Windkessel model-based Physics Informed Neural Networks for Blood Flow Estimation and Cardiovascular Parameters Assessment
Résumé
Cardiovascular system modeling is crucial due to the alarming rise in cardiovascular diseases worldwide. According to the WHO, cardiovascular diseases are the leading cause of death globally, accounting for 17.9 million deaths annually. This statistic underscores the need to better understand cardiovascular physiology and pathophysiology through accurate modeling and characterization. Arterial models vary in complexity, from simple yet less interpretable to highly intricate but precise ones. A prominent example is the arterial Windkessel model introduced by [1], which includes single and multiple-compartment models [2]. In practical applications, models offering interpretable parameters and manageable complexity are preferred. Estimating Blood Flow (BF) within the cardiovascular system is crucial to understanding its function and pathology [7]. However, measuring BF directly can be challenging due to the complex nature of blood circulation and the limitations of available measurement techniques. This report proposes a physics-informed neural network (PINN) approach for simultaneous BF and cardiovascular parameters estimation. Our proposed method evaluates the Windkessel model as a cardiovascular model, considering both 2 and 3 elements Windkessel models with integer and fractional-order derivatives. Fractional-order derivatives[3], incorporating non-integer orders, extend the concept of differentiability, capturing non-local and memory effects through fractional-order space and time derivatives.
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