Blind identification of the aortic pressure waveform from multiple peripheral artery pressure waveforms

We have developed a new technique to estimate the clinically relevant aortic pressure waveform from multiple, less invasively measured peripheral artery pressure waveforms. The technique is based on multichannel blind system identification in which two or more measured outputs (peripheral artery pressure waveforms) of a single-input, multi-output system (arterial tree) are mathematically analyzed so as to reconstruct the common unobserved input (aortic pressure waveform) to within an arbitrary scale factor. The technique then invokes Poiseuille's law to calibrate the reconstructed waveform to absolute pressure. Consequently, in contrast to previous related efforts, the technique does not utilize a generalized transfer function or any training data and is therefore entirely patient and time specific. To demonstrate proof of concept, we have evaluated the technique with respect to four swine in which peripheral artery pressure waveforms from the femoral and radial arteries and a reference aortic pressure waveform from the descending thoracic aorta were simultaneously measured during diverse hemodynamic interventions. We report that the technique reliably estimated the entire aortic pressure waveform with an overall root mean squared error (RMSE) of 4.6 mmHg. For comparison, the average overall RMSE between the peripheral artery pressure and reference aortic pressure waveforms was 8.6 mmHg. Thus the technique reduced the RMSE by 47%. As a result, the technique also provided similar improvements in the estimation of systolic pressure, pulse pressure, and the ejection interval. With further successful testing, the technique may ultimately be employed for more precise monitoring and titration of therapy in, for example, critically ill and hypertension patients.     

The Gurvich waveform has lower defibrillation threshold than the rectilinear waveform and the truncated exponential waveform in the rabbit heart

Implantable cardioverter defibrillator studies have established the superiority of biphasic waveforms over monophasic waveforms. However, external defibrillator studies of biphasic waveforms are not as widespread. Our objective was to compare the defibrillation efficacy of clinically used biphasic waveforms, i.e., truncated exponential, rectilinear, and quasi-sinusoidal (Gurvich) waveforms in a fibrillating heart model. Langendorff-perfused rabbit hearts (n = 10) were stained with a voltage-sensitive fluorescent dye, Di-4-ANEPPS. Transmembrane action potentials were optically mapped from the anterior epicardium. We found that the Gurvich waveform was significantly superior (p < 0.05) to the rectilinear and truncated exponential waveforms. The defibrillation thresholds (mean +/- SE) were as follows: Gurvich, 0.25 +/- 0.01 J; rectilinear-1, 0.34 +/- 0.01 J; rectilinear-2, 0.33 +/- 0.01 J; and truncated exponential, 0.32 +/- 0.02 J. Using optically recorded transmembrane responses, we determined the shock-response transfer function, which allowed us to predict the cellular response to waveforms at high accuracy. The passive parallel resistor-capacitor model (RC-model) predicted polarization superiority of the Gurvich waveform in the myocardium with a membrane time constant (taum) of less than 2 ms. The finding of a lower defibrillation threshold with the Gurvich waveform in an in vitro model of external defibrillation suggests that the Gurvich waveform may be important for future external defibrillator designs.     

Reverse flow in the major infrarenal vessels--a capacitive phenomenon

The arterial blood flow waveform is shown to change abruptly when passing from the thoracic aorta into the abdominal aorta in humans. Although this change has been accurately predicted by numerical solution of complicated pulse propagation equations, this paper demonstrates the ability of a simple lumped parameter model to explain this change in the waveforms using easily understood physical terms. The model correctly predicts changes in flow waveform under conditions of exercise and peripheral vascular disease. This analysis is useful in understanding abdominal artery physiology and explains the basis for clinical ultrasound Doppler examination of the legs.     

Computer simulation of blood flow in the human arm

This paper considers a finite element method to characterize blood flow in the human arm arteries. A set of different pressure waveforms, which represent normal and diseased heart pulses, is used for the proximal boundary conditions, and a modified Windkessel model is used for the distal arterial boundary conditions. A comparison of the distal pressure and flow waveforms, for each different proximal pressure, is made to determine whether such waveforms are significantly altered from normal waveforms. The results show that the distal pressure and/or flow waveforms in certain cases are sufficiently different to be possibly used as a diagnostic indicator of an abnormal heart condition. Also considered is the effect of stenosis, change of compliance, and dilatation of the distal beds on the pressure and flow waveforms. A stenosis which has an area reduction of greater than approximately 75% is found to significantly alter both the distal pressure and flow waveforms. Changes in arterial compliance, however, do not strongly influence the waveforms. Dilatation of distal vascular beds is simulated by reducing the lumped resistance of these beds, and this reduction increases mean flow and decreases mean distal pressure, but has little effect on the basic shape of either the pressure or flow waveform.     

