Estimation of the local fraction of cardiac output using a two-phase model of pulsatile hemodynamics

Estimation of the pulsatile component of stroke volume (SV) with thoracic rheography cannot be explained by the existing single-phase model of pulsatile hemodynamics, the theory of passive diastole, but can be satisfactorily explained by a two-phase model, the theory of active diastole. The local fraction of cardiac output, an original rheographic parameter for measuring blood flow in the examined area, is suggested, which can be calculated in the same way as the pulsatile component of SV but by a simpler formula and can be used for any region of the cardiovascular system.     

Anisotropic adaptive finite element method for modelling blood flow

In this study, we present an adaptive anisotropic finite element method (FEM) and demonstrate how computational efficiency can be increased when applying the method to the simulation of blood flow in the cardiovascular system. We use the SUPG formulation for the transient 3D incompressible Navier–Stokes equations which are discretised by linear finite elements for both the pressure and the velocity field.

Given the pulsatile nature of the flow in blood vessels we have pursued adaptivity based on the average flow over a cardiac cycle. Error indicators are derived to define an anisotropic mesh metric field. Mesh modification algorithms are used to anisotropically adapt the mesh according to the desired size field. We demonstrate the efficiency of the method by first applying it to pulsatile flow in a straight cylindrical vessel and then to a porcine aorta with a stenosis bypassed by a graft. We demonstrate that the use of an anisotropic adaptive FEM can result in an order of magnitude reduction in computing time with no loss of accuracy compared to analyses obtained with uniform meshes.     

Anisotropic adaptive finite element method for modelling blood flow

In this study, we present an adaptive anisotropic finite element method (FEM) and demonstrate how computational efficiency can be increased when applying the method to the simulation of blood flow in the cardiovascular system. We use the SUPG formulation for the transient 3D incompressible Navier-Stokes equations which are discretised by linear finite elements for both the pressure and the velocity field. Given the pulsatile nature of the flow in blood vessels we have pursued adaptivity based on the average flow over a cardiac cycle. Error indicators are derived to define an anisotropic mesh metric field. Mesh modification algorithms are used to anisotropically adapt the mesh according to the desired size field. We demonstrate the efficiency of the method by first applying it to pulsatile flow in a straight cylindrical vessel and then to a porcine aorta with a stenosis bypassed by a graft. We demonstrate that the use of an anisotropic adaptive FEM can result in an order of magnitude reduction in computing time with no loss of accuracy compared to analyses obtained with uniform meshes.     

On the paths of fluid particles in an axisymmetrical aneurysm

The aim of this study is the characterization of the pulsatile flow field by demonstration of the paths of single particles in a model of an axisymmetric aneurysm. The detailed analysis of the flow field can give additional information on the flow pattern and the time of transition of blood particles in the segment. The basis of the calculations is the system of the Navier-Stokes equations for incompressible Newtonian fluid flow. To solve these equations numerically the finite element method was used. The trajectory equations for a fluid particle were solved by use of a predictor-corrector procedure. The results of the computer simulation demonstrate the development, shift and disappearance of vortices in the excavation and give references to zones of stasis. This behavior can be an important factor in thrombogenesis.     

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.     

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.     

Optical flow sensor for continuous invasive measurement of blood flow velocity

Continuous monitoring of intrapulse measurement of blood flow in humans is currently not achievable with clinically available instruments. In this paper, we demonstrate a method of measuring the instantaneous variations in flow during pulsatile blood flow with an optical flow sensor comprising a fiber Bragg grating sensor and illumination from a 565 nm Light‐Emitting‐Diode. The LED illumination heats the blood and fluctuations in temperature, due to variations in flow, are detected by the fiber sensor. A set of experiments at different flow rates (20 to 900 mL/min) are performed in a simulated cardiac circulation setup with pulsatile flow. Data are compared with an in‐line time of flight ultrasound flow sensor. Our results show that the optical and ultrasonic signals correlate with Pearson coefficients ranging from ?0.83 to ?0.98, dependent on the pulsatile frequency. Average flow determined by ultrasound and the optical fiber sensor showed a parabolic relationship with R² = 0.99. An abrupt step change in flow induced by occlusion and release of the circuit tubing demonstrated that the optical fiber and ultrasound sensor had similar response. The method described is capable of intrapulse blood flow measurement under pulsatile flow conditions, with potential applications in medicine where continuous blood flow sensing is desired.     

Experimental study of pulsatile and steady flow through a smooth tube and an atherosclerotic coronary artery casting of man

In vitro investigation of pulsatile and steady flows through a smooth, straight circular tube and a diseased human coronary artery cast was conducted with sugar-water solutions simulating the viscosity of blood. Time averaged pressure drops for pulsatile flows measured in the circular tube over a Reynolds number ranging from 50 to 1,000 were found to be identical to those for steady flows in the same tube, both of which were in excellent agreement with the Poiseuille flow prediction. For the polyurethane case (# 124) made from a human main coronary with significant but 'non obstructive' diffuse atherosclerotic disease, pressure drops for steady flows were found to be greater than Poiseuille flow predictions by a factor of 3-8 in the physiological Reynolds number range from about 100 to 400. Pulsatile flows in the same artery cast resulted in additional 30% increases in time averaged pressure drops, and thus flow resistance, compared to the steady flow data. Steady and pulsatile flow data measured in a straight, axisymmetric model of cast # 124 showed considerably smaller increases in flow resistance than those observed in # 124 casting.     

