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Selection of sampling points for saturation recovery based myocardial T1 mapping
Journal of Cardiovascular Magnetic Resonance volume 16, Article number: W32 (2014)
Background
Quantitative myocardial T1 mapping allows assessment of focal and diffuse fibrosis in the myocardium, by sampling the T1 relaxation curve using inversion [1] or saturation recovery (SR) preparation [2] or a combination of both [3], followed by the acquisition of multiple images with different contrasts, which are subsequently fitted to a parametric equation pixel-wise to yield the T1 maps. In myocardial T1 mapping, there is a degree of freedom in selecting which points on the relaxation curve are sampled. However, this topic has not been studied. In this study, we sought to develop an estimation theoretic framework for optimal selection of sampling points and characterized the variance of the corresponding T1 estimator for sampling of the SR curve.
Methods
Based on the signal model, yk = a (1-b exp(-xk/T1))+nk, and the least squares model, we derived the Fisher information matrix [4]. This was used to derive the Bayesian Cramer-Rao bound [4] for the variance of the T1 estimator for T1 values of interest between 950 and 1250 ms (~pre-contrast myocardium). The bound was evaluated for the SASHA sequence [2] which allows sampling within a heart-beat between Tmin and Tmax with one point at full magnetization recovery (xk = ∞), and minimized over the choice of sampling points {xk} yielding the proposed point selection. Phantom imaging of NiCl2 doped agarose vials was performed to compare the proposed point selection with a uniform distribution of sampling points between Tmin and Tmax [3] using an SSFP sequence with body-coil (NSA = 5) for 11 sampling points. Standard deviation (std) of T1 values within the vials was used as a surrogate for the variance of the estimator. Imaging was also performed on 5 healthy adult subjects (4 women, 23.4 ± 3.3 years) with a 32-channel cardiac-coil to verify the gains predicted by the theory. Both proposed and uniform point selection acquisitions were repeated 5 times per subject to average out the effects of noise. ROIs were drawn in the myocardium and the blood. Both the T1 estimate (average T1 values in the ROI) and the std of the estimator (std of T1 values in the ROI) are reported as mean ± std across 5 scans.
Results
The point selection yielded a tri-modal distribution of points: 4 at Tmin, 6 at Tmax, 1 at ∞, with a theoretical gain in std of 24% compared to uniform selection. Figure 1 shows the results of phantom imaging for T1 values > 700 ms, indicating a good match between theory and experiment. Figure 2 depicts the measurements from the in-vivo data, averaged over five scans. Overall, there was a 23.6% and 26.8% reduction in the std of the T1 maps in the myocardium and blood respectively using the proposed approach.
Conclusions
The proposed framework allows for choosing the location of points on the T1 relaxation curve to achieve higher levels of precision without increasing the scan time.
Funding
NIH:K99HL111410-01; R01EB008743-01A2.
References
Messroghli : MRM. 2004
Chow : MRM. 2013
Weingartner : MRM. 2013
Gill : Bernoulli. 1995
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Akcakaya, M., Weingartner, S., Manning, W.J. et al. Selection of sampling points for saturation recovery based myocardial T1 mapping. J Cardiovasc Magn Reson 16 (Suppl 1), W32 (2014). https://doi.org/10.1186/1532-429X-16-S1-W32
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DOI: https://doi.org/10.1186/1532-429X-16-S1-W32