Examination of “The Tide,” CRI, and Physiologic Respiration: A Mathematical Analysis

Abstract

This study seeks to examine the inter-relationship of what William Garner Sutherland, DO called “The Tide,” the Cranial Rhythmic Impulse (CRI) palpated by practitioners of Osteopathy in the Cranial Field (OCF), and physiologic or pulmonary respiration. This study is different in that it proposes a mathematical analysis of these several phenomena to reconcile whether these are part of the same overarching natural wave or they are distinct. The pertinent medical literature is reviewed. The mathematics of Fourier analysis is briefly described. This study performed “reverse” Fourier analysis, that is, the combination of the various periodic signals into one periodic signal, across the range of normal physiological data values. Stochastic techniques were then applied to resolve these probabilistic data into 1 overarching periodic signal. From the mathematical analysis, it is not mathematically possible for “The Tide” to be in the range of the fundamental frequencies of the CRI, pulmonary respiration, and the Traube-Hering-Mayer oscillations that derive from it and are its harmonics. This mathematical analysis cannot be construed as negating the existence of “The Tide,” rather merely eliminates these fundamental frequencies as being “The Tide.” “The Tide” must be something else. More research is indicated.