Reliability of transfer function estimates in cardiovascular variability analysis

Transfer function (TF) analysis is a widely diffused technique in the assessment of the relationship between short-term cardiovascular variability signals, particularly blood pressure, heart rate and respiration. To guarantee the reliability of the estimates, a conventional threshold of 0.5 on the magnitude squared coherence (MSC) is commonly used, although (i) other analysis parameters play a role and (ii) lower values of MSC are frequently unavoidable in physiological systems. In this study, computer simulations are performed to assess the dependency of the bias and standard deviation (SD) of TF estimates on record length (RL), spectral window bandwidth (Bw) and MSC; to evaluate the accuracy of theoretical expressions for the computation of the confidence interval (CI) of the estimates; and to assess, in some representative situations, how faithfully observed TF shapes reproduce the underlying true functions in conditions of very low MSC. The accuracy of TF estimates increases non-linearly with increasing RL, and the benefit over 7 min is small. Using this RL, the relative bias for the TF modulus is 0.2. Estimates of TF phase are unbiased. The SD of both the modulus and phase increases linearly as the MSC decrease to 0.4 and then, for lower MSC, increases markedly with nonlinear behaviour. Bw=0.03 Hz appears to be most suitable to reduce the error, preserving spectral resolution. CIs for the TF phase are highly reliable, whereas those for the modulus tend to be slightly narrower than the nominal value at high coherence values. Major features of the TF shape appear to be preserved in simulations with very low MSC. The major problem in TF estimation is the sharp increase in the variability of the measurements as the coherence decreases towards the lowest values. The combination of RL≥420s and Bw=0.03 Hz should be suggested in short-term cardiovascular variability studies. Although basic features of the true TF can be recovered even when the MSC is <0.5, much greater values can be necessary when accurate point estimates are needed. Theoretical expressions for the computation of confidence intervals of the TF are adequate for practical purposes.