Comparison of Two Methods for In Vivo Estimation of the Glenohumeral Joint Rotation Center (GH-JRC) of the Patients with Shoulder Hemiarthroplasty

Determination of an accurate glenohumeral-joint rotation center (GH-JRC) from marker data is essential for kinematic and dynamic analysis of shoulder motions. Previous studies have focused on the evaluation of the different functional methods for the estimation of the GH-JRC for healthy subjects. The goal of this paper is to compare two widely used functional methods, namely the instantaneous helical axis (IHA) and symmetrical center of rotation (SCoRE) methods, for estimating the GH-JRC in vivo for patients with implanted shoulder hemiarthroplasty. The motion data of five patients were recorded while performing three different dynamic motions (circumduction, abduction, and forward flexion). The GH-JRC was determined using the CT-images of the subjects (geometric GH-JRC) and was also estimated using the two IHA and SCoRE methods. The rotation centers determined using the IHA and SCoRE methods were on average 1.47±0.62 cm and 2.07±0.55 cm away from geometric GH-JRC, respectively. The two methods differed significantly (two-tailed p-value from paired t-Test ∼0.02, post-hoc power ∼0.30). The SCoRE method showed a significant lower (two-tailed p-value from paired t-Test ∼0.03, post-hoc power ∼0.68) repeatability error calculated between the different trials of each motion and each subject and averaged across all measured subjects (0.62±0.10 cm for IHA vs. 0.43±0.12 cm for SCoRE). It is concluded that the SCoRE appeared to be a more repeatable method whereas the IHA method resulted in a more accurate estimation of the GH-JRC for patients with endoprostheses

Chemical graph transformation with stereo-information

Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms and their neighbours in space. Stereoisomers of chemical compounds thus cannot be distinguished, even though their chemical activity may differ substantially. In this contribution we propose an extended chemical graph transformation system with attributes that encode information about local geometry. The modelling approach is based on the socalled “ordered list method”, where an order is imposed on the set of incident edges of each vertex, and permutation groups determine equivalence classes of orderings that correspond to the same local spatial embedding. This method has previously been used in the context of graph transformation, but we here propose a framework that also allows for partially specified stereoinformation. While there are several stereochemical configurations to be considered, we focus here on the tetrahedral molecular shape, and suggest general principles for how to treat all other chemically relevant local geometries. We illustrate our framework using several chemical examples, including the enumeration of stereoisomers of carbohydrates and the stereospecific reaction for the aconitase enzyme in the citirc acid cycle