Three-Dimensional Analysis of the In Vivo Motion of Implantable Cardioverter Defibrillator Leads

Better understanding of the lead curvature, movement and their spatial distribution may be beneficial in developing lead testing methods, guiding implantations and improving life expectancy of implanted leads. Objective The aim of this two-phase study was to develop and test a novel biplane cine-fluoroscopy-based method to evaluate input parameters for bending stress in leads based on their in vivo 3D motion using precisely determined spatial distributions of lead curvatures. Potential tensile, compressive or torque forces were not subjects of this study. Methods A method to measure lead curvature and curvature evolution was initially tested in a phantom study. In the second phase using this model 51 patients with implanted ICD leads were included. A biplane cine-fluoroscopy recording of the intracardiac region of the lead was performed. The lead centerline and its motion were reconstructed in 3D and used to define lead curvature and curvature changes. The maximum absolute curvature Cmax during a cardiac cycle, the maximum curvature amplitude Camp and the maximum curvature Cmax@amp at the location of Camp were calculated. These parameters can be used to characterize fatigue stress in a lead under cyclical bending. Results The medians of Camp and Cmax@amp were 0.18 cm−1 and 0.42 cm−1, respectively. The median location of Cmax was in the atrium whereas the median location of Camp occurred close to where the transit through the tricuspid valve can be assumed. Increased curvatures were found for higher slack grades. Conclusion Our results suggest that reconstruction of 3D ICD lead motion is feasible using biplane cine-fluoroscopy. Lead curvatures can be computed with high accuracy and the results can be implemented to improve lead design and testing.

Nonpositive curvature foliations on 3-manifolds with bounded total absolute curvature of leaves

In this paper we introduce a new class of foliations on Rie-mannian 3-manifolds, called B-foliations, generalizing the class of foliations of non-negative curvature. The leaves of B-foliations have bounded total absolute curvature in the induced Riemannian metric. We describe several topological and geometric properties of B-foliations and the structure of closed oriented 3-dimensional manifolds admitting B-foliations with non-positive curvature of leaves.

Conformal transformations and curvature

In this paper, we discuss the relationship between conformal transformations of [Formula: see text] and the curvature of curves. First, for any non-circular closed curve, there exists a length-preserving inversion such that the maximum pointwise absolute curvature can be made arbitrarily large. In contrast, we show that the total absolute curvatures of a family of curves conformally equivalent to a given simple or simple closed curve are uniformly bounded. Furthermore, we show that the total absolute curvature of an inverted regular [Formula: see text] simple closed curve as a function of inversion center and radius is removably discontinuous along the curve with exactly a [Formula: see text] drop, and continuous elsewhere.

The Mask of Odd Pointsn-Ary Interpolating Subdivision Scheme

We present an explicit formula for the mask of odd pointsn-ary, for any oddn⩾3, interpolating subdivision schemes. This formula provides the mask of lower and higher arity schemes. The 3-point and 5-pointa-ary schemes introduced by Lian, 2008, and (2m+1)-pointa-ary schemes introduced by, Lian, 2009, are special cases of our explicit formula. Moreover, other well-known existing odd pointn-ary schemes including the schemes introduced by Zheng et al., 2009, can easily be generated by our formula. In addition, error bounds between subdivision curves and control polygons of schemes are computed. It has been noticed that error bounds decrease when the complexity of the scheme decreases and vice versa. Also, as we increase arity of the schemes the error bounds decrease. Furthermore, we present brief comparison of total absolute curvature of subdivision schemes having different arity with different complexity. Convexity preservation property of scheme is also presented.