Computer simulation of firefly flash sequences.

A new method is proposed for measuring nonsteady flow rates when this flow is pulsatile in nature. This method involves the use of indicators and does not require direct access to the vessel carrying the fluid. No knowledge of the associated mathematics is required for its application. The investigator infuses indator into the vessel leading into a capillary or similar labyrinth at a time-varying rate such that the indicator concentration at the outflow from the labyrinth remains constant in time. When this condition at the outflow has been achieved, the pulsatile flow rate at the inflow is given simply as the ratio of the varying infusion rate to the constant outflow indicator concentration.     

Bio-medico-mechanical behavior of natural artery blood vessel under constant and variable internal pulsatile pressure flow test in vitro

Studies have been carried out on the bio-medico-mechanical behavior in vitro of natural blood vessel (dogs) under constant and variable internal pulsatile pressure flow. The apparatus designed by us well simulated the arterial system. The studies were made for the case of pressure amplitude kept as constant, of the two-step-multi-duplicated pulsatile pressure and of the fluctuating pressure. For the case of the fluctuating pressure, the strength of the artery becomes considerably lower than those under constant amplitude and two-step-multi-duplicated pulsatile pressure. SEM observations of the inner walls of the artery shows that collagen fibers are more elongated under fluctuating pulsatile pressure flow. In conclusion, in order to avoid the mechanical deterioration of the artery strength, it is useful to keep the pulsatile blood pressure at constant amplitude. Even for the case of the blood pressure fluctuation, it is necessary to manage to keep the blood pressure as near a regular wave as possible, the total number of repeated pulse being equal.     

Pulsatile flow computational simulations of mitral regurgitation.

The noninvasive quantification of mitral regurgitation remains an important clinical goal. Recently, the flow convergence method was developed to estimate the regurgitant flow rate. This study used three-dimensional pulsatile flow computational simulations to evaluate the accuracy of the flow convergence method in the presence of complicating factors such as ventricular confinement, noncircular orifice shape, and the presence of aortic outflow. Results showed that in the absence of aortic outflow and ventricular confinement, there was a plateau zone where the calculated flow rate by the hemispheric formula approximated the true flow rate, independent of the orifice shape. In the presence of aortic outflow and in chambers of physiologic dimensions, there was no longer a clear zone where the hemispheric formula was valid. The hemi-elliptic modification of the flow convergence method worked in all cases, independent of the degree of ventricular confinement or the presence of aortic outflow. Therefore, application of the hemi-elliptic formula should be considered in future clinical studies.     

Organ vessel functions by pulsatile flow

It was found that changes of resistance, capacity and exchange vessel functions of the skeletal muscle depended on values of amplitude and frequency of perfusion blood flow in acute experiments on cats. Amplitude-frequency characteristics of hemodynamic parameters of these functions were nonlinear. Ranges of amplitude and frequency variation with significant shifts of these parameters were determined. Conditions of perfusion (constant flow or constant pressure) changed volume and direction of haemodynamic parameter shifts under the amplitude-frequency modulation of the pulsatile blood flow. The pulsatile blood flow oscillations exerted maximum influence on hemodynamic parameters of exchange vessel function. The author has proposed the wave regulation conception of organ vessel functions.     

Pulsatile flow during cardiopulmonary bypass preserves postoperative microcirculatory perfusion irrespective of systemic hemodynamics

