Myocardial T₁ mapping is an emerging cardiovascular magnetic resonance technique employed to characterize scar and diffuse myocardial fibrosis. Among all mapping techniques, inversion-recovery (IR) techniques such as MOLLI¹ have received more clinical interest due to their high precision (i.e. reproducibility), despite an underestimation of myocardial T₁ values. This underestimation is due to the reading of several images after each inversion pulse, leading to a deviation of the signal from the ideal IR curve. Saturation-recovery (SR) techniques such as SASHA² or SMART₁Map³ have shown better accuracy as they only acquire one image after each saturation pulse⁴. However they are less precise (i.e. less reproducible). This is due to the lower dynamic range of the SR curve compared to IR and to the acquisition of fewer data points, making SR more sensitive to acquisition noise. To overcome this limitation, we propose to combine SR acquisitions with a joint denoising method that exploits the spatiotemporal correlations in the native T1-weighted images, leading to an accurate and precise mapping technique.

Standard denoising approaches compute the regularization independently on each image, considering no combination between them and leading to no preservation of shared information (e.g. edges, structures). Motivated by recent work on Beltrami regularization⁵, we propose an extended multi-contrast Beltrami regularization by introducing a coupling between images, thus improving the denoising model by penalizing across a common edge (T₁ encoding) direction for all samples. Besides keeping the advantages of Beltrami (features preserving, staircasing reduction), a primal-dual formulation can be derived for the proposed vectorial Beltrami, which leads to a fast and efficient minimization algorithm⁶.The vectorial Beltrami denoising problem can be expressed as:

$$\rho = \underset{\rho}{argmin} \Bigl\lbrace \sum\limits_{TS=1}^n \| \rho_{TS} - S_{TS}\|_2^2 + \lambda \|\rho\|_{Bel} \Bigr\rbrace$$ where $$\quad \|\rho\|_{Bel} = \sqrt{1+C_{Bel} \sum\limits_{TS=1}^n \vert \nabla\rho_{TS} \vert^2}$$

Where $$$C_{Bel}$$$ is the Beltrami constant, set to 1 for simplicity, $$$\lambda$$$ is the regularization parameter controlling the desired noise reduction and $$$(S)_{TS=1..n}$$$ are the n acquired samples of the T₁ recovery curve. This noise-corrected technique is applied just after the acquisition to enable robust fitting to outliers.

Imaging: Phantom - A phantom including 13 tubes with a wide range of T₁ values was images using SMART₁Map on a 1.5T system (GE Healthcare, Milwaukee, WI) with the following parameters: matrix size = 256 x 256, FOV = 270 x 270 mm², slice thickness = 8 mm, TR = 3.78 ms, TE = 1.65 ms, acquiring 8 samples on the T₁ recovery curve at TS = [250, 420, 590, 1590, 2590, 3590, 4590, 20000] ms. Reference T₁ map was determined using a conventional IR-SE. T₁ values were assessed within each phantom compartment. The same ROI was used for all sequences. The average T₁ estimation for each phantom compartment was compared between the IR-SE gold standard and the denoised SMART₁Map. Patient - Imaging was performed in 6 patients with chronic myocardial infarction. The same imaging parameters were used as in the phantom section except TS = [100, 163, 226, 289, 1622, 2408, 2994, 3168, 20000] ms (typical values, depending on heart rate). Images were acquired 10min after Gadolinium injection on a 3T system using an 8-channel phased array coil.

Phantom - T₁ maps reconstructed using standard SMART₁Map and our method are shown in Fig.1a. Denoised SMART₁Map provided excellent T₁ agreement with the reference IR-SE method (Fig.1b). No statistically significant differences was observed between SMART₁Map and gold standard (p_non-denoised = 0.2 vs. p_denoised = 0.3) but significant differences between denoised and non-denoised (p = 0.02) with smaller error after denoising (6.7 ms vs 6.1 ms). Average standard deviation T₁ errors over all measurements were 37 ms for SMART₁Map and 21 ms for noise-corrected SMART₁Map (Fig.1c), showing improvement in T₁ values precision. Patient - The precision, measured as the signal homogeneity in the blood, was 206 ± 25 ms for SMART₁Map and 207 ± 19 ms for the proposed denoised T₁ mapping sequence (Fig.2). Better homogeneity and precision of T₁ values can also be observed on the denoised method for the patient with subendocardial myocardial infarction (Fig.3-4). Both methods exhibit differences in T₁ values between normal and infarcted myocardium, with clear depiction of the scar.Our results show that the developed joint denoising method maintains the features of SR techniques (accuracy) while improving the precision of T₁ values. The approach thus provides a promising tool for the measurement of myocardial and blood T₁ times and derived biomarkers such as ECV. The proposed strategy can also be applied to any parametric mapping applications such as T₂ or T₂* where precision is influenced by noise.