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At least 307 records · Page 17Linked to original sources
PubMedDate not supplied

Modification of DiFrancesco-Noble equations to simulate the effects of vagal stimulation on in vivo mammalian sinoatrial node electrical activity.

We present a new mathematical model for vagal control of rabbit sinoatrial (SA) node electrical activity based on the DiFrancesco-Noble equations. The original equations were found to be unstable, resulting in progressive cycle by cycle depletion or accumulation of ions in intra- and extracellular compartments. This problem was overcome by modifying the maximum Na-K pump current and the time constant for uptake of intracellular calcium. We also included a formulation for the acetylcholine (ACh)-activated potassium current which was consistent with experimental data. This formulation was based on kinetics first proposed by Osterrieder and later modified by Yanagihara. The resulting model exhibits cycle-cycle ionic stability, and includes an ACh-activated potassium current which accurately reproduces experimentally observed effects of vagal stimulation on both the membrane potential and its time-derivative. Simulations were performed for both brief-burst and prolonged vagal stimulation using simplified square wave profiles for the concentration of ACh in the synaptic cleft space. This protocol permits the isolation of cardiac period dynamics caused by changes in membrane potential and intra- and extracellular ionic concentrations from those caused by other mechanisms including the dynamics of ACh release, diffusion, hydrolysis and washout. Simulation results for the effects of brief-burst single cycle stimulation on the cardiac period agree closely with experimental data reported in the literature, accurately reproducing changes in membrane potential and the phasic dependency of the response to the position of vagal stimulus bursts within the cycle. Simulation of the effects of prolonged vagal stimulation accurately reproduced the steady-state characteristics of heart period response, but did not yield the complex multimodal dynamics of the recovery phase, or the pronounced post vagal tachycardia observed experimentally at the termination of the stimulus. Our results show that the major chronotropic effects of vagal stimulation on the SA cell membrane can be explained in terms of the ACh-activated potassium current. The effects of this membrane current however are generally fast acting and cannot contribute to any long lasting dynamics of the cardiac period response. The modified DiFrancesco-Noble model presented in this article provides a valuable theoretical tool for further analysis of the dynamics of vagal control of the cardiac pacemaker.

Acetylcholine↗
PubMedDate not supplied

SENSOP: a derivative-free solver for nonlinear least squares with sensitivity scaling.

Nonlinear least squares optimization is used most often in fitting a complex model to a set of data. An ordinary nonlinear least squares optimizer assumes a constant variance for all the data points. This paper presents SENSOP, a weighted nonlinear least squares optimizer, which is designed for fitting a model to a set of data where the variance may or may not be constant. It uses a variant of the Levenberg-Marquardt method to calculate the direction and the length of the step change in the parameter vector. The method for estimating appropriate weighting functions applies generally to 1-dimensional signals and can be used for higher dimensional signals. Sets of multiple tracer outflow dilution curves present special problems because the data encompass three to four orders of magnitude; a fractional power function provides appropriate weighting giving success in parameter estimation despite the wide range.

Capillaries↗
PubMed1985

Surface integration and least-squares procedures for the inverse recovery of cardiac multipole components.

A simulation study was performed to evaluate different recovery procedures for computing the multipole components of the cardiac electrical activity. A series of dipolar potential distributions was first generated on a realistic numerical model of the human torso. Then, different procedures based on surface integration (SI) and least-squares (LS) minimization were used to compute the multipole components. The parameters of a single moving dipole (SMD) computed from the estimated multipoles were compared with those of the original dipole source. For a finite and homogeneous simulation as well as recovery medium, the results showed that SI employing the potentials over all 1216 surface elements of the torso model was not affected by the various numerical approximations used to perform the integration (e.g., rms error for the SMD position, p = 0.7 mm). By integrating the potentials with truncated capping surfaces at the neck and the waist, the recovery errors increased (p = 2.1 mm). Sampling the potentials at 63 sites, followed by interpolation over the rest of the torso surface, severely affected the SI results for the SMD (p = 6.4 mm), as compared with LS minimization using also 63 values (p = 0.9 mm). With lungs and intraventricular blood masses in the simulation medium but a finite and homogeneous recovery medium, SI was less effective (p = 10.8 mm) than LS (p = 8.6 mm). Adequate compensation for the effects of lungs was obtained by including regions of lower electrical conductivity in the recovery medium for LS, and by a correction matrix for SI. In general, LS gave better results than SI, but with a higher initial computation time.

Electrocardiography↗
PubMed1989

Asymmetry of Doppler spectrum in stenosis differentiation.

