Impact of the training loss in deep learning-based CT reconstruction of bone microarchitecture

Abstract

Purpose: Computed tomography (CT) is a technique of choice to image bone structure at different scales. Methods to enhance the quality of degraded reconstructions obtained from low-dose CT data have shown impressive results recently, especially in the realm of supervised deep learning. As the choice of the loss function affects the reconstruction quality, it is necessary to focus on the way neural networks evaluate the correspondence between predicted and target images during the training stage. This is even more true in the case of bone microarchitecture imaging at high spatial resolution where both the quantitative analysis of bone mineral density (BMD) and bone microstructure is essential for assessing diseases such as osteoporosis. Our aim is thus to evaluate the quality of reconstruction on key metrics for diagnosis depending on the loss function that has been used for training the neural network.

Methods: We compare and analyze volumes that are reconstructed with neural networks trained with pixelwise, structural, and adversarial loss functions or with a combination of them. We perform realistic simulations of various low-dose acquisitions of bone microarchitecture. Our comparative study is performed with metrics that have an interest regarding the diagnosis of bone diseases. We therefore focus on bone-specific metrics such as bone volume and the total volume (BV and TV), resolution, connectivity assessed with the Euler number, and quantitative analysis of BMD to evaluate the quality of reconstruction obtained with networks trained with the different loss functions.

Results: We find that using $L_1$ norm as the pixelwise loss is the best choice compared to $L_2$ or no pixelwise loss since it improves resolution without deteriorating other metrics. Visual Geometry Group (VGG) perceptual loss, especially when combined with an adversarial loss, allows to better retrieve topological and morphological parameters of bone microarchitecture compared to Structural SIMilarity (SSIM) index. This however leads to a decreased resolution performance. The adversarial loss enhances the reconstruction performance in terms of BMD distribution accuracy.

Conclusions: In order to retrieve the quantitative and structural characteristics of bone microarchitecture that are essential for postreconstruction diagnosis, our results suggest to use $L_1$ norm as part of the loss function. Then, trade-offs should be made depending on the application: VGG perceptual loss improves accuracy in terms of connectivity at the cost of a deteriorated resolution, and adversarial losses help better retrieve BMD distribution while significantly increasing the training time.

Keywords: bone structure; deep learning; low-dose micro-CT; tomographic reconstruction; training loss.