Quantitative mapping of cerebrovascular reactivity using resting-state functional magnetic resonance imaging

1. A method for estimating a quantitative cerebrovascular reactivity from resting-state functional magnetic resonance imaging data, the method comprising:

(a) providing resting-state functional magnetic resonance imaging (rs-fMRI) data acquired from a subject with a magnetic resonance imaging (MRI) system, the rs-fMRI data comprising blood-oxygen level dependent (BOLD) signals;

(b) providing physiological data acquired from the subject while the rs-fMRI data were acquired, the physiological data comprising cardiac-rate variability (CRV) signals, respiratory-volume variability (RVT) signals, and passive end-tidal carbon dioxide (PETCO2) signals;

(c) processing the BOLD signals to remove BOLD signal variations attributable to the CRV and RVT signals by orthogonalizing the CRV signals, RVT signals, and PETCO2 signals to a common orthogonal basis and regressing out the orthogonalized CRV and RVT signals from the BOLD signals;

(d) estimating the quantitative cerebrovascular reactivity (qCVR) from the processed BOLD signals by further processing the BOLD signals to remove BOLD signal variations attributable to the PETCO2 signals, wherein further processing the BOLD signals includes estimating the qCVR based on a cross-correlation between the PETCO2 signals and the processed BOLD signals; and

(e) generating and displaying to a user, a qCVR map based on the qCVR estimated from the processed BOLD signals, wherein the qCVR maps depict a spatial distribution of qCVR values in the subject relative to anatomy of the subject.

2. The method as recited in claim 1 , wherein regressing out the orthogonalized CRV and RVT signals from the BOLD signals includes:

estimating a voxelwise hemodynamic response function (HRF) for the CRV signals and for the RVT signals;

generating convolved CRV signals by convolving the voxelwise HRF for the CRV signals with the orthogonalized CRV signals;

generating convolved RVT signals by convolving the voxelwise HRF for the RVT signals with the orthogonalized RVT signals; and

regressing out the convolved CRV and convolved RVT signals from the BOLD signals.

3. The method as recited in claim 2 , wherein estimating the voxelwise HRF for the CRV signals and the voxelwise HRF for the RVT signals includes estimating each HRF using a multivariate deconvolution model.

4. The method as recited in claim 1 , wherein step (c) includes downsampling the CRV signals, RVT signals, and PETCO2 signals to a sampling rate of the BOLD signals.

5. The method as recited in claim 1 , wherein estimating the qCVR includes:

determining a time lag that maximizes the cross-correlation between the PETCO2 signals and the processed BOLD signals;

truncating the PETCO2 signals and the processed BOLD signals based on the time lag;

performing a regression of the truncated PETCO2 signals and the truncated BOLD signals; and

selecting the qCVR as a slope of the regression.

6. A method for estimating a quantitative cerebrovascular reactivity from resting-state functional magnetic resonance imaging data, the method comprising:

(a) providing resting-state functional magnetic resonance imaging (rs-fMRI) data acquired from a subject with a magnetic resonance imaging (MRI) system, the rs-fMRI data comprising blood-oxygen level dependent (BOLD) signals;

(b) providing physiological data acquired from the subject while the rs-fMRI data were acquired, the physiological data comprising cardiac-rate variability (CRV) signals, respiratory-volume variability (RVT) signals, and passive end-tidal carbon dioxide (PETCO2) signals;

(c) processing the BOLD signals to remove BOLD signal variations attributable to the CRV and RVT signals by orthogonalizing the CRV signals, RVT signals, and PETCO2 signals to a common orthogonal basis and regressing out the orthogonalized CRV and RVT signals from the BOLD signals;

(d) estimating the quantitative cerebrovascular reactivity (qCVR) from the processed BOLD signals by further processing the BOLD signals to remove BOLD signal variations attributable to the PETCO2 signals, wherein further processing the BOLD signals includes estimating the qCVR using a parametric deconvolution based on the PETCO2 signals and the processed BOLD signals; and

(e) generating and displaying to a user, a qCVR map based on the qCVR from the processed BOLD signals, wherein the qCVR maps depict a spatial distribution of qCVR values in the subject relative to anatomy of the subject.

7. The method as recited in claim 6 , wherein estimating the qCVR includes:

determining a CO2 hemodynamic response function (HRFCO2) from the PETCO2 signals;

performing a regression of the HRFCO2 and the processed BOLD signals; and

selecting the qCVR as a slope of the regression.

8. The method as recited in claim 7 , wherein determining the HRFCO2 includes:

determining a canonical hemodynamic response function (HRF);

computing a temporal derivative of the canonical HRF;

computing a dispersion derivative of the canonical HRF; and

computing the HRFCO2 based on a basis function set defined by the canonical HRF, the temporal derivative of the canonical HRF, and the dispersion derivative of the canonical HRF.

9. The method as recited in claim 8 , wherein computing the HRFCO2 includes determining relative contributions of each basis function in the basis function set based on a least-squares minimization of a difference between the processed BOLD signals and a convolution between the HRFCO2 and the PETCO2 signals.

10. The method as recited in claim 8 , wherein the temporal derivative of the canonical HRF is computed as a Taylor expansion of the canonical HRF in time, and the dispersion derivative of the canonical HRF is computed as a Taylor expansion of the canonical HRF width.

11. The method as recited in claim 8 , wherein the canonical HRF is determined based on an initialized HRF characterized by a parameter set.

12. The method as recited in claim 6 , wherein regressing out the orthogonalized CRV and RVT signals from the BOLD signals includes:

estimating a voxelwise hemodynamic response function (HRF) for the CRV signals and for the RVT signals;

generating convolved CRY signals by convolving the voxelwise HRF for the CRV signals with the orthogonalized CRV signals;

generating convolved RVT signals by convolving the voxelwise HRF for the RVT signals with the orthogonalized RVT signals; and

regressing out the convolved CRV and convolved RVT signals from the BOLD signals.

13. The method as recited in claim 12 , wherein estimating the voxelwise HRF for the CRY signals and the voxelwise HRF for the RVT signals includes estimating each HRF using a multivariate deconvolution model.

14. The method as recited in claim 6 , wherein step (c) includes downsampling the CRV signals, RVT signals, and PETCO2 signals to a sampling rate of the BOLD signals.