Julien Songeon^{1}, Sebastien Courvoisier^{1}, Antoine Klauser^{1}, Alban Longchamp^{2}, Jean-Marc Corpataux^{2}, Leo Buhler^{3}, and François Lazeyras^{1}

^{1}Department of Radiology and Medical Informatics, University of Geneva, Geneva, Switzerland, ^{2}Department of Vascular Surgery, Centre Hospitalier Universitaire Vaudois and University of Lausanne, Lausanne, Switzerland, ^{3}Faculty of Science and Medicine, Section of Medicine, University of Fribourg, Fribourg, Switzerland

Phosphorus magnetic resonance spectroscopy imaging (^{31}P-MRSI) allows the probing of biological compounds that hold fundamental cellular information. High resolution MRSI at 3T suffers from low signal-to-noise ratio (SNR) inherent to the nuclear low sensitivity. This is accentuated in the MRSI in comparison to unlocalized free induction decay (FID) where acquired volumes are smaller and consequently lower the SNR. Our Convolutional Neural Network (CNN) based algorithm perform efficient quantification of metabolite and is compared to last-square fitting algorithm. Our model was trained with a simulated dataset and tested with both simulated spectra and real spectra from 3D ^{31}P-MRSI acquired in kidneys.

First, spectra were quantified with a fitting method that is based on prior knowledge for spectral signature, peaks chemical shift and coupling constant. Once identified, the peaks are estimated with Gaussian shape curves, as illustrated in Figure 1.

As second analysis, quantification was performed with the CNN. Supervised learning approach was achieved with a simulated and labeled training data-set. Following exact density matrix computation for each metabolite resonance, 10

From the 10

Figure 4 shows a slice of a 3D

The gain provided by the use of CNN is the instantaneous processing time in comparison with traditional fitting methods. Also the ability to create training set with widely distributed parameters should provide more robustness to CNN spectral analysis.

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Figure 1 : Fitting of true data FID with non-linear least-square algorithm. Pi and ATPs concentrations were estimated after phases and baseline correction.

Figure 2: MRS signal simulation is performed with the top formula with the listed independent variables. The metabolite signal M_{m}(t) is the sum of all metabolite resonances, and the peak width is estimated with combination of a Lorentzian and a Gaussian function. An example of simulated spectrum is displayed at the bottom.

Figure 3: Values of the coeffcients of determination R^{2} for each metabolite.

Figure 4: T2 image of kidneys MRI with its corresponding mapping of ATP level.