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The T1 measurement of flowing blood using standard DCE- MRI sequences are subject to large measurement errors which are non-linear in relation to flow velocity. This work qualitatively and quantitatively demonstrates the difficulties of accurately measuring the T1 of flowing blood using DCE-MRI over a wide range of physiologically realistic flow velocities and pulsatilities. Sources of error are identified and proposals made to reduce these. This work qualitatively and quantitatively demonstrates the difficulties of accurately measuring