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Purpose: To implement physics‐based regularization as a stopping condition in tuning an untrained deep neural network for reconstructing MR images from accelerated data. Methods: The ConvDecoder (CD) neural network was trained with a physics‐based regularization term incorporating the spoiled gradient echo equation that describes variable‐flip angle data. Fully‐sampled variable‐flip angle k‐space data were retrospectively accelerated by factors of R = {8, 12, 18, 36} and reconstructed with CD, CD with the proposed regularization (CD + r), locally low‐rank (LR) reconstruction, and compressed sensing with L1‐wavelet regularization (L1). Final images from CD + r training were evaluated at the "argmin" of the regularization loss; whereas the CD, LR, and L1 reconstructions were chosen optimally based on ground truth data. The performance measures used were the normalized RMS error, the concordance correlation coefficient, and the structural similarity index. Results: The CD + r reconstructions, chosen using the stopping condition, yielded structural similarity indexs that were similar to the CD (p = 0.47) and LR structural similarity indexs (p = 0.95) across R and that were significantly higher than the L1 structural similarity indexs (p = 0.04). The concordance correlation coefficient values for the CD + r T1 maps across all R and subjects were greater than those corresponding to the L1 (p = 0.15) and LR (p = 0.13) T1 maps, respectively. For R ≥ 12 (≤4.2 min scan time), L1 and LR T1 maps exhibit a loss of spatially refined details compared to CD + r. Conclusion: The use of an untrained neural network together with a physics‐based regularization loss shows promise as a measure for determining the optimal stopping point in training without relying on fully‐sampled ground truth data. [ABSTRACT FROM AUTHOR]

Purpose: A method is presented to select the optimal time points at which to measure DCE‐MRI signal intensities, leaving time in the MR exam for high‐spatial resolution image acquisition. Theory: Simplicial complexes are generated from the Kety‐Tofts model pharmacokinetic parameters Ktrans and ve. A geometric search selects optimal time points for accurate estimation of perfusion parameters. Methods: The DCE‐MRI data acquired in women with invasive breast cancer (N = 27) were used to retrospectively compare parameter maps fit to full and subsampled time courses. Simplicial complexes were generated for a fixed range of Kety‐Tofts model parameters and for the parameter ranges weighted by estimates from the fully sampled data. The largest‐area manifolds determined the optimal three time points for each case. Simulations were performed along with retrospectively subsampled data fits. The agreement was computed between the model parameters fit to three points and those fit to all points. Results: The optimal three‐point sample times were from the data‐informed simplicial complex analysis and determined to be 65, 204, and 393 s after arrival of the contrast agent to breast tissue. In the patient data, tumor‐median parameter values fit using all points and the three selected time points agreed with concordance correlation coefficients of 0.97 for Ktrans and 0.67 for ve. Conclusion: It is possible to accurately estimate pharmacokinetic parameters from three properly selected time points inserted into a clinical DCE‐MRI breast exam. This technique can provide guidance on when to capture images for quantitative data between high‐spatial‐resolution DCE‐MRI images. [ABSTRACT FROM AUTHOR]