<p>Perfusion through a liver lobule is influenced by a range of physiological parameters such as lobule geometry, permeability, blood viscosity, and pressure gradients. We present a hybrid reduced-order modeling approach for real-time simulation of perfusion profiles in 2D lobular structures of the liver that addresses all these parametric aspects. Building on our previous work in Siddiqui et al. (Adv Model Simul Eng Sci 11:22, 2024), we extend the methodology to incorporate a broader range of physiological parameters and multiple interconnected lobules, and introduce hybrid reduced-order representations, thereby achieving even greater computational speedups. We illustrate our reduced-order representations through a stepwise construction, sequentially incorporating different aspects of the parameterized perfusion model. To demonstrate the viability of our approach, we first focus on a model of a single lobule. It is then extended to a model of several interconnected lobules via the formulation of suitable coupling terms. Our simulation results show that our hybrid reduced-order modeling approach is up to three orders of magnitude faster than corresponding high-fidelity finite element computations. At the same time, it maintains responsiveness to physical stimuli and produces results for variations in health conditions that are consistent with clinical experience.</p>