INTRODUCTION

In the field of cardiac electrophysiology, "isochrones" are lines that connect points of equal activation time. Isochronal maps are the common means of depicting an activation pattern. They are sometimes annotated with arrows to indicate the major propagation paths. An example is shown in Fig. 1. Creation of isochronal maps is a complicated process, which must be performed with care [1]. Spatial and temporal undersampling can easily lead to incorrect conclusions. Investigators therefore sometimes decided to draw isochrones by hand, based on computer-generated tables of activation times [2, 3]. An investigator who manually draws an isochronal map may use the drawn isochrones to change activation times that were used to create the map. This can be an advantage; for example, it may help in deciding which deflection corresponds to a local activation front. On the other hand, it allows for complicated methodology that is hard to reproduce, and allows preconceptions to have an influence on the results.

For efficiency and objectivity it may be desirable to have a computer program draw isochrones. Contour drawing routines are a standard part of most data analysis and visualization software, such as MATLAB. Some algorithms were previously described by Barr [4] and by Linnenbank [5]. However, isochrone drawing is more difficult than ordinary contour drawing of, e.g., potential maps because zones of conduction block have to be treated in a special way. Two situations that need special care are: (1) Activation times in adjacent electrodes differ to the extent that the apparent conduction velocity is lower than considered possible [6, 7], which implies that they cannot be part of the same activation front. This can happen if conduction block is present and if a reentrant activation returns at the point where it started. In both cases, a standard contour algorithm would draw a set of crowding isochrones. This would inadvertently suggest the presence of very slow conduction. Instead, a line with a special style should be plotted; either a block line to indicate a total stop (the line with "T" marks in Fig. 1), or a line that indicates the beginning and end of an interval of reentrant activation. This cannot be accomplished with standard contouring programs. (2) In some electrodes, no activation occurs within the given interval. If a standard contouring program is used, such situations can be handled by treating the region of this electrode as if it was not included in the grid, i.e. making a "hole" in the grid before feeding it to the contouring algorithm. No contours will then be drawn in this region. In case of an isochronal map, such regions would look similar to regions of very high conduction velocity, where isochrones are also at large distances from each other; the observer would have to discriminate these phenomena from the context of the entire map. Ideally, a block line or a patch with a different shade should be drawn for regions of conduction block.

A specialized program is thus necessary; however, to a large extent it can use existing algorithms.

Figure 1: Example of a hand-crafted isochronal map, reproduced from Van Capelle et al. [3]. The line with "T" symbols attached to it indicates a line of conduction block.

METHODS AND RESULTS

An experimental program for electrocardiographic isochrone drawing, called "isomap," was developed. This program can handle lines of conduction block (Fig. 2) and reentrant activation (Fig. 3) correctly. It can work on surfaces in 3-D as well as in 2-D, and with both triangulated and rectangular grids. In its current implementation it decomposes rectangles into triangles, so that only an algorithm for contour drawing on a triangulated grid is needed. This decomposition is performed in such a way that saddle points are treated correctly. Output of the isomap program is shown in Figs. 2 and 3.

DISCUSSION

An important feature of the isomap program is that it can automatically indicate lines of conduction block: if the activation time difference between neigbouring electrodes is so large that the apparent conduction velocity is below a user-specified limit, the program assumes conduction block between these electrodes, and will indicate this with a special line style. Ordinary isochrones are not drawn in such regions. Since isomap can handle a typical activation map in a few milliseconds, the software operates fast enough to allow experimentation with limit values in an interactive way.