Experimental study of hemodynamics in the circle of willis

Background

The Circle of Willis (CoW) is an important collateral pathway of the cerebral blood flow. An experimental study of the cerebral blood flow (CBF) distribution in different anatomical variations may help to a better understanding of the collateral mechanism of the CoW.

Methods

An in-vitro test rig was developed to simulate the physiological cerebral blood flow in the CoW. Ten anatomical variations were considered in this study, include a set of different degrees of stenosis in L-ICA and L-ICA occlusion coexist with common anatomical variations. Volume flow rates of efferent arteries and pressure signals at the end of communicating arteries of each case were recorded. Physiological pressure waveforms were applied as inlet boundary condition.

Results

In the development of L-ICA stenosis, the total CBF decreases with the increase of stenosis degree. The blood supply of ipsilateral middle cerebral artery (MCA) was affected most by the stenosis of L-ICA. Anterior communicating artery (ACoA) and ipsilateral posterior communicating artery (PCoA) function as important collateral pathways of cerebral collateral circulation when unilateral stenosis occurred. The blood supply of anterior cerebral circulation was compensated by the posterior cerebral circulation through ipsilateral PCoA when L-ICA stenosis degree is greater than 40% and the affected side was compensated immediately by the unaffected side through ACoA. Blood flow of the anterior circulation and the total CBF reached the minimum among all cases studied when L-ICA occlusion coexist with the absence of PCoA.

Conclusion

The results demonstrated the flow distribution patterns of the CoW under anatomical variations and clarified the collateral mechanism of the CoW. The flow ACoA is the most sensitive indexes to the morphology change of ipsilateral ICA. The relative independence of the circulation in anterior and posterior sections of the CoW is not broken and the function of ipsilateral PCoA is not activated until a severe stenosis of unilateral ICA occurs. PCoA is the most important collateral pathway of the collateral circulation and the missing of PCoA has the highest risk of stroke when the ipsilateral ICA has severe stenosis. These findings may provide the basis for future therapeutic and diagnosis applications.

     

Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows

Blood flow in the circle of Willis (CoW) is modelled using the 1-D equations of pressure and flow wave propagation in compliant vessels. The model starts at the left ventricle and includes the largest arteries that supply the CoW. Based on published physiological data, it is able to capture the main features of pulse wave propagation along the aorta, at the brachiocephalic bifurcation and throughout the cerebral arteries. The collateral ability of the complete CoW and its most frequent anatomical variations is studied in normal conditions and after occlusion of a carotid or vertebral artery (VA). Our results suggest that the system does not require collateral pathways through the communicating arteries to adequately perfuse the brain of normal subjects. The communicating arteries become important in cases of missing or occluded vessels, the anterior communicating artery (ACoA) being a more critical collateral pathway than the posterior communicating arteries (PCoAs) if an internal carotid artery (ICA) is occluded. Occlusions of the VAs proved to be far less critical than occlusions of the ICAs. The worst scenario in terms of reduction in the mean cerebral outflows is a CoW without the first segment of an anterior cerebral artery combined with an occlusion of the contralateral ICA. Furthermore, in patients without any severe occlusion of a carotid or VA, the direction of flow measured at the communicating arteries corresponds to the side of the CoW with an absent or occluded artery. Finally, we study the effect of partial occlusions of the communicating arteries on the cerebral flows, which again confirms that the ACoA is a more important collateral pathway than the PCoAs if an ICA is occluded.     

A 3D numerical study of the collateral capacity of the circle of Willis with anatomical variation in the posterior circulation

Background

The Circle of Willis (CoW) is the most important collateral pathway of the cerebral artery. The present study aims to investigate the collateral capacity of CoW with anatomical variation when unilateral internalcarotid artery (ICA) is occluded.

Methods

Basing on MRI data, we have reconstructed eight 3D models with variations in the posterior circulation of the CoW and set four different degrees of stenosis in the right ICA, namely 24%, 43%, 64% and 79%, respectively. Finally, a total of 40 models are performed with computational fluid dynamics simulations. All of the simulations share the same boundary condition with static pressure and the volume flow rate (VFR) are obtained to evaluate their collateral capacity.