The asymmetry of the spectral distribution of ultrasonic Doppler flow velocity signals, assessed using the coefficient of skewness, is discussed as a criterion of stenosis differentiation. Its performance is compared with that of the index of turbulence intensity for both in vitro and in vivo flow Doppler signals, recorded distal to a stenosis. The power spectral distributions are computed using the direct Fourier transform and maximum likelihood method. The asymmetry of spectral distribution has proved to be a more efficient criterion than the turbulence intensity. The maximum likelihood method ensures better stenosis differentiation than the direct FFT method.

Animals↗
PubMed1989

Mathematical model for interpretation of Doppler velocity waveform indices.

Various empirical indices such as the pulsatility index (PI) are widely used for quantitative analysis of Doppler ultrasound velocity waveforms. The physical interpretation of these indices was studied using a mathematical model. Although the method has more general applicability, this particular study was concerned with the umbilical-placental circulation. A lumped element electrical circuit equivalent was used, with each arterial branch represented by a resistor and a capacitor. The placental villous bed was modelled by a two-step parallel branching structure. Placental vascular disease was modelled either as obliteration of a fraction of the terminal branches, or as a fractional decrease in the radius of the vessels. The main features of both normal and abnormal umbilical artery waveforms can be reproduced by this simple model. Theoretical relationships between the velocity waveform indices and the lumped resistances and capacitance of the system were obtained for different input pressure functions. Over a wide range of physically reasonable conditions, the umbilical artery PI is approximately proportional to the ratio of the placental resistance to the umbilical artery resistance. The PI also depends on the pulsatility of the input pressure waveform. The Fourier pulsatility index was evaluated for an arbitrary pressure function, and shown to behave like (PI)2 for the umbilical artery waveform.

Biomedical Engineering↗
PubMed1992

Segmentation, modelling and reconstruction of arterial bifurcations in digital angiography.

The paper presents a method to model an arterial bifurcation from a pair of X-ray angiographic images. It is the initial step of a reconstruction process aiming at detecting and quantifying abnormal sites located on bifurcations. The method proposed consists of two steps. First, each image is independently segmented to extract the vessels in the images. The algorithm uses dynamic programming first to find the bifurcation centrelines from the original images, and secondly to extract vessel edges from the morphological gradient images, under a constraint of parallelism with the previously detected centrelines. Then, a three-dimensional bifurcation model is built by adapting cylinders around the three-dimensional bifurcation centrelines. These cylinders are obtained as a stack of binary orientable ellipses fitted to the projection densities in the corresponding cross-sections. Results obtained on simulated data, phantom and femoral bifurcations are displayed.

Angiography, Digital Subtraction↗
PubMed1995

A kinetic model of coronary reactive hyperemic response to transient ischemia.

A kinetic model is proposed to delineate the factors that determine the coronary reactive hyperemic response (RHR) to transient ischemia. The model comprises of myocardial-interstitial (M) and vascular (V) compartments. Vasodilator metabolites (VM) are produced in the M compartment during the interval of coronary occlusion. The rate of VM production is dependent on the flow rate during the ischemic period, the ratio of excess flow above the control level (R) to the loss of flow during occlusion period (D), the amount of oxygen stored and the degree of vasodilation in the V compartment prior to occlusion. Following a complete release of occlusion, VM are transported from the M to V compartment and are washed out or degraded with time. The time course of RHR is determined by the coronary patency which is proportional to VM concentration in the V compartment. Based on a set of numerical constants, the model is tested by simulating RHR to the various occlusion manoeuvres: a pair of 10 sec occlusions separated by brief release, a 15 sec release followed by a second brief occlusion, a brief release of an occlusion followed by restricted inflow and a period of restricted inflow after occlusion. The simulated results fit the experimental R/D and RH durations data of canine hearts. Factors that determine the impairment of RH capacity in coronary stenosis are suggested in terms of the model scheme.

Animals↗
PubMed1996

Drug delivery to brain tumors.

We develop a macroscopic model for delivering drug to brain tumors. The model accounts for bulk convective and diffusive transport across the blood-brain barrier and through the interstitial space. Through mathematical analysis and simulations, we assess the effects of changing parameters (within physiological bounds) on drug delivery. We find that there is an optimal treatment for convective drug delivery to the center of the tumor. We interpret this phenomenon in terms of traffic flow. The implications of our analyses on existing chemotherapeutic protocols are discussed.

Antineoplastic Agents↗
PubMed1989

Some applications of the P-V relation to the study of left ventricular performance.

There is still controversy as to which characteristics of the pressure-volume relation should be used to define myocardial contractility. In the present study a mathematical model for the left ventricle as a two-dimensional cylinder contracting radially and symmetrically was used to establish a relation between a calculated intramyocardial pressure (Dh) and the P-V relation (PVR) at end-systole. Four new indices are introduced that allow a better assessment of change in inotropic state of the myocardium, namely the calculated intramyocardial pressure (Dh), the calculated resultant pressure across the inner surface of the myocardium (Dh-P) (P = cavity pressure), the work Wt related to the pressure (Dh) and the work Wd related to the pressure (Dh-P). A relation between Wt and Wd and different parts of the area under the PVR is established. Indices derived in this manner from the PVR to study changes in myocardial contractility appear to have a clear physical meaning.

