The roles of cerebral blood flow, capillary transit time heterogeneity, and oxygen tension in brain oxygenation and metabolism

Abstract

Normal brain function depends critically on moment-to-moment regulation of oxygen supply by the bloodstream to meet changing metabolic needs. Neurovascular coupling, a range of mechanisms that converge on arterioles to adjust local cerebral blood flow (CBF), represents our current framework for understanding this regulation. We modeled the combined effects of CBF and capillary transit time heterogeneity (CTTH) on the maximum oxygen extraction fraction (OEF(max)) and metabolic rate of oxygen that can biophysically be supported, for a given tissue oxygen tension. Red blood cell velocity recordings in rat brain support close hemodynamic-metabolic coupling by means of CBF and CTTH across a range of physiological conditions. The CTTH reduction improves tissue oxygenation by counteracting inherent reductions in OEF(max) as CBF increases, and seemingly secures sufficient oxygenation during episodes of hyperemia resulting from cortical activation or hypoxemia. In hypoperfusion and states of blocked CBF, both lower oxygen tension and CTTH may secure tissue oxygenation. Our model predicts that disturbed capillary flows may cause a condition of malignant CTTH, in which states of higher CBF display lower oxygen availability. We propose that conditions with altered capillary morphology, such as amyloid, diabetic or hypertensive microangiopathy, and ischemia-reperfusion, may disturb CTTH and thereby flow-metabolism coupling and cerebral oxygen metabolism.

Figure 1

Model overview. On the left, the single capillary model is sketched. It consists of three compartments, oxygen bound to hemoglobin, oxygen in plasma, and oxygen in tissue. Oxygen in plasma is assumed to be in equilibrium with oxygen bound to hemoglobin, their concentrations related by the Hill equation. Transfer of oxygen across the capillary membrane is modeled as a first-order exchange process with the rate constant k. The capillary has a length L, and blood moves with a velocity v resulting in transit time τ=L/v. The capillary bed on the right is then obtained as a collection of capillaries modeled as described, but with different transit times τ taken from the transit time distribution h(τ), as shown in the middle. Total capillary volume CBV′ was assumed to either remain constant, or to vary with CBF in the same way as total blood volume, modeled here by Grubb's relation. CBF, cerebral blood flow; CBV, cerebral blood volume; CBV′, capillary blood volume.

Figure 2

Oxygen extraction as a function of capillary transit time. (A) The maximum attainable oxygen extraction fraction versus transit time is shown. Note that oxygen extraction becomes inefficient toward short mean transit times, μ=CBV′/CBF. The same principle applies to individual transit times along separate paths in the capillary tree. However, the effect is nonlinear, and because of the concave nature of the curve, a broad capillary transit time distribution (illustrated here by two populations with transit times μ−σ/2 and μ+σ/2) yields considerably lower OEF^max (indicated by the asterisk) for this distribution than the corresponding homogenous distribution, where all capillary transits have identical transit time μ. The same phenomenon may result in a decreased net oxygen extraction despite an increased net flow: in (B), maximum CMRO₂ is plotted versus flow using our model, and here the green line indicates the flow and associated CMRO₂^max from a homogeneous population of capillaries with a net flow F_hom. A slightly larger flow F_het>F_hom, indicated by the red line is now accommodated by the same capillary bed, but divided into two populations, where one population has flow f₁ and the other f₂, f₁+f₂=F_het. However, the net oxygen extraction in this case (intersection of the dashed diagonal line with the red vertical line) is in fact smaller than that obtained for the homogenous, lower flow case, as indicated by the double asterisk. CBF, cerebral blood flow; CBV′, capillary blood volume; OEF^max, maximum oxygen extraction fraction; CMRO₂, cerebral metabolic rate of oxygen; CMRO₂^max, maximum CMRO₂.

Figure 3

Effects of capillary transit time heterogeneity (CTTH) on oxygen extraction. (A, B) Compare the extraction of oxygen from individual capillaries according to commonly accepted Crone-Renkin kinetics when the same flow is distributed across the same number of parallel capillary paths with homogenous (B) capillary flow velocities (arrows), and heterogeneous flow velocities (A), respectively. Transit times in the resting, heterogeneous case were obtained by sampling a gamma distribution with parameters corresponding to recordings of mean and standard deviation of transit times in a rat (Stefanovic et al, 2008). Notice that venous outflow oxygen concentration is affected by the heterogeneity of capillary flows, in spite of identical total blood flows and number of open capillaries.

Figure 4

General model of the effects of transit time and capillary transit time heterogeneity (CTTH) on maximum oxygen extraction. Contour plot of maximum oxygen extraction fraction (OEF^max) (A) for a given mean transit time (μ) and capillary flow heterogeneity (σ). The corresponding maximum oxygen delivery is shown in (B) assuming fixed cerebral blood volume (CBV′)=1.6%, and Grubb's relation (Grubb et al, 1974) in (C). Resting state values were assumed to be cerebral blood flow (CBF)=60 mL/100 mL per minute and C_aO₂=19 mL/100 mL. Note that maximum oxygen delivery increases with decreasing flow heterogeneity. The yellow line in (B) separates states in which shorter transit times lead to decreased oxygen availability (dubbed malignant CTTH) from states where decreasing transit times lead to increased oxygen availability. Also shown are (μ,σ) values obtained in a range of physiological conditions—the symbols below refer to conditions listed in Table 1. The roman numeral accompanying each symbol allows identification of the corresponding physiological data in Table1. Symbols: ○=functional activation (Stefanovic et al, 2008); □=cortical electrical stimulation (Schulte et al, 2003); ▿=hypotension (Hudetz et al, 1995); ⋆=mild hypoxia (Hudetz et al, 1997); Δ=severe hypoxia (Krolo and Hudetz, 2000); ◊=mild hypocapnia (Villringer et al, 1994); ^*=severe hypercapnia (Hudetz et al, 1997).

Figure 5

Maximum oxygen extraction fraction and maximum oxygen utilization for fixed CTTH. This figure illustrates the biophysical effects of reduced oxygen tension (as a result of tissue oxygen utilization) in the case of fixed CTTH (σ=1.33 seconds). A reduction in tissue oxygen tension can seemingly maintain high OEF^max (A) and thus CMRO₂^max, except toward short mean transit times (high CBF). Values as in Figure 4. CTTH, capillary transit time heterogeneity; OEF^max, maximum oxygen extraction fraction; CBF, cerebral blood flow; CMRO₂^max, maximum cerebral metabolic rate of oxygen.

Figure 6

Net oxygen availability as a function of tissue oxygen tension and CTTH for fixed CBF. In this figure, CBF and CBV′ were kept constant (CBF=60 mL/100 mL per minute; CBV′=1.6% mean transit time μ=1.4 seconds) to illustrate how tissue oxygen tension and CTTH contribute to the metabolic needs of tissue during rest and as metabolic needs are increased with blocked CBF. Note that observed oxygen tension increases of 5% typically support CMRO₂ increases of 25%. CTTH, capillary transit time heterogeneity; OEF^max, maximum oxygen extraction fraction; CBF, cerebral blood flow; CBV, cerebral blood volume; CMRO₂, cerebral metabolic rate of oxygen.