Results

As for the middle cerebral artery (MCA) and the anterior cerebral artery (ACA), the transitional-type model possesses the best collateral capacity. But for the posterior cerebral artery (PCA), unilateral stenosis of ICA has the weakest influence on the unilateral posterior communicating artery (PCoA) absent model. We also find that the full fetal-type posterior circle of Willis is an utmost dangerous variation which must be paid more attention.

Conclusion

The results demonstrate that different models have different collateral capacities in coping stenosis of unilateral ICA and these differences can be reflected by different outlets. The study could be used as a reference for neurosurgeon in choosing the best treatment strategy.

     

Metabolic model of autoregulation in the Circle of Willis

The Circle of Willis (CoW) is a ringlike structure of blood vessels found at the base of the brain. Its main function is to distribute oxygen-rich arterial blood to the cerebral mass. In a previous study, a one-dimensional (1D) model of the CoW was created to simulate a series of possible clinical scenarios such as occlusions in afferent arteries, absent or stringlike circulus vessels, or arterial infarctions (Moorhead et al., 2004, Comput. Methods Biomech. Biomed. Eng., 7(3), pp. 121-130). The model captured cerebral haemodynamic autoregulation by using a proportional-integral-derivative (PID) controller to modify efferent artery resistances. Although some good results and correlations were achieved, the model was too simple to capture all the transient dynamics of autoregulation. Hence a more physiologically accurate model has been created that additionally includes the oxygen dynamics that drive the autoregulatory response. Results very closely match accepted physiological response and limited clinical data. In addition, a set of boundary conditions and geometry is presented for which the autoregulated system cannot provide sufficient perfusion, representing a condition with increased risk of stroke and highlighting the importance of modeling the haemodynamics of the CoW. The system model created is computationally simple so it can be used to identify at-risk cerebral arterial geometries and conditions prior to surgery or other clinical procedures.     

Integration of jugular venous return and circle of Willis in a theoretical human model of selective brain cooling.

A three-dimensional mathematical model was developed to examine the induction of selective brain cooling (SBC) in the human brain by intracarotid cold (2.8 degrees C) saline infusion (ICSI) at 30 ml/min. The Pennes bioheat equation was used to propagate brain temperature. The effect of cooled jugular venous return was investigated, along with the effect of the circle of Willis (CoW) on the intracerebral temperature distribution. The complete CoW, missing A1 variant (mA1), and fetal P1 variant (fP1) were simulated. ICSI induced moderate hypothermia (defined as 32-34 degrees C) in the internal carotid artery (ICA) territory within 5 min. Incorporation of the complete CoW resulted in a similar level of hypothermia in the ICA territory. In addition, the anterior communicating artery and ipsilateral posterior communicating artery distributed cool blood to the contralateral anterior and ipsilateral posterior territories, respectively, imparting mild hypothermia (35 and 35.5 degrees C respectively). The mA1 and fP1 variants allowed for sufficient cooling of the middle cerebral territory (30-32 degrees C). The simulations suggest that ICSI is feasible and may be the fastest method of inducing hypothermia. Moreover, the effect of convective heat transfer via the complete CoW and its variants underlies the important role of CoW anatomy in intracerebral temperature distributions during SBC.     

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.     

Lumped parameter and feedback control models of the auto-regulatory response in the Circle of Willis

The Circle of Willis (CoW) is a ring-like structure of blood vessels found beneath the hypothalamus at the base of the brain. Its main function is to distribute oxygen-rich arterial blood to the cerebral mass. A 1-dimensional model of the CoW has been created to simulate a series of possible clinical scenarios such as occlusions in afferent arteries, absent or string-like circulus vessels, or arterial infarctions. The model captures cerebral haemodynamic auto-regulation by using a proportional-integral-derivative (PID) controller to modify efferent resistances and maintain optimal efferent flowrates for a given circle geometry and afferent blood pressure. Results match limited clinical data and results obtained in prior studies to within 6%. In addition, a set of boundary conditions and geometry is presented for which the auto-regulated system cannot provide the necessary efferent flowrates and perfusion, representing a condition with increased risk of stroke and highlighting the importance of modelling the haemodynamics of the CoW. The system model created is computationally simple so it can be used to identify at-risk cerebral arterial geometries and conditions prior to surgery or other clinical procedures.     

