Use of Phase-Contrast MRA to Assess Intracranial Venous Sinus Resistance to Drainage in Healthy Individuals

Discussion

It has been suggested that cerebral venous sinus insufficiency is a major factor in certain neurovascular diseases.^{4,5,8⇓–10,23} Apart from evaluations of anatomic abnormalities and the quantification of narrowed vessels and abnormal flow/pressure patterns,^24,25 little is known about resistance to blood flow in the cerebral venous sinus drainage system. Here, we describe a novel approach for calculating the Rd through the cerebral venous tree; it is based on the application of the Poiseuille equation for laminar flow to data from phase-contrast MRA, a highly sensitive technique for noninvasive imaging of the cerebral venous sinus system.²⁶

In the present study, we hypothesized that turbulent flow conditions occur very infrequently. To confirm this hypothesis, we calculated the Reynolds number (Re) for the study participants' superior sagittal sinus and IJVs according to the following equation: Re = ρVD / μ, where V is the maximum velocity, D is the diameter of the luminal cross-section, ρ is the attenuation of blood, and μ is the viscosity of blood. The highest Reynolds number that we obtained was 392, well below the value of 2000 at which turbulent flow conditions can be expected.²⁷

The blood flows through the IJVs measured in our study agree with the literature data.²⁸ We also observed relatively high interindividual variations in both the calculated Rd and outflows. These flow variations have been reported by others² and may reflect anatomic variants rather than changes in physiologic conditions.¹¹ The total venous flow appeared to be correlated with the overall Rd of the venous sinus tree, though the relationship did not achieve statistical significance. One possible explanation is that our representation of the very complex venous sinus pathway was oversimplified; some branches of the venous drainage network were not taken into account in our calculation of the overall resistance. For example, the straight sinus drains the deep venous system through the inferior sagittal sinus and the vein of Galen.²⁹ The transverse sinus also receives the superior petrosal sinuses and the veins of Labbé, which drain blood from the temporo-occipital cortex. Moreover, the drainage pathways include the emissary veins, vertebral veins, and pterygoid plexus; this network may also explain the lack of a statistically significant correlation between the values of the overall Rd and the total IJV flow measurements. We chose to limit our measurements to the major dural sinuses, in view of the high interindividual variations in the venous sinus system.³⁰

Another unique feature of the cerebral venous drainage system is its dependence on posture. In the upright position, the IJVs tend to collapse and thus prompt a concomitant rise in flow in the vertebral veins³¹; in the supine position, they are the main drainage pathways for the cerebral outflow. Our participants were imaged in the supine position, which minimized the impact of position on both flow and Rd measurements of the IJVs.

The present findings and previous reports^2,32 show that venous drainage is dominated by the right outflow, reflecting the asymmetry in the resistance between the left and right sides of the venous sinus pathway. Furthermore, the relationship between resistance and flow was highlighted by our observation of a strong, inverse correlation between the resistance AIs and the flow AIs. The presence of an inverse association may indicate a lateralization effect, whereby one side compensates for the other.^2,28 It may also underline the importance of flow resistance in the regulation of cerebral blood outflow. Although our results are preliminary, they suggest that the cumulative effects of resistance to flow along vessel segments may have repercussions on the intracranial hydrodynamics, insofar as cerebral blood outflow may be influenced by the venous sinus resistance to flow. It is also possible that an elevated Rd across the cerebral sinus pathways contributes to the elevation of blood pressure on the venous side of the cerebral vascular tree. An elevation in venous pressure makes the cortical veins stiffer and induces a decrease in craniospinal compliance.³³ Furthermore, several researchers have emphasized the relevance of the venous sinus drainage system in hydrocephalus.^9,10 One hypothesis is that elevated pressure in the venous system may lead to alterations in CSF resorption through the arachnoid granulations. Moreover, other researchers have suggested that reduced cortical vein compliance and reduced superior sagittal sinus flow in normal-pressure hydrocephalus indicate the presence of a significant elevation in the resistance to flow through these vessels.^34,35 The balance between cerebral arterial inflow and venous outflow contributes to the maintenance of normal intracranial pressure, which depends not only on the arterial volume input and CSF volume but also on venous outflow.

