Th. J. C. Faes

Spectra of data sampled at frequency-modulated rates in application to cardiovascular signals: Part 1 analytical derivation of the spectra

Beat-to-beat cardiovascular signals, e.g. a series of systolic pressure values, can be considered as time series which are pulse amplitude modulated (PAM) and pulse frequency modulated (PFM). The latter process, due to variations in heart rate, causes the series to become non-uniformly spaced in time. If PAM is to be quantified by spectral analysis, the influence of PFM must be known. An analytical expression is therefore derived for the spectrum of sinusoids which are sampled according to the output event series of a linear integral pulse frequency modulator (IPFM). We conclude that two spectral components arise at the difference and sum of the PFM and PAM frequencies, fp±fx, with amplitudes proportional to the PFM modulation depth. These components appear as a DC component and as a first harmonic if both modulating frequencies are equal. In addition, a cluster of spectral components appears around the mean pulse frequency fo (i.e. mean heart rate), at frequencies fo-nfp±fx, which may leak into the signal band. From these theoretical considerations, we conclude that the amplitude spectrum of a sinusoidally varying systolic blood pressure series can contain up to 20–30% spurious components, owing to the heart rate modulation process.

Estimation of non-cardiogenic pulmonary oedema using dual-frequency electrical impedance

The study investigates the effects of non-cardiogenic oedema, especially the accumulation of protein in extracellular fluid, on thoracic impedance and proposes a new method of oedema measurement based on an impedance ratio from a dual-frequency measurement. In vitro measurements in a cell containing an albumin-in-saline solution yield a resistance increase when the albumin concentration increases. Subsequently, 13 patients having acute respiratory failure are measured. The single-frequency Z0 measurements and the proposed impedance ratio are compared with extravascular lung water (EVLW) determined by the double indicator dilution method. The single-frequency measurement correlates poorly with EVLW (r=−0.24, p=0.56). In some patients, a total thoracic impedance increase is found with increasing EVLW. The correlation between the impedance ratio and EVLW is r=−0.79 (p<0.0005). The ratio decreases as EVLW increases. Thus, when oedema is measured using bio-impedance, cardiogenic and noncardiogenic oedema yield different results. It is well recognised that cardiogenic oedema decreases total thoracic impedance. In non-cardiogenic oedema, however, protein accumulation causes an impedance increase. The decrease in the impedance ratio as EVLW increases can be explained by the accumulation of albumin in the extracellular compartment.

Thoracic geometry and its relation to electrical current distribution: consequences for electrode placement in electrical impedance cardiography

In thoracic impedance cardiography (TIC) measurements the neck electrodes are often positioned at the basis of the neck, close to the neck-thorax transition. Theoretically, this neck-thorax transition will cause inhomogeneities in the current density and potential distribution. This was simulated using a 3D finite element method, solely representing the geometrical neck-thorax transition. The specific conductivity was 7 10−3 (Ωcm)−1 and the injected current was 1 mA. As expected, the model generated inhomogeneities in the current distribution at the neck-thorax transition, which reached as far as 5 cm into the neck and 20 cm into the thorax. These results are supported by in vivo measurements performed in 10 young male subjects, in which the position of the neck electrodes was varied. A two-way ANOVA revealed that the stroke volume of the lowest neck position was significantly different from the other positions. Small shifts in the position of the neck electrode resulted in large changes in impedance and stroke volume (127 to 82 ml for the Kubicek equation). To standardise the electrode position, the authors strongly recommend placement of the neck electrodes at least 6 cm above the clavicula.

Spectra of data sampled at frequency-modulated rates in application to cardiovascular signals: Part 2 evaluation of Fourier transform algorithms

For three direct Fourier transform algorithms we quantified the influence of pulse frequency modulation (PFM) on the spectral estimation of pulse amplitude modulation (PAM). The simulation study is based on sinusoid functions sampled according to a pulse sequence which is the output of an integral pulse frequency modulator (IPFM). One algorithm exactly reproduces the theoretical spectrum derived in Part 1. The other two, including the classical FFT, scale all PFM-induced components in a different way, and in addition, generate higher modulating frequency harmonics. For a PFM depth below 30%, the sum of spurious PFM components is almost linearly dependent on this modulation depth, for all three algorithms. Dividing the effect of PFM in a ‘harmonic’ and ‘aliasing’ distortion, we found that the FFT has a relatively high harmonic distortion, compared to an algorithm that takes into account the non-uniform character of the data. In the cardiovascular (worst) case of 30% modulation in heart rate (PFM) at a frequency of 0.1 Hz, the FFT spectrum of beat-to-beat systolic blood pressure variations contains approximately 20% of spurious components caused solely by the modulation in time occurrences of the blood pressure samples. The ‘non-uniform’ algorithm performs twice as well in this case.