The Dynamic Characteristics of Color-Coded S-Potentials

A linear analysis approach has been applied to determine the dynamic characteristics of the color-coded S-potentials. Using a sinusoidally modulated light stimulus it could be shown that the monophasic S-potential as well as each of the different components of biphasic and triphasic S-potentials behaves linearly. However, for high modulation depths and high average intensities nonlinear effects, such as saturation, become obvious. The transfer characteristics of the monophasic potentials and each component of the biphasic and triphasic potentials are indistinguishable. Their latencies, however, differ. These findings suggest that the three different types of S-potentials not only originate from functionally comparable cells but also that the dynamic characteristics of the cells presynaptic to the S-potential sources are identical.     

The effect of blood viscoelasticity on pulsatile flow in stationary and axially moving tubes

An analytical solution for pulsatile flow of a generalized Maxwell fluid in straight rigid tubes, with and without axial vessel motion, has been used to calculate the effect of blood viscoelasticity on velocity profiles and shear stress in flows representative of those in the large arteries. Measured bulk flow rate Q waveforms were used as starting points in the calculations for the aorta and femoral arteries, from which axial pressure gradient ▿P waves were derived that would reproduce the starting Q waves for viscoelastic flow. The ▿P waves were then used to calculate velocity profiles for both viscoelastic and purely viscous flow. For the coronary artery, published ▿P and axial vessel acceleration waveforms were used in a similar procedure to determine the separate and combined influences of viscoelasticity and vessel motion.Differences in local velocities, comparing viscous flow to viscoelastic flow, were in all cases less than about 2% of the peak local velocity. Differences in peak wall shear stress were less than about 3%.In the coronary artery, wall shear stress differences between viscous and viscoelastic flow were small, regardless of whether axial vessel motion was included. The shape of the wall shear stress waveform and its difference, however, changed dramatically between the stationary and moving vessel cases. The peaks in wall shear stress difference corresponded with large temporal gradients in the combined driving force for the flow.     

Exercise reduces arterial pressure augmentation through vasodilation of muscular arteries in humans

Exercise markedly influences pulse wave morphology, but the mechanism is unknown. We investigated whether effects of exercise on the arterial pulse result from alterations in stroke volume or pulse wave velocity (PWV)/large artery stiffness or reduction of pressure wave reflection. Healthy subjects (n = 25) performed bicycle ergometry. with workload increasing from 25 to 150 W for 12 min. Digital arterial pressure waveforms were recorded using a servo-controlled finger cuff. Radial arterial pressure waveforms and carotid-femoral PWV were determined by applanation tonometry. Stroke volume was measured by echocardiography, and brachial and femoral artery blood flows and diameters were measured by ultrasound. Digital waveforms were recorded continuously. Other measurements were made before and after exercise. Exercise markedly reduced late systolic and diastolic augmentation of the peripheral pressure pulse. At 15 min into recovery, stroke volume and PWV were similar to baseline values, but changes in pulse wave morphology persisted. Late systolic augmentation index (radial pulse) was reduced from 54 +/- 3.9% at baseline to 42 +/- 3.7% (P < 0.01), and diastolic augmentation index (radial pulse) was reduced from 37 +/- 1.8% to 25 +/- 2.9% (P < 0.001). These changes were accompanied by an increase in femoral blood flow (from 409 +/- 44 to 773 +/- 48 ml/min, P < 0.05) and an increase in femoral artery diameter (from 8.2 +/- 0.4 to 8.6 +/- 0.4 mm, P < 0.05). In conclusion, exercise dilates muscular arteries and reduces arterial pressure augmentation, an effect that will enhance ventricular-vascular coupling and reduce load on the left ventricle.     

1D simulation of blood flow characteristics in the circle of Willis using THINkS

One-dimensional (1D) simulation of the complete vascular network, so called THINkS (Total Human Intravascular Network Simulation) is developed to investigate changes of blood flow characteristics caused by the variation of CoW. THINkS contains 158 major veins, 85 major arteries, and 77 venous and 43 arterial junctions. THINkS is validated with available in vivo blood flow waveform data. The overall trends of flow rates in variations of the CoW, such as the missing anterior cerebral artery (missing-A1) or missing posterior cerebral artery (missing-P1), are confirmed by in vivo experimental data. It is demonstrated that the CoW has the ability to shunt blood flow to different areas in the brain. Flow rates in efferent arteries remain unaffected under the variation of CoW, while the flow rates in afferent vessels can be subject to substantial changes. The redistribution of blood flow can cause particular vessels to undergo extra flow rate and hemodynamic stresses.     

