Jiaren Zou^{1}, James Balter^{1,2}, and Yue Cao^{1,2,3}

^{1}Department of Radiation Oncology, University of Michigan, Ann Arbor, MI, United States, ^{2}Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI, United States, ^{3}Department of Radiology, University of Michigan, Ann Arbor, MI, United States

Conventional nonlinear least squares (LS) methods to fit DCE-MRI to a pharmacokinetic (PK) model are time-consuming. We propose a long Short-Term Memory (LSTM) network that is capable of efficiently learning temporal dependency in sequence data to map PK parameters from single-voxel DCE signals with their corresponding AIFs. The LSTM model showed 90 folds of computation time reduction with comparable performance to LS fitting, while outperforming it for temporally sparsely sampled DCE-MRI. The proposed model can potentially accelerate the data acquisition and PK parameter inference of DCE-MRI.

DCE MR images were acquired from 105 patients with head and neck cancers using a dynamic scanning sequence (TWIST) on a 3 Tesla MRI scanner (Skyra, Siemens Healthineers, Erlangen Germany). Of 105 patients, 80 cases were randomly selected for training, and 25 for testing. For all cases, the subject-specific AIFs were extracted manually

For network training with fully sampled synthetic data, concentration time-curves were generated on-the-fly from randomly drawn AIFs, PK parameters, and time steps ($$$\Delta t$$$) from the training data. Figure 2 shows the data generating process during network training. Random scaling (70%-130%)

To evaluate our model, the performance of the LSTM model was compared to both the conventional DMF approach and a CNN model

For temporally subsampled simulated signals, the LSTM method consistently outperformed the DMF approach when the sampling time interval of the dynamic signals is 4s or greater (figure 4). While the average rMSE and SSIM from the DMF degraded significantly with an increase in the sampling interval, the LSTM approach showed a robust performance for sparse temporal sampling data.

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Figure 1 Illustration of the network architecture used for PK parameter estimation from an input of a CA concentration time-series and an AIF as two separate channels.

Figure 2 Training data generating scheme with bolus arrival time simulation and AIF augmentation by random scaling

Table 1 Quantitative performance of different methods on 25 test DCE-MRI volumes in terms of SSIM and rMSE (mean ± std) with respect to the ground truth parameter maps.

Figure 3 An exemplary slice of the ground truth parameter maps (left
column) and the residual maps of estimated K^{trans}
(top row), v_{e} (middle row), and v_{p} (bottom
row) by the LSTM3 (second left column), CNN (second right column), and DMF (right
column) models from a testing case. The residual maps are displayed in 3 times
of the absolute error for display purposes.

Figure 4 Quantitative results of the
estimated parameters from the 25 synthesized testing datasets with different temporal
sampling time intervals (3, 4, 5, and 6 s) by the LSTM and DMF approaches. The
proposed LSTM shows a more stable performance than the DMF when increasing the
sampling interval in DCE-MRI.