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Proposal for the usefulness of the first and second derivatives for measuring the duration of time during REM sleep
Proposal for the usefulness of the first and second derivatives for measuring the duration of time during REM sleep
Emilio Arch-Tirado 1 
, Miguel A. Collado-Corona 2 , Ana L. Lino-González 3 , Óscar Sánchez-Escandón 2
1 Centro Neurológico, Centro Médico ABC Sede Santa Fe, Ciudad de México, México; 2 Centro Neurológico, Centro Médico ABC, Sede Santa Fe, Ciudad de México, México; 3 Área de Neurociencias Clínica, Instituto Nacional de Rehabilitación Luis Guillermo Ibarra Ibarra, Secretaría de Salud, Ciudad de México, México
*Correspondence: Emilio Arch-Tirado. Email: arch.tirado@gmail.com
Abstract
This study aims to demonstrate the applicability of first and second derivative criteria (namely, instantaneous velocity and instantaneous acceleration) as a mathematical model for estimating REM sleep duration. The model is based on the discrepancy observed between perceived time during the REM phase and actual elapsed time. The findings indicate that the application of differential calculus yields varying results depending on the rate of change (velocity), instantaneous rate of change (instantaneous velocity), and the rate of change of the rate of change (instantaneous acceleration), reflecting patterns analogous to those observed during REM sleep.
Keywords: REM sleep. Paradoxical sleep. Differential calculus. Instantaneous velocity. Instantaneous acceleration.
