Pia Christine Høy^{1}, Kristine Storm Sørensen^{1}, Lasse Riis Østergaard^{1}, Kieran O'Brien^{2,3}, Markus Barth^{2}, and Steffen Bollmann^{2}

Quantitative susceptibility mapping (QSM) aims to solve an ill-posed field-to-source inversion to extract magnetic susceptibility of tissue. QSM algorithms based on deep convolutional neural networks have shown to produce artefact-free susceptibility maps. However, clinical scans often have a large variability, and it is unclear how a deep learning-based QSM algorithm is affected by discrepancies between the training data and clinical scans. Here we investigated the effects of different B0 orientations and noise levels of the tissue phase on the final quantitative susceptibility maps.

We found that the studied DL-QSM algorithm performs best, when the dipole kernel direction of the input resembles the direction of the training data. We also found that the studied network was not robust to high levels of image noise. Future optimization should focus on more complex mitigations such as improvement of training data or application of a QSM tailored error metric during learning with the goal to increase robustness to the described parameters.

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Figure 1: The architecture of our network based on the U-Net ^{9}. The
architecture contains a convolutional and transposed convolutional part linked
by skip connections. The convolutional part has convolutional layers of filter
size 3x3x3 with dropout of 0.05 and relu activation function and max pooling
layers. The transposed convolutional part contains convolutional layers with
filter size 3x3x3 and relu activation function and transposed convolutional
layers. The output layer is a convolutional layer with filter size 1x1x1. The
output has the same size as the input.

Figure 2: The effect of the B0 orientation. In the top left corner the χ_{33} reference image is shown. The reference image is convolved with dipole kernels of different directions to simulate different B0 orientations. The first two columns show slices from image and k-space representations of the input and the image, k-space, difference map and error metric values of the algorithm prediction. The third column shows that the effect of a non-trained B0 direction can be mitigated by rotating the input. The red arrows show the areas in k-space affected by the kernel.

Figure 3:Investigation of the effect of noise level of the input. In the top left corner
the χ_{33}
reference image is shown. Rician noise of different levels was added to the
phase tissue, and the four columns show the input image to the deep learning
algorithm as well as the prediction image, difference map and error metrics for
the examined SNR levels. The inversion ability of the
algorithm decreases as the noise level increases, which is expressed as
darkening in the centre of the brain.