Mechanical simulation of shear stress on the walls of peripheral arteries

In the last few years many attempts were made to line artificial vascular grafts with in vitro grown endothelial cell layers and thereby to minimize the risk of thromboembolism. However, adherence and resistance against shear stress forces were not tested under physiological pulsatile shear stress forces. In this paper, a mock-circulation apparatus is described, which simulates various forms of pulsatile shear stress, and which at the same time meets the requirements of cell cultivation. It can be sterilized and needs less than 700 ml of culture medium for priming. The generated flow profile can be adapted to a wide range of shear stress and also to different viscosities of used media. To take account of the different viscosities of culture medium and blood, a computerized calculation of the shear stress pattern was performed. Using the results of this computer model, the flow pattern was modified to obtain normal physiological shear stress when using culture medium. Results of pulse generation and simulation for the superficial femoral artery are presented.     

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.     

Pulsatile flow and mass transport over an array of cylinders: gas transfer in a cardiac-driven artificial lung

The pulsatile flow and gas transport of a Newtonian passive fluid across an array of cylindrical microfibers are numerically investigated. It is related to an implantable, artificial lung where the blood flow is driven by the right heart. The fibers are modeled as either squared or staggered arrays. The pulsatile flow inputs considered in this study are a steady flow with a sinusoidal perturbation and a cardiac flow. The aims of this study are twofold: identifying favorable array geometry/spacing and system conditions that enhance gas transport; and providing pressure drop data that indicate the degree of flow resistance or the demand on the right heart in driving the flow through the fiber bundle. The results show that pulsatile flow improves the gas transfer to the fluid compared to steady flow. The degree of enhancement is found to be significant when the oscillation frequency is large, when the void fraction of the fiber bundle is decreased, and when the Reynolds number is increased; the use of a cardiac flow input can also improve gas transfer. In terms of array geometry, the staggered array gives both a better gas transfer per fiber (for relatively large void fraction) and a smaller pressure drop (for all cases). For most cases shown, an increase in gas transfer is accompanied by a higher pressure drop required to power the flow through the device.     

In Vitro Model of Physiological and Pathological Blood Flow with Application to Investigations of Vascular Cell Remodeling

Vascular disease is a common cause of death within the United States. Herein, we present a method to examine the contribution of flow dynamics towards vascular disease pathologies. Unhealthy arteries often present with wall stiffening, scarring, or partial stenosis which may all affect fluid flow rates, and the magnitude of pulsatile flow, or pulsatility index. Replication of various flow conditions is the result of tuning a flow pressure damping chamber downstream of a blood pump. Introduction of air within a closed flow system allows for a compressible medium to absorb pulsatile pressure from the pump, and therefore vary the pulsatility index. The method described herein is simply reproduced, with highly controllable input, and easily measurable results. Some limitations are recreation of the complex physiological pulse waveform, which is only approximated by the system. Endothelial cells, smooth muscle cells, and fibroblasts are affected by the blood flow through the artery. The dynamic component of blood flow is determined by the cardiac output and arterial wall compliance. Vascular cell mechano-transduction of flow dynamics may trigger cytokine release and cross-talk between cell types within the artery. Co-culture of vascular cells is a more accurate picture reflecting cell-cell interaction on the blood vessel wall and vascular response to mechanical signaling. Contribution of flow dynamics, including the cell response to the dynamic and mean (or steady) components of flow, is therefore an important metric in determining disease pathology and treatment efficacy. Through introducing an in vitro co-culture model and pressure damping downstream of blood pump which produces simulated cardiac output, various arterial disease pathologies may be investigated.     

Numerical simulations of pulsatile blood flow using a new constitutive model

In the present paper we use a new constitutive equation for whole human blood [R.G. Owens, A new microstructure-based constitutive model for human blood, J. Non-Newtonian Fluid Mech. (2006), to appear] to investigate the steady, oscillatory and pulsatile flow of blood in a straight, rigid walled tube at modest Womersley numbers. Comparisons are made with the experimental results of Thurston [Elastic effects in pulsatile blood flow, Microvasc. Res. 9 (1975), 145-157] for the pressure drop per unit length against volume flow rate and oscillatory flow rate amplitude. Agreement in all cases is very good. In the presentation of the numerical and experimental results we discuss the microstructural changes in the blood that account for its rheological behaviour in this simple class of flows. In this context, the concept of an apparent complex viscosity proves to be useful.     

