vessel-based analysis, we estimated the quasi-static strain that had existed in the suture in vivo from 2 to 60 days. Sutural thickness, width, and stiffness per length were notable properties found to be age dependent. Sutural thickness increased 4.5-fold (0.11-0.50mm) between 2 and 60 days. Sutural width increased transiently between 2 and 20 days, peaking around 8 days; at 8 days, mean sutural width was 75% larger than mean sutural width at two days (0.35+/-0.07 (SD) vs. 0.20+/-0.06 mm). Sutural stiffness per length increased 4.4-fold (8.77-38.3N/mm/mm) between 2 and 60 days. The quasi-static sutural strain estimated to exist in vivo averaged 270+/-190 muepsilon between 2 and 60 days and was not age dependent. These findings provide data on the age-dependent sutural properties of infant to mature rats and provide the first estimate of quasi-static sutural strain in vivo in the rat. The findings show that during development the rat sagittal suture, as a structure, changes significantly and is exposed to quasi-static tensile strain in vivo due to intracranial pressure.

Selection criteria for preparatory object rotation in manual lifting actions.

Participants lifted a canister by its handle while balancing a ball on the lid. Experiment 1 allowed object rotation prior to lifting. A lifting comfort zone was measured by the variability in object orientation at lift; its size depended on the object mass and required task precision. The amount of prelift rotation correlated with the resulting change in lifting capability, as measured for different object orientations. Experiment 2 required direct grasping without preparatory rotation. Task completion time and success rate decreased, and initial object orientation affected prelift time. Results suggest that lifting from the comfort zone produces more robust performance at a cost of slower completion; moreover, physical rotation could be replaced by mental planning when direct grasping is enforced.

Method for determining kinematic parameters of the in vivo thumb carpometacarpal joint.

The mobility of the thumb carpometacarpal (CMC) joint is critical for functional grasping and manipulation tasks. We present an optimization technique for determining from surface marker measurements a subject-specific kinematic model of the in vivo CMC joint that is suitable for measuring mobility. Our anatomy-based cost metric scores a candidate joint model by the plausibility of the corresponding joint angle values and kinematic parameters rather than only the marker trajectory reconstruction error. The proposed method repeatably determines CMC joint models with anatomically-plausible directions for the two dominant rotational axes and a lesser range of motion (RoM) for the third rotational axis. We formulate a low-dimensional parameterization of the optimization domain by first solving for joint axis orientation variables that then constrain the search for the joint axis location variables. Individual CMC joint models were determined for 24 subjects. The directions of the flexion--extension (FE) axis and adduction--abduction (AA) axis deviated on average by 9 degrees and 22 degrees , respectively, from the mean axis direction. The average RoM for FE, AA, and pronation--supination (PS) joint angles were 76 degrees , 43 degrees , and 23 degrees for active CMC movement. The mean separation distance between the FE and AA axes was 4.6 mm, and the mean skew angle was 87 degrees from the positive flexion axis to the positive abduction axis.