Introduction

The accurate quantification of SNR is important for quantitative MRI and quality control in general¹. This is particularly true for modalities working in the low SNR limit due to the need for high spatio-temporal resolution, such as DCE-MRI for quantitative perfusion and permeability measurements. For example, a precise knowledge of SNR enables the determination of expected statistical errors for native tissue T₁-mapping and contrast-agent (CA) concentration determination. A real-time estimate of SNR would allow to adjust the imaging sequence before contrast-agent injection and avoid sub-standard scans, which cannot be used for robust quantitative analysis. Nevertheless, efforts to quantify SNR rarely go beyond the “two-region” method², which is known to be wrong when multi-channel receiver arrays, parallel imaging, and other modern MRI methods are employed. To overcome this limitation, a Monte-Carlo based method, similar to Robson et al.³, is applied in this work, which is based on resampling noise-calibration data for determining and predicting SNR in DCE-MRI exams.

Background

Two important parts of a DCE-MRI exam are T1-mapping based on the Variable Flip-Angle (VFA) method, followed by a dynamic scan (DCE scan) during CA injection. To predict the SNR of the dynamic scan, the SNR is first determined from at least one of the VFA scans using the method described below. Applying a suitable signal model, the obtained signal for any of the VFA scans can be scaled to predict the expected signal of the DCE scan. Here, for simplicity, the Ernst equation is employed, which describes the signal of fully transverse spoiled gradient-echo sequences. The same noise calibration measurement can be used to generate noise images of the dynamic scan even before the scan is started, thus leaving time for intervention. Creation of noise images: Given a set of samples $$$s_j$$$, representing complex noise measured for the j-th element of a multi-channel receive array with N channels, the noise covariance matrix C is defined as $$$C_{ij}=<s_i^* s_j>$$$. Following diagonalization, $$$C=UDU^{H}$$$, a single noise sample is computed by drawing from N independent, complex Gaussian random variables $$$\rho_k$$$, to compute $$$s_i=U_{ij} \sqrt{D_{jk}}\rho_k$$$. The k-space of the sequence of interest is filled with noise samples, and reconstruction proceeds as usual, this including effects of coil-combination, filtering, etc. The statistical noise distribution can be determined on a voxel-by-voxel basis from a suitable number of individual noise realizations, allowing the estimation of pure noise image⁴.

Methods

T₁-weighted gradient echo scans (FOV: 216×216×95 mm³, acquisition voxel: 1.5×1.5×5 mm³, TE/TR: 2.5/7 ms, 10 dynamics) with different flip-angles (2,5,10,20,30) were acquired for a gel phantom with 12 tubes of varying T₁ and T₂ values (Diagnostic Sonar, Livingston, UK) using 13-ch head coil at 1.5T (Ingenia, Philips, Best, The Netherlands). The noise resampling was implemented as a new node within the scanner manufacturer’s reconstruction software framework (Recon 2.0). Noise images were generated computing the standard-deviation across the stack of resampled noise images and for the acquired dynamics. From the scans with flip-angles from 2°-20°, a T₁-map was created using the variable-flip angle method (VFA)⁵. Based on the Ernst equation, $$$S(\alpha, T_1, T_R)=M_0\sin(\alpha)\frac{1-\exp(-T_R/T_1)}{1-\cos(\alpha)\exp(-T_R/T_1)}$$$, assuming M₀=1, and the T₁-map, the mean magnitude signal of the scan with flip-angle 30° was predicted by scaling the signals obtained from the other scans. Finally, directly determined SNR and predicted SNR were compared within ROIs defined within the tubes of the phantom, and sorted according to the determined T₁ values.

Results

Figure 1 shows obtained SNR maps computed from pure noise images obtained via resampling and by using the direct method. Tubes with short T₁ show high SNR. Also clearly visible is the variation in SNR across the field-of-view due to the spatially varying noise level. The spatial variation of the noise level, also presented directly in Figure 2, reflects the variation of coil-sensitivities but also from parallel imaging. Figure 3 demonstrates the excellent agreement between the directly measured SNR of the scan with flip-angle 30° and the SNR predicted from the scan at 5°.

Discussion and Conclusion

Noise-level maps determined using a Monte-Carlo method were used to predict SNR of a different scan with high accuracy over a large range of T1 values. This prediction is useful for quality assurance and workflow support, for example, for quantitative DCE-MRI, where scans cannot be repeated once the CA is injected. The presented method requires no additional measurements and generalizes to different acquisition and reconstruction methods. The method allows the reliable determination of an upper bound across the imaged region and characterization of spatial noise-correlations. Furthermore, the noise-level maps obtained using the resampling method in combination with the direct method applied to dynamic scans, could be used to determine quality criteria for motion compensation techniques or image registration.

Acknowledgements

No acknowledgement found.