The onset of nonpulsatile cardiopulmonary bypass is known to deteriorate microcirculatory perfusion, but it has never been investigated whether this may be prevented by restoration of pulsatility during extracorporeal circulation. We therefore investigated the distinct effects of nonpulsatile and pulsatile flow on microcirculatory perfusion during on-pump cardiac surgery. Patients undergoing coronary artery bypass graft surgery were randomized into a nonpulsatile (n = 17) or pulsatile (n = 16) cardiopulmonary bypass group. Sublingual mucosal microvascular perfusion was measured at distinct perioperative time intervals using sidestream dark field imaging, and quantified as the level of perfused small vessel density and microvascular flow index (vessel diameter < 20 μm). Microcirculation measurements were paralleled by hemodynamic and free hemoglobin analyses. The pulse wave during pulsatile bypass estimated 58 ± 17% of the baseline blood pressure waveform. The observed reduction in perfused vessel density during aorta cross-clamping was only restored in the pulsatile flow group and increased from 15.5 ± 2.4 to 20.3 ± 3.7 mm/mm(2) upon intensive care admission (P < 0.01). The median postoperative microvascular flow index was higher in the pulsatile group [2.6 (2.5-2.9)] than in the nonpulsatile group [2.1 (1.7-2.5); P = 0.001]. Pulsatile flow was not associated with augmentation of free hemoglobin production and was paralleled by improved oxygen consumption from 70 ± 14 to 82 ± 16 ml·min(-1)·m(-2) (P = 0.01) at the end of aortic cross-clamping. In conclusion, pulsatile cardiopulmonary bypass preserves microcirculatory perfusion throughout the early postoperative period, irrespective of systemic hemodynamics. This observation is paralleled by an increase in oxygen consumption during pulsatile flow, which may hint toward decreased microcirculatory heterogeneity during extracorporeal circulation and preservation of microcirculatory perfusion throughout the perioperative period.     

The effect of asymmetry in abdominal aortic aneurysms under physiologically realistic pulsatile flow conditions

In the abdominal segment of the human aorta under a patient's average resting conditions, pulsatile blood flow exhibits complex laminar patterns with secondary flows induced by adjacent branches and irregular vessel geometries. The flow dynamics becomes more complex when there is a pathological condition that causes changes in the normal structural composition of the vessel wall, for example, in the presence of an aneurysm. This work examines the hemodynamics of pulsatile blood flow in hypothetical three-dimensional models of abdominal aortic aneurysms (AAAs). Numerical predictions of blood flow patterns and hemodynamic stresses in AAAs are performed in single-aneurysm, asymmetric, rigid wall models using the finite element method. We characterize pulsatile flow dynamics in AAAs for average resting conditions by means of identifying regions of disturbed flow and quantifying the disturbance by evaluating flow-induced stresses at the aneurysm wall, specifically wall pressure and wall shear stress. Physiologically realistic abdominal aortic blood flow is simulated under pulsatile conditions for the range of time-average Reynolds numbers 50 < or = Rem < or = 300, corresponding to a range of peak Reynolds numbers 262.5 < or = Repeak < or = 1575. The vortex dynamics induced by pulsatile flow in AAAs is depicted by a sequence of four different flow phases in one period of the cardiac pulse. Peak wall shear stress and peak wall pressure are reported as a function of the time-average Reynolds number and aneurysm asymmetry. The effect of asymmetry in hypothetically shaped AAAs is to increase the maximum wall shear stress at peak flow and to induce the appearance of secondary flows in late diastole.     

Platelet near-wall excess in porcine whole blood in artery-sized tubes under steady and pulsatile flow conditions

Platelet margination (enhanced platelet concentration in the near wall region of a blood vessel) has been well documented in small vessels. In artery-sized vessels margination has only been demonstrated in one study, using ghost cell suspensions and under relatively non-physiologic conditions of steady flow and 50 cm development length. Local sampling experiments were performed to confirm platelet margination in artery-sized stainless steel tubes, for a typical anatomical length and under pulsatile flow, using fresh EDTA-anticoagulated porcine whole blood (N=21). Experiments were designed using three-dimensional Computational Fluid Dynamics (CFD) to model the sample region with greater fidelity. Steady flow experiments in 50 cm long tubes verify published laser Doppler measurements of platelet margination in 3 mm ID tubes at normal arterial shear rate (500 s(-1). Margination persists under pulsatile flow conditions (63.8 pulses/min), but in steady flow at length of 10 cm, margination is reduced. Platelet margination ratio (the ratio of the platelet concentration near the wall to bulk average platelet count) ranges from 1.21 to 2.48. No significant effects of calculated sampling thickness (20 microm and 50 microm) or pulsatility were detected. Hematocrit margination ratio is 0.68 to 0.90. Two model platelet concentration profiles are fit to the experimental results.     