A finite-element model of blood flow in arteries including taper, branches, and obstructions

A nonlinear mathematical model of arterial blood flow, which can account for tapering, branching, and the presence of stenosed segments, is presented. With the finite-element method, the model equations are transformed into a system of algebraic equations that can be solved on a high-speed digital computer to yield values of pressure and volume rate of flow as functions of time and arterial position. A model of the human femoral artery is used to compare the effects of linear and nonlinear modeling. During periods of rapid alternations in pressure or flow, the nonlinear model shows significantly different results than the linear model. The effect of a stenosis on pressure and flow waveforms is also simulated, and the results indicate that these waveforms are significantly altered by moderate and severe stenoses.     

The role of biphasic shocks for transthoracic cardioversion of atrial fibrillation

The modern generation of transthoracic defibrillators now employ impedance compensated biphasic waveforms. These new devices are superior to those with monophasic waveforms and practice is currently switching to biphasic defibrillators for the treatment of both ventricular and atrial fibrillation. However, there is no universal guideline for the use of biphasic defibrillators in direct current cardioversion of atrial fibrillation. This article reviews the use of biphasic defibrillation waveforms for transthoracic cardioversion of atrial fibrillation.     

Distally based free flap using retrograde arterial flow

In lower extremity injuries, the major arteries are frequently damaged and the remaining artery may be located in the traumatized zone. Recently, vascular anastomoses to recipient vessels distal to the zone of injuries have been advocated in the lower limb reconstruction and flaps by using retrograde arterial flow are well established in island flaps. Twelve patients with soft-tissue defects below the knee underwent lower extremity reconstruction with distally based free flaps by using retrograde arterial flow. For assessment of retrograde flow, the intraoperative retrograde arterial pressure was quantitated and compared with the systolic blood pressure taken at the same time (n = 6). In this study, suitable candidates had been chosen with pulsatile retrograde flow from the distal cut end of the vessel because patients without pulsatile flow had recorded diastolic and systolic retrograde arterial pressures that were very low. Four different free flaps were used. All flaps were successful. Retrograde flow anastomosis could not interrupt the major blood vessels, which were essential for survival of the distal limb, the compromise of fracture or wound healing might be prevented. In cases in which arteriography demonstrates significant vascular flow interruption within the zone of injury, retrograde arterial anastomosis may also be a candidate.     

Analysis of electric field stimulation of single cardiac muscle cells.

Electrical stimulation of cardiac cells by imposed extracellular electric fields results in a transmembrane potential which is highly nonuniform, with one end of the cell depolarized and the other end hyperpolarized along the field direction. To date, the implications of the close proximity of oppositely polarized membranes on excitability have not been explored. In this work we compare the biophysical basis for field stimulation of cells at rest with that for intracellular current injection, using three Luo-Rudy type membrane patches coupled together as a lumped model to represent the cell membrane. Our model shows that cell excitation is a function of the temporal and spatial distribution of ionic currents and transmembrane potential. The extracellular and intracellular forms of stimulation were compared in greater detail for monophasic and symmetric biphasic rectangular pulses, with duration ranging from 0.5 to 10 ms. Strength-duration curves derived for field stimulation show that over a wide range of pulse durations, biphasic waveforms can recruit and activate membrane patches about as effectively as can monophasic waveforms having the same total pulse duration. We find that excitation with biphasic stimulation results from a synergistic, temporal summation of inward currents through the sodium channel in membrane patches at opposite ends of the cell. Furthermore, with both waveform types, a net inward current through the inwardly rectifying potassium channel contributes to initial membrane depolarization. In contrast, models of stimulation by intracellular current injection do not account for the nonuniformity of transmembrane potential and produce substantially different (even contradictory) results for the case of stimulation from rest.     

