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PubMed2005

Kinematic characterization of valvular opening.

The evaluation of the valvular opening due to a pulse flow, as is the case of cardiac valves, requires the knowledge of the leaflets material properties and the coupled solution of the fluid and solid equations. This approach is not commonly feasible. A different approach is introduced here to describe the opening behavior of valvular leaflets by a functional kinematic relationship. The asymptotic analysis, in the limit of leaflet opening without vortex shedding, is presented for a two-dimensional rigid leaflet model under the irrotational scheme. The approach is then verified by numerical solution of the Navier-Stokes equation in asymptotic and nonasymptotic conditions.

Aortic Valve↗
PubMed2005

Phase transition in a healthy human heart rate.

A healthy human heart rate displays complex fluctuations which share characteristics of physical systems in a critical state. We demonstrate that the human heart rate in healthy individuals undergoes a dramatic breakdown of criticality characteristics, reminiscent of continuous second order phase transitions. By studying the germane determinants, we show that the hallmark of criticality--highly correlated fluctuations--is observed only during usual daily activity, and a breakdown of these characteristics occurs in prolonged, strenuous exercise and sleep. This finding is the first reported discovery of the dynamical phase transition phenomenon in a biological control system and will be a key to understanding the heart rate control system in health and disease.

Adult↗
PubMed2005

Asymmetric bound states of spiral pairs in excitable media.

We present a stable regime of asymmetric bound states for spiral pairs in a generic numerical model of a homogeneous excitable medium. In this regime, one spiral tip (slave) rotates around the other (master). Master-slave dynamics occur for both same-chirality and opposite-chirality spiral pairs in a range of parameters and initial conditions. We study the dependency of master-slave characteristics on the medium's excitation threshold and present a phenomenological model that accounts for the qualitative properties of master-slave dynamics.

Models, Cardiovascular↗
PubMed1992

A flexible blood flow phantom capable of independently producing constant and pulsatile flow with a predictable spatial flow profile for ultrasound flow measurement validations.

The validation of the ultrasound time-domain correlation method of measuring blood flow has required the development of a flexible blood flow phantom capable of generating predictable flow profiles under a wide variety of conditions. The purpose of the phantom is to generate flow with well-known flow properties and not to mimic actual in vivo vessels. This paper describes a flow phantom which can independently generate both constant and pulsatile flow over a wide range of flow rates with a spatially fully developed laminar flow profile. It incorporates a computer-controlled pulsatile pump, which can produce different temporal pulsatile waveforms. The flow phantom also supports multiple vessels, different vessel sizes, as well as different attenuating media. The fluid most commonly used in the phantom is Sephadex mixed with water, and the probability density function of ultrasound reflected from Sephadex is experimentally determined and compared with that of blood. Examples of different constant and pulsatile flow experiments using the phantom are presented.

Adult↗
PubMed1992

A physiologic regurgitant cardiac valve phantom for magnetic resonance imaging or color Doppler ultrasound study.

Noninvasive imaging has proven successful in the evaluation of valvular heart disease; primarily with magnetic resonance imaging (MRI) and color Doppler ultrasound (CFM). However, the relationship between the morphology of regurgitant flow in MRI and CFM, as a function of hemodynamic parameters (chamber pressure difference, lesion size, compliance, etc.) is not understood. The goals for this work were: 1) to develop a computer-controlled regurgitant cardiac valve phantom, compatible with artifact-free CFM and MR imaging, 2) to create regurgitant lesions in the phantom which appear similar to those detected clinically, 3) to produce and measure physiologic pressure differences between chambers, compliances, and regurgitant fractions as seen in mild, moderate, and severe regurgitation. Mean chamber pressure differences ranged from 43-142 mmHg over the range of diseases simulated. Similarly, regurgitant flow rates ranged from approximately 0.54-18.6 L/min. Compliance values ranged from 0.83 to 21.95 cc/mmHg. No coherent or incoherent artifacts were observed in MRI or CFM images. Images show a high degree of similarity to regurgitant lesions detected with each modality, confirming that all design goals were met. The system should allow extensive comparative analysis of Doppler ultrasound and MRI flow jets under a wide range of controllable hemodynamic conditions in future experiments.

Aortic Valve Insufficiency↗
PubMed1993

Conductance volumetric model of an eccentrically positioned catheter within a three-compartment ellipsoidal ventricle.

This paper presents a mathematical model of the electric field generated and resistance measured by a conductance catheter within a three-compartment ellipsoidal approximation of a cardiac ventricle. The model is based on a novel combination of analytical and numerical techniques. The numerical component of the model predicts displacement of the catheter along the central longitudinal ventricular axis, as well as eccentric positions off that axis. The analytical component of the model enables interactive definition of model parameters during simulation. This versatile combination enables performance of validation studies that include simulations of various catheter movements within a ventricle of changing geometry. The results of our simulation studies agree with the results of previous investigators studying ex-vivo systems.

