Quantification of blood flow patterns in the cerebral arterial circulation of individual (human) subjects

There is a growing research interest in quantifying blood flow distribution for the entire cerebral circulation to sharpen diagnosis and improve treatment options for cerebrovascular disease of individual patients. We present a methodology to reconstruct subject‐specific cerebral blood flow patterns in accordance with physiological and fluid mechanical principles and optimally informed by in vivo neuroimage data of cerebrovascular anatomy and arterial blood flow rates. We propose an inverse problem to infer blood flow distribution across the visible portion of the arterial network that best matches subject‐specific anatomy and a given set of volumetric flow measurements. The optimization technique also mitigates the effect of uncertainties by reconciling incomplete flow data and by dissipating unavoidable acquisition errors associated with medical imaging data. We present the theoretical basis and implementation of a distributed deterministic constrained optimization problem whose optimality condition precisely quantifies the subject‐specific arterial blood flow with minimum difference between observed and predicted hemodynamic states. Robust problem formulations and numerical solution for incorporating in vivo time‐averaged (stationary) and dynamic measurements are derived. We successfully recreate global cerebral circulation patterns in five human subjects based on quantitative magnetic resonance angiography data acquired in main cerebral arteries. The method is a milestone towards subject‐specific blood flow simulations for the entire cerebral circulation.