Generative Modelling of 3D In-Silico Spongiosa with Controllable Micro-structural Parameters

Research in vertebral bone micro-structure generally requires costly procedures to obtain physical scans of real bone with a specific pathology under study, since no methods are available yet to generate realistic bone structures in-silico. Here we propose to apply recent advances in generative adversarial networks (GANs) to develop such a method. We adapted style-transfer techniques, which have been largely used in other contexts, in order to transfer style between image pairs while preserving its informational content. In a first step, we trained a volumetric generative model in a progressive manner using a Wasserstein objective and gradient penalty (PWGAN-GP) to create patches of realistic bone structure in-silico. The training set contained 7660 purely spongeous bone samples from twelve human vertebrae (T12 or L1) with isotropic resolution of \(164~\upmu \)m and scanned with a high resolution peripheral quantitative CT (Scanco XCT). After training, we generated new samples with tailored micro-structure properties by optimizing a vector \(\textit{\textbf{z}}\) in the learned latent space. To solve this optimization problem, we formulated a differentiable goal function that leads to valid samples while compromising the appearance (content) with target 3D properties (style). Properties of the learned latent space effectively matched the data distribution. Furthermore, we were able to simulate the resulting bone structure after deterioration or treatment effects of osteoporosis therapies based only on expected changes of micro-structural parameters. Our method allows to generate a virtually infinite number of patches of realistic bone micro-structure, and thereby likely serves for the development of bone-biomarkers and to simulate bone therapies in advance.