Simulation study of brain blood flow regulation by intra-cortical arterioles in an anatomically accurate large human vascular network. Part II: flow variations induced by global or localized modifications of arteriolar diameters.

In a companion paper (Lorthois et al., Neuroimage, in press), we perform the first simulations of blood flow in an anatomically accurate large human intra-cortical vascular network (~10000 segments), using a 1D non-linear model taking into account the complex rheological properties of blood flow in microcirculation. This model predicts blood pressure, blood flow and hematocrit distributions, volumes of functional vascular territories, regional flow at voxel and network scales, etc. Using the same approach, we study flow reorganizations induced by global arteriolar vasodilations (an isometabolic global increase in cerebral blood flow). For small to moderate global vasodilations, the relationship between changes in volume and changes in flow is in close agreement with Grubb's law, providing a quantitative tool for studying the variations of its exponent with underlying vascular architecture. A significant correlation between blood flow and vascular structure at the voxel scale, practically unchanged with respect to baseline, is demonstrated. Furthermore, the effects of localized arteriolar vasodilations, representative of a local increase in metabolic demand, are analyzed. In particular, localized vasodilations induce flow changes, including vascular steal, in the neighboring arteriolar trunks at small distances (<300 µm), while their influence in the neighboring veins is much larger (about 1 mm), which provides an estimate of the vascular point spread function. More generally, for the first time, the hemodynamic component of various functional neuroimaging techniques has been isolated from metabolic and neuronal components, and a direct relationship with several known characteristics of the BOLD signal has been demonstrated.

Simulation study of brain blood flow regulation by intra-cortical arterioles in an anatomically accurate large human vascular network: Part I: methodology and baseline flow.

Hemodynamically based functional neuroimaging techniques, such as BOLD fMRI and PET, provide indirect measures of neuronal activity. The quantitative relationship between neuronal activity and the measured signals is not yet precisely known, with uncertainties remaining about the relative contribution by their metabolic and hemodynamic components. Empirical observations have demonstrated the importance of the latter component and suggested that micro-vascular anatomy has a potential influence. The recent development of a 3D computer-assisted method for micro-vascular cerebral network analysis has produced a large quantitative library on the microcirculation of the human cerebral cortex (Cassot et al., 2006), which can be used to investigate the hemodynamic component of brain activation through fluid dynamic modeling. For this purpose, we perform the first simulations of blood flow in an anatomically accurate large human intra-cortical vascular network (~10000 segments), using a 1D non-linear model taking account of the complex rheological properties of blood flow in microcirculation. This model predicts blood pressure, blood flow and hematocrit distributions, as well as volumes of functional vascular territories, and regional flow at voxel and network scales. First, the influence of the prescribed boundary conditions (BCs) on the baseline flow structure is investigated, highlighting relevant lower- and upper-bound BCs. Independent of these BCs, large heterogeneities of baseline flow from vessel to vessel and from voxel to voxel, are demonstrated. These heterogeneities are controlled by the architecture of the intra-cortical vascular network. In particular, a correlation between the blood flow and the proportion of vascular volume occupied by arterioles or venules, at voxel scale, is highlighted. Then, the extent of venous contamination downstream to the sites of neuronal activation is investigated, demonstrating a linear relationship between the catchment surface of the activated area and the diameter of the intra-cortical draining vein.

Velocity field of a Björk-Shiley valve prosthesis: influence of the disc orientation.

An experimental investigation was carried out on the development of physiological flows downstream of a Björk-Shiley valve prosthesis. The post-valvular velocity field was determined by an ultrasonic method in an elastic model of the aortic arch. The flow development in the ascending aorta was strongly dependent on the orientation of the tilting disc. The rotating direction of the vortices and the site of the maximum velocity were influenced by the orientation.

Velocity profiles in the wake of two prosthetic heart valves using a new cardiovascular simulator.

In this paper we present a study of the post valvular flow field on a new cardiovascular simulator including an elastic model of the aortic arch. Transverse and vertical two-dimensional velocity measurements are performed with an ultrasonic velocimeter. Two prosthetic heart valves are tested in the aortic position. The behaviour of the velocity vectors patterns during one pulsatile cycle is one of the most striking features of the flow.

