Numerical simulations of the blood flow through vertebral arteries

Vertebral arteries are two arteries whose structure and location in human body result in development of special flow conditions. For some of the arteries, one can observe a significant difference between flow rates in the left and the right arteries during ultrasonography diagnosis. Usually the reason of such a difference was connected with pathology of the artery in which a smaller flow rate was detected. Simulations of the flow through the selected type of the vertebral artery geometry for twenty five cases of artery diameters have been carried out. The main aim of the presented experiment was to visualize the flow in the region of vertebral arteries junction in the origin of the basilar artery. It is extremely difficult to examine this part of human circulation system, thus numerical experiments may be helpful in understanding the phenomena occurring when two relatively large arteries join together to form one vessel. The obtained results have shown that an individual configuration and diameters of particular arteries can exert an influence on the flow in them and affect a significant difference between flow rates for vertebral arteries. It has been assumed in the investigations that modelled arteries were absolutely normal, without any pathology. In the numerical experiment, the non-Newtonian model of blood was employed.     

Numerical simulation of blood pulsatile flow in a stenosed carotid artery using different rheological models

Symmetrical 30-60% stenosis in a common carotid artery under unsteady flow condition for Newtonian and six non-Newtonian viscosity models are investigated numerically. Results show power-law model produces higher deviations, in terms of velocity and wall shear stress in comparison with other models while generalized power-law and modified-Casson models are more prone to Newtonian state. Comparing separation length of recirculation region at different critical points of cardiac cycle confirms the necessity of considering blood flow in unsteady mode. Increasing stenosis intensity causes flow patterns more disturbed downstream of the stenosis and WSS appear to develop remarkably at the stenosis throat.     

Numerical models of auto-regulation and blood flow in the cerebral circulation

A two-dimensional time-dependent computational fluid dynamics model of the Circle of Willis has been developed. To simulate, not only the peripheral resistance of the cerebrovascular tree but also its auto-regulation function, a new "active" boundary condition has been defined and developed using control theory to provide a model of the feedback mechanism. The model was then used to simulate different common abnormalities of the Circle of Willis while a pressure drop, simulating a rapid compression of the right internal carotid artery, was imposed. Test results using a simple tube compared excellently with experiment. The total time-dependent flux for each efferent artery was tabulated and showed the important relationship between geometrical variations in the Circle of Willis and the auto-regulation of blood flow by vascular vaso-dilation and contraction. From this study, it was found that the worst case seemed to be that of a missing or dysfunctional right A1 segment of the anterior cerebral artery. The use of valid physiological models of the peripheral resistance allows for more realistic models of the blood flow in the Circle whilst allowing an easy extension to 3D patient specific simulations.     

Hemodynamics of local cerebral blood flow induced by somatosensory stimulation under normoxia and hyperoxia in rats.

We observed changes in the local cerebral blood flow (LCBF), red blood cell (RBC) concentration and RBC velocity in alpha-chloralose anesthetized rats using laser-Doppler flowmetry during activation of the somatosensory cortex following electrical stimulation of the hind paw under hyperoxia (PaO(2)=513.5+/-48.4 mmHg; mean+/-S.D.) and normoxia (PaO(2)=106.4+/-8.4 mmHg). Electrical stimuli of 5 and 10 Hz (pulse width 0.1 ms) with an intensity of 1.5 mA were applied for 5 s (n=13 at 5 Hz, n=9 at 10 Hz). Baseline levels of LCBF and RBC concentration under hyperoxia were, respectively, 5.6+/-3.3 and 8.8+/-3.0% lower than those under normoxia (P<0.05), and that of RBC velocity under hyperoxia was slightly higher than that under normoxia (NS), suggesting mild vasoconstriction at rest under hyperoxia. At 5 Hz stimulation, after normalization to each baseline level, normalized response magnitudes of LCBF, RBC concentration and RBC velocity under hyperoxia were, respectively, 68.2+/-48.0, 71.1+/-65.5 and 66.0+/-56.3% greater than those under normoxia (P<0.05). At 10-Hz stimulation, normalized response magnitudes of LCBF and RBC concentration under hyperoxia were, respectively, 44.6+/-32.0 and 55.9+/-43.5% greater than those under normoxia (P<0.05), although a significant difference in the normalized response magnitude of RBC velocity was not detected between both conditions. The evoked LCBF under hyperoxia increased earlier, by approximately 0.15 s, than that under normoxia regardless of the stimulus frequency (P<0.05). These results suggest the involvement of oxygen interaction on the regulation of LCBF during neuronal activation.     

