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Letters to the Editor |

Low-Dimensional Chaos in Bipolar Disorder?—Reply

Allan Gottschalk, MD, PhD; Mark S. Bauer, MD; Peter C. Whybrow, MD
Arch Gen Psychiatry. 1998;55(3):275-276. doi:.
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We would like to thank Drs Krystal and Greenside for their interest in our recent article1 and for their comments, which further elucidate the caution that must be applied when interpreting data in this fashion. They raise an important issue regarding the analysis of the power spectra in our article. Our presentation of the power spectra in Figure 4 of the article was in a log-log coordinate system, and the parameter α of the power-law relationship (1/fα) was a natural means of quantifying the increase in power that was clearly present toward the lower frequencies (f). We did not present any material that considered alternate models for these power spectra. Krystal and Greenside point out recent work2 where it is asserted that the presence of a finite region of exponential decay (ekf) in the power spectrum of a process is sufficient to characterize the process as one with deterministic chaotic dynamics.

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Power spectral densities for the 7 bipolar patients from the time series of Figure 2 of the original article,1 presented in a log-linear coordinate system to emphasize their exponential character. The pair of solid lines represents the best fit of each spectrum to the sum of an exponential and a white process. These spectra were obtained directly from the definition of the discrete Fourier transform without zero-padding the time series, and after subtraction of the mean and removal of linear trend. The square magnitude of the resulting transform was then smoothed with a 5-point triangular filter.

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March 1, 1998
Allan Gottschalk, MD, PhD; Mark S. Bauer, MD; Peter C. Whybrow, MD
Arch Gen Psychiatry. 1998;55(3):275-276. doi:.
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