Biomedical subjects

Marius Lysaker

Publications and source records attributed to Marius Lysaker.

3 recordsLinked to original sources

PubMed2006

Computing the size and location of myocardial ischemia using measurements of ST-segment shift.

It is well known that the presence of myocardial ischemia can be observed as a shift in the ST segment of an electrocardiogram (ECG) recording. The question we address in this paper is whether or not ST shift can be used to compute approximations of the size and location of the ischemic region. We begin by investigating a cost functional (measuring the difference between synthetic recorded data and simulated values of ST shift) for a parameter identification problem to locate the ischemic region. We then formulate a more flexible representation of the ischemia using a level set framework and solve the associated minimization problem for the size and position of the ischemia. We apply this framework to a set of ECG data generated by the Bidomain model using the cell model of Winslow et al. Based on this data, we show that values of ST shift recorded at the body surface are capable of identifying the position and (roughly) the size of the ischemia.

Animals↗

PubMed2006

A binary level set model and some applications to Mumford-Shah image segmentation.

In this paper, we propose a PDE-based level set method. Traditionally, interfaces are represented by the zero level set of continuous level set functions. Instead, we let the interfaces be represented by discontinuities of piecewise constant level set functions. Each level set function can at convergence only take two values, i.e., it can only be 1 or -1; thus, our method is related to phase-field methods. Some of the properties of standard level set methods are preserved in the proposed method, while others are not. Using this new method for interface problems, we need to minimize a smooth convex functional under a quadratic constraint. The level set functions are discontinuous at convergence, but the minimization functional is smooth. We show numerical results using the method for segmentation of digital images.

Algorithms↗

PubMed2004

Noise removal using smoothed normals and surface fitting.

In this work, we use partial differential equation techniques to remove noise from digital images. The removal is done in two steps. We first use a total-variation filter to smooth the normal vectors of the level curves of a noise image. After this, we try to find a surface to fit the smoothed normal vectors. For each of these two stages, the problem is reduced to a nonlinear partial differential equation. Finite difference schemes are used to solve these equations. A broad range of numerical examples are given in the paper.

Algorithms↗