Analysis of the timing parameters of blood flow in the carotid basin arteries of hypertensive patients

Vascular duplex ultrasound study with simultaneous ECG recording was performed to estimate the timing parameters of blood flow in the common carotid, internal carotid, and middle cerebral arteries in patients with grades 1 and 2 arterial hypertension. There was an increase in the blood flow acceleration phase index in the common carotid and middle cerebral arteries and a reduction in the systolic phase index in the internal carotid arteries. There were correlations of phasic blood flow parameters in the extra- and intracranial arteries with age and lipidogram readings.     

Emesis, radiation exposure, and local cerebral blood flow in the ferret

We examined the sensitivity of the ferret to emetic stimuli and the effect of radiation exposure near the time of emesis on local cerebral blood flow. Ferrets vomited following the administration of either apomorphine (approx 45% of the ferrets tested) or peptide YY (approx 36% of those tested). Exposure to radiation was a very potent emetic stimulus, but vomiting could be prevented by restraint of the hindquarters of the ferret. Local cerebral blood flow was measured using a quantitative autoradiographic technique and with the exception of several regions in the telencephalon and cerebellum, local cerebral blood flow in the ferret was similar to that in the rat. In animals with whole-body exposure to moderate levels of radiation (4 Gy of 137Cs), mean arterial blood pressure was similar to that in the control group. However, 15-25 min following irradiation there was a general reduction of local cerebral blood flow ranging from 7 to 33% of that in control animals. These cerebral blood flow changes likely correspond to a reduced activation of the central nervous system.     

Numerical technique of blood flow through catheterized arteries with overlapping stenosis

This study is concerned with the surgical technique for the injection of a catheter through arteries with overlapping stenosis in the presence of externally applied magnetic field and Hall currents influences. The nature of blood is analyzed mathematically by considering it as a micropolar fluid. The analysis is carried out for an artery with a mild stenosis. The governing equations with the corresponding boundary conditions solved numerically using Crank–Nicolson implicit finite difference scheme. The numerical technique give excellent agreement for axial velocity of the fluid, the circumferential microrotation, the wall shear stress distribution and the contour plots of stream lines. The obtained results show that the value of axial velocity is higher for a Newtonian fluid than that for a micropolar fluid model, the effect of suitable moving magnetic field (Hall currents influences) accelerates the speed of blood, the size of trapped bolus for the stream lines decrease if the spinning movement of the fluid molecules have considerable value regardless of small or large size of the fluid molecules and the flow of fluid is better with increasing the Hall current effect and the size of trapping bolus increase clearly by increasing the maximum height of stenosis where the fluid moves as a bulk.     

Behavioral state transition and local cerebral blood flow in fetal sheep.

Local cerebral blood flow in four near term fetal sheep was evaluated continuously before and after natural alternations in fetal behavioral state. Measurements were made in fetuses several days following an aseptic surgery to place electrodes for behavioral state recordings as well as heated and reference thermojunctions in cortical and subcortical tissue. These thermojunctions were used to qualitatively assess local cerebral blood flow. The time of transition between rapid eye movement sleep (REMS) and non-rapid eye movement sleep (NREMS) was based on visual inspection of strip chart recordings of electrocortical, electroocular, and neck electromyographic activity and application of published criteria for their assessment. To confirm that transition had occurred, the amplitude of the spectrum of the electrocorticogram in one-third octave bands centered around 1 Hz and 20 Hz was measured before and after the transition point. Mean cerebral blood flow rose significantly by 24 s (P less than 0.05) after the transition from NREMS to REMS and fell by 12 s after the transition from REMS to NREMS (P less than 0.05).     