Cardiac Catheterization↗
PubMed1993

A model study of extracellular stimulation of cardiac cells.

Point source extracellular stimulation of a myocyte model was used to study the efficacy of excitation of cardiac cells, taking into account the shape of the pulse stimulus and its time of application in the cardiac cycle. The myocyte was modeled as a small cylinder of membrane (10 microns in diameter and 100 microns in length) capped at both ends and placed in an unbounded volume conductor. A Beeler-Reuter model modified for the Na+ dynamics served to simulate the membrane ionic current. The stimulus source was located on the cylinder axis, close to the myocyte (50 microns) in order to generate a nonlinear extracellular field (phi e). The low membrane impedance associated with the high frequency component of the make and break of the rectangular current pulse leads to a current flow across the membrane and an abrupt change in intracellular potential (phi i). Because the intracellular space is very small, phi i is nearly uniform over the length of the myocyte and the membrane potential (V = phi i-phi e) is governed by the applied field phi e. There is then a longitudinal gradient of membrane polarization which is the inverse of the gradient of extracellular potential. With an anodal (positive) pulse, for instance, the proximal portion of the myocyte is hyperpolarized and the distal portion is depolarized. Based on this principle and considering the voltage-dependent activation/inactivation dynamics of the membrane, it is shown that a cathodal (negative) pulse is the most efficacious stimulus at diastolic potentials, an anodal current is preferable during the plateau phase of the action potential, and a biphasic pulse is optimal during the relative refractory phase. Thus a biphasic pulse would constitute the best choice for maximum efficacy at all phases of the action potential.

Action Potentials↗
PubMed1992

Calculating endocardial potentials from epicardial potentials measured during external stimulation.

This paper presents a boundary integral method for calculating the potential field generated by external stimulation at locations within the heart using realistic heart geometry and samples of the potential taken from the epicardial surface. This method assumes the heart is homogeneous and isotropic. To test the method we made epicardial and endocardial measurements in dogs during transthoracic pacing stimuli. From the epicardial potential measurements we predicted the endocardial potential values and compared them with the measured data. Despite the seemingly gross assumptions, the mean correlation coefficient between the measured and predicted potentials for three dogs and eleven stimulation electrode configurations was 0.985, and the mean rms error was 17%.

Action Potentials↗
PubMed1994

Transfer-function analysis of UFCT myocardial time-density curves by time-varying recursive least squares analysis.

Techniques which assume linear, time-invariant systems have been used to characterize indicator dilution pairs. As a basis for fully describing the relation between left ventricular (LV) and myocardial (MYC) time-density curves, produced by an intravenous contrast medium as measured by ultrafast CT, the assumption of time invariance was tested using recursive least squares regression and CUSUM, a test for time variability of regression parameters. Using data from anesthetized dogs with concomitant microsphere information, constant and time-varying regression models, MYC(t) = b(t)LV(t-1), were generated from time-density curves of flows from two groups: Group 1 (MBF < 2 ml/min/gm, n = 11) and Group 2 (MBF > 2 ml/min/gm, n = 10). The time-varying regression models had reduced root mean square error: 0.6 +/- 1.1 and 0.5 +/- 0.8 versus 7.3 +/- 3.5 and 4.1 +/- 1.6 for Groups 1 and 2, respectively. Significant time variability (p < 0.05) by CUSUM was found in 9/11 Group 1 models and 7/10 Group 2 models. Myocardial blood volume was estimated as the average value of b(t) over the rising portion of the LV curve. Myocardial blood flow was then calculated as myocardial blood volume divided by coronary transit time, determined from gamma variate fits of the LV and scaled, shifted LV curve, with excellent results over a wide range of flows (r = 0.93, y = 0.92 x + 0.28, range of 0.4 to 6.7 ml/min/gm). These results show that measurements of increased myocardial blood flow are possible with an intravenous contrast media, and that movement of contrast medium from intravascular space to extravascular space occurs during the course of the contrast medium's first pass.

Animals↗
PubMed1995

Magnetic backprojection imaging of the vascular lumen.

Current injected into a phantom model generated a magnetic field which was distorted above a simulated atherosclerotic lesion. The output of a Hall effect magnetic sensor was used in a backprojection to reconstruct the centroid of the simulated blood flow and thus localize the modeled atherosclerotic plaque region.

Arteries↗
PubMed1996

Maximum likelihood analysis of cardiac late potentials.

