Reliable estimation of capillary transit time distributions using DSC-MRI

Abstract

The regional availability of oxygen in brain tissue is traditionally inferred from the magnitude of cerebral blood flow (CBF) and the concentration of oxygen in arterial blood. Measurements of CBF are therefore widely used in the localization of neuronal response to stimulation and in the evaluation of patients suspected of acute ischemic stroke or flow-limiting carotid stenosis. It was recently demonstrated that capillary transit time heterogeneity (CTH) limits maximum oxygen extraction fraction (OEF(max)) that can be achieved for a given CBF. Here we present a statistical approach for determining CTH, mean transit time (MTT), and CBF using dynamic susceptibility contrast magnetic resonance imaging (DSC-MRI). Using numerical simulations, we demonstrate that CTH, MTT, and OEF(max) can be estimated with low bias and variance across a wide range of microvascular flow patterns, even at modest signal-to-noise ratios. Mean transit time estimated by singular value decomposition (SVD) deconvolution, however, is confounded by CTH. The proposed technique readily identifies malperfused tissue in acute stroke patients and appears to highlight information not detected by the standard SVD technique. We speculate that this technique permits the non-invasive detection of tissue with impaired oxygen delivery in neurologic disorders such as acute ischemic stroke and Alzheimer's disease during routine diagnostic imaging.

Figures

Figure 1

The phantoms in the left column represent the true capillary transit time heterogeneity (CTH) and maximum oxygen extraction fraction (OEFmax) values of the digital phantom. Mean transit time (MTT) and CTH values vary from 2 to 20 seconds along columns (MTT) and rows (CTH). The center and right column shows estimated values at signal-to-noise ratio (SNR)=100 (center) and SNR=20 (right column). The unit of the color bar is seconds for the CTH maps, while the OEFmax maps are dimensionless. Little bias is observed at SNR=100. At SNR=20, the CTH estimates exhibit minor bias for very high MTT, while OEFmax is well estimated except for combinations of very high flow and CTH.

Figure 2

Standard deviation (alternating dot and dashed line) and bias (dashed line) of the capillary transit time heterogeneity (CTH) (cross) and maximum oxygen extraction fraction (OEFmax) (open diamonds) parameters as a function of signal-to-noise ratio (SNR). The units of CTH are in seconds.

Figure 3

Mean transit time (MTT) maps computed by the proposed parametric, standard singular value decomposition (sSVD), and oscillatory SVD (oSVD) methods for signal-to-noise ratio (SNR)=20 and SNR=100. The true values are shown in the left column. Mean transit time is well estimated at SNR=100 with the parametric model, whereas both the SVD methods demonstrate pronounced bias, even at high SNR. The SVD estimates are apparently confounded by capillary transit time heterogeneity (CTH) (which varies across rows), whereas the parametric technique appears able to produce independent estimates of MTT and CTH.

Figure 4

Standard deviation (A) and bias (B) of the mean transit time (MTT) for the different models as a function of the signal-to-noise ratio (SNR). Mean transit time values were fixed at 30 seconds if the estimates exceeded this value. The bias for the parametric model continues to decrease with increasing SNR, whereas for singular value decomposition (SVD), there is no considerable improvement beyond and SNR of ∼60. oSVD, oscillatory SVD; sSVD, standard SVD.

Figure 5

Standard deviation (A) and bias (B) as a function of delay using the parametric model (blue), standard singular value decomposition (sSVD) (green), and oscillatory SVD (oSVD) (red). The delay is given in seconds. CBF, cerebral blood flow; CTH, capillary transit time heterogeneity; MTT, mean transit time; OEF, maximum oxygen extraction fraction.

Figure 6

The effect of scale changes in the prior covariance matrix on s.d. (A) and bias (B). The exact maximization (blue curves) derived in this study provides robustness to scale changes whereas a sudden increase in bias of parameter estimates is observed with the iterative approach (red curves). CTH, capillary transit time heterogeneity; MTT, mean transit time.

Figure 7

Perfusion markers for a set of clinically acquired stroke data. Variation for the transit time distribution (CoV) denotes the coefficient of variation, and is a measure of the dissimilarity between the parametric capillary transit time heterogeneity (CTH) and mean transit time (MTT) maps. In general, the perfusion lesions appear more distinct on the parametric MTT and CTH maps compared with singular value decomposition (SVD)-based MTT. We also note the large difference in lesion volumes between the parametric and SVD techniques in patients E, F, and G, where the parametric maps appear in better correspondence with follow-up T2 fluid-attenuated inversion recovery shown in the bottom row. OEF, maximum oxygen extraction fraction; oSVD, oscillatory SVD; sSVD, standard SVD.