Computationally Efficient Fluid-Particle Dynamics Simulations of Arterial Systems

Realistic and accurate computer simulations of the particle-hemodynamics in arterial systems can be a valuable tool for numerous biomedical applications. Examples include optimal by-pass grafting and optimal drug-delivery, as well as best medical management concerning the cardio-vascular system. However, such numerical analyses require large computer resources which may become prohibitive for extended sets of arterial bifurcations. A remedy is to develop a hybrid model where the first few generations of the bifurcating arteries of interest are simulated in full 3-D, while a 1-D model is then coupled for subsequent bifurcations. Alternatively, a 1-D computer model can be directly employed to simulate fluid-particle transport in complex bifurcating networks.Relying on a representative axial velocity profile, a physiological 1-D model has been developed and validated, which is capable of predicting with reasonable accuracy arterial flow, pressure field and elastic wall interaction as well as particle transport. The usefulness of the novel 1-D simulation approach is demonstrated via a comparison to 3-D blood flow and microsphere transport in a hepatic artery system, featuring as outlets one major branch and four small daughter vessels. Compared to the 3-D simulation, the 1-D analysis requires only about 1% of computational time. The hybrid modeling approach would be also applicable to the human respiratory tract to evaluate the fate of inhaled aerosols.A simple and cost-effective way to simulate particle-hemodynamics is using a 1-D model for simulating arterial pressures and flow rates as well as microsphere transport, based on assumptions involving the use of a simple algebraic pressure-area relation, an exponential elasticity model for the vessels, and considering only unidirectional flow with a representative skewed velocity profile. In summary, the novel contributions are:• Particle tracking in arteries via 1-D fluid modeling and selection of an averaged, skewed velocity profile based on 3-D simulation results to provide more realistic friction and inertia term values for modeling a flow system with bifurcations.• The 1-D model can be coupled to a 3-D model so that simulations can be run for larger regions of vascular or lung-airway systems.     

A New Method for Calculating Total Respiratory System Compliance Theory and Model Experiments

A new method for calculating total respiratory system compliance is described, based on simple modelling of a ventilator-respiratory system circuit that assumes linear characteristics of the circuit parameters compliances and resistances. The method requires only that flow measurement be conducted continuously to obtain compliance, if the internal compliance of the circuit is known beforehand. Model experiments showed that the compliance of a child test lung, calculated from the flow recording, differed at most by 10% from the compliance obtained by separate measurements of pressure and volume under static conditions, over a wide range of respiratory flows and airway resistances.     

Hemodynamic Impact of the C‐Pulse Cardiac Support Device: A One‐Dimensional Arterial Model Study

The C‐Pulse is a novel extra‐aortic counter‐pulsation device to unload the heart in patients with heart failure. Its impact on overall hemodynamics, however, is not fully understood. In this study, the function of the C‐Pulse heart assist system is implemented in a one‐dimensional (1‐D) model of the arterial tree, and central and peripheral pressure and flow waveforms with the C‐Pulse turned on and off were simulated. The results were studied using wave intensity analysis and compared with in vivo data measured non‐invasively in three patients with heart failure and with invasive data measured in a large animal (pig). In all cases the activation of the C‐Pulse was discernible by the presence of a diastolic augmentation in the pressure and flow waveforms. Activation of the device initiates a forward traveling compression wave, whereas a forward traveling expansion wave is associated to the device relaxation, with waves exerting an action in the coronary and the carotid vascular beds. We also found that the stiffness of the arterial tree is an important determinant of action of the device. In settings with reduced arterial compliance, the same level of aortic compression demands higher values of external pressure, leading to stronger hemodynamic effects and enhanced perfusion. We conclude that the 1‐D model may be used as an efficient tool for predicting the hemodynamic impact of the C‐Pulse system in the entire arterial tree, complementing in vivo observations.     

Design and initial testing of a mock human circulatory loop for left ventricular assist device performance testing

A mock circulatory loop, which simulates the human circulatory system, is needed to bench test the various versions of continuous flow (CF) left ventricular assist devices (LVADs). This article describes the design and initial testing of such a loop. The loop consists of: (1) pulsatile left and right cardiac simulators; (2) air/water tanks to model the venous and arterial compliances; (3) tygon tubes to model the venous, arterial, and other system flow resistances; and (4) a tuning clamp to model the variation in system resistance characteristics under different cardiac pressure/flow conditions. Several loop measurements were carried out without an LVAD to verify the cardiovascular modeling of a healthy person in sleep, rest, and physical activity, and in different pathological states, and compared to the data found in the literature to validate the loop performance prior to LVAD testing.     

