Fig. 1: Validation of ANNCEST with numerical simulation.
From: In vivo imaging of phosphocreatine with artificial neural networks
a Diagrammatic representation of the feed-forward artificial neural network used in this study. This network comprises three layers: an input layer, fully connected hidden layers, and an output layer. The input of the neural network is the intensity of the Z spectrum at different frequency offsets, and the outputs are the predicted values of metabolite concentrations, exchange rates of exchangeable protons, and B1/B0. b Representative Z spectra of PCr phantom generated by three-pool Bloch–McConnell equations. Z spectra from 0.5 to 4.0 ppm were sampled with a 50-saturation offset over equal intervals. Gaussian white noise with a standard deviation of 0.35% and B0 inhomogeneity offsets were added to the Z spectra. The saturation power and length were set to 0.6 µT and 10 s, respectively. c The performance of neural networks as a function of the number of hidden layers. The error bar was obtained by repeating the neural network training five times. d–f The ground truth maps of concentration, exchange rate at 2.5 ppm, and B0 for generating validated Z spectra. The matrix size of maps is 256 × 256. The maps of concentration, exchange rate, and B0 obtained by Bloch equation fitting (g, h) and ANNCEST (j–l), respectively. m, n Quantified concentrations and exchange rates, respectively. The bar and error bar indicate the mean value and standard deviation across each phantom, respectively (n = 4523, 3655, 2770, 2610, and 2790 pixels for phantom numbers 1–5, respectively).
