Application of fractal geometry to the analysis of ventricular premature contractions.

Fractals are a group of irregularly irregular geometric objects, first described by Mandelbrot.ln2 We have previously suggested that a patient’s distribution of ventricular premature contractions (VPCs) over time can be represented by a particular kind of fractal-the fractal dust.3 This makes it possible to measure dimension (D), a number that quantifies the uniformity or nonuniformity of that patient’s ventricular ectopy. When applied to a group of patients with severe congestive heart failure, dimension was found to have prognostic significance: Patients with nonuniform (clustered) ectopy had a higher risk of early death than those with more uniform distributions. We now present some technical comments on the use of this technique. Fructuls are defined as objects whose HausdorffBesicovitch dimension exceeds their topologic dimension. In general they are complicated in appearance and irregular at any scale of measurement. 1*2,5 Many natural shapes have this property, among them coastlines, clouds, and the branching of Purkinje fibers in the heart or capillaries in the lung. A fractul dust is an object composed of topologically unconnected points. Any such object has a topologic dimension of zero. Hence, any dust with a fractal dimension greater than zero is, by definition, a fractal dust. A set of events occurring over time can be thought of as a shape in which each event marks a point along a time axis. In this manner a set of ventricular premature contractions recorded during a defined period of ambulatory electrocardiography can be transformed into a “VPC-shape.” Because any two VPCs