Jiaxin Shao^{1}, Vahid Ghodrati ^{1}, Kim-Lien Nguyen^{2,3}, and Peng Hu^{1,4}

Bloch equation simulation provides accurate estimation of soft tissue relaxation parameters for many applications. To speed up using Bloch equation for relaxation parameter estimation, we propose a general approach - deep learning with Bloch equation simulations (DeepBLESS) - to learn inverse Bloch equation for rapid myocardial relaxation parameter prediction. Using the Modified Look-Locker inversion recovery (MOLLI) sequence and a self-designed simultaneous radial T1 and T2 mapping sequence as examples, we demonstrated that DeepBLESS was adaptive to heart rate variation with good estimation accuracy and precision while reducing the inline computation time compared to the conventional Bloch-equation-based approaches.

**Introduction**

**Methods**

Fig.1
illustrates the proposed deep learning model for DeepBLESS. The self-designed
radial T1/T2 mapping sequence is explained in Fig.2. Similar to raMOLLI^{5},
compressed sensing with view sharing were used to reconstructed 10 images for
each heartbeat, resulting in 110 image signal in total. In DeepBLESS model, the
input signal was formatted as an 8×2 matrix (one image signal row and
one acquisition time row) for the MOLLI 5-(3)-3 sequence and was formatted as an
11×11 matrix (ten acquired signal + one time signal as a column for each
heartbeat) for the simultaneous radial T1-T2 mapping sequence.

Bloch equation simulations were used to generate the training sets (1,000,000 samples) and validation sets (100,000 samples) for each sequence (the MOLLI or radial T1/T2 mapping sequence). Random T1, flip angle α and heart rate (HR) were uniformly sampled for the range 200 ms – 2000 ms, 20°- 45° for MOLLI / 3° - 8° for the radial sequence, and 40 bpm -100 bpm, respectively. For T2, 90% was uniformly random-sampled between 20 ms – 100 ms and 10% was uniformly random-sampled between 100 ms – 200 ms. For each group of T1, T2, α, and HR, 10% Gaussian noise was added to each heartbeat interval before simulation. For the MOLLI/radial sequence, either 1% or 5% Gaussian noise was respectively added to the simulated signal. For training, we used mean square error (MSE) as the loss function with a batch size of 2000. Model parameters with the best MSE from the validation set were saved and used for phantom and in vivo studies.

After
training, DeepBLESS was evaluated and compared with a conventional Bloch equation-based-approach
(BLESSPC^{3}) using phantoms at simulated heart rates of 40 - 100 bpm
and in 8 healthy volunteers for MOLLI at 1.5T and in 10 healthy volunteers for the simultaneous radial
T1-T2 mapping sequence at 3.0 T. Two-tailed Student’s t-tests were used for pair-wise comparisons.
Both the inversion and T2 preparation pulses were simulated in detail for the radial
T1-T2 mapping sequence, while for MOLLI, a fixed inversion factor of 0.96^{3}
was used.

**Results**

**Discussion**

The proposed DeepBLESS approach enabled in-line estimation of myocardial relaxation parameters to be almost instantaneous and removed the rate-limiting step for estimation of relaxation parameters by off-loading the time-consuming task of Bloch equation simulations to off-line. Phantom and in vivo results showed that DeepBLESS can achieve 490 – 18,000 times acceleration compared to BLESSPC with similar accuracy and precision.

**Conclusion**

1.Cohen et al. MRM, 2018;80(3):885-94.

2. Messroghli et al. MRM, 2004; 52(1):141-146.

3. Shao et al. MRM, 2017;78(5):1746-1756.

4. Christos et al. JCMR, 2015;17:104.

5. Marth et al. MRM, 2018;79:1387-1398.

Figure 1. Illustration of the deep learning network used for DeepBLESS
in this work.

Figure 2: Diagram of simultaneous radial T1 and T2
mapping sequence. Golden angle radial FLASH readout is applied in every R-R
interval. An adiabatic inversion pulse is applied in the first R-R interval
with the inversion time TI = 150 ms. An adiabatic T2-prep with echo length
TEprep from 30ms to 55ms is applied in each R-R interval from the 6th
R-R interval to 11th R-R interval.

Figure 3: DeepBLESS
vs. BLESSPC for both the MOLLI and radial T1-T2 mapping sequences in phantom (Table
1) and in vivo (Table 2) studies

Figure 4: Short
axis T1 maps of a normal myocardium using DeepBLESS and BLESSPC for the MOLLI
sequence acquired at 1.5T. In the septal region, the average myocardial T1
values were 1038±16 ms for both DeepBLESS and BLESSPC. The time required to
generate T1 maps using DeepBLESS was ~0.2 s, which was 490 times faster than
using BLESSPC (~98 s)

Figure
5: Short axis T1 and T2 maps of normal
myocardium using DeepBLESS and BLESSPC for the simultaneous radial T1-T2
mapping sequence acquired at 3.0T. The image quality and T1/T2 values were
similar between DeepBLESS and BLESSPC while DeepBLESS generated T1 and T2 maps
over 18,000 times faster.