Changes in cerebral compartmental compliances during mild hypocapnia in patients with traumatic brain injury

The benefit of induced hyperventilation for intracranial pressure (ICP) control after severe traumatic brain injury (TBI) is controversial. In this study, we investigated the impact of early and sustained hyperventilation on compliances of the cerebral arteries and of the cerebrospinal (CSF) compartment during mild hyperventilation in severe TBI patients. We included 27 severe TBI patients (mean 39.5 ± 3.4 years, 6 women) in whom an increase in ventilation (20% increase in respiratory minute volume) was performed during 50 min as part of a standard clinical CO(2) reactivity test. Using a new mathematical model, cerebral arterial compliance (Ca) and CSF compartment compliance (Ci) were calculated based on the analysis of ICP, arterial blood pressure, and cerebral blood flow velocity waveforms. Hyperventilation initially induced a reduction in ICP (17.5 ± 6.6 vs. 13.9 ± 6.2 mmHg; p < 0.001), which correlated with an increase in Ci (r(2)?= 0.213; p = 0.015). Concomitantly, the reduction in cerebral blood flow velocities (CBFV, 74.6 ± 27.0 vs. 62.9 ± 22.9 cm/sec; p < 0.001) marginally correlated with the reduction in Ca (r(2)?= 0.209; p = 0.017). During sustained hyperventilation, ICP increased (13.9 ± 6.2 vs. 15.3 ± 6.4 mmHg; p < 0.001), which correlated with a reduction in Ci (r(2)?= 0.297; p = 0.003), but no significant changes in Ca were found during that period. The early reduction in Ca persisted irrespective of the duration of hyperventilation, which may contribute to the lack of clinical benefit of hyperventilation after TBI. Further studies are needed to determine whether monitoring of arterial and CSF compartment compliances may detect and prevent an adverse ischemic event during hyperventilation.     

Effects of phenylephrine on transmural distribution of myocardial blood flow in regions supplied by normal and collateral arteries during cardiopulmonary bypass.

Cardiopulmonary bypass is frequently accompanied by decreased peripheral vascular resistance with resultant hypotension that is unresponsive to increased flow rates. Alpha adrenergic agonists are routinely used to increase peripheral vascular resistance and augment blood pressure. In this study, the effects of the alpha adrenergic stimulant phenylephrine on blood flow distribution during cardiopulmonary bypass in myocardium supplied by normal and collateral arteries were studied in eight mongrel dogs. Microsphere determinations of blood flow were made following augmentation of perfusion pressure with phenylephrine and were compared with intraoperative normotensive and hypotensive control levels. With systemic flow rates held constant, phenylephrine was infused in doses adequate to raise perfusion pressure to normotensive levels following hypotension. In the normal region (NR), blood flow was returned to normotensive control levels with flow favoring the subendocardium. In the region supplied by collateral vessels (CR), however, phenylephrine infusion failed to return flow to the normotensive control level in the subendocardial layer, and the flow imbalance present during hypotension was not corrected. An analogue model of the calculable resistances in the CR is presented, which indicates that phenylephrine increased resistance in the collateral vessels. Associated with this inflow restriction is decreased resistance or vasodilatation of the intramyocardial vessels supplied by collateral coronary arteries.     

THE HALOSCALE "INFANTA" WRIGHT RESPIROMETER: An In Vitro and In Vivo Assessment

The performance of the Haloscale "Infanta" respirometer hasbeen assessed in vitro using ISO test compliances and resistances,and in vivo by comparison with pneumotachograph volumes in 13spontaneously breathing children and 13 children during intermittentpositive pressure ventilation. The Infanta was shown to be capableof registering volumes between 15 and 200 ml with an accuracyof ±5%. The registered volume decreased rapidly below15 ml, whilst above 200 ml over-registration developed.     

Intraluminal velocity profile analyzed from flow waveforms

Normal and abnormal flow waveforms, electromagnetically measured in the reconstructed arteries of patients with peripheral occlusive diseases of the lower extremity, were analyzed in terms of luminal velocity profile, using a newly designed flow wave simulation pump. The blood flow with normal flow wave was characterized by a large fluctuation in the velocity profile in the limited layer adjacent to the wall, where a reversal stream was characteristically noted during the phase of cardiac diastole. In contrast, in the abnormal flow wave, the velocity profile in the limited layer adjacent to the wall was always stagnant with little change in the velocity during each phase of a cardiac cycle. These observations clearly explain why an artery with a normal flow waveform remains patent, while an artery with an abnormal waveform tends to occlude. It was also found that the electromagnetically determined flow waveforms do provide the required information on the luminal velocity distribution.     