Lumped Parameter and Feedback Control Models of the Auto-regulatory Response in the Circle of Willis

The Circle of Willis (CoW) is a ring-like structure of blood vessels found beneath the hypothalamus at the base of the brain. Its main function is to distribute oxygen-rich arterial blood to the cerebral mass. A 1-dimensional model of the CoW has been created to simulate a series of possible clinical scenarios such as occlusions in afferent arteries, absent or string-like circulus vessels, or arterial infarctions. The model captures cerebral haemodynamic auto-regulation by using a proportional-integral-derivative (PID) controller to modify efferent resistances and maintain optimal efferent flowrates for a given circle geometry and afferent blood pressure. Results match limited clinical data and results obtained in prior studies to within 6%. In addition, a set of boundary conditions and geometry is presented for which the auto-regulated system cannot provide the necessary efferent flowrates and perfusion, representing a condition with increased risk of stroke and highlighting the importance of modelling the haemodynamics of the CoW. The system model created is computationally simple so it can be used to identify at-risk cerebral arterial geometries and conditions prior to surgery or other clinical procedures.     

3D models of blood flow in the cerebral vasculature

The circle of Willis (CoW) is a ring-like arterial structure located in the base of the brain and is responsible for the distribution of oxygenated blood throughout the cerebral mass. To investigate the effects of the complex 3D geometry and anatomical variability of the CoW on the cerebral hemodynamics, a technique for generating physiologically accurate models of the CoW has been created using a combination of magnetic resonance data and computer-aided design software. A mathematical model of the body's cerebral autoregulation mechanism has been developed and numerous computational fluid dynamics simulations performed to model the hemodynamics in response to changes in afferent blood pressure. Three pathological conditions were explored, namely a complete CoW, a fetal P1 and a missing A1. The methodology of the cerebral hemodynamic modelling is proposed with the potential for future clinical application in mind, as a diagnostic tool.     

One-dimensional and three-dimensional models of cerebrovascular flow

The Circle of Willis is a ring-like structure of blood vessels found beneath the hypothalamus at the base of the brain. Its main function is to distribute oxygen-rich arterial blood to the cerebral mass. One-dimensional (1D) and three-dimensional (3D) computational fluid dynamics (CFD) models of the Circle of Willis have been created to provide a simulation tool which can potentially be used to identify at-risk cerebral arterial geometries and conditions and replicate clinical scenarios, such as occlusions in afferent arteries and absent circulus vessels. Both models capture cerebral haemodynamic autoregulation using a proportional-integral (PI) controller to modify efferent artery resistances to maintain optimal efferent flow rates for a given circle geometry and afferent blood pressure. The models can be used to identify at-risk cerebral arterial geometries and conditions prior to surgery or other clinical procedures. The 1D model is particularly relevant in this instance, with its fast solution time suitable for real-time clinical decisions. Results show the excellent correlation between models for the transient efferent flux profile. The assumption of strictly Poiseuille flow in the 1D model allows more flow through the geometrically extreme communicating arteries than the 3D model. This discrepancy was overcome by increasing the resistance to flow in the anterior communicating artery in the 1D model to better match the resistance seen in the 3D results.     

Endothelium-dependent vasodilation of cerebral arteries is altered with simulated microgravity through nitric oxide synthase and EDHF mechanisms.

Cephalic elevations in arterial pressure associated with microgravity and prolonged bed rest alter cerebrovascular autoregulation in humans. Using the head-down tail-suspended (HDT) rat to chronically induce headward fluid shifts and elevate cerebral artery pressure, previous work has likewise shown cerebral perfusion to be diminished. The purpose of this study was to test the hypothesis that 2 wk of HDT reduces cerebral artery vasodilation. To test this hypothesis, dose-response relations for endothelium-dependent (2-methylthioadenosine triphosphate and bradykinin) and endothelium-independent (nitroprusside) vasodilation were determined in vitro in middle cerebral arteries (MCAs) from HDT and control rats. All in vitro measurements were done in the presence and absence of the nitric oxide synthase inhibitor N(G)-nitro-L-arginine methyl ester (10(-5) M) and cyclooxygenase inhibitor indomethacin (10(-5) M). MCA caveolin-1 protein content was measured by immunoblot analysis. Endothelium-dependent vasodilation to 2-methylthioadenosine triphosphate and bradykinin were both lower in MCAs from HDT rats. These lower vasodilator responses were abolished with N(G)-nitro-L-arginine methyl ester but were unaffected by indomethacin. In addition, HDT was associated with lower levels of MCA caveolin-1 protein. Endothelium-independent vasodilation was not altered by HDT. These results indicate that chronic cephalic fluid shifts diminish endothelium-dependent vasodilation through alterations in the endothelial nitric oxide synthase signaling mechanism. Such decrements in endothelium-dependent vasodilation of cerebral arteries could contribute to the elevations in cerebral vascular resistance and reductions in cerebral perfusion that occur after conditions of simulated microgravity in HDT rats.     

