Real-time simulation of blood perfusion in parameterized lobular structures of the liver

This work focuses on the development of efficient simulation techniques for enabling the acquisition of real-time perfusion profiles within functional units of liver, known as “lobules”, forming the liver parenchyma. To motivate the work, liver anatomy is briefly reviewed, along with few pathological conditions, and their associated influences on the perfusion characteristics of the parenchyma. An existing mathematical modeling framework for the blood perfusion within the lobular domains is presented, and the parametric aspects of the associated physiology is incorporated as the model parameters. Specifically, the parameterization of lobular domains, parenchyma’s permeability, blood viscosity, and flow driving forces are taken into consideration. The resulting parameterized model demands efficient computational methods. Thus, the parameterized formulation is efficiently presented to facilitate the construction of reduced-order models, which enable faster computations and acquisition of perfusion profiles in real-time. For the construction of reduced-order models. various techniques are reviewed, and put into practice for addressing different aspects of the parameterized problem. These techniques are implemented in combinations, leading to the constructions of unique hybrid reduced-order models. In particular, a hybrid reduced-order model for the parameterized lobular domains is devised based on the combination of Proper Orthogonal Decomposition and Discrete Empirical Interpolation Method. This model accurately mimics the velocity fields within varying lobular domains and is an order of magnitude faster than the high-fidelity model. Moreover, novel hybrid reduced-order representations based on Proper Generalized Decomposition are constructed as the next step, where the variations in parenchyma’s permeability, blood viscosity, and driving forces are also taken into consideration. These novel representations bypass the intermediate steps of the reduced-order model developed initially, and therefore, offer even higher speedups. Lastly, the novel hybrid reduced-order representations are extended for tessellated lobular structures, where interconnections among them are enabled through appropriate couplings based on certain assumptions. A unique lobular patch is considered for the purpose of demonstration, where three different health conditions of the patch are taken into account. The novel representations for these tessellated lobular patches are designed in the next step, where multivariate representations of the parametric functions are leveraged to efficiently deal with the high dimensional nature of the problem. The performance of these representations are assessed based on computational speedups and imitation of clinical observations. The results demonstrate speedups of at least three orders of magnitudes, where the novel representations are capable of mimicking clinical observations when subjected to pathological stimuli.