A Strong Stability-Preserving Predictor-Corrector Method for the Simulation of Elastic Wave Propagation in Anisotropic Media

In this paper, we propose a strong stability-preserving predictor-corrector (SSPC) method based on an implicit Runge-Kutta method to solve the acoustic- and elastic-wave equations. We first transform the wave equations into a system of ordinary differential equations (ODEs) and apply the local extrapolation method to discretize the spatial high-order derivatives, resulting in a system of semi-discrete ODEs. Then we use the SSPC method based on an implicit Runge-Kutta method to solve the semi-discrete ODEs and introduce a weighting parameter into the SSPC method. On top of such a structure, we develop a robust numerical algorithm to effectively suppress the numerical dispersion, which is usually caused by the discretization of wave equations when coarse grids are used or geological models have large velocity contrasts between adjacent layers. Meanwhile, we investigate the performance of the SSPC method including numerical errors and convergence rate, numerical dispersion, and stability criteria with different choices of the weighting parameter to solve 1-D and 2-D acoustic- and elastic-wave equations. When the SSPC is applied to seismic simulations, the computational efficiency is also investigated by comparing the SSPC, the fourth-order Lax-Wendroff correction (LWC) method, and the staggered-grid (SG) finite difference method. Comparisons of synthetic waveforms computed by the SSPC and analytic solutions for acoustic and elastic models are given to illustrate the accuracy and the validity of the SSPC method. Furthermore, several numerical experiments are conducted for the geological models including a 2-D homogeneous transversely isotropic (TI) medium, a two-layer elastic model, and the 2-D SEG/EAGE salt model. The results show that the SSPC can be used as a practical tool for large-scale seismic simulation because of its effectiveness in suppressing numerical dispersion even in the situations such as coarse grids, strong interfaces, or high frequencies.     

Brachial arterial pressure to assess cardiovascular structural damage: an overview and lessons from clinical trials

Epidemiological studies have emphasized the relationship between blood pressure (BP) and the incidence of cardiovascular diseases. Severity of hypertension was in the past judged on the basis of diastolic BP. More recent epidemiological studies have directed attention to systolic pressure as a better guide to cardiovascular and all-cause mortality. Traditionally, hypertension was appreciated by measures of BP recorded in peripheral arteries, usually brachial artery which was assumed to reflect pressures in all parts of arterial system. All these studies neglected that peripheral systolic BP differs from pressure recorded in the aorta and central arteries. While mean and diastolic pressures are almost constant along the arterial tree, due to the stiffness and geometric heterogeneity of large arteries and the timing and magnitude of wave reflections systolic BP and pulse pressure are amplified from the aorta to peripheral arteries, and brachial systolic BP only indirectly reflects the systolic BP in the aorta and central arteries. Several recent studies have shown that the effects of antihypertensive drugs are not the same in peripheral and central arteries, fact which could account for different effects of various drugs on end-organ damage, such as regression of left ventricular hypertrophy. Moreover, it has been shown that aortic and central artery pressure (or their determinants) are stronger predictors of end-organ damage and cardiovascular outcome than conventionally measured brachial pressure. These studies have focused the attention on the physical properties of large arteries and on the way they influence the level of systolic and pulse pressures along the arterial tree.     

A Parallel Domain Decomposition Algorithm for Simulating Blood Flow with Incompressible Navier-Stokes Equations with Resistive Boundary Condition

We introduce and study a parallel domain decomposition algorithm for the simulation of blood flow in compliant arteries using a fully-coupled system of nonlinear partial differential equations consisting of a linear elasticity equation and the incompressible Navier-Stokes equations with a resistive outflow boundary condition. The system is discretized with a finite element method on unstructured moving meshes and solved by a Newton-Krylov algorithm preconditioned with an overlapping restricted additive Schwarz method. The resistive outflow boundary condition plays an interesting role in the accuracy of the blood flow simulation and we provide a numerical comparison of its accuracy with the standard pressure type boundary condition. We also discuss the parallel performance of the implicit domain decomposition method for solving the fully coupled nonlinear system on a supercomputer with a few hundred processors.     

