Problem: There is a lack of big data for the training of deep learning models in medicine, characterized by the time cost of data collection and privacy concerns. Generative adversarial networks (GANs) offer both the potential to generate new data, as well as to use this newly generated data, without inclusion of patients' real data, for downstream applications. Approach: A series of GANs were trained and applied for a downstream computer vision spine radiograph abnormality classification task. Separate classifiers were trained with either access or no access to the original imaging. Trained GANs included a conditional StyleGAN2 with adaptive discriminator augmentation, a conditional StyleGAN2 with adaptive discriminator augmentation to generate spine radiographs conditional on lesion type, and using a novel clinical loss term for the generator a StyleGAN2 with adaptive discriminator augmentation conditional on abnormality (SpineGAN). Finally, a differential privacy imposed StyleGAN2 with adaptive discriminator augmentation conditional on abnormality was trained and an ablation study was performed on its differential privacy impositions. Key Results: We accomplish GAN generation of synthetic spine radiographs without meaningful input for the first time from a literature review. We further demonstrate the success of synthetic learning for the spine domain with a downstream clinical classification task (AUC of 0.830 using synthetic data compared to AUC of 0.886 using the real data). Importantly, the introduction of a new clinical loss term for the generator was found to increase generation recall as well as accelerate model training. Lastly, we demonstrate that, in a limited size medical dataset, differential privacy impositions severely impede GAN training, finding that this is specifically due to the requirement for gradient perturbation with noise.