The influence of extravascular lung water on cardiac output measurements using thoracic impedance cardiography

The purpose of this study was to investigate the influence of pulmonary oedema as measured with the double indicator dilution technique on the accuracy of cardiac output (CO) measurement using thoracic impedance cardiography (TIC) compared with thermodilution in thirteen sepsis patients. Differences in the Kubicek and Sramek-Bernstein equation with respect to pulmonary oedema were explored theoretically and experimentally. From a parallel two cylinder model a hypothesis can be derived that CO determined with the Kubicek equation is oedema independent, whereas CO determined using the Sramek-Bernstein equation is oedema dependent. Experimentally, CO determined using Kubiceks equation correlated better with thermodilution CO (r = 0.75) than CO determined with the Sramek-Bernstein equation (r = 0.25). The effect of oedema on the accuracy of TIC was investigated by comparing the differences in the CO of impedance and thermodilution to the extravascular lung water index. For the Kubicek equation the difference was not influenced by oedema (r = 0.04, p = 0.84), whereas for the Sramek-Bernstein equation the difference was affected by oedema (r = 0.39, p = 0.05). Thus, the effects of pulmonary oedema on the accuracy of TIC measurements can better be understood with the parallel cylinder model. Moreover, the Kubicek equation still holds when pulmonary oedema is present, in contrast to the Sramek-Bernstein equation.

Extra-cellular volume estimation by electrical impedance - phase measurement or curve fitting: a comparative study

In order to determine body fluid shifts between the intra- and extra-cellular spaces, multifrequency impedance measurement is performed. According to the Cole-Cole extrapolation, lumped values of intra- and extra-cellular conduction can be estimated which are commonly expressed in resistances Ri and Re respectively. For this purpose the magnitude and phase of the impedance under study are determined at a number of frequencies in the range between 5 kHz and 1 MHz. An approach to determine intra- and extra-cellular conduction on the basis of Bode analysis is presented in this article. On this basis, estimation of the ratio between intra- and extra-cellular conduction could be performed by phase measurement only, midrange in the bandwidth of interest. An important feature is that the relation between intra- and extra-cellular conduction can be continuously monitored by phase measurement and no curve fitting whatsoever is required. Based on a two frequency measurement determining Re at 4 kHz and phi(max) at 64 kHz it proved possible to estimate extra-cellular volume (ECV) more accurately compared with the estimation based on extrapolation according to the Cole-Cole model in 26 patients. Reference values of ECV were determined by sodium bromide. The results show a correlation of 0.90 with the reference method. The average error of ECV estimation was -3.6% (SD 8.4), whereas the Cole-Cole extrapolation showed an error of 13.2% (SD 9.5). An important feature of the proposed approach is that the relation between intra- and extra-cellular conduction can be continuously monitored by phase measurement and no curve fitting whatsoever is required.

A wideband high common mode rejection ratio amplifier and phase-locked loop demodulator for multifrequency impedance measurement

Design considerations and implementation of a multifrequency measuring channel for application in the field of bio-impedance measurement are discussed in this paper. The input amplifier has a differential configuration which is electrically isolated from the remaining circuits. Transformer coupling provides improved common mode rejection when compared to non-isolated input stages. The frequency characteristic of the section between input and demodulator is flat within ±0.1 dB between 4kHz and 1024 kHz. The synchronous demodulator is based on a wideband switched video amplifier. In contrast to commonly used lock-in techniques, the carrier for demodulation is recovered from the input signal by means of a phase-locked loop. This method ensures zero phase shift with respect to the input signal and improves the accuracy of measurement. The system has been developed primarily for thoracic impedance cardiography (TIC) but has also succesfully been applied in the field of total body bio-impedance analysis (BIA). At present an electrical impedance tomograph is under development based on the instrumentation described. Results regarding the measurement range and accuracy are given and some recordings of patient data are shown.

Frequency synthesis of digital filters based on repeatedly applied unweighed moving average operations

Simple formulae are presented for designing filters based on repeatedly applied moving average operations with unit coefficients. Design formulae are derived to synthesise the filter in a way that satisfies specified passband and stopband specifications. These filters are attractive because of the reasonable frequency characteristics, the computational efficiency of the design and filter algorithms, and the uncomplicated implementation in software.

A Parametric Method to Resolve the Ill-Posed Nature of the EIT Reconstruction Problem: A Simulation Study

Abstract: The reconstruction problem of electrical impedance tomography (EIT) is to estimate the distribution of the conductivity inside an object from measured potential distributions on the circumference caused by injected current patterns. Mathematically, this reconstruction problem is an ill‐posed nonlinear inverse problem, with many unknowns. In this paper, the ill‐posed nature is demonstrated by analyzing the condition of the sensitivity matrix; the associated inverse problem can only be solved on a very coarse grid. To circumvent the ill‐posed nature of the EIT reconstruction problem, we present a new parametric formulation. In this formulation, it is assumed that the object consists of compartments with homogeneous conductivity. The position, orientation, size, and conductivity of these compartments are treated as unknown parameters, which are determined by solving the forward problem (using the boundary element method) and optimizing the parameters (using Powells or the simplex method) in order to fit the parameters to the EIT data. Simulations show that the parametric method is stable and adequately solves the EIT problem.

The influence of pulsatile flow on blood resistivity in impedance cardiography

The purpose of the study was to investigate the resistivity change over the cardiac cycle. This is important for the correct application of thoracic impedance cardiography (TIC). The ratio of spatial mean velocity over the vessel radius of the ascending and descending aorta of two female and eight male subjects (age ranging from 23 to 69 years) were measured in supine position using MRI. Based on Vissers (1989) equation the relative resistivity change was calculated. In all subjects the authors found a change of less than 15%, which is smaller than rigid tube experiments predicted. However, the peak resistivity change occurs at the same time as the peak in the impedance signal. Thus, the effects of resistivity changes on stroke volume calculation in TIC needs further investigation.