Heart↗
PubMed1996

Analysis of effect of two concurrent ischaemic zones on left ventricular function.

Left ventricular (LV) function due to two concurrent ischaemic zones (IZs) is investigated using a cardiovascular system model. The model comprises a three-compartment LV, the venous return and the arterial system. Haemodynamic responses of the LV to changes in the IZ size and myocardial contraction timings are explored. Results show that the greater the degree of asynschonisation is between the normal zone and the IZ, and the larger the ischaemic size, the more severe the LV dysfunction. Pre-load augmentation improves LV function. Model-predicted features are consistent with reported observations associated with myocardial ischaemia. The extent of the usefulness and limitations of this model is also discussed.

Computer Simulation↗
PubMed1997

Time-frequency analysis of heart murmurs. Part I: Parametric modelling and numerical simulations.

The object of this study is to compare the performance of two new bilinear time-frequency representation techniques with the spectrogram to characterise the behaviour of heart murmurs produced by bioprosthetic heart valves implanted in the mitral or aortic position. The murmurs are those of mitral stenosis, mitral regurgitation, aortic stenosis, aortic regurgitation, a diastolic musical murmur and a systolic musical murmur. In the first part of the study, the general characteristics of the amplitude and the spectral content of these murmurs are determined by visual observation of the spectrogram of phonocardiograms obtained from several patients with known valvular pathology complemented with a literature review. A parametric model is then generated for each murmur signal. Stenotic and regurgitant murmurs are modelled as the sequential output of a bank of low-pass filters excited by a white noise input signal. The basic parameters of each filter are selected to simulate, as a function of time, the basic characteristics of random heart murmurs. Musical murmurs are modelled as a frequency-modulated deterministic sinusoid of constant amplitude. Numerical simulations of these random and musical heart murmurs are then generated and will be used in Part II to determine the best of three time-frequency representation techniques for analysing heart murmur signals.

Aortic Valve↗
PubMed1997

Time-frequency analysis of heart murmurs. Part II: Optimisation of time-frequency representations and performance evaluation.

The basic parameters of the spectrogram, the Choi-Williams, and the Bessel distributions are adjusted to provide the best time-frequency representations (TFRs) of the simulated murmur signals of mitral stenosis, mitral regurgitation, aortic stenosis, aortic regurgitation, and of two musical murmurs. The initial adjustment of the parameters of each TFR technique is performed by computing and minimising the relative averaged absolute error between the frequency contours at -3 dB and -10 dB of each TFR of the simulated murmurs and those of the theoretical distribution of the same signals. The results show that the spectrogram generally provides very good to excellent performance in representing the TFRs of stenotic and regurgitant murmurs. Improvements provided by the Choi-Williams and the Bessel distributions are minor but not systematic for the two signal-to-noise ratios tested (0 and 30 dB) and for the two frequency contours estimated. The Bessel and the Choi-Williams distributions provide the best performance for the musical murmurs. The study shows that although a single technique cannot be optimal for all six murmurs, the spectrogram using a Hamming window of 30 ms is an acceptable compromise to detect the six simulated heart murmurs.

Computer Simulation↗
PubMedDate not supplied

Local intraarterial thrombolysis: in vitro comparison between automatic and manual pulse-spray infusion.

PURPOSE: Manual and automatic pulse-spray infusion techniques are compared in vitro to evaluate the efficacy of thrombolysis and the distribution of urokinase and saline solution within thrombus using a pulse-spray catheter. METHODS: A pulse-spray catheter was introduced into a human thrombus within a stenotic flow model. Automatic and manual pulsed infusion of urokinase and automatic pulsed infusion of saline solution were compared. To quantify the efficacy of thrombolysis, pressure gradients were recorded proximal and distal to the thrombus and during the course of infusion. Distribution of infused urokinase was assessed radiographically. RESULTS: The fastest and most homogeneous dissolution of the thrombus was achieved with automatic pulsed infusion of urokinase, shown by decreasing transthrombotic pressure gradients (p < 0.001, Wilcoxon, matched pairs). Manual pulsed infusion of urokinase or saline solution resulted in inhomogeneous thrombus dissolution and delayed thrombolysis. CONCLUSION: Application of automatic pulse-spray injectors seems beneficial for more effective and homogeneous intraarterial pulse-spray thrombolysis when compared with conventional manual pulsed technique.

Humans↗