Uncertainty quantification in cerebral circulation simulations focusing on the collateral flow: Surrogate model approach with machine learning

Collateral circulation in the circle of Willis (CoW), closely associated with disease mechanisms and treatment outcomes, can be effectively investigated using one-dimensional–zero-dimensional hemodynamic simulations. As the entire cardiovascular system is considered in the simulation, it captures the systemic effects of local arterial changes, thus reproducing collateral circulation that reflects biological phenomena. The simulation facilitates rapid assessment of clinically relevant hemodynamic quantities under patient-specific conditions by incorporating clinical data. During patient-specific simulations, the impact of clinical data uncertainty on the simulated quantities should be quantified to obtain reliable results. However, as uncertainty quantification (UQ) is time-consuming and computationally expensive, its implementation in time-sensitive clinical applications is considered impractical. Therefore, we constructed a surrogate model based on machine learning using simulation data. The model accurately predicts the flow rate and pressure in the CoW in a few milliseconds. This reduced computation time enables the UQ execution with 100 000 predictions in a few minutes on a single CPU core and in less than a minute on a GPU. We performed UQ to predict the risk of cerebral hyperperfusion (CH), a life-threatening condition that can occur after carotid artery stenosis surgery if collateral circulation fails to function appropriately. We predicted the statistics of the postoperative flow rate increase in the CoW, which is a measure of CH, considering the uncertainties of arterial diameters, stenosis parameters, and flow rates measured using the patients’ clinical data. A sensitivity analysis was performed to clarify the impact of each uncertain parameter on the flow rate increase. Results indicated that CH occurred when two conditions were satisfied simultaneously: severe stenosis and when arteries of small diameter serve as the collateral pathway to the cerebral artery on the stenosis side. These findings elucidate the biological aspects of cerebral circulation in terms of the relationship between collateral flow and CH.     

Cerebral hemodynamics response to low intensity physical exercise

The aim of this research was to study the cerebral hemodynamics reaction to step increase of physical exercises intensity during bicycle ergometer test in young healthy male subjects. Hemodynamics parameters were registered with the transcranial Doppler ultrasonography of middle cerebral artery (MCA) prior to the study and during the last seconds of every step of physical exercise. Cerebral hemodynamics response to physical exercise was characterized by a significant increase of peak systolic blood velocity in the MCA up to 0.25 W/kg of the body weight (90 rpm with regard to 0 W/kg) without further increase of blood velocity in the same physical exercise becoming more intensive up to 0.5 W/kg of the body weight. The stabilization mechanism of blood velocity in cerebral arteries in case of physical exercise increase and, hence, the autoregulation mechanism of cerebral circulation means that the increase of regional cerebral vascular resistance depends on the value of arterial pressure. The autoregulation mechanism of cerebral circulation starts working with he exercise intensity of 0.25 W/kg and the value of systolic blood pressure about 140-145 mm Hg.     

Cerebral perfusion changes in patients with internal carotid artery stenoses after surgical revascularization

Changes of cerebral perfusion and the condition of collateral blood supply in patients with internal carotid artery stenoses may have a prognostic value for effective blood flow restoration after revascularization of the internal carotid arteries (ICAs). To determine the patterns of cerebral perfusion changes in patients with ICA stenoses before and after surgical treatment, a clinical CT perfusion study of 41 patients with moderate to severe ICA stenoses was performed. Perfusion CT (PCT) had been conducted in 17 patients with moderate ICA stenoses (50–69%) and in 24 patients with severe ICA stenoses (70–99%) 3 times: before intervention (balloon angioplasty with stenting or carotid endarterectomy), on the 3rd to 7th day, and within 1 to 3 months after surgery. Scanning was performed at the level of the basal ganglia and semioval centers. In patients without ICA stenosis (control group of 39 individuals), PCT was conducted once. We found that surgical recanalization of the ICA leads to normalization of the cerebral blood flow parameters in the perfusion area of the middle cranial artery, as evidenced by a decrease of MTT and CBV and an increase of CBF to values comparable to those in the control group. However, blood flow restoration in the anterior and posterior watershed areas, which are known to be mostly affected under chronic hypoperfusion conditions, was observed only in patients with a complete circle of Willis (CW) and moderate ICA stenosis. Therefore, severe stenosis (>70%) and the incomplete CW are the prognostic factors for inadequate blood flow restoration after revascularization in patients with ICA stenoses.     