Computational assessment of model-based wave separation using a database of virtual subjects

The quantification of arterial wave reflection is an important area of interest in arterial pulse wave analysis. It can be achieved by wave separation analysis (WSA) if both the aortic pressure waveform and the aortic flow waveform are known. For better applicability, several mathematical models have been established to estimate aortic flow solely based on pressure waveforms. The aim of this study is to investigate and verify the model-based wave separation of the ARCSolver method on virtual pulse wave measurements.The study is based on an open access virtual database generated via simulations. Seven cardiac and arterial parameters were varied within physiological healthy ranges, leading to a total of 3325 virtual healthy subjects. For assessing the model-based ARCSolver method computationally, this method was used to perform WSA based on the aortic root pressure waveforms of the virtual patients. As a reference, the values of WSA using both the pressure and flow waveforms provided by the virtual database were taken.The investigated parameters showed a good overall agreement between the model-based method and the reference. Mean differences and standard deviations were −0.05 ± 0.02 AU for characteristic impedance, −3.93 ± 1.79 mmHg for forward pressure amplitude, 1.37 ± 1.56 mmHg for backward pressure amplitude and 12.42 ± 4.88% for reflection magnitude.The results indicate that the mathematical blood flow model of the ARCSolver method is a feasible surrogate for a measured flow waveform and provides a reasonable way to assess arterial wave reflection non-invasively in healthy subjects.     

The effect of inlet waveforms on computational hemodynamics of patient-specific intracranial aneurysms

Due to the lack of patient-specific inlet flow waveform measurements, most computational fluid dynamics (CFD) simulations of intracranial aneurysms usually employ waveforms that are not patient-specific as inlet boundary conditions for the computational model. The current study examined how this assumption affects the predicted hemodynamics in patient-specific aneurysm geometries. We examined wall shear stress (WSS) and oscillatory shear index (OSI), the two most widely studied hemodynamic quantities that have been shown to predict aneurysm rupture, as well as maximal WSS (MWSS), energy loss (EL) and pressure loss coefficient (PLc). Sixteen pulsatile CFD simulations were carried out on four typical saccular aneurysms using 4 different waveforms and an identical inflow rate as inlet boundary conditions. Our results demonstrated that under the same mean inflow rate, different waveforms produced almost identical WSS distributions and WSS magnitudes, similar OSI distributions but drastically different OSI magnitudes. The OSI magnitude is correlated with the pulsatility index of the waveform. Furthermore, there is a linear relationship between aneurysm-averaged OSI values calculated from one waveform and those calculated from another waveform. In addition, different waveforms produced similar MWSS, EL and PLc in each aneurysm. In conclusion, inlet waveform has minimal effects on WSS, OSI distribution, MWSS, EL and PLc and a strong effect on OSI magnitude, but aneurysm-averaged OSI from different waveforms has a strong linear correlation with each other across different aneurysms, indicating that for the same aneurysm cohort, different waveforms can consistently stratify (rank) OSI of aneurysms.     

Effect of alterations in femoral artery flow on abdominal vessel hemodynamics in swine

In support of an in vivo investigation in swine of the influence of changes in fluid dynamic wall shear on arterial macromolecular permeability, a procedure has been developed to alter the flows in the porcine posterior arterial vasculature by opening and closing a reversible arteriovenous shunt placed on one of the femoral arteries. Laparoscopic techniques were used to place appropriately modified Transonic Systems ultrasonic flow probes on both external and circumflex iliac arteries, and on the terminal aorta. Flow measurements were made prior to shunt placement, and with the shunt open and closed, to measure the influence of altered external iliac artery flow on the distribution to the infrarenal abdominal vessels. Similar experiments were carried out to relate the flow rates in the external iliac arteries to those in the femoral arteries, which are more accessible. Based on the relationships among the measured flow rates, rules have been developed to estimate the major infrarenal flows in the pig, at baseline and with the shunt opened and closed, from only the flow rates measured at the two femoral arteries.     

Abnormal arterial flows by a distributed model of the fetal circulation

Modeling the propagation of blood pressure and flow along the fetoplacental arterial tree may improve interpretation of abnormal flow velocity waveforms in fetuses. The current models, however, either do not include a wide range of gestational ages or do not account for variation in anatomical, vascular, or rheological parameters. We developed a mathematical model of the pulsating fetoumbilical arterial circulation using Womersley's oscillatory flow theory and viscoelastic arterial wall properties. Arterial flow waves are calculated at different arterial locations from which the pulsatility index (PI) can be determined. We varied blood viscosity, placental and brain resistances, placental compliance, heart rate, stiffness of the arterial wall, and length of the umbilical arteries. The PI increases in the umbilical artery and decreases in the cerebral arteries, as a result of increasing placental resistance or decreasing brain resistance. Both changes in resistance decrease the flow through the placenta. An increased arterial stiffness increases the PIs in the entire fetoplacental circulation. Blood viscosity and peripheral bed compliance have limited influence on the flow profiles. Bradycardia and tachycardia increase and decrease the PI in all arteries, respectively. Umbilical arterial length has limited influence on the PI but affects the mean arterial pressure at the placental cord insertion. The model may improve the interpretation of arterial flow pulsations and thus may advance both the understanding of pathophysiological processes and clinical management.     