Numerical investigation of the non-Newtonian pulsatile blood flow in a bifurcation model with a non-planar branch

The pulsatile flow of non-Newtonian fluid in a bifurcation model with a non-planar daughter branch is investigated numerically by using the Carreau-Yasuda model to take into account the shear thinning behavior of the analog blood fluid. The objective of this study is to deal with the influence of the non-Newtonian property of fluid and of out-of-plane curvature in the non-planar daughter vessel on wall shear stress (WSS), oscillatory shear index (OSI), and flow phenomena during the pulse cycle. The non-Newtonian property in the daughter vessels induces a flattened axial velocity profile due to its shear thinning behavior. The non-planarity deflects flow from the inner wall of the vessel to the outer wall and changes the distribution of WSS along the vessel, in particular in systole phase. Downstream of the bifurcation, the velocity profiles are shifted toward the flow divider, and low WSS and high shear stress temporal oscillations characterized by OSI occur on the outer wall region of the daughter vessels close to the bifurcation. Secondary motions become stronger with the addition of the out-of-plane curvature induced by the bending of the vessel, and the secondary flow patterns swirl along the non-planar daughter vessel. A significant difference between the non-Newtonian and the Newtonian pulsatile flow is revealed during the pulse cycle; however, reasonable agreement between the non-Newtonian and the rescaled Newtonian flow is found. Calculated results for the pulsatile flow support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology.     

Investigation of the influence of blood flow rate on large vessel cooling in hepatic radiofrequency ablation.

Radiofrequency (RF) ablation using high-frequency current has become an important treatment method for patients with non-resectable liver tumors. Tumor recurrence is associated with tissue cooling in the proximity of large blood vessels. This study investigated the influence of blood flow rate on tissue temperature and lesion size during monopolar RF ablation at a distance of 10 mm from single 4- and 6-mm vessels using two different approaches: 1) an ex vivo blood perfusion circuit including an artificial vessel inserted into porcine liver tissue was developed; and 2) a finite element method (FEM) model was created using a novel simplified modeling technique for large blood vessels. Blood temperatures at the inflow/outflow of the vessel and tissue temperatures at 10 and 20 mm from the electrode tip were measured in the ex vivo set-up. Tissue temperature, blood temperature and lesion size were analyzed under physiological, increased and reduced blood-flow conditions. The results show that changes in blood flow rate in large vessels do not significantly affect tissue temperature and lesion size far away from the vessel. Monopolar ablation could not produce lesions surrounding the vessel due to the strong heat-sink effect. Simulated tissue temperatures correlated well with ex vivo measurements, supporting the FEM model.     

Experimental determination of wall shear rate in canine carotid arteries perfused in vitro

The mathematical model of Hung (Tsai and Hung, 1984) is employed to determine the wall shear rate acting on canine carotid arteries perfused in vitro. Model equations for pulsatile flow in a deformable vessel are coupled with experimental data of dynamic pressure drop, flow rate, vessel radius and radial wall motion. Derived quantities, e.g. velocity profiles and wall shear, are obtained for vessels exposed to 'normotensive' hemodynamics, 'hypertension' simulations and perfusions in which the compliance of the vessel wall is deliberately altered. Our results indicate that wall shear varies markedly as a function of the hemodynamic environment. The effects of vessel radius vs flow rate on the development of wall shear are also demonstrated. It is found that convective processes correlate with the magnitude of wall shear in the 'hypertension' simulations. The present findings and complementary published data may explain, at least in part, the variations in vessel wall transport and endothelial cell biology we observe as a function of the hemodynamic environment. For example we have documented that the exposure of canine carotids to 'hypertensive' (vs 'normotensive') hemodynamics is associated with an increased flux of lipoproteins (LDL) into the intima and luminal media. Alternations in wall compliance, on the other hand, profoundly influence endothelial shape, orientation and cytoskeletal array.     