Three-dimensional hemodynamics analysis of the circle of Willis in the patient-specific nonintegral arterial structures

The hemodynamic alteration in the cerebral circulation caused by the geometric variations in the cerebral circulation arterial network of the circle of Wills (CoW) can lead to fatal ischemic attacks in the brain. The geometric variations due to impairment in the arterial network result in incomplete cerebral arterial structure of CoW and inadequate blood supply to the brain. Therefore, it is of great importance to understand the hemodynamics of the CoW, for efficiently and precisely evaluating the status of blood supply to the brain. In this paper, three-dimensional computational fluid dynamics of the main CoW vasculature coupled with zero-dimensional lumped parameter model boundary condition for the CoW outflow boundaries is developed for analysis of the blood flow distribution in the incomplete CoW cerebral arterial structures. The geometric models in our study cover the arterial segments from the aorta to the cerebral arteries, which can allow us to take into account the innate patient-specific resistance of the arterial trees. Numerical simulations of the governing fluid mechanics are performed to determine the CoW arterial structural hemodynamics, for illustrating the redistribution of the blood flow in CoW due to the structural variations. We have evaluated our coupling methodology in five patient-specific cases that were diagnosed with the absence of efferent vessels or impairment in the connective arteries in their CoWs. The velocity profiles calculated by our approach in the segments of the patient-specific arterial structures are found to be very close to the Doppler ultrasound measurements. The accuracy and consistency of our hemodynamic results have been improved (to \(16.1 \pm 18.5\) %) compared to that of the pure-resistance boundary conditions (of 43.5 \(\pm \) 28 %). Based on our grouping of the five cases according to the occurrence of unilateral occlusion in vertebral arteries, the inter-comparison has shown that (i) the flow reduction in posterior cerebral arteries is the consequence of the unilateral vertebral arterial occlusion, and (ii) the flow rate in the anterior cerebral arteries is correlated with the posterior structural variations. This study shows that our coupling approach is capable of providing comprehensive information of the hemodynamic alterations in the pathological CoW arterial structures. The information generated by our methodology can enable evaluation of both the functional and structural status of the clinically significant symptoms, for assisting the treatment decision-making.     

Impaired cerebrovascular autoregulation and reduced CO₂ reactivity after long duration spaceflight

Long duration habitation on the International Space Station (ISS) is associated with chronic elevations in arterial blood pressure in the brain compared with normal upright posture on Earth and elevated inspired CO(2). Although results from short-duration spaceflights suggested possibly improved cerebrovascular autoregulation, animal models provided evidence of structural and functional changes in cerebral vessels that might negatively impact autoregulation with longer periods in microgravity. Seven astronauts (1 woman) spent 147 ± 49 days on ISS. Preflight testing (30-60 days before launch) was compared with postflight testing on landing day (n = 4) or the morning 1 (n = 2) or 2 days (n = 1) after return to Earth. Arterial blood pressure at the level of the middle cerebral artery (BP(MCA)) and expired CO(2) were monitored along with transcranial Doppler ultrasound assessment of middle cerebral artery (MCA) blood flow velocity (CBFV). Cerebrovascular resistance index was calculated as (CVRi = BP(MCA)/CBFV). Cerebrovascular autoregulation and CO(2) reactivity were assessed in a supine position from an autoregressive moving average (ARMA) model of data obtained during a test where two breaths of 10% CO(2) were given four times during a 5-min period. CBFV and Doppler pulsatility index were reduced during -20 mmHg lower body negative pressure, with no differences pre- to postflight. The postflight indicator of dynamic autoregulation from the ARMA model revealed reduced gain for the CVRi response to BP(MCA) (P = 0.017). The postflight responses to CO(2) were reduced for CBFV (P = 0.056) and CVRi (P = 0.047). These results indicate that long duration missions on the ISS impaired dynamic cerebrovascular autoregulation and reduced cerebrovascular CO(2) reactivity.     

