Cerebrovascular Resistance: The Basis of Cerebrovascular Reactivity

Abstract

The cerebral vascular network regulates blood flow distribution by adjusting vessel diameters, and consequently resistance to flow, in response to metabolic demands (neurovascular coupling) and changes in perfusion pressure (autoregulation). Deliberate changes in carbon dioxide (CO₂) partial pressure may be used to challenge this regulation and assess its performance since CO₂ also acts to change vessel diameter. Cerebrovascular reactivity (CVR), the ratio of cerebral blood flow (CBF) response to CO₂ stimulus is currently used as a performance metric. However, the ability of CVR to reflect the responsiveness of a particular vascular region is confounded by that region's inclusion in the cerebral vascular network, where all regions respond to the global CO₂ stimulus. Consequently, local CBF responses reflect not only changes in the local vascular resistance but also the effect of changes in local perfusion pressure resulting from redistribution of flow within the network. As a result, the CBF responses to CO₂ take on various non-linear patterns that are not well-described by straight lines. We propose a method using a simple model to convert these CBF response patterns to the pattern of resistance responses that underlie them. The model, which has been used previously to explain the steal phenomenon, consists of two vascular branches in parallel fed by a major artery with a fixed resistance unchanging with CO₂. One branch has a reference resistance with a sigmoidal response to CO₂, representative of a voxel with a robust response. The other branch has a CBF equal to the measured CBF response to CO₂ of any voxel under examination. Using the model to calculate resistance response patterns of the examined branch showed sigmoidal patterns of resistance response, regardless of the measured CBF response patterns. The sigmoid parameters of the resistance response pattern of examined voxels may be mapped to their anatomical location. We show an example for a healthy subject and for a patient with steno-occlusive disease to illustrate. We suggest that these maps provide physiological insight into the regulation of CBF distribution.

Keywords: carbon dioxide; cerebrovascular reactivity; cerebrovascular resistance; humans; magnetic resonance imaging; model.

FIGURE 1

A conceptual schematic of cerebral blood flow (CBF) pathways and resistances. Resistances are represented with electrical resistance symbols with variability indicated by an arrow. Mean arterial pressure (MAP) forces flow through the high resistance of the source arteries to anastomose around the circle of Willis (CoW) where they are distributed to vascular territories, via the anterior, middle and posterior cerebral arteries (ACA, MCA, and PCA, respectively) in each hemisphere. The interconnected pial networks supply the brain parenchyma via penetrating arterioles, with flow finally reaching the tissue volumes seen in magnetic resonance imaging (MRI) scans through regulating resistances to venous pressure (Pv).

FIGURE 2

The resistance model; determining the pattern of resistance change from the pattern of blood flow change during a ramp CO₂ stimulus. MAP, mean arterial blood pressure; Pv, venous blood pressure; Rart, major arteries resistance; Pbranch, perfusion pressure at branch; Rref, standard reference branch resistance; Fref, standard reference branch blood flow; Rvox, examined voxel branch resistance; Fvox, examined voxel branch blood flow; Ftotal, total blood flow through Rart.

FIGURE 3

The test protocol. The CO₂ stimulus (blue squares) and the whole brain average BOLD response scaled to 100 nL/s at resting PETCO₂ (magenta squares) in a control subject. The step change is used for measuring the speed of response in a separate analysis, and the ramp portion shown between the dashed lines is used in assessing the resistance response.

FIGURE 4

Examples of the four types of response patterns for model flow (left) and the calculated resistance response patterns (right) with the reference resistance (black line). The four voxel branch flow patterns (color coded solid lines) are increasing (A, red), inverted U-shaped (B, light blue), declining (C, dark blue) and U-shaped (D, orange), with the accompanying reference branch flow patterns shown as dashed lines. The dotted vertical line indicates the subject’s resting PETCO₂. Note that despite the varying shapes of the BOLD curves, the resistance curves are all sigmoidal in shape as expected except type C, which is unresponsive. The choice of BOLD scaling to model flow of 100 nL/s at the resting PETCO₂ brings the model resistances at resting PETCO₂ to approximately the same value for all patterns.

FIGURE 5

Histograms of the resistance sigmoid parameters observed in the survey of 38 healthy control subjects.

FIGURE 6

The resistance sigmoids of the healthy regions for all 38 healthy control subjects surveyed. The dotted line shows the reference sigmoid chosen for the model from the median values of the cohort sigmoid parameters.

FIGURE 7

Histograms of the resistance sigmoid parameters for all voxels in the 10 patients with cerebrovascular disease.

FIGURE 8

Example maps for a single axial slice and their color scales from a healthy control subject with analysis graphs and resistance sigmoids from two example voxels. The maps show the locations of example voxels 1 (high amplitude, midpoint at resting PETCO₂) and 2 (low amplitude, high midpoint). The analysis graph shows the model fitting process, using the reference resistance (black solid line) and its calculated flow (black dashed line): model voxel branch flow pattern of response to PETCO₂, scaled from the % changes in BOLD vs. PETCO₂ (magenta points), is converted to resistance (blue points), then fitted with a sigmoid (blue line). The flow patterns of response for the voxel branch and reference resistance branch are then calculated from the resistance response patterns (voxel, blue line and reference black dashed line) The resistance sigmoids graphs show the relation of the fitted voxel sigmoid resistances (blue line) to the reference resistance sigmoid (black line), with their respective midpoints indicated by the vertical lines. The dashed vertical line shows the subject’s resting PETCO₂.

FIGURE 9

Example maps for a single axial slice and their color scales, with analysis graphs and resistance sigmoids from two example voxels for a patient with a near occlusion of the right carotid and bilateral foci of stenosis in the vertebral arteries. The maps show the locations of example voxels 1 (low amplitude, midpoint at resting PETCO₂) and 2 (high amplitude, high midpoint). The rest of the caption is the same as for Figure 8.

FIGURE 10

Example maps for a single axial slice of r² fit assessments for the subjects shown in Figure 8 (top row) and 9 (bottom row), with histograms of the r² fits for all voxels.