Velocity field of pulsatile flow in a porous tube

This paper describes velocity fields for fully developed periodic laminar flow in a rigid tube with a porous wall. We obtained an analytical solution of the flow by the linear approximation of the Navier-Stokes equation. Unlike the previous works with a constant seepage rate along the axis, we used a wall velocity which contained hydraulic permeation constant Lp. The axial velocity profile shows a local maximum velocity near the wall at a large Womersley number alpha. This suggests that concentration polarization in porous tubular membrane may be reduced at high frequencies if a membrane device is operated under pulsatile flow conditions. The magnitude of wall permeation velocity decreases linearly along the tube axis because the damping of the pressure difference between the inside and the outside of the tube is very small.     

Wall shear stress estimates in coronary artery constrictions.

Wall shear stress estimates from laminar boundary layer theory were found to agree fairly well with the magnitude of shear stress levels along coronary artery constrictions obtained from solutions of the Navier Stokes equations for both steady and pulsatile flow. The relatively simple method can be used for in vivo estimates of wall shear stress in constrictions by using a vessel shape function determined from a coronary angiogram, along with a knowledge of the flow rate.     

A model of pulsatile flow in a uniform deformable vessel.

Simulations of blood flow in natural and artificial conduits usually require large computers for numerical solution of the Navier-Stokes equations. Often, physical insight into the fluid dynamics is lost when the solution is purely numerical. An alternative to solving the most general form of the Navier-Stokes equations is described here, wherein a functional form of the solution is assumed in order to simplify the required computations. The assumed forms for the axial pressure gradient and velocity profile are chosen such that conservation of mass is satisfied for fully established pulsatile flow in a straight, deformable vessel. The resulting equations are cast in finite-difference form and solved explicitly. Results for the limiting cases of rigid wall and zero applied pressure are found to be in good agreement with analytical solutions. Comparison with the experimental results of Klanchar et al. [Circ. Res. 66, 1624-1635 (1990]) also shows good agreement. Application of the model to realistic physiological parameter values provides insight as to the influence of the pulsatile nature of the flow field on wall shear development in the presence of a moving wall boundary. Specifically, the model illustrates the dependence of flow rate and shear rate on the amplitude of the vessel wall motion and the phase difference between the applied pressure difference and the oscillations of the vessel radius. The present model can serve as a useful tool for experimentalists interested in quantifying the magnitude and character of velocity profiles and shearing forces in natural and artificial biologic conduits.     

Mathematical Modeling of Ischemia–Reperfusion Injury and Postconditioning Therapy

Reperfusion (restoration of blood flow) after a period of ischemia (interruption of blood flow) can paradoxically place tissues at risk of further injury: so-called ischemia–reperfusion injury or IR injury. Recent studies have shown that postconditioning (intermittent periods of further ischemia applied during reperfusion) can reduce IR injury. We develop a mathematical model to describe the reperfusion and postconditioning process following an ischemic insult, treating the blood vessel as a two-dimensional channel, lined with a monolayer of endothelial cells that interact (respiration and mechanotransduction) with the blood flow. We investigate how postconditioning affects the total cell density within the endothelial layer, by varying the frequency of the pulsatile flow and the oxygen concentration at the inflow boundary. We find that, in the scenarios we consider, the pulsatile flow should be of high frequency to minimize cellular damage, while oxygen concentration at the inflow boundary should be held constant, or subject to only low-frequency variations, to maximize cell proliferation.     

