A novel method for estimating the fractional Cole impedance model using single-frequency DC-biased sinusoidal excitation.

OBJECTIVE: The Cole model is a widely used fractional circuit model in electrical bioimpedance applications for evaluating the content and status of biological tissues and fluids. Existing methods for estimating the Cole impedance parameters are often based on multi-frequency data obtained from stepped-sine measurements fitted using a complex non-linear least square (CNLS) algorithm. Newly emerged numerical methods from the magnitude of electrical bio-impedance data-only do not need CNLS fitting, but they still require multi-frequency stepped-sine data. This study proposes a novel approach to estimating the Cole impedance parameters that combines a numerical and time-domain fitting method based on a single-frequency DC-biased sinusoidal current excitation. APPROACH: First, the transient and steady-state voltage response along with the current excitation are acquired in electrical bio-impedance measurement. From the sampled data, a numerical method is applied to provide the initial estimation of the Cole impedance parameters, which are then used in a time-domain iterative fitting algorithm. RESULTS: The accuracy of the algorithm proposed is tested with noisy electrical bio-impedance simulations. The maximum relative error of the estimated Cole impedance parameters is 1% considering 2% (34 dB) additive Gaussian noise. Experimental measurements performed on a 2R-1C circuit and some fruit samples show a mean difference less than 1% and 5% respectively compared to the Cole impedance parameters estimated from a commercial electrical bio-impedance analyzer performing stepped-sine measurements and CNLS fitting. SIGNIFICANCE: This is the first method that allows estimating the Cole impedance parameters from single-frequency electrical bio-impedance data. The approach presented could find broad use in many applications, including single-frequency body impedance analysis.

Numerical estimation of Fricke-Morse impedance model parameters using single-frequency sinusoidal excitation.

OBJECTIVE: The Fricke-Morse impedance model is widely used in bioelectrical impedance analysis (BIA), which is usually fitted by multi-frequency electrical impedance data. Here, we propose a novel numerical method for estimating the model parameters using single-frequency sinusoidal excitation. APPROACH: A single-frequency sinusoidal signal is used as the current excitation, from which the initial transient, the steady-state and the ending transient voltage responses along with the current excitation are recorded. The model parameters can be then estimated with numerical calculations from the acquired signals. MAIN RESULTS: Simulation and experimental measurements are verified on a 2R1C circuit by using a 50 kHz sinusoidal current excitation. The results show that the maximum relative errors of the estimated model parameters are <1% in simulation with 2% noise and <2% in experimental measurement. SIGNIFICANCE: The proposed method could extend the applications of wideband BIA by using single-frequency excitation, rather than multi-frequency excitation as is done today.

A Noise-Filtering Method for Link Prediction in Complex Networks.

Link prediction plays an important role in both finding missing links in networked systems and complementing our understanding of the evolution of networks. Much attention from the network science community are paid to figure out how to efficiently predict the missing/future links based on the observed topology. Real-world information always contain noise, which is also the case in an observed network. This problem is rarely considered in existing methods. In this paper, we treat the existence of observed links as known information. By filtering out noises in this information, the underlying regularity of the connection information is retrieved and then used to predict missing or future links. Experiments on various empirical networks show that our method performs noticeably better than baseline algorithms.

Design of tri-level excitation signals for broadband bioimpedance spectroscopy.

Bioimpedance spectroscopy (BIS) measurement methods have been evolving from the traditional frequency-sweep approach to the multi-frequency simultaneous measurement technique which can drastically reduce measuring time and will be increasingly attractive for time-varying biological applications. Multi-frequency mixed (MFM) signals with sparsely distributed spectra are desirable for broadband BIS measurement. This paper proposes a synthesis method to design a series of tri-level MFM signals which contain only three values (+1, 0, -1), and has majority energy distributed on its (2(n))th primary harmonics. Tri-level MFM signals have both high energy efficiency and a low crest factor. An impedance measurement experiment excited by an 8th-order tri-level MFM signal on a RC three-element equivalent model has been performed, and the results on 8 primary harmonic frequencies ranging from 8 to 1024 kHz show a high accuracy with the mean amplitude relative error of 0.41% and mean phase absolute error of 0.18°, which has validated the feasibility of the tri-level MFM signals for broadband BIS measurement.

An improved crest factor minimization algorithm to synthesize multisines with arbitrary spectrum.

Multisine signal with a low crest factor (CF) can bring a high signal-to-noise ratio for fast frequency response function (FRF) estimation. Synthesis of a low CF multisine with the given amplitude spectrum depends on optimum selection of the initial phases of its cosinusoidal components. The solutions investigated can be generally divided into two branches: (1) the analytical method based on direct formula calculation; and (2) the numerical method based on iterative computations. The analytical method works well only for an equidistant and flat amplitude spectrum, while the numerical method can generally output better results, even for a sparse or non-flat spectrum, but the number of iterations might be huge. This paper presents an improved CF minimization algorithm to synthesize multisine signals based on the combination of the previous Schroeder analytical method and the Van der Ouderaa (VDO) iteration procedure. The improved algorithm adopts the Schroder phases as the iterative initial phases, and employs a logarithmic clip function of the iterative index i in the VDO iteration procedure. Comprehensive experiments of multisine synthesis on three types of cosinusoidal amplitude spectra are performed, and the resulting CFs remain the lowest level in all cases compared with the earlier methods. The proposed algorithm provides a fast and efficient solution to synthesize multisine with the lowest CF for an arbitrary user-prescribed spectrum.

Multi-frequency simultaneous measurement of bioimpedance spectroscopy based on a low crest factor multisine excitation.

Bioimpedance spectroscopy (BIS) is becoming a powerful diagnostic tool for a wide variety of medical applications, and the multi-frequency simultaneous (MFS) measurement of BIS can greatly reduce measurement time and record the transient physiological status of a living body compared with traditional frequency-sweep measurement technology. This paper adopts the Van der Ouderaa's multisine, which has 31 equidistant and flat amplitude spectra and a low crest factor of 1.405 as the broadband excitation, and realizes the MFS measurement of BIS by means of spectral analysis using the fast Fourier transform algorithm. The approach to implement the multisine based on a field-programmable gate array and a digital to analog converter is described in detail, and impedance measurement experiments are performed on three resistance-capitance three-element phantoms. Experimental results show a commendable accuracy with a mean relative error of 0.55% for the impedance amplitudes, and a mean absolute error of 0.20° for the impedance phases on the 31 frequencies ranging linearly from 32 to 992 kHz. This paper validates the feasibility of the MFS technology for BIS measurement based on the multisine excitation.

Improved Cole parameter extraction based on the least absolute deviation method.

The Cole function is widely used in bioimpedance spectroscopy (BIS) applications. Fitting the measured BIS data onto the model and then extracting the Cole parameters (R0, R∞, α and τ) is a common practice. Accurate extraction of the Cole parameters from the measured BIS data has great significance for evaluating the physiological or pathological status of biological tissue. The traditional least-squares (LS)-based curve fitting method for Cole parameter extraction is often sensitive to noise or outliers and becomes non-robust. This paper proposes an improved Cole parameter extraction based on the least absolute deviation (LAD) method. Comprehensive simulation experiments are carried out and the performances of the LAD method are compared with those of the LS method under the conditions of outliers, random noises and both disturbances. The proposed LAD method exhibits much better robustness under all circumstances, which demonstrates that the LAD method is deserving as an improved alternative to the LS method for Cole parameter extraction for its robustness to outliers and noises.