Definition of biological rhythm

In the preceding paragraphs, bioperiodic phe­nomena have been treated as temporal signals whose variation may be expressed by discrete values co- incinding with the sampling time.

It must be stressed that a discrete time series is not a faithful reconstruction of the signal as the approximation depends on timing and density of collected data (Fig. 5).

Fig. 5. - Diagram illustrating how both sampling time and interval cause the same discrete series to show different values.

In the discretization of bioperiodic phenomena there is the risk of systematic errors, any temporal series being constituted by an intrinsic component which is superimposed by occasional or random elements. The discrete series can, therefore, be contaminated by aberrant values, the so called «biological noise», not belonging to the systematic component of the periodic variation (Fig. 6).

Fig. 6. - Abnormal values can be included within tem­poral data due to casual effects.

In order to remove the biological noise due to aberrant values, the so called «outliers», the periodic signal has to be geometrically approximated by a curve adjusted to the raw series of data (Fig. 7).

Fig. 7. - Sine or cosine function fitting a time series of discrete data.

As the signal is periodic, the analytical curve has to be .representative of the harmonic oscillation. Therefore, one can assume that a biological rhythm is better expressed by the oscillating wave which optimally fits the discrete signal in its periodic fluctuation. In line with this thought, one can suggest that a biological rhythm is by definition «the periodic component of a temporal series of biological data whose waveform profile has been analytically validated». In other words, a biological rhythm is «a biosignal whose period of oscillation has been validated by analytical models of periodic regression using one or more harmonic components». Assuming such a definition, one can argue that a discrete variation of temporal biodata is not impli­citly a pattern demonstrating a biological rhythm. Obviously, the analytical resolution of a discrete biosignal doesn’t imply that the biological rhythm is arranged in a perfect sinusoidal shape. The sinusoidalization is just a model for removing the aleatory components which causes biological noise and, thus, biometric disturbance.

Furthermore, there are other valid biostatistical reasons that recognize the harmonic representation as the ideal signal of biological cycles] As a vari­ation occurring over the 24 h scale is not an implicit demonstration that the pattern varies ac­cording to a 24 h period, there is the need to statistically validate the oscillation in its periodicity. The rhythm detection level may be statistically verified assuming an «alpha» probability (P) of. less than 5% for the null-hypothesis of non-oscil­lation (zero-amplitude). Using the harmonic model, the biological rhythmicity may be, thus, statistically validated in its significance against the P probabil­ity less than 0.05 that the oscillation is due to a casual phenomenon.