Circular motion analysis of time-varying bioimpedance.

This paper presents a step forward towards the analysis of a linear periodically time-varying (PTV) bioimpedance ZPTV(jw, t), which is an important subclass of a linear time-varying (LTV) bioimpedance. Similarly to the Fourier coefficients of a periodic signal, a PTV impedance can be decomposed into frequency dependent impedance phasors, [Formula: see text], that are rotating with an angular speed of wr = 2πr/TZ. The vector length of these impedance phasors corresponds to the amplitude of the rth-order harmonic impedance |Zr( jw)| and the initial phase is given by Φr(w, t0) = [Symbol: see text]Zr( jw) + 2πrt0/TZ, with t0∈[0, T] being a time instant within the measurement time T. The impedance period TZ stands for the cycle length of the bio-system under investigation; for example, the elapsed time between two consecutive R-waves in the electrocardiogram or the breathing periodicity in case of the heart or lungs, respectively. First, it is demonstrated that the harmonic impedance phasor [Formula: see text], at a particular measured frequency k, can be represented by a rotating phasor, leading to the so-called circular motion analysis technique. Next, the two dimensional (2D) representation of the harmonic impedance phasors is then extended to a three-dimensional (3D) coordinate system by taking into account the frequency dependence. Finally, we introduce a new visualizing tool to summarize the frequency response behavior of ZPTV( jw, t) into a single 3D plot using the local Frenet-Serret frame. This novel 3D impedance representation is then compared with the 3D Nyquist representation of a PTV impedance. The concepts are illustrated through real measurements conducted on a PTV RC-circuit.

Time-invariant measurement of time-varying bioimpedance using vector impedance analysis.

When stepped-sine impedance spectroscopy measurements are carried out on (periodically) time-varying bio-systems, the inherent time-variant (time-periodic) parts are traditionally ignored or mitigated by filtering. The latter, however, lacks theoretical foundation and, in this paper, it is shown that it only works under certain specific conditions. Besides, we propose an alternative method, based on multisine signals, that exploits the non-stationary nature in time-varying bio-systems with a dominant periodic character, such as cardiovascular and respiratory systems, or measurements interfered with by their physiological activities. The novel method extracts the best­in a mean square sense­linear time-invariant (BLTI) impedance approximation ZBLTI(jω) of a periodically time-varying (PTV) impedance ZPTV(jω, t) as well as its time-periodic part. Relying on the geometrical interpretation of the BLTI concept, a new impedance analysis tool, called vector impedance analysis (VIA), is also presented. The theoretical and practical aspects are validated through measurements performed on a PTV dummy circuit and on an in vivo myocardial tissue.

Harmonic impedance spectra identification from time-varying bioimpedance: theory and validation.

The harmonic impedance spectra (HIS) of a time-varying bioimpedance Z(ω, t) is a new tool to better understand and describe complex time-varying biological systems with a distinctive periodic character as, for example, cardiovascular and respiratory systems. In this paper, the relationship between the experimental setup and the identification framework for estimating Z(ω, t) is set up. The theory developed applies to frequency response based impedance measurements from noisy current-voltage observations. We prove theoretically and experimentally that a voltage source (VS) and a current source (CS) analogue front end-based measurement lead, respectively, to a closed-loop and an open-loop HIS identification problem. Next, we delve into the estimation of the HIS by treating Z(ω, t), on the one hand, as a linear time-invariant (LTI) system within a short time window; and, on the other hand, as a linear periodically time-varying (PTV) system within the entire measurement interval. The LTI approach is based on the short-time Fourier transform (STFT), while the PTV approach relies on the information that is present in the skirts of the voltage and/or current spectra. In addition, direct and indirect methods are developed for estimating the HIS by using simple as well as more sophisticated techniques. Ultimately, the HIS and their uncertainty bounds are estimated from real measurements conducted on a periodically varying dummy impedance.

A new measuring and identification approach for time-varying bioimpedance using multisine electrical impedance spectroscopy.

The bioimpedance measurement/identification of time-varying biological systems Z(ω, t) by means of electrical impedance spectroscopy (EIS) is still a challenge today. This paper presents a novel measurement and identification approach, the so-called parametric-in-time approach, valid for time-varying (bio-)impedance systems with a (quasi) periodic character. The technique is based on multisine EIS. Contrary to the widely used nonparametric-in-time strategy, the (bio-)impedance Z(ω, t) is assumed to be time-variant during the measurement interval. Therefore, time-varying spectral analysis tools are required. This new parametric-in-time measuring/identification technique has experimentally been validated through three independent sets of in situ measurements of in vivo myocardial impedance. We show that the time-varying myocardial impedance Z(ω, t) is dominantly periodically time varying (PTV), denoted as ZPTV(ω, t). From the temporal analysis of ZPTV(ω, t), we demonstrate that it is possible to decompose ZPTV(ω, t) into a(n) (in)finite sum of fundamental (bio-)impedance spectra, the so-called harmonic impedance spectra (HIS) Zk(ω)s with [Formula: see text]. This is similar to the well-known Fourier series of a periodic signal, but now understood at the level of a periodic system's frequency response. The HIS Zk(ω)s for [Formula: see text] actually summarize in the bi-frequency (ω, k) domain all the temporal in-cycle information about the periodic changes of Z(ω, t). For the particular case k = 0 (i.e. on the ω-axis), Z0(ω) reflects the mean in-cycle behavior of the time-varying bioimpedance. Finally, the HIS Zk(ω)s are directly identified from noisy current and voltage myocardium measurements at the multisine measurement frequencies (i.e. nonparametric-in-frequency).

Frequency-selective quantification of biomedical magnetic resonance spectroscopy data.

In this paper the possibility of obtaining accurate estimates of parameters of selected peaks in the presence of unknown or uninteresting spectral features in biomedical magnetic resonance spectroscopy (MRS) signals is investigated. This problem is denoted by frequency-selective parameter estimation. A new time-domain technique based on maximum-phase finite impulse response (FIR) filters is presented. The proposed method is compared to a number of existing approaches: the application of a weighting function in the time domain, frequency domain fitting using a polynomial baseline, and the time-domain HSVD filter method. The ease of use and low computational complexity of the FIR filter method make it an attractive approach for frequency-selective parameter estimation. The methods are validated using simulations of relevant (13)C and (31)P MRS examples.

Learning neural networks with noisy inputs using the errors-in-variables approach.

Currently, most learning algorithms for neural-network modeling are based on the output error approach, using a least squares cost function. This method provides good results when the network is trained with noisy output data and known inputs. Special care must be taken, however, when training the network with noisy input data, or when both inputs and outputs contain noise. This paper proposes a novel cost function for learning NN with noisy inputs, based on the errors-in-variables stochastic framework. A learning scheme is presented and examples are given demonstrating the improved performance in neural-network curve fitting, at the cost of increased computation time.

Identification of parametric models for ultrasonic wave propagation in the presence of absorption and dispersion.

Acoustic wave propagation in an absorptive and dispersive medium is usually described using models derived from a nearly local form of the Kramers-Kronig relationship, e.g., Q- and relaxation models. A modeling approach based on rational transfer function models for the generalized Hooke's law is presented. The assumptions and restrictions of models based on the nearly local absorption-dispersion relations and rational transfer function models are discussed. Using identification techniques, it is experimentally shown that the rational transfer function models explain the ultrasonic wave propagation in an absorptive-dispersive medium much better than the classical Q-models.