Towards Better SNR for In Vivo Applications

The theoretical upper limit of the iDQC signal is 40% of the full equilibrium magnetization. However, when relaxation is included, the maximum achievable signal from a prototypical CRAZED sequence, in the linear regime, is proportional to T2/τ_d This means that for samples with a short T2, as encountered in vivo, signals from intermolecular multiple quantum coherences (iMQCs) reach very diminished signal intensities. However, with simple modifications to the sequence, the signal can be increased beyond the T2 limit.

The prototypical iMQC pulse sequence is the “CRAZED” sequence, θ₁-{delay t₁}-{z-gradient pulse, area GT}-θ₂-{z-gradient pulse, area nGT}-{delay t₂}, which can be shown analytically in either the classical or quantum pictures to give a signal of the form In this expression, M_o is the equilibrium magnetization, and τ_d = 1/(γμ_oM_o), called the demagnetizing time, sets the time scale for the appearance of iMQC resonances, which is approximately 170 ms for tissue at room temperature in a 7 Tesla imager. If we can ignore relaxation, the signal will grow linearly in time until it will reaches its maximum value for T2=tau.
However, when we include transverse relaxation, the signal will grow linearly only for a time t2~T2, and then relaxation will dominate. The maximum signal achievable will drop from the theoretical 40% to only a few percent.
There is however an escape for this. In a CRAZED sequence, the mixing time transfers part of modulation along the z axis . The evolution of the transverse magnetization under the dipolar field created by the longitudinal magnetization causes the signal to “bunch up” and produce a non zero signal. If the sample has a short T2 and a fairly long T1, then even after the transverse magnetization has dissipated, modulated longitudinal magnetization remains. Therefore, an additional pulse can turn some of the longitudinal into transverse, and again both magnetizations will be well spatially correlated. Thus, in principle, more signal can be recovered by dipolar evolution, even though the system has not been restored to equilibrium. Figure 1 shows how the signal from a standard iZQC CRAZED sequence can be increased by simply adding an extra mixing pulse to the standard sequence.