Extra permeability is required to model dynamic oxygen measurements: evidence for functional recruitment?

Abstract

Neural activation triggers a rapid, focal increase in blood flow and thus oxygen delivery. Local oxygen consumption also increases, although not to the same extent as oxygen delivery. This 'uncoupling' enables a number of widely-used functional neuroimaging techniques; however, the physiologic mechanisms that govern oxygen transport under these conditions remain unclear. Here, we explore this dynamic process using a new mathematical model. Motivated by experimental observations and previous modeling, we hypothesized that functional recruitment of capillaries has an important role during neural activation. Using conventional mechanisms alone, the model predictions were inconsistent with in vivo measurements of oxygen partial pressure. However, dynamically increasing net capillary permeability, a simple description of functional recruitment, led to predictions consistent with the data. Increasing permeability in all vessel types had the same effect, but two alternative mechanisms were unable to produce predictions consistent with the data. These results are further evidence that conventional models of oxygen transport are not sufficient to predict dynamic experimental data. The data and modeling suggest that it is necessary to include a mechanism that dynamically increases net vascular permeability. While the model cannot distinguish between the different possibilities, we speculate that functional recruitment could have this effect in vivo.

Figure 1

Schematic diagram of the oxygen transport model showing O₂ concentrations (CO₂), mean oxygen partial pressures (PO₂), and cerebral metabolic rate of oxygen consumption (CMRO₂). Subscripts 1, 2, 3 and t refer to arterial, capillary, venous, and tissue compartments, while subscripts 0 and 4 refer to notional larger arterial and venous compartments, respectively. Movement of O₂ by convection (i.e., via blood flow) is shown with single arrowheads, while movement via diffusion is shown with double arrowheads. All mathematical notation is as per the equations in the Methods section.

Figure 2

Model predictions (left) and experimental observations (right) of oxygen partial pressure (PO₂) at baseline. Model predictions are shown with the femoral artery (Fem. Art.) and mean compartmental PO₂ values in solid shapes, and the PO₂ values into or out of compartments as ‘x'.

Figure 3

Model predictions of data from Masamoto et al in response to 10-second electrical forepaw stimulation. (A–D) Optimal predictions of cerebral blood flow (CBF), cerebral metabolic rate of oxygen consumption (CMRO₂), and tissue oxygen partial pressure (PO₂) under control (Ctrl, panels A and C) and sodium nitroprusside (SNP) induced vasodilated conditions (panels B and D). (E) Changes from baseline CBF, tissue PO_2, and CMRO₂ induced by stimulation. Predictions show median±s.d. of n=29 simulations obtained by varying model parameters in the sensitivity analysis. Experiments show mean±s.e.m. of n=5 measurements. Predictions of CMRO₂ and PO₂ are shown with either increased capillary permeability (CapPerm, green) or without any additional mechanisms (NoMech, black). Asterisk (*) indicates P<0.05 versus CapPerm simulations. See Supplementary Figure 1 for results from remaining mechanisms.

Figure 4

Model predictions of data from Vazquez et al in response to 20-second electrical forepaw stimulation. (A–D) Optimal predictions of cerebral blood flow (CBF) and cerebral metabolic rate of oxygen consumption (CMRO₂, panel A), tissue oxygen partial pressure (PO₂, panel B), arterial PO₂ (panel C), and venous PO₂ (panel D). (E) Changes from baseline induced by stimulation. Predictions show median±s.d. of n=35 simulations obtained by varying model parameters in the sensitivity analysis. Experiments show mean±s.e.m. of n=6 or 9 measurements. Predictions of CMRO₂ and PO₂ are shown either with increased capillary permeability (CapPerm, green) or without any additional mechanisms (NoMech, black), although these mechanisms overlap in panel C. Asterisk (*) indicates P<0.05 versus CapPerm simulations. See Supplementary Figure 2 for results from remaining mechanisms.

Figure 5

Root mean square (RMS) error associated with fitting the model to data for all of the mechanisms considered. Data shown as mean±standard error of means (s.e.m.); asterisk (*) indicates P<0.05 versus CapPerm simulations; n=29 simulations for data from Masamoto et al and n=35 simulations for data from Vazquez et al.