Theoretical studies of the effect of the dipolar field in multiple spin-echo sequences with refocusing pulses of finite duration

It has been observed recently that the finite duration of refocusing rf pulses in a multiecho acquisition of the signal formed under the influence of the dipolar field leads to significant signal attenuation [S. Kennedy, Z. Chen, C.K. Wong, E.W.-C. Kwok, J. Zhong, Investigation of multiple-echo spin-echo signal acquisition under distant dipole-dipole interactions, Proc. Int. Soc. Magn. Reson. Med. 13 (2005) 2288]. Hereto, we quantify the phenomenon by evaluating analytically the influences of both the distant dipolar field (DDF) and transverse relaxation T2 on the magnetization in a multiecho pulse sequence based on correlation spectroscopy revamped by asymmetric z-gradient echo detection (CRAZED). Analytic expressions for the magnetization were obtained, which demonstrate explicitly the origin of rephased signal in the presence of the finite π pulses in the multiecho train. The expressions also explain the effects of the DDF and T2 during the refocusing pulses on the signal strength, and show the substantial signal dependence on the phase of the rf pulses. We show that when the DDF effect during the pulse is canceled, the signal rises primarily during the free evolution time in the acquisition period. This elucidates the signal attenuation when the rf pulses cover a significant proportion of time in the sequence. In addition, we performed an optimization on the number of refocusing pulses that maximizes the total acquired signal using parameters for water, brain white matter, and muscle. We found that maximal signal-to-noise ratio is obtained when the pulse duration approximately equals the free evolution time in the samples with a wide range of T2.