A Neural Network for Rapid Generation of Cardiac MR Fingerprinting Dictionaries with Arbitrary Heart Rhythms
Jesse Ian Hamilton1, Danielle Currey2, Mark Griswold1,3, and Nicole Seiberlich1,3

1Biomedical Engineering, Case Western Reserve University, Cleveland, OH, United States, 2Computer Science, Johns Hopkins University, Baltimore, MD, United States, 3Radiology, University Hospitals, Cleveland, OH, United States


Cardiac MR Fingerprinting with ECG gating typically requires that a new Bloch equation simulation be performed after each scan so that the subject’s cardiac rhythm is incorporated in the dictionary. However, this may be challenging for clinical translation and online reconstruction. This study proposes to use a neural network to rapidly generate the dictionary when given input ranges for T1 and T2, 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.


Cardiac MR Fingerprinting (cMRF) enables the simultaneous quantification of T1, T2, and M0.1,2 However, since the scan is ECG-gated, the cardiac rhythm must be incorporated in the dictionary simulation to obtain accurate measurements. This may impede clinical translation, especially if computationally expensive corrections are modeled, such as slice profile or preparation pulse efficiency.3 Inspired by recent work combining machine learning and MRF,4–6 this study uses a neural network to rapidly generate cMRF dictionaries for arbitrary heart rhythms.


A 16-heartbeat cMRF sequence was used as described previously.2 Figure 1 shows a diagram of the neural network, which takes as inputs T1, T2, 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 efficiency3 were used to simulate 4392 signal timecourses for each rhythm with T1 50-3000ms and T2 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 (T1=1400ms, T2=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 T2 array of the ISMRM/NIST system phantom7 was scanned at 3T (Siemens Skyra) using an 18-channel head coil array. Data were acquired using a variable density spiral8 with golden angle rotation,9 192x192 matrix, 300mm2 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 T1 and T2 discretization were generated using the Bloch equations and the neural network. Undersampled images were gridded using the NUFFT10 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. T1 and T2 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


After training for 4 hours, the time to generate a dictionary with 26,680 entries was 0.8s (neural network) vs 158s (Bloch equations using parallelized MATLAB Mex code). Figure 2 shows the Monte Carlo simulation results. The neural network estimates under constant heart rate conditions (0% noise) are nearly perfect. Errors increase as heart rates become more variable but remain small (RMSE<1%) up to a noise level of 20%. Figure 3 shows results from the phantom scan. The neural network produced accurate T1 and T2 measurements for constant heart rates between 40-120bpm, although high T2 values (near 200ms) were slightly underestimated at high heart rates. Accurate measurements were also obtained when the heart rate changed abruptly halfway during the scan. Representative in vivo maps are shown in Figure 4. Excellent agreement between the Bloch equation and neural network approaches was observed, as corroborated by the Bland-Altman plots in Figure 5.


This study demonstrates that a neural network can generate cMRF timecourses for arbitrary cardiac rhythms. Once trained, the network can output a dictionary over 100 times faster than a Bloch equation simulation with parallelized Mex code. Eliminating the need perform a Bloch equation simulation after every scan could accelerate online reconstructions and facilitate clinical translation of cMRF. Corrections for system imperfections, which may be time-consuming to model, can be included upfront in the network training. Future work will investigate new network architectures and the use of actual, rather than simulated, cardiac rhythms for training to improve performance.


A neural network is introduced for rapidly generating cMRF dictionaries for arbitrary heart rhythms, eliminating the need to perform a Bloch equation simulation after every cMRF scan.


NIH R01HL094557, R01DK098503, R01EB016728; NSF CBET 1553441, Siemens Healthineers (Erlangen, Germany)


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Diagram of the neural network architecture. The inputs to the network are T1, T2, 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 T1, T2, 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 T1 and T2 values obtained by matching signals generated using the Bloch equations with a dictionary produced by the neural network. The reference values are T1=1400ms and T2=50ms. The mean RMSE is reported for each case.

Results from the NIST phantom study. (A) cMRF T1 and T2 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) T1 and (B) T2. 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.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)