Flow-induced control of arterial lumen

Blood flow velocity is a factor that affects the diameter of arteries. In order to investigate the flow-induced arterial dilatation, the outer diameter of the femoral, common carotid or renal arteries of anaesthetized cats was measured during perfusion of these arteries with blood or plasma-substituting solutions under conditions of stabilized perfusion pressure. It has been shown that, whatever the perfusate, blood or a substituent, an increase in flow makes the artery to dilate. Consequently, the flow-induced dilatation is not due to any blood-borne humoral factor. As an increase in the solution's viscosity causes dilatation even at constant flow-rate and pressure in the artery, the effect is to be ascribed to the ability of the vascular wall to perceive shear stress. As far as removal of endothelium eliminates the dilatation evoked by increasing flow or fluid viscosity, it may be concluded that the flow-induced dilatation is due to the sensitivity to shear stress of the endothelium.     

Toward a noninvasive subject-specific estimation of abdominal aortic pressure

A method for estimation of central arterial pressure based on linear one-dimensional wave propagation theory is presented in this paper. The equations are applied to a distributed model of the arterial tree, truncated by three-element windkessels. To reflect individual differences in the properties of the arterial trees, we pose a minimization problem from which individual parameters are identified. The idea is to take a measured waveform in a peripheral artery and use it as input to the model. The model subsequently predicts the corresponding waveform in another peripheral artery in which a measurement has also been made, and the arterial tree model is then calibrated in such a way that the computed waveform matches its measured counterpart. For the purpose of validation, invasively recorded abdominal aortic, brachial, and femoral pressures in nine healthy subjects are used. The results show that the proposed method estimates the abdominal aortic pressure wave with good accuracy. The root mean square error (RMSE) of the estimated waveforms was 1.61 +/- 0.73 mmHg, whereas the errors in systolic and pulse pressure were 2.32 +/- 1.74 and 3.73 +/- 2.04 mmHg, respectively. These results are compared with another recently proposed method based on a signal processing technique, and it is shown that our method yields a significantly (P < 0.01) lower RMSE. With more extensive validation, the method may eventually be used in clinical practice to provide detailed, almost individual, specific information as a valuable basis for decision making.     

Particle deposition in arteries ex vivo: effects of pressure,flow, and waveform

The goal of this study was to quantify the effect of hemodynamic pressure, flow and waveform perturbations on the deposition of protein-sized particles in porcine carotid arteries ex vivo. An ex vivo perfusion system was used to control the pressure and flow environment for excised arterial tissue. Confocal laser microscopy images revealed that 200 nm particles were deposited intimally and that more spheres were evident along vessels perfused under oscillatory waveform conditions than all others. Under all pressure, flow and waveform conditions, particles were excluded from the media and adventitia of the vessel wall. The steady flow data support the use of Darcy's Law with pressure-dependent hydraulic permeability to model arterial tissue.     

Wave propagation in a model of the arterial circulation

The propagation of the arterial pulse wave in the large systemic arteries has been calculated using a linearised method of characteristics analysis to follow the waves generated by the heart. The model includes anatomical and physiological data for the 55 largest arteries adjusted so that the bifurcating tree of arteries is well matched for forward travelling waves. The peripheral arteries in the model are terminated by resistance elements which are adjusted to produce a physiologically reasonable distribution of mean blood flow. In the model, the pressure and velocity wave generated by the contraction of the left ventricle propagates to the periphery where it is reflected. These reflected waves are re-reflected by each of the bifurcations that they encounter and a very complex pattern of waves is generated. The results of the calculations exhibit many of the features of the systemic arteries, including the increase of the pulse pressure with distance away from the heart as well as the initial decrease and then the large increase in the magnitude of back flow during late systole going from the ascending aorta to the abdominal aorta to the arteries of the leg. The model is then used to study the effects of the reflection or absorption of waves by the heart and the mechanisms leading to the incisura are investigated. Calculations are carried out with the total occlusion of different arterial segments in order to model experiments in which the effects of the occlusion of different arteries on pressure and flow in the ascending aorta were measured. Finally, the effects of changes in peripheral resistance on pressure and velocity waveforms are also studied. We conclude from these calculations that the complex pattern of wave propagation in the large arteries may be the most important determinant of arterial haemodynamics.