The effect of intracranial fluid dynamics on intracranial pressure is a major component of the Monro-Kellie^36,37 doctrine. As presented in Wilson's recent review,³⁸ increasing evidence suggests that a venous pathology is central to the multiple conditions that cause a rise in intracranial pressure. A better understanding of the role of the venous system in neurocritical care is essential. In a prospective controlled study based on a grading system, Farb et al²⁵ showed sinovenous stenosis in 27 of 29 patients with idiopathic intracranial hypertension and in only 4 of 59 control patients. Moreover, the severity of intracranial hypertension (which depends on the degree of venous congestion) was found to be closely related to the intradural sinus pressure.³⁹ As the latter rises, slight parenchymal damage may progress to severe cerebral edema and/or hematoma if thrombolysis is delayed. Furthermore, some researchers have suggested that benign intracranial hypertension may be caused by venous hypertension,^19,20 mostly due to stenosis or occlusions of the lateral sinuses. Moreover, it has been shown that dilation of one of the sinuses with a stent may reduce the pressure gradient and produce a striking reduction in symptoms.⁴⁰ This venous sinus stent placement technique had a high technical success rate and was highly effective (80%) in reducing the headache associated with benign intracranial hypertension.⁴¹ Nevertheless, sinus stenosis appears to result from elevated CSF pressure (rather than hypertension) in some cases.⁴²

Also, there is some evidence that idiopathic intracranial hypertension may be characterized by elevated central venous pressure²⁰ in the absence of ventricular dilation, a mass lesion, or venous sinus thrombosis.^43,44 Thus, it is possible that the cumulative effects of resistance to blood flow across the venous sinus pathways may lead to a substantial pressure increase in the intracranial drainage system. This question could be addressed (at least in part) by comparing venous sinus Rd measurements in patients versus healthy individuals. However, in the absence of such data, it seems premature to draw conclusions with regard to a possible causal link between venous sinus resistance to blood flow and intracranial hypertension.

The relationships between blood flow velocity, cross-sectional area, pressure drop, and resistance are very complex. A simplified relationship between fluid velocity and pressure can be described by the Bernoulli law, which is based on the fundamental physical law of energy conservation. The equation based on the Bernoulli law can take various forms, which differ in their complexity as a function of the type of fluid flow⁴⁵ but can be represented as (½)·ρ·V² + P + ρ·g·z = Constant, where ρ is the fluid attenuation, V is the velocity, P is the pressure, z the vertical height relative to a reference location, and g is the gravity constant. The first term of this equation accounts for the kinetic energy, and the 2 last terms represent the potential energy resulting from pressure and gravity. According to this principle, an increase in fluid velocity implies a concomitant decrease in pressure and vice versa. Therefore, if vessel resistance is increased by lumen constriction, the flow velocity rise would imply a decrease in pressure.

However, several assumptions must be made before applying the Bernoulli equation. In particular, the velocities must be uniformly distributed at the cross-sectional area, the fluid must be incompressible, and there must be no loss of energy. These assumptions tend to limit the applicability of the Bernoulli law to structures that are subject to deformation. Moreover, Cebral et al⁴⁶ used phase-contrast MR imaging to investigate the flow-area relationship in the internal carotid and vertebral arteries. To the best of our knowledge, a similar study on the cerebral veins has not been performed. The pressure/area/flow relationships in compliant veins are much more complicated to evaluate than in the venous sinuses because the veins are prone to hydrostructural instability and are much more sensitive to slight pressure variations.

The present study had a number of limitations. First, the relatively small sample size must be taken into account when interpreting the results. A second limitation relates to the calculated Rd possibly being influenced by the hydrostatic pressure gradient across the venous sinus wall, which might influence the compliance of the vessels. Third, given that patterns of complex and disturbed flow may occur at branch points in the venous sinus network, the laminar flow required for the validity of the Poiseuille equation may not be met. It is also possible that the image quality was worsened by intravascular signal loss due to turbulence and intravoxel dephasing.⁴⁷ Moreover, although the PC-MRA technique may be useful for imaging slowing blood flow⁴⁸ and can depict multidirectional flow (such as recirculating flow patterns) with good sensitivity,⁴⁹ the choice of an optimal velocity-encoding value that enables avoiding velocity aliasing also constitutes a study limitation.²⁶ Last, our data were collected from a group of young, healthy participants. Extending this investigation to more representative samples of older individuals (including patients with cerebrovascular/neurovascular disease) would be a valuable goal in the near future.