A Numerical Thermal-Hydraulic Model to Simulate the Fast Transients in a Supercritical Water Channel Subjected to Sharp Pressure Variations

The present work demonstrates the extension of a thermal-hydraulic model, THRUST, with an objective to simulate the fast transient flow dynamics in a supercritical water channel of circular cross section. THRUST is a 1-D model which solves the nonlinearly coupled mass, axial momentum and energy conservation equations in time domain based on a characteristics-dependent fully implicit finite difference scheme using an Eulerian approach. The model developed accounts for the compressibility of the supercritical flow by considering the finite value of acoustic speed in the solution algorithm and treats the boundary conditions naturally. A supercritical water channel of circular cross section, for which the experimental data is available at steady state operating conditions, is chosen for the transient simulations to start with. Two different case studies are undertaken with a purpose to assess the capability of the model to analyze the fast transient processes caused by the large reduction in system pressure. The first transient case study is where the initial exit pressure is reduced by 1 MPa exponentially in a time span of 5 s. In the second case study, the transient is initiated with a sudden step decrease in the exit pressure by the same amount. Results obtained for both the case studies show the desired performance from the model developed.     

Analysis of Cleveland Clinic continuous-flow total artificial heart performance using the Virtual Mock Loop: Comparison with an in vivo study

The Virtual Mock Loop (VML) is a mathematical model designed to simulate mechanism of the human cardiovascular system interacting with mechanical circulatory support devices. Here, we aimed to mimic the hemodynamic performance of Cleveland Clinic’s self-regulating continuous-flow total artificial heart (CFTAH) via VML and evaluate the accuracy of the VML compared with an in vivo acute animal study. The VML reproduced 124 hemodynamic conditions from three acute in vivo experiments in calves. Systemic/pulmonary vascular resistances, pump rotational speed, pulsatility, and pulse rate were set for the VML from in vivo data. We compared outputs (pump flow, left and right pump pressure rises, and atrial pressure difference) between the two systems. The pump performance curves all fell in the designed range. There was a strong correlation between the VML and the in vivo study in the left pump flow (r² = 0.84) and pressure rise (r² = 0.80), and a moderate correlation in right pressure rise (r² = 0.52) and atrial pressure difference (r² = 0.59). Although there is room for improvement in simulating right-sided pump performance of self-regulating CFTAH, the VML acceptably simulated the hemodynamics observed in an in vivo study. These results indicate that pump flow and pressure rise can be estimated from vascular resistances and pump settings.     

Guidelines for inspiratory flow setting when measuring the pressure-volume relationship

Acquisition of pressure-volume (PV) curves to improve ventilation strategy is time consuming when using static methods. Low-flow techniques use less time, but compliance values can be decreased by the resistance to flow in airways and tracheal tube (P-t). In this study, we determined the impact of three flows on the resistive component of airway pressure during anesthesia. We studied 10 ASA status P1/P2 patients with normal respiratory function. Airway and esophageal pressures were measured while volume-control ventilated with 6, 12, and 30 L/min continuous flows. PV curves, lower inflection point, respiratory system, and chest wall compliances at 250, 500, 750, and 1000 mL tidal volume were established before and after removing P-t. Data were submitted to analysis of variance. The inflection point was lower for the lower flow when comparing 6 and 12 with 30 L/min (P < 0.001). No difference was found between 6 and 12 L/min. Removal of P-t showed a difference only for 30 L/min (P = 0.004). Higher flows generated lower compliances. P-t subtraction reduced compliances only for 30 L/min. Chest wall compliances showed no difference between flows. We concluded that flows < or =12 L/min minimize P-t during intraoperative PV curves acquisition. Compliances suggest 6 L/min as the most adequate flow. IMPLICATIONS: We suggest guidelines for inspiratory flow setting when measuring the pressure-volume relationship during anesthesia based on the comparison among three different continuous flow values, aiming at better intraoperative respiratory settings in patients with normal respiratory function.     

Effect of tapered grafts on hemodynamics and flow rate in dialysis access grafts

AIM: Aside from the high incidence of venous stenosis, high-output failure and peripheral steal syndromes remain serious problems of vascular access. Meanwhile commercial tapered grafts are available to address this topic, but little is known about its effect neither on graft flow nor on hemodynamics. METHODS: Anastomotic models were constructed using a clear silicon elastomer. The arterial anastomosis was shaped in two ways: 1) like a direct connection of artery and 7-mm graft and 2) with a 4-mm diameter segment between artery and graft. Hemodynamic measurements were performed in a pulsatile flow circuit to simulate blood flow at physiological conditions. Flow patterns were obtained by direct dye injection. Additionally, the correlation between the length of narrow segment and mean arterial pressure was investigated. RESULTS: In all models using a 4-mm segment, the oscillating anastomotic vortex was disappeared. This vortex was shifted to the area behind the well-rounded expansions of the graft demonstrating a new separation region, but the flow direction was constant during the whole simulated cycle. At identical pressure rates and waveforms the length of narrow segment determined the graft flow rate directly (e.g., at mean pressure 100 mmHg, flow reduction up to 28% in 4-mm segments, and up to 55% in 3-mm segments). CONCLUSION: These findings indicate that taper is an important consideration in the design of vascular access grafts.     

