The difference signal between the longitudinal magnetisation of the control and label images ([DELTA]M) is
A modification of the Bloch equation for longitudinal magnetisation to include the flow effect according to Fick's principle (difference between delivery and clearance of substance in blood is proportional to the local flow) has been introduced by Detre and Williams :
where [M.sub.0] is the longitudinal magnetisation of the tissue at the equilibrium and M, Ma, and Mv are the time-dependent longitudinal magnetizations of the tissue, arterial, and venous blood, respectively.
Additionally, labelled blood flow leads to a time-dependent decrease in the longitudinal magnetisation [M.sub.0] with an apparent time constant T1 app; its magnitude depends on the T1 relaxation time of tissue and blood flow, given by
and in the case of a steady state, [M.sub.0] decrease to longitudinal magnetisation in steady state [M.sub.ss], and the solution is given by
(iii) And the magnetisation relaxation function, M (t), is the fraction of the remaining longitudinal magnetisation that is carried by the tagged water at time t after arrival.