Reconstructing in-vitro and in-vivo signals and parameters in networks of elastic vessels using physics-informed neural networks

The reconstruction of waveforms and hidden parameters is crucial for the physical modeling of steady and transient flows in networks of elastic vessels (arteries), where many mechanical properties are not directly measurable. This work investigates the potential of Physics-Informed Neural Networks (PINNs) to address the challenge of reconstructing pressure and flow signals and inferring parameters from experimental data. We incorporate the zero-dimensional (0D) system of coupled differential equations that describe flow in elastic vessels into the neural network, which we call 0D-PINN. We evaluate our methodology with several test cases representing different dynamical systems, including an experimental mock arterial network with 37 silicone vessels replicating the human arterial system, as well as a clinical case based on in-vivo MRI data from a healthy adult's thoracic aorta. It is shown that coupling 0D models with Physics-Informed Neural Networks (PINNs) enables the recovery of parameters and waveforms from experimental in-vitro or in-vivo data.