Theoretical investigation of estimation of steady and pulsatile blood flow and blood vessel cross section by CW NMR excitation

In this paper we show theoretically that when a magnetised blood bolus enters a CW NMR excitor coil of length Le at resonance and the signal from the T2-decaying, processing transverse magnetisation of the flowing blood spins is subsequently detected by a detector coil of length L separated from the excitor coil by a distance delta l, then by recording CW NMR signals at three positions such as delta l = 0, 0.5 and 1.0 cm one can eliminate the static tissue signal and measure non-invasively the steady component V0 as well as the total vessel cross section, beta accurately. The time dependent part of the CW NMR signal which depends on Vpulse(t), is also dependent on V0 non-linearly unless both L and Le are greater than 50 cm and delta l is zero. Finally, methods of obtaining true Vpulse(t) from the CW NMR signal after applying proper correction due to the steady flow are discussed.