A Stochastic and Mathematically Integrative Model of the Gender Modulation of Cardiorespiratory Activity.

Breath-to-breath interval (BBI) and heartbeat-toheartbeat interval (RRI) variability intrinsically contain a combination of random and temporally scaled characteristics. The objective of this study was to design and test a stochastic and mathematically integrative model (SIM) of cardiorespiratory function that could replicate any genderbased differences in breathing or heartrate variability during a calm, resting state. BBI and RRI sequences were recorded from 12 healthy subjects. Inter-breath and inter-beat memory were estimated with an autocorrelation function, and discrete probability density functions were created by fitting polynomial curves to the normalized histograms of each sequence. The SIM generated an artificial BBI or RRI sequence by constructing a random series of interval values selected from a discrete PDF, and then integrating the series with parameters from the autocorrelation analysis. Fractal scaling was quantified with detrended fluctuation analysis. A significant gender difference was identified in the autocorrelation coefficients of the BBI. The SIM produced artificial BBI and RRI sequences with significant fractal scaling as compared to randomly-shuffled surrogate data (p < 0.001), and with fractal-scaling characteristics similar to the original human data. The SIMgenerated BBI sequences also exhibited the same significant gender-based differences as identified in the human data (p < 0.01). In conclusion, this research demonstrated a stochastic and integrative model that replicated the gender-based differences in fractal scaling in resting human breathing patterns.