This study presents a new time-domain method for the detection of late potentials in individual leads. Basic statistical properties of the ECG samples are modeled in order to estimate the amplitude and duration of late potentials. The signal model accounts for correlation in both time and across the ensemble of beats. Late potentials are modeled as a colored process with unknown amplitude which is disturbed by white, Gaussian noise. Maximum likelihood estimation is applied to the model for estimating the amplitude of the late potentials. The resulting estimator consists of an eigenvector-based filter followed by a nonlinear operation. The performance of the maximum likelihood procedure was compared to that obtained by traditional time-domain analysis based on the vector magnitude. It was found that the new technique yielded a substantial improvement of the signal-to-noise ratio in the function used for endpoint determination. This improvement leads to a prolongation of the filtered QRS duration in cases with late potentials.

Action Potentials↗
PubMed1996

The surface Laplacian of the potential: theory and application.

The use of the surface Laplacian of the potential (Ls) in bioelectricity is discussed. Different estimates of Ls, in particular the field measured by coaxial electrodes, are compared to that of the true Laplacian. A method to compute Ls on the surface of an inhomogeneous volume conductor of arbitrary shape resulting from assumed electrical sources in introduced. In two applications the sensitivity of the body surface Laplacian is carried to that of body surface potentials. This comparison is carried out for dipolar sources within the human brain as well as for distributed sources within the heart.

Body Surface Potential Mapping↗
PubMed1996

Power Doppler ultrasound evaluation of the shear rate and shear stress dependences of red blood cell aggregation.

The use of power Doppler ultrasound at 10 MHz is evaluated as a method to study the shear rate and the shear stress dependences of red blood cell aggregation. This evaluation was based on six in vitro experiments conducted in a 1.27-cm diameter tube under steady flow conditions. Porcine whole blood was circulated in the flow model at flow rates ranging between 125 to 1500 ml/min (mean shear rate across the tube ranging between 6 and 74 s-1). For each flow condition, the variation of the Doppler power across the tube and the velocity profile were measured by moving the Doppler sample volume across the tube diameter. For each radial position, the shear rate within the Doppler sample volume was also determined by considering the radial power pattern of the ultrasound beam. To estimate the shear stress within the Doppler sample volume, the apparent viscosity of blood samples withdrawn from the flow model was measured for each experiment. The variation of the Doppler power as a function of the shear rate within the sample volume showed a rapid reduction of the power between 1 and 5 s-1, a transition region between 5 and 10 s-1, and a very slow reduction beyond 10 s-1. Little variation of the Doppler power was measured for shear stress higher than 2 dyn/cm2. The maximum Doppler power for all flow rates was usually found near the center of the tube. Based on the ultrasonic scattering models, which predict that the Doppler power is related to the volume square of the scatterers, the method described in the present study showed a very high sensitivity to the presence of red blood cell aggregation for shear rates below 10 s-1.

Animals↗
PubMed1990

An adaptive aortic pressure observer for the Penn State Electric Ventricular Assist Device.

This paper addresses the development of an aortic pressure observer for the Penn State Electric Ventricular Assist Device (EVAD). The observer estimates the aortic blood pressure by measuring the voltage of the electric motor and the pusher plate position. The estimated pressure is fedback to the EVAD's blood flow controller, which adjusts the beat rate of the device to accommodate the varying demand of cardiac output. The gains of the observer are deterministically optimized such that the optimal values are independent of the (often unknown) system state initial conditions. To improve the performance of the pressure observer an adaptation scheme is developed. In this scheme the initial pressure estimate of the succeeding systolic cycle is adjusted when the pressure does not match its corresponding second estimated value. In vitro test runs of the developed observer show that is is robust to parameter variations, and the error of the resultant estimated pressure is less than 5%.

Aorta↗
PubMed1996

A model of ultrasound backscatter for the assessment of myocardial tissue structure and architecture.

A statistical parametric model of returning echoes from myocardium is theorized in order to investigate the relationship between normal myocardium structure and spectral signatures with the use of ultrasonic tissue characterization. It is hypothesized, that in a clinical setting the normal myofiber architecture in the left ventricular wall is structured as a matrix of cylinder scatterers whose orientation and spatial distribution vary according to two different statistical distribution laws: 1) a Gaussian law to approximate parametric angular myofiber variability at each site within the myocardial wall; 2) a gamma distribution law to describe parametric regularity in scatterer interdistance. In the model, the effect of the angle of insonification with respect to the alignment of myofibers on ultrasound backscatter was considered. The slope of the power spectral density (PSD) evaluated within the echocardiographic transducer bandwidth has been used as a ultrasonic tissue characterization parameter. The model has been tested by computer simulation and in vitro measurements on myocardial pig tissue specimens. The concordance between experimental and simulated results confirms that the model accounts for the process underlying the echo formation from normal myocardium. Moreover, it provides a simple method of simulation which can be easily implemented and used for the assessment of pathologic alterations.