In vitro hemodynamic investigation of the embryonic aortic arch at late gestation

This study focuses on the dynamic flow through the fetal aortic arch driven by the concurrent action of right and left ventricles. We created a parametric pulsatile computational fluid dynamics (CFD) model of the fetal aortic junction with physiologic vessel geometries. To gain a better biophysical understanding, an in vitro experimental fetal flow loop for flow visualization was constructed for identical CFD conditions. CFD and in vitro experimental results were comparable. Swirling flow during the acceleration phase of the cardiac cycle and unidirectional flow following mid-deceleration phase were observed in pulmonary arteries (PA), head-neck vessels, and descending aorta. Right-to-left (oxygenated) blood flowed through the ductus arteriosus (DA) posterior relative to the antegrade left ventricular outflow tract (LVOT) stream and resembled jet flow. LVOT and right ventricular outflow tract flow mixing had not completed until approximately 3.5 descending aorta diameters downstream of the DA insertion into the aortic arch. Normal arch model flow patterns were then compared to flow patterns of four common congenital heart malformations that include aortic arch anomalies. Weak oscillatory reversing flow through the DA junction was observed only for the Tetralogy of Fallot configuration. PA and hypoplastic left heart syndrome configurations demonstrated complex, abnormal flow patterns in the PAs and head-neck vessels. Aortic coarctation resulted in large-scale recirculating flow in the aortic arch proximal to the DA. Intravascular flow patterns spatially correlated with abnormal vascular structures consistent with the paradigm that abnormal intravascular flow patterns associated with congenital heart disease influence vascular growth and function.     

Analytical solutions for the specific activities of a traced substance within the component parts of a simulated kidney-ureter system

Two models for a kidney-ureter system are considered: one model of one vessel in which a traced substance, undergoing exchange between the vessel and an external compartment, is emptying into the ureter; the second model of two approximately parallel, identical vessels in which a traced substance, undergoing exchange between each vessel and an external compartment, is emptying into the ureter. A single impulsive input of label into a vessel is assumed. For mathematical simplicity, the major conditions imposed on each system are: (1) rapid mixing transverse to a vessel axis and no mixing longitudinal to a vessel axis within the plasma; (2) small variation of the specific activity within the plasma in the longitudinal direction to a vessel axis; (3) constant flow rate of urine into the ureter and (4) constant exchange coefficients, tubule flow velocity and traced substance concentrations within individual compartments.     

Fast blood-flow simulation for large arterial trees containing thousands of vessels

Blood flow modelling has previously been successfully carried out in arterial trees to study pulse wave propagation using nonlinear or linear flow solvers. However, the number of vessels used in the simulations seldom grows over a few hundred. The aim of this work is to present a computationally efficient solver coupled with highly detailed arterial trees containing thousands of vessels. The core of the solver is based on a modified transmission line method, which exploits the analogy between electrical current in finite-length conductors and blood flow in vessels. The viscoelastic behaviour of the arterial-wall is taken into account using a complex elastic modulus. The flow is solved vessel by vessel in the frequency domain and the calculated output pressure is then used as an input boundary condition for daughter vessels. The computational results yield pulsatile blood pressure and flow rate for every segment in the tree. This solver is coupled with large arterial trees generated from a three-dimensional constrained constructive optimisation algorithm. The tree contains thousands of blood vessels with radii spanning ~1 mm in the root artery to ~30 μm in leaf vessels. The computation takes seconds to complete for a vasculature of 2048 vessels and less than 2 min for a vasculature of 4096 vessels on a desktop computer.     

