Figure 2

Illustration of the four-dimensional data set. Drawing a curved M-mode along the wall (1a) in one plane, results in velocity data along a straight line. As data are recorded over a time period, adding the time sequence in each pixel of the line, results in a traditional curved M-mode plot. This is equivalent to a 2-dimensional surface (1b) with one spatial and one temporal dimension. However, the curved M-mode contains more information; the curvature itself defines the location of each point in space relative to all the others. With this information added, the M-mode is a curve in a plane, i.e. a two-dimensional figure (2a) instead of a straight line. If the time-sequence is added to this figure, analogous to the transition 1c, it results in a curved plane, a three-dimensional figure, with two spatial and one temporal dimension (2b). This kind of display is not used in practice; it is included here for reasons of analogy only. Adding two more curved M-modes from the two other standard planes and information about their angular separation, results in a three-dimensional figure, a grid (3a) the spatial interpolation is done by cubic spline. When the time-sequence is added in this case, the data set becomes four-dimensional (3b). This cannot be shown directly, but is illustrated by the analogy to 1 and 2b. Only part of the information can be extracted at a time, for the various display modalities: Bull's eye at any point in the heart cycle (4a), M-mode array (4b), 3D surface (4c). Only the processing to the full data set, however, allows the figures to be scrolled through the heart cycle, and the data set remains quantitative, allowing the curves to be extracted from each point.