Quantifying the microvascular origin of BOLD-fMRI from first principles with two-photon microscopy and an oxygen-sensitive nanoprobe

Abstract

The blood oxygenation level-dependent (BOLD) contrast is widely used in functional magnetic resonance imaging (fMRI) studies aimed at investigating neuronal activity. However, the BOLD signal reflects changes in blood volume and oxygenation rather than neuronal activity per se. Therefore, understanding the transformation of microscopic vascular behavior into macroscopic BOLD signals is at the foundation of physiologically informed noninvasive neuroimaging. Here, we use oxygen-sensitive two-photon microscopy to measure the BOLD-relevant microvascular physiology occurring within a typical rodent fMRI voxel and predict the BOLD signal from first principles using those measurements. The predictive power of the approach is illustrated by quantifying variations in the BOLD signal induced by the morphological folding of the human cortex. This framework is then used to quantify the contribution of individual vascular compartments and other factors to the BOLD signal for different magnet strengths and pulse sequences.

Keywords: BOLD-fMRI; Monte Carlo; modeling; two-photon microscopy.

Figure 1.

Overview of the modeling framework. Green arrows represent validations of the model against experimental measurements.

Figure 2.

Construction of realistic vascular networks. A, TPM FITC angiogram of the mouse cortex. B, FEM mesh of the vasculature displaying arteries, capillaries, and veins. C, Blood flow distribution simulated across the vascular network assuming a global perfusion value of 100 ml/min/100 g. D, Distribution of the partial pressure of oxygen (pO₂) simulated across the vascular network using the finite element method model. E, TPM experimental measurements of pO₂ in vivo using PtP-C343 dye. F, Quantitative comparison of simulated and experimental pO₂ and SO₂ distributions across the vascular network for a single animal. Traces represent arterioles and capillaries (red) and venules and capillaries (blue) as a function of the branching order from pial arterioles and venules, respectively.

Figure 3.

Modeling the physiological response to forepaw stimulus. A, TPM experimental measurements or arterial dilation following forepaw stimulus. B, Simulated flow changes, (C) simulated volume changes, and (D) simulated SO₂ changes (all relative to baseline) in the different vascular compartments. E, Comparison of simulated SO₂ changes (n = 6 animals) with experimental SO₂ changes (n = 10 animals) measured in pial vessels during a forepaw stimulus with confocal microscopy. F, Vessel type. G, Spatiotemporal evolution of simulated SO₂ changes following forepaw stimulus.

Figure 4.

Modeling the fMRI signals from realistic vascular networks. A, Time series of SO₂ volumes. B, Resulting time series of magnetic field perturbation volumes (contour lines) computed from the SO₂ volumes at each time instant. C, Simulation of nuclear spins (n = 10⁷) diffusing in the magnetic field perturbation volume. D, Spatial gradients applied to simulate GRE and SE signals. E, Time series of the simulated extravascular GRE and SE signals. F, Comparison of simulated GRE signal against experimental GRE signal measured during the same forepaw stimulus.

Figure 5.

BOLD dependence on local folding of the cortex. A, Convention for the angle (θ_z) between the vector normal to the local cortical surface and the external magnetic field (represented by the arrow). B, Variation in the extravascular BOLD response at 3T predicted from simulations with θ_z ranging from 0° to 180° normalized by the BOLD response simulated for θ_z = 90°. C, Difference in the extravascular BOLD response simulated at θ_z = 0° relative to θ_z = 90° (in percentage relative to θ_z = 90°) for different B-field strengths (TE = T_{2, tissue}^*). D, Illustration of θ_z values computed in the gray matter of the human brain. E, Averaged BOLD responses measured in the gray matter of human subjects during a hypercapnic challenge as a function of θ_z. F, Comparison of angular dependence predicted from our simulations with angular dependence measured during the hypercapnic challenge in humans (n = 5 human subjects for experimental, n = 6 animals for simulations).

Figure 6.

Statistics for vessel orientations and sizes. A, Histogram of vessel orientation with respect to the z-axis for arteries, capillaries, and veins. B, Mean vessel diameter as a function of vessel orientation with respect to the z-axis.

Figure 7.

Compartment-specific contributions to the extravascular BOLD effect for different magnetic field strengths and cortical orientations. A, Averaged blood volume fractions and (B) averaged vascular volume fractions for individual vascular compartments computed across the six VAN models. C, Contributions of individual vascular compartment to the BOLD signal computed from the simulations (n = 6 animals).

Figure 8.

Independent contributions of (A) oxygenation changes and (B) blood volume changes to the extravascular BOLD signal for different magnetic field strengths and cortical orientations (n = 6 animals).