Hemodynamic role of the circle of Willis in stenoses of internal carotid arteries. An analytical solution of a linear model.

A mathematical model of blood flow through the circle of Willis was developed, within a linear framework. Comprehensive analytical solutions, including a remarkably small number of parameters, were derived in the cases of obstructive lesions of extracranial carotid arteries. The influence of these lesions and the role of anterior and posterior communicating arteries on the blood pressure at the entry of the cerebral territories were quantified and analyzed emphasizing that the responses of the system of Willis to obstructive carotid lesions are extremely varied, depending on the communicating artery anatomy. Comparison with numerical results obtained by using a non-linear model showed no physiologically significant differences. Such a model might be an essential tool for an accurate assessment of the cerebral hemodynamics in carotid diseases.

Near velocity field downstream prosthetic valves in aortic position.

Using a cardiovascular simulator to duplicate in vitro the flow conditions through valves in aortic position, bidimensional velocity maps very near the valve are reconstructed, from an ultrasonic 8 Mhz doppler system, in an elastic model of the ascending aortic arch. Three mechanical heart valves representative of the different types of commercial models (a tilting disc, a ball in cage and a two-leaflet valve) and a new bileaflet prototype were investigated. From examination of the velocity field, it is possible to define the main characteristics of the valve wake and to observe the development of negative velocities associated with regurgitant flows. From a comparison with tests in rigid tubes, the role played by the arch elasticity is analysed.

Flow analysis within the left ventricle using an integral equation method: interest in left ventricular function assessment.

The following parameters are derived from a hydrodynamic analysis of left ventricular ejection: pressure distribution along ventricular long axis and walls, regional and net forces applied to the blood within the ventricle. They are computed from human ventricular contours (angiograms), using an original application of integral equation method and numerical analysis. This technique enables flow analysis inside bodies of any shape. Comparison of each parameter computed from normal and infarcted (akinetic or bulged) ventricles shows that hydrodynamic analysis within the human left ventricle may provide better documented and quantitative assessment of its muscular and pump function than does morphological analysis of cardiac imaging.

Mechanical aspect of the heart sound emission.

The present paper deals with a physical study of the relation between the phonocardiogram and left ventricular pressure (LVP) fluctuations. Fourier analysis comparison of the two signals-simultaneously recorded either on pathologic human hearts or during experiments on dogs-does not point out an obvious relation between the phonocardiogram and a linear combination of the first pressure derivatives.-A mechanical model of the heart enabling the description of the sound emission mechanism provides a qualitative relation between the phonocardiogram and LVP fluctuations: the acceleration of the thoracic area is equal to the product of LVP by a time function depending on the mechanical properties of the muscle. - A theoretical thoracic acceleration obtained by transformation of the experimental LVP is compared with the experimental phonocardiogram through linear filtering analysis. The theoretical signal is in good agreement with the experimental one.

Heat and mass transfer of a thermal indicator in pulsatile flow through the cardio-pulmonary system. II. Identification of cardiac output.

Hamilton's celebrated formula for cardiac output measurement is simple but its validity is dependent on several methodologic requirements which are not generally fulfilled, particularly in thermal dilution. A quite different method, based on a physico-mathematical model of the indicator dispersion in the circulation, is proposed. It allows direct derivation of cardiac output once the model's parameters have been identified. Combined deconvolution and least squares procedures are used with truncated data for this identification. Numerical tests and application to clinical observations are presented. Both limitations and possibilities of further developments in estimation of pulsatile flow conditions from TD technique are discussed.

Heat and mass transfer of a thermal indicator in pulsatile flow through the cardio-pulmonary system. I. Modeling.