Study of human cerebral blood flow by corrosion casts of the carotid system

20 corrosion casts of human anterior cerebral arteries and middle cerebral arteries were analyzed. In 588 vessel sections in between 2 bifurcations, the relation of vessel length and vessel diameter was investigated. Measurements were taken starting from the arterial trunk down to vessels with a diameter of 0.4 mm. The mean values of the lengths show that both the anterior cerebral artery and the middle cerebral artery can be grouped into 5 diameter ranges with significant different lengths. With decreasing diameter there are short vessels in the groups 1, 3 and 5 and long vessels in the groups 2 and 4. However, the long branches in the groups 2 and 4 of the middle cerebral artery are longer and thinner than in the anterior cerebral artery. Due to the higher pressure loss in thin and long vessels, blood pressure drop occurs earlier in the branches of the middle cerebral artery than in those of the anterior cerebral artery.     

WISE-2005: reduced cerebral blood flow velocity with nitroglycerin--comparison with common carotid artery blood flow

During the WISE-2005 study of 24 women, we observed a reduction (21.6 +/- 0.89%, mean +/- SEM) in cerebral blood flow velocity (CBV) measured by transcranial Doppler ultrasound, following 0.3 mg sublingual nitroglycerin (NG). In parallel, we observed quantitative reductions in leg blood flow (47.3 +/- 7.0%) and corresponding reductions in calculated conductance (Conductance = Femoral Flow / Mean Arterial Pressure; 45.7 +/- 7.2%). To determine if the reduction in CBV was the result of reduced cerebral blood flow or dilation of the middle cerebral artery (MCA), the change in CBV in the MCA was compared with changes in quantitative flow measured in the common carotid artery (CCA). The relationship between CBV and CCA blood flow was tested in five men and four women using hyper- and hypo-ventilation to manipulate arterial PCO2. Changes in CCA blood flow were positively correlated with changes in CBV (p<0.001). We then investigated the CBV and CCA flow responses to sublingual NG in an additional two men and six women. Concurrent with the reduction in CBV there was no change in blood flow through the CCA (p>0.05). These results indicate that the decrease in CBV observed in response to NG was probably the result of dilation of the MCA and that total cerebral blood flow was similar after administration of NG. These results suggest regional differences in the vascular responses to NG during the WISE bed rest. Conduit vessels of both the peripheral and cerebral vasculature dilated; however, the resistance vessels in skeletal muscle constricted causing a reduction in blood flow, while the resistance vessels of the brain appeared to be unaffected by NG so that cerebral blood flow remained constant. These results highlight the need to obtain quantitative measures of cerebral blood flow if there is reason to suspect that the diameter of the MCA might not remain constant.     

Numerical simulations of the blood flow in the patient-specific arterial cerebral circle region

The Cerebral Circle Region, also known as the Circle of Willis (CoW), is a loop of arteries that form arterial connections between supply arteries to distribute blood throughout the cerebral mass. Among the population, only 25% to 50% have a complete system of arteries forming the CoW. 3D time-varying simulations for three different patient-specific artery anatomies of CoW were performed in order to gain a better insight into the phenomena existing in the cerebral blood flow. The models reconstructed on the basis of computer tomography images start from the aorta and include the largest arteries that supply the CoW and the arteries of CoW. Velocity values measured during the ultrasound examination have been compared with the results of simulations. It is shown that the flow in the right anterior artery in some cases may be supplied from the left internal carotid artery via the anterior communicating artery. The investigations conducted show that the computational fluid dynamic tool, which provides high resolution in both time and space domains, can be used to support physicians in diagnosing patients of different ages and various anatomical arterial structures.     

The importance of blood rheology in patient-specific computational fluid dynamics simulation of stenotic carotid arteries

Biomechanics and Modeling in Mechanobiology - The initiation and progression of atherosclerosis, which is the main cause of cardiovascular diseases, correlate with local haemodynamic factors such...     

