Abstract
Theories of deterministic chaos have been applied to mammalian systems and specifically to arrhythmogenesis however controversy persists as to whether fibrillation [atrial (AF) or ventricular] obeys the laws of dynamical chaos. We addressed this question by analyzing the frequency spectra of left atrial appendage (LAA) Doppler flow in AF (n = 17), describing these spectra using fractions or multiples of the dominant frequency (D f ) or by a function of two basic frequencies ( f ) along with their harmonics and frequency combinations ( mf 1 ± nf 2 ), and correlating these signals with a mathematical model for deterministic chaos using the Lorentz equations. Spectral analysis demonstrated a mean D f of 6.3 ± 0.7 Hz (range 5.6–7.8 Hz) which was associated with a wide range of subharmonics (12% to 59% of total spectral power, avg 32 ± 12%). Three patients exhibited very narrow based spectral patterns with very little subharmonics. Twelve of 17 LAA Doppler fourier spectra (71%) could be defined by the equation mf 1 ± nf 2 The transition to a chaotic state was modeled by solving the Lorenz equations, with the solutions and Fourier transform of the signal exhibiting striking similarity to the signal generated by LAA Doppler flow as well as to the Fourier spectra of LAA flow in AF. (1) Fourier analysis of LAA Doppler flow in AF demonstrates behavior consistent with deterministic chaos in most but not all cases. (2) Mathematical modeling of a chaotic system closely resembles LAA flow in AF. Fourier analysis of LAA flow should provide insight into structural and electrophysiologic mechanisms of AF.
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