Improving temporal resolution of pulmonary perfusion imaging in rats using the partially separable functions model

Abstract

Dynamic contrast-enhanced MRI (or DCE-MRI) is a useful tool for measuring blood flow and perfusion, and it has found use in the study of pulmonary perfusion in animal models. However, DCE-MRI experiments are difficult in small animals such as rats. A recently developed method known as Interleaved Radial Imaging and Sliding window-keyhole (IRIS) addresses this problem by using a data acquisition scheme that covers (k,t)-space with data acquired from multiple bolus injections of a contrast agent. However, the temporal resolution of IRIS is limited by the effects of temporal averaging inherent in the sliding window and keyhole operations. This article describes a new method to cover (k,t)-space based on the theory of partially separable functions (PSF). Specifically, a sparse sampling of (k,t)-space is performed to acquire two data sets, one with high-temporal resolution and the other with extended k-space coverage. The high-temporal resolution training data are used to determine the temporal basis functions of the PSF model, whereas the other data set is used to determine the spatial variations of the model. The proposed method was validated by simulations and demonstrated by an experimental study. In this particular study, the proposed method achieved a temporal resolution of 32 msec.

Figure 1

Sparse (k, t)-space sampling patterns for dynamic imaging of partially separable functions where k_y is the phase encoding axis, and k_x, the frequency encoding axis, is into the page. The open circles represent the training data, s₁(k, t), and the filled circles represent the imaging data, s₂(k, t). (a) A conceptual (k, t)-space sampling pattern for partially separable functions of order 1. (b) A realizable (k, t)-space sampling pattern for higher order partially separable functions.

Figure 2

The k-space sampling over time for the proposed method. The dark radial is the one acquired for that T_R, while the light gray radials represent the full set. The training data cover 8 equally spaced angles and are incremented by 45° every T_R. The imaging data cover 720 equally spaced angles that are divided into 4 unique sets for acquisition during separate contrast injections. The imaging data’s angle step size is 66.5° every T_R.

Figure 3

Results from the pulmonary perfusion simulation reconstructed using the proposed method and the sliding window method. (a) The singular values of the training data normalized by the square root sum of squares of the singular values and converted to dB. The 6^th singular value has a normalized value of −70.8 dB or 0.029%. (b) The gold standard signal-intensity curves shown at 4 ms resolution. (c) The sliding window signal-intensity curves have a normalized RMSE between 7 and 15%. The curves have been reconstructed at 32 ms spacing with a 720 ms sliding window. (d) The proposed method’s signal-intensity curves have a normalized RMSE between 0.4 and 3.2%. The curves have been reconstructed at 32 ms resolution.

Figure 4

Representative experimental DCE-MRI results. (a) The singular values of the training data normalized by the square root sum of squares of the singular values and converted to dB. The 6^th singular value has a normalized value of −37.7 dB or 1.3%. (b) The regions of interest analyzed to produce the signal-intensity curves. (c) The sliding window method’s signal-intensity curves with 32 ms spacing. (d) The proposed method’s signal-intensity curves at 32 ms resolution.