Atherosclerosis and flow in carotid arteries with authentic geometries

The influence of blood flow on the depositions and development of atherosclerotic lesions have been observed and described since the 19th century. Observations have shown that depositions correlate with regions of low wall shear stress. However, the exact correlations between depositions, vessel geometry and flow parameters are not yet known. The purpose of this study was the quantification of atherosclerosis risk factors in carotid bifurcation. This artery has attracted particular interest because lesions are often found in this bifurcation. Post mortem, the arteries are excised and vessel casts are produced. Afterwards, the arteries are analyzed morphometrically. The vessel casts are used for the assessment of some geometrical parameters. 31 carotid bifurcations were analyzed in this study. Eight vessel casts were digitized and rendered three-dimensional mathematical models of the arteries. These data were imported by the computational fluid dynamics program FLUENT. Further, the blood flow was reconstructed in a computer model based on the individual vessel geometry. The flow parameters, such as velocity, pressure and wall shear stress were computed. At the same time the geometrical parameters and wall alterations are known. This permits the comparison of the anatomical shape and its flow with the distribution and level of the wall alterations.     

Numerical simulation and comparative analysis of flow field in axial blood pumps

The objective study was to estimate the rheological properties and physiological compatibility of the blood pump by simulating the internal flow field of the blood pump. In this study we use computational fluid dynamics method to simulate and analyse two models of axial blood pumps with a three-blade diffuser and a six-blade diffuser, named pump I and pump II, respectively, and to compare the flow patterns of these two kinds of blood pumps while both of them satisfy the conditions of the normal human blood differential pressure and blood flow. Results indicate that (i) the high shear force occurs between the diffuser and the rotor in which the crucial place leads to haemolysis and (ii) under the condition of 100 mmHg pressure head and 5 l/min flow rate, the difference between the two kinds of blood pumps, as far as the haemolytic performance is concerned, is notable. The haemolysis index of the two pumps is 0.32% and 0.2%. In conclusion, the performance of the blood pump is influenced by the diffusers' blade number. Pump II performed better than pump I, which can be the basic model for blood pump option.     

Numerical simulation of non-Newtonian blood flow dynamics in human thoracic aorta

Three non-Newtonian blood viscosity models plus the Newtonian one are analysed for a patient-specific thoracic aorta anatomical model under steady-state flow conditions via wall shear stress (WSS) distribution, non-Newtonian importance factors, blood viscosity and shear rate. All blood viscosity models yield a consistent WSS distribution pattern. The WSS magnitude, however, is influenced by the model used. WSS is found to be the lowest in the vicinity of the three arch branches and along the distal walls of the branches themselves. In this region, the local non-Newtonian importance factor and the blood viscosity are elevated, and the shear rate is low. The present study revealed that the Newtonian assumption is a good approximation at mid-and-high flow velocities, as the greater the blood flow, the higher the shear rate near the arterial wall. Furthermore, the capabilities of the applied non-Newtonian models appeared at low-flow velocities. It is concluded that, while the non-Newtonian power-law model approximates the blood viscosity and WSS calculations in a more satisfactory way than the other non-Newtonian models at low shear rates, a cautious approach is given in the use of this blood viscosity model. Finally, some preliminary transient results are presented.     

Numerical simulation of blood and interstitial flow through a solid tumor

A theoretical framework is presented for describing blood flow through the irregular vasculature of a solid tumor. The tumor capillary bed is modeled as a capillary tree of bifurcating segments whose geometrical construction involves deterministic and random parameters. Blood flow along the individual capillaries accounts for plasma leakage through the capillary walls due to the transmural pressure according to Sterling’s law. The extravasation flow into the interstitium is described by Darcy’s law for a biological porous medium. The pressure field developing in the interstitium is computed by solving Laplace’s equation subject to derived boundary conditions at the capillary vessel walls. Given the arterial, venous, and tumor surface pressures, the problem is formulated as a coupled system of integral and differential equations arising from the interstitium and capillary flow transport equations. Numerical discretization yields a system of linear algebraic equations for the interstitial and capillary segment pressures whose solution is found by iterative methods. Results of numerical computations document the effect of the interstitial hydraulic and vascular permeability on the fractional plasma leakage. Given the material properties, the fractional leakage reaches a maximum at a particular grade of the bifurcating vascular tree.