Chapter 56 Mathematical principles and physiologic applications of coherence analysis

Abstract

Coherence analysis is a measure in the frequency domain. It was applied in the context of oscillatory activity in different parts of the nervous system. It has been established that there is rhythmic activity in the cortex that is coherent with the electromyography (EMG) signal. It has been argued that it might be the motor equivalent of the binding phenomenon encountered in the visual system. Apart from the application to basic motor physiology, coherence analysis is widely used in tremor research. Starting with some basic definitions and the assumptions about the data made before applying spectral analysis, this chapter develops the mathematical algorithm that is used to arrive at the coherence spectrum. The superiority of the coherence to a mere comparison of tremor frequencies in different limbs and the concept of multiple independent oscillators, causing parkinsonian and essential tremor, is discussed in the chapter. Using the study on coherence between the electrocorticography (EeoG) and physiologic tremor (PT) activity established is the capability of the coherence function to detect correlated processes in two spectra with differing frequency contents and show a cortical correlate of PT. The calculation of phase spectra has been shown. Difficulties in interpreting the phase spectrum in terms of the timing relation between the two processes are pointed out and also offered is a possible mathematical solution. Equal frequencies in the power spectra are not tantamount to the correlated or coherent processes. The tremor oscillations in Parkinsonian disease (PD) and essential tremor (ET) are independent between different limbs. Therefore, both pathological tremors seem to be caused by multiple independent oscillators. The coherence function can detect correlated processes also in power spectra that do not share the same frequency peaks or contents.