A least-squares algorithm for the equiform transformation from spatial marker co-ordinates.

The present paper describes an algorithm for estimating the translation vector and the rotation matrix of a moving body from noisy measurements on the spatial co-ordinates of at least three non-collinear markers. A sensitivity analysis of the estimated parameters and of the helical axis is presented in terms of characteristics of the marker distribution. The implementation of the proposed algorithm in a FORTRAN-subroutine is appended.

Finite centroid and helical axis estimation from noisy landmark measurements in the study of human joint kinematics.

Recent work on joint kinematics indicates that the finite centroid (centre of rotation) and the finite helical axis (axis of rotation, screw axis, twist axis) are highly susceptible to measurement errors when they are experimentally determined from landmark position data. This paper presents an analytical model to describe these effects, under isotropic conditions for the measurement errors and for the spatial landmark distribution. It appears that the position and direction errors are inversely proportional to the rotation magnitude, and that they are much more error-prone than the relatively well-determined rotation and translation magnitudes. Furthermore, the direction and rotation magnitude errors are inversely proportional to the landmark distribution radius, and the position and translation magnitude errors are minimal if the mean position of the landmarks coincides with the centroid or helical axis. For the planar centroid, the use of rigid-body constraints results in considerable precision improvement relative to the classical, finite Reuleaux method for centroid reconstruction. These analytical results can be used to define suitable measurement configurations, and they are used in this paper to explain experimental results on Röntgenphotogrammetrically acquired in vitro wrist joint movement.

The mechanical properties of porcine aortic valve tissues.

In uniaxial tensile experiments in vitro mechanical properties of the different parts of porcine aortic valves, i.e. the leaflets, the sinus wall and the aortic wall, have been dealt with. Tissue strips cut in different directions were investigated. The collagen bundles in the leaflets show a stiffening effect and cause a marked anisotropy: within the physiological range of strains the largest slopes of the stress-strain curves of leaflet specimens in the bundle direction are a factor of about 20 larger than those of specimens taken along the perpendicular direction. For the sinus and aortic tissues, these values are 50-200 times smaller than those obtained from the leaflet specimens in the bundle direction. Two aspects of viscoelastic behaviour were examined: the strain rate sensitivity of the stress-strain curves and the relaxation behaviour. The stress-strain curves of the different valve parts appeared to be rather insensitive to the strain rate: the most pronounced sensitivity observed in our experiments, was a doubling of the stress at the same strain caused by a hundredfold increase of the strain rate. In analyzing the relaxation behaviour, use was made of the relaxation model proposed by Fung (1972, in Biomechanics, its Foundations and Objectives; Fung, Perrone and Anliker. Prentice Hall). In the leaflets, about 45% stress relaxation was found whereas this amounted to 30% in the sinus and aortic walls. Predictions based upon the model indicate that on cyclic loading the larger viscous losses have to be expected in the leaflets.