Tracheal tube resistance and airway and alveolar pressures during mechanical ventilation in the neonate

The relationship between peak airway pressure, alveolar pressure and respiratory frequency was calculated for the range of compliances and airway resistances which might be encountered during mechanical ventilation of a 3-kg neonate. The pressure/flow relationships of 2.5, 3.0, 3.5 and 4-mm tracheal tubes were determined at a series of flows from 0.5 to 4 litres/minute. Peak airway and alveolar pressures were then measured at various frequencies and inspiratory:expiratory ratios with the tubes incorporated in a model lung. Large differences between peak airway and alveolar pressures developed when frequency was increased or inspiratory time decreased; the differences were greatest with the smaller tubes. Shortening expiratory time by increasing the frequency or altering the inspiratory:expiratory ratio resulted in increased end-expiratory pressure because of incomplete emptying of the lung.     

The analysis of radial artery pressure waveforms using 4 element model

BACKGROUND: The pressure wave transmission from the aorta to the peripheral artery has rarely been analyzed using the physiological model linked to the entire vascular system. The goal of the present study is to clarify the law of causality between distortions of waveforms and cardiovascular conditions using a model. METHODS: The arterial system was quantitatively analyzed with a 4-element model consisting of aortic characteristic impedance, inertance, peripheral resistance, and compliance, which shows the nature of second-order response. In order to elucidate the influence of the 4 elements on transmitting waveforms, we simulated cases in which these 4 elements change independently. RESULTS: Large aortic characteristic impedance, low peripheral resistance, and increased compliance cause the damping of radial artery pressure wave. CONCLUSIONS: The model approach enabled us to grasp the hemodynamics-related changes to the pressure waveforms, since each of the 4 elements corresponds to the vascular system with physical meanings.     

Investigation of Parameter Estimator and Adaptive Controller for Assist Pump by Computer Simulation

The multi-output adaptive controller of a left ventricular assist device (LVAD) was studied by computer simulation. The controller regulated two outputs--mean aortic pressure (mAoP) and mean atrial pressure (mLAP)--by regulating vacuum pressure (input). The autoregressive models were used to describe the circulatory system. The parameters of the models were estimated by the recursive least squares method. Based on the autoregressive models, the vacuum pressure minimizing a performance index was searched. The index used was the weighted summation of the square errors. Responses of the adaptive controller were simulated when the contractility of the left ventricle was decreased at various rates and the peripheral resistance was changed. Both the mAoP and mLAP were controlled to their predicted values in the steady state. The steady-state errors of the mAoP were less than a few mm Hg, and those of the mLAP were lower than 1 mm Hg. Consequently, the estimated parameters can be regarded as true parameters, and the adaptive controller has the potential to control more than two outputs. The multioutput adaptive controller studied is useful in controlling the LVAD according to the change in circulatory condition.     

SODIUM NITROPRUSSIDE AND REGIONAL ARTERIAL HAEMODYNAMICS IN THE DOG

Blood flow to functionally different vascular beds was examinedduring a sodium nitroprusside infusion in 10 dogs anaesthetizedwith halothane (1 MAC) in oxygen. Blood flows were measuredin the ascending aorta, and the coeliac, superior mesenteric,renal and iliac arteries. In two dogs, regional vascular impedanceand related power were calculated. Regional pressure-flow relationshipswere measured at systemic pressure reductions of approximately15, 35 and 55% of control. At pressure reductions of 15–35%,coeliac, mesenteric and aortic blood flow exceeded control values(P<0.025); renal and iliac blood flows were reduced, butnot significantly. At pressure reductions of 55% a more significantreduction of iliac, renal and aortic blood flow occurred (P<0.05).All vascular resistances showed significant monotonic reductions(P<0.01) over the entire range of pressure reduction. Totalpower dissipation was reduced in all beds with a reduction ofcharacteristic impedance in the coeliac, renal and iliac beds;aortic oscillatory pressure power increased.