Jesse Ian Hamilton^{1}, Danielle Currey^{2}, Mark Griswold^{1,3}, and Nicole Seiberlich^{1,3}

Cardiac MR Fingerprinting with ECG gating typically requires that a new Bloch equation simulation _{1} and T_{2}, as well as the cardiac rhythm (RR intervals). The network produces dictionaries for arbitrary cardiac rhythms and is more than 100 times faster than performing a Bloch equation simulation.

A 16-heartbeat cMRF sequence was used as described previously.^{2} Figure 1 shows a diagram of the neural network, which takes as inputs T_{1}, T_{2}, and the RR interval times between heartbeats, and outputs a complex-valued signal evolution. The network was trained using 510 simulated cardiac rhythms with average heart rates 40-120bpm (5bpm step size). For each average heart rate, 30 cardiac rhythms were simulated by adding random Gaussian noise with standard deviation 0-50% of the mean RR interval. The Bloch equations with corrections for slice profile and preparation pulse efficiency^{3} were used to simulate 4392 signal timecourses for each rhythm with T_{1} 50-3000ms and T_{2} 2-600ms. The total number of cMRF timecourses available for training was 510(cardiac rhythms) x 4392(parameter combinations) = 2.2x106. Training was performed in MATLAB using an ADAM optimizer, mini-batch size 256, 100 epochs, and learning rate 0.01.

Monte Carlo simulations were conducted to test performance under variable heart rate conditions. Reference signals representative of myocardium (T_{1}=1400ms, T_{2}=50ms) were simulated for cardiac rhythms having an average 63bpm, chosen because this heart rate was not present during training, and matched to a dictionary produced by the network. Random Gaussian noise with standard deviations of 0%,10%, 20%, and 50% of the mean RR interval was added to the cardiac cycle. The simulation was repeated 250 times for each noise level, and errors were quantified using normalized RMSE. Next, the T_{2} array of the ISMRM/NIST system phantom^{7} was scanned at 3T (Siemens Skyra) using an 18-channel head coil array. Data were acquired using a variable density spiral^{8} with golden angle rotation,^{9} 192x192 matrix, 300mm^{2} FoV, and 8mm slice thickness. Data were collected with constant heart rates of 40-120bpm (step size 10bpm) simulated at the scanner. Two scans were acquired where the heart rate changed abruptly from 60 to 80bpm (and 80 to 60bpm) after 8 heartbeats. Dictionaries with identical T_{1} and T_{2} discretization were generated using the Bloch equations and the neural network. Undersampled images were gridded using the NUFFT^{10} and matched to each dictionary using the inner product to generate parameter maps. A similar experiment was conducted using in vivo data acquired in 8 volunteers in an IRB-approved, HIPAA-compliant study after obtaining written informed consent. T_{1} and T_{2} values were measured in the septal wall, and the agreement between Bloch equation vs neural network approaches was assessed using a Bland-Altman analysis.^{11}

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- Hamilton JI, Jiang Y, Chen Y, et al. MR fingerprinting for rapid quantification of myocardial T1, T2, and proton spin density. Magn Reson Med. 2017;77:1446-1458.
- Hamilton JI, Jiang Y, Ma D, et al. Investigating and reducing the effects of confounding factors for robust T1 and T2 mapping with cardiac MR fingerprinting. Magn Reson Imaging. 2018;53:40-51.
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- Yang M, Jiang Y, Ma D, Mehta BB, Griswold MA. Game of Learning Bloch Equation Simulations for MR Fingerprinting. Proc. ISMRM 2018; #673.
- Russek SE, Boss M, Jackson EF, et al. Characterization of NIST/ISMRM MRI System Phantom. Proc. ISMRM 2012; #2456.
- Hargreaves B. Variable-Density Spiral Design Functions. http://mrsrl.stanford.edu/~brian/vdspiral/. Published 2005. Accessed June 1, 2017.
- Winkelmann S, Schaeffter T, Koehler T, Eggers H, Doessel O. An optimal radial profile order based on the Golden Ratio for time-resolved MRI. IEEE Trans Med Imaging. 2007;26(1):68-76.
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Diagram of the neural network architecture. The inputs to the network are T_{1}, T_{2}, and the RR interval times for the 16 heartbeats in the sequence. These are followed by two fully-connected layers with 300 nodes. The output of each fully-connected layer passes through a batch normalization layer and then a rectified linear unit (ReLu) activation function. The final output is a 768x2 matrix (real part in column 1, and imaginary part in column 2) that is reshaped to a complex-valued signal timecourse for the given T_{1}, T_{2}, and cardiac rhythm. Note that this sequence has a total of 768 time points (TRs).

Monte Carlo simulation results under conditions
with variable heart rates. Random Gaussian noise with standard deviations of
0%, 10%, 20%, and 50% of the average RR interval was added to a cardiac cycle
with average heart rate 63bpm. The histograms show the distribution of T_{1}
and T_{2} values obtained by matching signals generated using the
Bloch equations with a dictionary produced by the neural network. The reference
values are T_{1}=1400ms and T_{2}=50ms. The mean RMSE is
reported for each case.

Results from the NIST phantom study. (A) cMRF T_{1}
and T_{2} measurements using a dictionary generated by the neural
network are plotted against NIST reference values (the identity line is also
plotted in black). Constant heart rates were simulated at the scanner ranging
from 40 to 120bpm. (B) Results from scans with an abrupt change in heart rate.
In one scan, the heart rate instantaneously changed from 60 to 80bpm after the
eighth heartbeat. In a second scan, the heart rate changed from 80 to 60bpm
after the eighth heartbeat.

In vivo maps from a volunteer at 3T. Maps were
reconstructed by pattern matching to a dictionary generated by a Bloch equation
simulation (leftmost column) and by matching to a dictionary output by the
neural network (middle column). Difference maps are shown in the rightmost
column.

Bland-Altman results from the in vivo study for
(A) T_{1} and (B) T_{2}. The bias (solid black line) and 95%
limits of agreement (dotted black line) are indicated on the plots. Note that a
positive bias indicates higher measurements were obtained with the neural
network approach.