Hemodynamic-kinetic controlled extracorporeal circulation in heart surgery]

Mimicking the physiological characteristics of the circulatory system, pulsatile bloodflow has also been introduced into extracorporeal perfusion to avoid known postoperative complications. In a mathematical consideration of the situation bloodflow is seen as a function of time F(t) for approximately constant vessel diameter over a given time. The kinetic energy of a column of blood produced by the heart-lung machine is transmitted directly to the arterial circulation via the aorta. The nature of the energy release can give rise to both positive (organ perfusion) and negative (damage to endothelium) effects. This study investigates how this energy release can be optimised, using the following experimental approach. A Doppler flow-measuring probe is placed on the ascending aorta to monitor the extracorporeal circulation. At the same time, the blood pressure is measured and converted to a pressure-flow curve via an A/D converter. On the basis of the parameters thus obtained, the energy released by the heart-lung machine is calculated. By regulating the functional parameters of a new generation of heart-lung machines, the bloodflow can then be adapted to the physiological requirements. Within the pulse period (cycle) a 20% rise phase ending in a slightly increasing plateau is established. The energy increase within a cycle should not exceed 150 joules. To optimize the mode of functioning of the heart-lung machine, we introduced the "energy-equivalent pressure" (EEP). Adaptation of the EEP to the physiological conditions required a basic flow of 60% at a pulse rate of 60/min and a pulse duration of 35% within the pulsatile flow interval.     

Blood flow patterns and pressure loss in the ascending aorta: A comparative study on physiological and aneurysmal conditions

An aortic aneurysm is defined as a balloon-shaped bulging of all three histologic components of the aortic vessel walls (intima, media and adventitia). This dilation results from vessel weakening owing to remodeling, i.e. due to cystic degeneration of the Tunica media (Marfan), progression of atherosclerosis or presence of a bicuspid aortic valve. The growth rate of the aortic diameter varies from patient to patient and may progress until the aneurysm ultimately ruptures. The role of hemodynamics, i.e. blood flow patterns, and shear stresses that are supposed to intensify during aneurysm growth are not yet fully understood, but thought to play a key role in the enlargement process. The aim of this study is to characterize the aortic blood flow in a silicone model of a pathological aorta with ascending aneurysm, to analyze the differences in the blood flow pattern compared to a healthy aortic model, and to single out possible blood flow characteristics measurable using phase contrast magnetic resonance imaging (MRI) that could serve as indicators for aneurysm severity. MRI simulations were performed under physiological, pulsatile flow conditions using data obtained from optical three dimensional particle tracking measurements. In comparison to the healthy geometry, elevated turbulence intensity and pressure loss are measured in the diseased aorta, which we propose as a complimentary indicator for assessing the aneurysmal severity. Our results shed a light on the interplay between the blood flow dynamics and their contribution to the pathophysiology and possible role for future risk assessment of ascending aortic aneurysms.     

The insect abdomen--a heartbeat manager in insects?

Different possibilities of coordination between circulation, respiration and abdominal movements were found in pupae of Pieris brassicae, Tenebrio molitor, Galleria mellonella and Leptinotarsa decemlineata. Coordination principles depend on metabolic rate: the need to support circulation with abdominal movements appears only at higher metabolic rates. Integration between different abdominal movements and circulation depends on species, on physiological state and, supposedly, on internal morphology. At low metabolic rates, there is no need for a very intensive hemolymph flow, and the dorsal vessel is capable of initiating and/or maintaining necessary hemolymph flow. Starting from a certain metabolic level, it is possible that the abdomen is used to accelerate hemolymph flow in the case of a large amount of hemolymph. When the necessary flow speed has been reached, relatively weak pulsation of the dorsal vessel with accessory pulsatile organs and diaphragms can easily maintain the necessary flow intensity. Heart activity may sometimes be initiated by abdominal movements via cardiac reflex or mechanical excitation. Sometimes, when heart function is weakened by histolysis, the abdomen may temporarily take over the main circulatory function or occasionally contribute to acceleration of low-speed hemolymph flow. In this case the functions are simultaneous and may be triggered by some mediator(s). In active adult insects the whole body is moving, and hence hemolymph circulates and the tracheal system is effectively ventilated by a whole body ensemble consisting of the dorsal vessel, moving organs, body appendages and accessory pulsatile organs. The mechanism of autocirculation (analogous to autoventilation in gas exchange) is a probable mechanism in circulation in adult insects.