GL-PINN algorithm for inferring velocity and pressure fields from sparse concentration field

The distributions of velocity and pressure in blood vessels are essential information for the diagnosis and treatment of vascular diseases. Conventional medical imaging techniques such as ultrasound Doppler and computer tomography are suitable for point measurement of blood velocity. The reconstruction of velocity and pressure distributions are challenging and time-consuming. Even digital subtraction angiography provides the spatiotemporal concentration of the contrast medium in blood vessels, the blood velocity is evaluated empirically by physicians in the clinic. It is still challenging to infer the flow field information from the concentration distribution. In this study, we propose a novel inferring method to reconstruct the velocity field and the pressure field from a fractional sampling of the concentration field. This method combines the physics-informed neural network (PINN) algorithm with gradient limitations, referring to as the gradient-limited PINN (GL-PINN). The results demonstrate that the GL-PINN algorithm is capable of inferring the velocity field and pressure field from the concentration field. The calculation error is less than 1% compared with Comsol results. Moreover, the GL-PINN algorithm with gradient constraints shows a better accuracy than the traditional PINN algorithm. The proposed GL-PINN is promising in inferring the blood velocity and pressure from DSA for the diagnosis of vascular diseases.