Complexity, Scaling, and Fractals in Biological Signals

A biological signal carries information about the complex biological phenomena being measured and is typically a time series having both a regular and random component. This chapter focuses on dynamic physiologic phenomena, in order to reduce the number of time series discussed to a manageable size. The output of dynamical physiologic systems, such as the cardiac system, the respiratory system and the motor control system, have all been shown to be fractal or multifractal statistical time series. Consequently, the fractal dimension turns out to be a significantly better indicator of health than the more traditional measures, such as heart rate, breathing rate, and stride rate, all average quantities. Fractal physiology, as this field has come to be called, focuses on the complexity of the human body and the characterization of that complexity through fractal measures and the dynamics of such measures. These new measures reveal that the traditional interpretation of disease as the loss of regularity is not adequate and a better interpretation of disease is the loss of variability, or more accurately, the loss of complexity. Keywords: physiologic time series; fractal statistics; allometric control; scaling; variability