The construction of a physico-mathematical model which describes the mechanism of indicator dispersion in the circulation and which fits the thermal dilution curves (TDC) is presented. Because of its more evident physical meaning, formulation of the problem in terms of heat and mass transfer is preferred to stochastic theory. Hypotheses necessary to simplify the general system of governing equations are clearly defined and discussed. This deductive method leads to a one-dimensional convective heat transfer model in which pulsatility and form of injection appear naturally. Simulations of TDC in constant and pulsatile flow cases are performed on a digital mini-computer which demonstrates the model's ability to represent different experimental or clinical observations. This will facilitate hemodynamic parameter identification from TD techniques and will increase the accuracy of this identification.

Relationship of pulmonary diastolic and pulmonary wedge pressures to left ventricular diastolic pressures: role of acute myocardial infarction localization.

Right and left hemodynamics have been simultaneously studied in 127 patients with acute myocardial infarction with respect to electrocardiographic localization. Hemodynamic profiles of the different localizations suggest a high incidence of right ventricular dysfunction in infero-posterior infarcts. The comparison with the other localizations suggests that such a right ventricular dysfunction is likely to be responsible for an additional underestimation of left ventricular end-diastolic pressure when estimated by pulmonary diastolic pressure.

[In vitro determination of the pressure-diameter relationship and velocity profiles by ultrasonic technics. In vivo application]. / Détermination in vitro de la relation pression-diamètre et des profils de vitesse par des techniques ultrasonores. Application in vivo.

A good knowledge of arterial flow mechanics and of the phenomena associated with fluid-boundary interactions is necessary for the determination of some fundamental parameters such as velocity, pressure and pressure-diameter relationship during a cardiac cycle. Ultrasonic techniques were developed on a test bench and directly applied to animals without major modification. On such a test bench allowing a good simulation of physiological type flows, velocity field and pressure-diameter relationship were determined. In vivo application of these techniques allowed a systematic analysis of velocity profiles in the rabbit abdominal aorta and a precise approach of rheological properties of the vascular wall.

Maximal wall shear stress in arterial stenoses: application to the internal carotid arteries.

Maximal wall shear stress (MWSS) in the convergent part of a stenosis is calculated by the interactive boundary-layer theory. A dimensional analysis of the problem shows that MWSS depends only on a few measurable parameters. A simple relationship between MWSS and these parameters is obtained, validated, and used to calculate the magnitude of MWSS in a carotid stenosis, as a function of the patency of the circle of Willis and the stenotic pattern. This demonstrates the huge effect of collateral pathways. Elevated MWSS are observed even in moderate stenoses, provided they are associated with a contralateral occlusion, a large anterior, and narrow posterior communicating arteries, suggesting a potential risk of embolus release in this configuration.

Effects of anterior communicating artery diameter on cerebral hemodynamics in internal carotid artery disease. A model study.

BACKGROUND: Collateral circulatory pathways are considered the primary determinant of cerebral hemodynamics in patients with obstructive lesions of the internal carotid arteries (ICaAs). However, the hemodynamic effects of the diameter of the anterior communicating artery (ACoA) have never been assessed quantitatively in humans. METHODS AND RESULTS: Two different mathematical models were used to simulate changes affecting blood pressures and flows in cerebral arteries as a function of ACoA diameter and ICaA stenoses or occlusions. Small changes in ACoA diameter were found to have marked hemodynamic effects when they occurred within the range of 0.4 to 1.6 mm, a situation observed in 80% of the cases. Outside this range, changes in ACoA diameter had no effect. Simulated pressure drops through a stenotic ICaA were consistent with those observed. They were found to depend on the degrees of the stenoses in both ICaAs and on ACoA diameter according to a simple equation. Pressure reserve in the middle and anterior cerebral arteries decreased to below the lower limit of autoregulation, despite a normal mean arterial blood pressure, when the arteries were distal to a unique 70% ICaA stenosis associated with a small-diameter ACoA or to a 50% ICaA stenosis associated with a contralateral ICaA occlusion and a large-diameter ACoA. Above these thresholds, the circle of Willis allowed for an almost complete global cerebral blood flow compensation that involved all the afferent and communicating vessels. CONCLUSIONS: ACoA diameter strongly modulates the effects of ICaA lesions on cerebral hemodynamics. Some proposals for endarterectomy indications can be derived from our study.