Partial Carotid Occlusion as Treatment for Intracranial Internal Carotid Aneurysms

A study was undertaken to investigate the possibility of using partial carotid occlusion instead of complete carotid ligation for the treatment of intracranial internal carotid aneurysms with a view to avoiding such complications of the latter procedure as neurological deficit resulting from cerebral ischemia, and ascending thrombus formation. The beneficial effect of carotid ligation has been explained by the interruption of pulsatile flow which can cause rupture of an aneurysm by resonance phenomena. Studies on blood flow in the aorta in dogs, as well as in a human carotid artery in vivo and in vitro, showed that the same object could be achieved by the use of constriction by a Poppen clamp. This changed the pulsatile blood flow to a relatively non-pulsatile state with slight diminution in mean flow. Partial occlusion of the common carotid artery is recommended for those cases of intracranial aneurysm in which complete carotid occlusion would not likely be tolerated.     

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.     

Comparison of physiological and simple pulsatile flows through stenosed arteries.

Most experimental and numerical studies of pulsatile flow through stenosed arteries have been performed for a first harmonic oscillatory flow. In this paper, numerical solutions are presented for a physiological pulsatile flow as well as for an equivalent simple pulsatile flow, having the same stroke volume as the physiological flow, and the differences in their flow behavior are discussed. The analysis is restricted to laminar flow, Newtonian fluid and axisymmetric rigid stenosis. Comparison of results shows that the behaviors of the two flows are similar at some instances of time, however, important observed differences indicate that for thorough understanding of pulsatile flow behavior in stenosed arteries, the actual physiological flow should be simulated.     

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.     

Pulsatile pressure and flow in the skeletal muscle microcirculation

Although blood flow in the microcirculation of the rat skeletal muscle has negligible inertia forces with very low Reynolds number and Womersley parameter, time-dependent pressure and flow variations can be observed. Such phenomena include, for example, arterial flow overshoot following a step arterial pressure, a gradual arterial pressure reduction for a step flow, or hysteresis between pressure and flow when a pulsatile pressure is applied. Arterial and venous flows do not follow the same time course during such transients. A theoretical analysis is presented for these phenomena using a microvessel with distensible viscoelastic walls and purely viscous flow subject to time variant arterial pressures. The results indicate that the vessel distensibility plays an important role in such time-dependent microvascular flow and the effects are of central physiological importance during normal muscle perfusion. In-vivo whole organ pressure-flow data in the dilated rat gracilis muscle agree in the time course with the theoretical predictions. Hemodynamic impedances of the skeletal muscle microcirculation are investigated for small arterial and venous pressure amplitudes superimposed on an initial steady flow and pressure drop along the vessel.     

Mechanical buckling of artery under pulsatile pressure

Tortuosity that often occurs in carotid and other arteries has been shown to be associated with high blood pressure, atherosclerosis, and other diseases. However the mechanisms of tortuosity development are not clear. Our previous studies have suggested that arteries buckling could be a possible mechanism for the initiation of tortuous shape but artery buckling under pulsatile flow condition has not been fully studied. The objectives of this study were to determine the artery critical buckling pressure under pulsatile pressure both experimentally and theoretically, and to elucidate the relationship of critical pressures under pulsatile flow, steady flow, and static pressure. We first tested the buckling pressures of porcine carotid arteries under these loading conditions, and then proposed a nonlinear elastic artery model to examine the buckling pressures under pulsatile pressure conditions. Experimental results showed that under pulsatile pressure arteries buckled when the peak pressures were approximately equal to the critical buckling pressures under static pressure. This was also confirmed by model simulations at low pulse frequencies. Our results provide an effective tool to predict artery buckling pressure under pulsatile pressure.     

Pulsatile extracorporeal circulation during on-pump cardiac surgery enhances aortic wall shear stress

Controversy on superiority of pulsatile versus non-pulsatile extracorporeal circulation in cardiac surgery still continues. Stroke as one of the major adverse events during cardiopulmonary bypass is, in the majority of cases, caused by mobilization of aortic arteriosclerotic plaques that is inducible by pathologically elevated wall shear stress values. The present study employs computational fluid dynamics to evaluate the aortic blood flow and wall shear stress profiles under the influence of antegrade or retrograde perfusion with pulsatile versus non-pulsatile extracorporeal circulation. While, compared to physiological flow, a non-pulsatile perfusion resulted in generally decreased blood velocities and only moderately increased shear forces (48 Pa versus 20 Pa antegradely and 127 Pa versus 30 Pa retrogradely), a pulsatile perfusion extensively enhanced the occurrence of turbulences, maximum blood flow speed and maximum wall shear stress (1020 Pa versus 20 Pa antegradely and 1178 Pa versus 30 Pa retrogradely). Under these circumstances arteriosclerotic embolism has to be considered. Further simulations and experimental work are necessary to elucidate the impact of our findings on the scientific discourse of pulsatile versus non-pulsatile extracorporeal circulation.