Digitally reconstructed radiographs (DRRs) are simulated 2D X-ray images generated from 3D CT volumes, widely used in preoperative settings but limited in intraoperative applications due to computational bottlenecks. Physics-based Monte Carlo simulations provide accurate representations but are extremely computationally intensity. Analytical DRR renderers are much more efficient, but at the price of ignoring anisotropic X-ray image formation phenomena such as Compton scattering. We propose a novel approach that balances realistic physics-inspired X-ray simulation with efficient, differentiable DRR generation using 3D Gaussian splatting (3DGS). Our direction-disentangled 3DGS (DDGS) method decomposes the radiosity contribution into isotropic and direction-dependent components, able to approximate complex anisotropic interactions without complex runtime simulations. Additionally, we adapt the 3DGS initialization to account for tomography data properties, enhancing accuracy and efficiency. Our method outperforms state-of-the-art techniques in image accuracy and inference speed, demonstrating its potential for intraoperative applications and inverse problems like pose registration.