ObjectiveClassic methods for assessing cerebral autoregulation involve a transfer function analysis performed using the Fourier transform to quantify relationship between fluctuations in arterial blood pressure (ABP) and cerebral blood flow velocity (CBFV). This approach usually assumes the signals and the system to be stationary. Such an presumption is restrictive and may lead to unreliable results. The aim of this study is to present an alternative method that accounts for intrinsic non-stationarity of cerebral autoregulation and the signals used for its assessment.MethodsContinuous recording of CBFV, ABP, ECG, and end-tidal CO2 were performed in 50 young volunteers during normocapnia and hypercapnia. Hypercapnia served as a surrogate of the cerebral autoregulation impairment. Fluctuations in ABP, CBFV, and phase shift between them were tested for stationarity using sphericity based test. The Zhao-Atlas-Marks distribution was utilized to estimate the time—frequency coherence (TFCoh) and phase shift (TFPS) between ABP and CBFV in three frequency ranges: 0.02–0.07 Hz (VLF), 0.07–0.20 Hz (LF), and 0.20–0.35 Hz (HF). TFPS was estimated in regions locally validated by statistically justified value of TFCoh. The comparison of TFPS with spectral phase shift determined using transfer function approach was performed.ResultsThe hypothesis of stationarity for ABP and CBFV fluctuations and the phase shift was rejected. Reduced TFPS was associated with hypercapnia in the VLF and the LF but not in the HF. Spectral phase shift was also decreased during hypercapnia in the VLF and the LF but increased in the HF. Time-frequency method led to lower dispersion of phase estimates than the spectral method, mainly during normocapnia in the VLF and the LF.ConclusionThe time—frequency method performed no worse than the classic one and yet may offer benefits from lower dispersion of phase shift as well as a more in-depth insight into the dynamic nature of cerebral autoregulation.

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In this paper, a Lie-algebraic nonholonomic motion planning technique, originally designed to work in a configuration space, was extended to plan a motion within a task-space resulting from an output function considered. In both planning spaces, a generalized Campbell–Baker–Hausdorff–Dynkin formula was utilized to transform a motion planning into an inverse kinematic task known for serial manipulators. A complete, general-purpose Lie-algebraic algorithm is provided for a local motion planning of nonholonomic systems with or without output functions. Similarities and differences in motion planning within configuration and task spaces were highlighted. It appears that motion planning in a task-space can simplify a planning task and also gives an opportunity to optimize a motion of nonholonomic systems. Unfortunately, in this planning there is no way to avoid working in a configuration space. The auxiliary objective of the paper is to verify, through simulations, an impact of initial parameters on the efficiency of the planning algorithm, and to provide some hints on how to set the parameters correctly.