Animals↗
PubMed1997

Estimation of the ventricular fibrillation duration by autoregressive modeling.

An accurate estimation of ventricular fibrillation (VF) duration could be critical in selecting the most effective therapeutic intervention. We test the hypothesis that changes in frequency content of VF signals can be quantified by using autoregressive (AR) modeling, and the duration since the onset of VF can be estimated by using this method. VF signals were recorded for up to 300 s in five isolated rabbit hearts. Fourth-order AR parameters of successive segments were estimated, and frequencies of the first poles (the pole with lower frequency) were pooled together and a curve was fitted: F(t) = A exp (-alpha t) + B, where F(t) is the estimated frequency of the first pole at t'th time instant, alpha is the decay constant, B is the offset frequency, and A is the frequency at time zero minus the offset frequency. The utility of this curve in estimating the VF duration was tested in four new experiments, and the difference between the actual and the estimated VF duration (estimation error) was calculated. F(t), the frequency of the first pole, decreased from 12 to 6 Hz with duration of:VF, while the frequency of the other pole decreased from 25 to 20 Hz. Parameters of the fitted curve were calculated as A = 7.8, alpha = 0.0041 and B was selected as four. Testing on a new set of VF signals produced very little estimation error for the first 100 s of VF, although this error increased with VF duration. For these new signals, the mean value of the absolute estimation error was 26 s. Results of this study show that changes in the frequency content of electrocardiogram (ECG) during VF can be quantified by AR modeling and that the frequency changes associated with a pole of this model can be used to estimate the VF duration.

Algorithms↗
PubMed1998

Incorporating O2-Hb reaction kinetics and the Fåhraeus effect into a microcirculatory O2-CO2 transport model.

The influence of O2-Hb reaction kinetics and the Fåhraeus effect on steady state O2 and CO2 transport in cat brain microcirculation was investigated using our refined multicompartmental model. The most important model predictions include: 1) capillaries are the sites in the microcirculation where the effect of O2-Hb kinetics is most pronounced; 2) while there is only a small difference between equilibrium and actual oxygen saturation, this effect is not negligible; 3) O2-Hb kinetics tends to make the PO2 level at the venous entrance higher than in venules; 4) the influence of the Fåhraeus effect leads to a lower tissue PO2 level than in venules and the outlet vein. The resultant decline in tissue PO2 may lead to a decrease in O2 consumption rate and extraction ratio; 5) although the Fåhraeus effect changes the ratio between arteriolar flux and capillary flux, incorporating the Fåhraeus effect and O2-Hb kinetics into the simulation does not change our previous conclusion, that most of the O2 and CO2 exchange takes place at the capillary level; 6) in general, influences of O2-Hb kinetics and Fåhraeus effect are synergistic; 7) a model that excludes these two mechanisms might overestimate the tissue oxygenation level especially during severe hypoxia.

Algorithms↗
PubMed1998

A mathematical analysis on the biological zero problem in laser Doppler flowmetry.

The biological zero (BZ) problem is a critical issue inherent in laser Doppler flowmetry (LDF). It causes confusion when measuring low tissue blood flows. Many experimental studies have been done on the question of whether the BZ flux should be subtracted from the normally measured flux in various situations. However this problem can only be solved after a proper mathematical analysis. Only then can we clearly define and formulate what flux is truly meaningful in blood perfusion measurement and what movement generates the BZ flux and how can we correctly remove it. Following this motivation, the movement of moving blood cells (MBC's) is decomposed into a net translation and a random wondering based on in vivo observations. This important step leads to a clear definition of the BZ and net perfusion flux and reveals that subtraction of BZ flux from the normal flux will certainly cause an underestimation of the net flux. Using this decomposition, the relationship between the net, BZ and normal flux is established which leads to the correct formula to recover the net flux from the BZ and normal fluxes. This recovered net flux is shown to be bounded by the normal flux and the normal flux minus the BZ flux. Numerical studies, preliminary phantom model and clinical evaluations manifest that the new approach is more accurate and reasonable at measuring low net fluxes. In contrast, subtracting BZ flux causes a systematic underestimation of perfusion and is apparently inappropriate even from a methodological point of view. In addition to the novel BZ solution, a general density function of the speed of MBC's is given which is more faithful than the Maxwell density used in [4]. This general density function offers new possibilities for further theoretical developments in LDF.

Capillaries↗