Jan Strackee

Comparing Spectra of a Series of Point Events Particularly for Heart Rate Variability Data

Different methods for spectral analysis of the heart rate signal¿considered as series of point events¿are used in studies on heart rate variability. This paper compares these methods, focusing on the two principal ones: the interval spectrum, i.e., the spectrum of the interval series, and the spectrum of counts, which is related to the representation of the event series as a series of spikes (delta functions). Both autospectra are estimated for experimental heart rate data and are shown to produce similar results. This similarity is proven analytically, and it is shown that for small variations in interval length, the ratio of these spectra is PI(f)/PC(f) = [sin(¿f¿)/(¿f¿)]2, with PI and PC the interval spectrum and the spectrum of counts, respectively, f the frequency, and ¿the mean interval length. It is concluded that both autospectra are equivalent for the considered heart rate data, but that, when relating the heart rate signal to other signals (e.g., respiration, blood pressure) by means of cross spectra, the technique to be used depends on the characteristics of the second signal.

Relationships between short-term blood-pressure fluctuations and heart-rate variability in resting subjects I: a spectral analysis approach

A method to attribute the short-term variability of blood pressure and heart rate of resting subjects to their various causes, using spectral techniques, is presented. Power spectra and cross-spectra are calculated for beat-to-beat values of R-R interval and blood pressure from subjects who were seated in a comfortable chair. Interval values as well as systolic, mean and pulse pressures show variations linked to respiration and to the so-called 10 s rhythm. The diastolic pressure values are scarcely influenced by respiration in the normal respiratory range (0·20–0·35 Hz), but do show 10 s variability. Relationships between pressure and interval variability which indicate that the 10 s variability in systolic pressure leads the interval variation by two to three beats become manifest in cross-spectra; however, no such lag is found between the respiration-linked variations in systolic pressure and intervals. It is argued that the technique presented provides a critical test for models of the fast regulation of the cardiovascular system.

The Solid Angle of a Plane Triangle

An analytical expression is presented for the solid angle subtended by a plane triangle at some arbitrary point in space. Using this expression, the time required for numerical computation is cut down to one third.

Relationships between short-term blood-pressure fluctuations and heart-rate variability in resting subjects. II: A simple model

A simple model of the beat-to-beat properties of the cardiovascular system is used to interpret the results of spectral analysis of blood-pressure and interval data. The model consists of two equations, one representing the fast regulation of interval by the systolic pressure (baroreflex), the other one representing a Windkessel approximation of the systemic arterial system. The model, when applied to interval and blood-pressure data from resting subjects, explains the lack of respiratory variability in the diastolic pressure values. The baroreflex equation seems to describe the data only in the region of respiratory frequencies. The shape of the phase spectrum of systolic pressures against intervals is modelled by difference equations, but no physiological interpretation of these equations is given.

The Excitability Cycle of the Dog's Left Ventricle Determined by Anodal, Cathodal, and Bipolar Stimulation

Investigations are reported in which the excitability cycle of the dogs heart was tested successively by unipolar anodal and cathodal square wave shocks as well as by bipolar stimulation. The classical view that excitability decreases smoothly during the relative refractory phase was substantiated. The excitability for anodal stimulation reached its maximum of the cardiac cycle immediately after the absolute refractory period and exceeded cathodal excitability at that moment. Evidence is presented that the dip phenomenon described by Orias, Brooks and their associates is due to their arrangement of driving and testing electrodes. The coincidence of the dip phenomenon with the vulnerable period may be related to simultaneous spreading of two fronts of activation from cathode and anode of bipolar electrodes which would create favorable conditions for reentry.