Regulation of middle cerebral artery blood velocity during recovery from dynamic exercise in humans.

We sought to examine the regulation of cerebral blood flow during 10 min of recovery from mild, moderate, and heavy cycling exercise by measuring middle cerebral artery blood velocity (MCA V). Transfer function analyses between changes in arterial blood pressure and MCA V were used to assess the frequency components of dynamic cerebral autoregulation (CA). After mild and moderate exercise, the decreases in mean arterial pressure (MAP) and mean MCA V (MCA Vm) were small. However, following heavy exercise, MAP was rapidly and markedly reduced, whereas MCA Vm decreased slowly (-23 +/- 4 mmHg and -4 +/- 1 cm/s after 1 min for MAP and MCA Vm, respectively; means +/- SE). Importantly, for each workload, the normalized low-frequency transfer function gain between MAP and MCA Vm remained unchanged from rest to exercise and during recovery, indicating a maintained dynamic CA. Similar results were found for the systolic blood pressure and systolic MCA V relationship. In contrast, the normalized low-frequency transfer function gain between diastolic blood pressure and diastolic MCA V (MCA Vd) increased from rest to exercise and remained elevated in the recovery period (P < 0.05). However, MCA Vd was quite stable on the cessation of exercise. These findings suggest that MCA V is well maintained following mild to heavy dynamic exercise. However, the increased transfer function gain between diastolic blood pressure and MCA Vd suggests that dynamic CA becomes less effective in response to rapid decreases in blood pressure during the initial 10 min of recovery from dynamic exercise.     

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

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

Assessment of Dynamic Cerebral Autoregulation in Patients with Basilar Artery Stenosis

Background and Aims

Previous studies have shown impaired cerebral autoregulation (CA) in carotid and middle cerebral artery (MCA) stenosis/occlusion. Little is known about CA in patients with basilar artery (BA) stenosis. We therefore investigated dynamic CA patterns in BA stenosis using transfer function analysis (TFA).

Methods

We measured spontaneous oscillations of blood flow velocity (CBFV) in the right posterior cerebral artery (PCA), and left MCA and mean arterial pressure (ABP) continuously in 25 patients with BA stenosis (moderate n=16 with 50-69% occlusion and severe n=9 with ≥70% occlusion) and 22 healthy volunteers in supine position during 6 circles per minute deep breath. Analysis was based on the ‘black-box’ model of transfer function deriving phase and gain in both PCA and MCA.

Results

Though changes of phase shift and gain between the patients and healthy controls were observed in MCA, the differences are however not significant. Phase shift in PCA was significantly decreased in severe stenosis when comparing with healthy controls and moderate stenosis (4.2±34.2° VS 41.1±40.4°, 4.2±34.2° VS 34.2±27.2°, both p<0.05), whilst the gain in PCA is increased for moderate BA stenosis and decreased for severe BA stenosis. Furthermore, we found that phase shift were almost abolished in patients with ischemic stroke who developed unfavorable clinical outcome (mRs>2) on the 90 days after stroke onset.

Conclusion

Dynamic CA in PCA reduces in patients with severe BA stenosis and those with ischemic stroke who present poor outcome in 90 days after stroke onset. Phase shift might be a sensitive index prompting impaired CA in posterior circulation.     

A global mathematical model of the cerebral circulation in man

A mathematical model of the cerebral circulation has been formulated. It was based on non-linear equations of pulsatile fluid flow in distensible conduits and applied to a network simulating the entire cerebral vasculature, from the carotid and vertebral arteries to the sinuses and the jugular veins. The quasilinear hyperbolic system of equations was numerically solved using the two-step Lax-Wendroff scheme. The model's results were in good agreement with pressure and flow data recorded in humans during rest. The model was also applied to the study of autoregulation during arterial hypotension. A close relationship between cerebral blood flow (CBF) and capillary pressure was obtained. At arterial pressure of 80 mmHg, the vasodilation of the pial arteries was unable to maintain CBF at its control value. At the lower limit of autoregulation (60 mm Hg), CBF was maintained with a 25% increase of zero transmural pressure diameter of nearly the whole arterial network.