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# Statistical Models of 4D flow MRI Velocity Error using Principles of Fluid Dynamics and Imaging Physics

4D flow magnetic resonance imaging (MRI) has emerged as an imaging modality capable of assessing cardiovascular flow non-invasively. Despite interest in using these *in vivo* measurements for cardiovascular disease diagnostics and progression assessment, there are no adequate models of 4D flow MRI’s measurement error. Error models are essential in evaluating accurate hemodynamic biomarkers and judging the quality of 4D flow MRI scans. Here, we present a comprehensive error model of 4D flow MRI velocity measurements using fluid dynamics and imaging physics principles. 4D flow MRI velocity error is described as a multivariate normal distribution which is a function of space and time. The error distribution’s scale is assessed using the principle of conservation of mass, and error correlations are assessed using the novel standardized difference of means (SDM) velocity metric. We define the SDM velocity as the difference between the local mean velocity and the global background mean velocity relative to the standard error of the local mean velocity. We also demonstrate the SDM velocity’s utility in segmenting vessels in 4D flow MRI measurements. This work also introduces a bias error model, which accounts for insufficient spatial resolution and partial volume effects. These bias error estimates serve as one means of validating our proposed 4D flow MRI error model. All algorithms presented are validated in 4D flow MRI measurements in scaled *in vitro* cerebral aneurysms and *in vivo* 4D flow measurements. This work ultimately supports the development of reliable biomarkers indicative of cardiovascular disease progression.