Spectrum of a series of point events, generated by the integral pulse frequency modulation model

The paper deals with the relationship between the spectra of the input signal and the output signal of the integral pulse frequency modulation (IPFM) model. The IPFM model is a physiologically attractive device for the conversion of a continuous input signal into an output signal, consisting of a series of events (e.g. nerve spikes, heart beats). Two different spectra are used in the analysis of a series of events; the interval spectrum and the spectrum of counts. The latter spectrum is known analytically for the event series belonging to a sinusoidal input signal. An approximation to the interval spectrum of this series is presented. Using data from a simulated IPFM model, it is shown that, for an input signal consisting of the sum of two sinusoids, terms at sum and difference frequencies appear in the interval spectrum but not in the spectrum of counts. However, the spectrum of counts is contaminated by sidebands of the mean repetition frequency. It is concluded that in general the spectral properties of the input signal cannot be recovered fully from the interval spectrum, nor from the spectrum of counts, the more so as physiological series of events will seldom be generated by an ideal IPFM model.

A Handwriting Simulator

A description of a handwriting simulator is given based on the same principles as real cursive handwriting are thought to be. Some results are presented.

Computing the lead field of electrodes with axial symmetry

The computation of the lead field of a plane bipolar electrode with axial symmetry is discussed. The numerical technique used is based on an analogy of the ‘charge density method’. An explicit analytical formula describing the potential arising from a plane annulus having uniform (current) density is presented. A verification of the technique is given by comparing the results with both a known analytical expression describing the field of a disc electrode and measurements inside a tank. The lead field is computed for several values of the radii involved and is shown to posses a pronounced directional sensitivity. Possible applications are discussed.

Computer Analysis of the RR Interval-Contractility Relationship during Random Stimulation of the Isolated Heart

Hemodynamic variability in patients with atrial fibrillation may originate from a direct influence of the variations in RR intervals on myocardial contractility. With the aid of a computer the serial autocorrelation function and the histogram of the RR intervals of patients with atrial fibrillation receiving no medication were produced. The RR intervals were randomly distributed and the histograms rather skew. Next, random rhythms with histograms matching those of the patients were produced with a radioactive source and a Geiger-Müller counter. These rhythms were used to stimulate isolated perfused rat hearts to study the relationship between the RR interval and a number of contractile parameters. The ECG and the isotonic contractions were digitized and processed by the computer. Serial crosscorrelation coefficients were computed between the RR interval on the one hand, and contraction height, contraction area, and maximum of the first derivative of the contraction on the other hand. The zero order crosscorrelation coefficient between the RR interval and contraction height was 0.6, between the RR interval and contraction area 0.8, and between the RR interval and maximum of first derivative 0.5. Although small, the first and second to approximately the tenth order coefficients were definitely negative. It is concluded that during a random rhythm the contractile parameters of an isolated heart are strongly related to the preceding RR interval. It is conceivable that this relation contributes to the variability of hemodynamic parameters during atrial fibrillation in man.

Syllectometry: the effect of aggregometer geometry in the assessment of red blood cell shape recovery and aggregation

Syllectometry is a measuring method that is commonly used to assess red blood cell (RBC) aggregability. In syllectometry, light is incident on a layer of whole blood initially exposed to shear flow. The backscattered light is measured after abruptly stopping the driving mechanism. The resultant time-dependent intensity plot is called the syllectogram. Parameters that quantify RBC aggregability are obtained by analyzing the syllectogram. As we will show in this paper, the upstroke in the initial part of the syllectogram contains the information for measurement of RBC-shape recovery in whole blood as well. To estimate RBC-shape recovery, we extended the existing two-exponential mathematical representation of the syllectogram by a third exponent that describes the upstroke. To investigate the feasibility of RBC-shape recovery measurement from the upstroke, we derived an analytical model of the flow decay that follows after abruptly stopping the driving mechanism. The model reveals that for large gaps the flow decay may interfere with the true RBC-shape recovery process. These theoretical findings were confirmed by velocity measurements in a Couette-type aggregometer. Syllectograms obtained using large gaps differ in many respects from those obtained using small gaps. As predicted by our model large gaps show a prolonged apparent shape-recovery time-constant. Moreover, a delayed intensity peak, a reduced upstroke of the intensity peak and a considerable increase of the half-life parameter are observed. The aggregation indices for large gaps are lower than for small gaps. This paper yields a better understanding of the velocity and shear-rate decay following upon abruptly stopping the driving mechanism. A better mathematical representation of the syllectogram and recommendations for a maximum gap width enables both RBC-shape recovery and aggregation measurements in whole blood using syllectometry.