Zero Echo Time (ZTE) imaging is a technique with clinical potential for imaging tissues with very short T2 relaxation times. With ZTE, the readout gradient is ramped to a constant value prior to a hard RF excitation pulse, therey enabling signal acquisition along a radial k-space trajectory immediately after the RF pulse. Because the read gradient amplitude is generally high to provide a suitable point spread function of short T2 signals, the hard RF pulse may result in a sinc-shaped excitation profile in the direction of the readout gradient. To avoid the resulting artefacts in the reconstructed image, the slice profile effect on signal from each full radial sampling across k-space can be corrected prior to 3D image reconstruction¹, at the cost of image signal to noise ratio (SNR). In addition, quadratic phase modulation of the hard RF pulse is used to avoid the zero crossings of the sinc excitation profile². The slice profile effect during excitation (and the associated SNR penalty for correcting it) can be reduced by reducing the duration of the RF excitation pulse, thereby broadening the profile; however, in the typical ZTE scenario where RF amplitude is already maximized, a shorter duration RF pulse results in a lower flip angle and lower SNR. Therfore, an optimum pulse duration exists to balance these sources of SNR loss.

The raw signal equation in ZTE is $$[1]~~~~~~~S(k)=\int_{}^{} M(r)\rho(r)e^{-i2{\pi}kr}dr + \epsilon$$where M(r) is the magnetization as a function of radial position, r, ρ(r) is the quadratic phase modulated excitation profile, and ε is added noise. To remove the profile contribution to the signal, data from each full radial projection (i.e., from –kmax to +kmax) must be corrected by dividing by the profile¹, $$[2]~~~~~~~S_{corr}=FT\begin{bmatrix}\frac{IFT[S(k)]}{\rho(r)} \end{bmatrix}$$The SNR of S_corr is $$[3]~~~~~~~SNR\propto \frac{\int_{}^{}M(r)dr }{\sqrt{\int_{}^{}\frac{1}{\rho(r)^{2}}dr}}$$where the numerator is the sum of transverse magnetization after RF excitation and the denominator is the factor by which the standard deviation of the noise is increased by the profile correction step in Eq [2]. The transverse magnetization depends on pulse duration, τ, as $$[4]~~~~~~~M(\tau)\propto \frac{\sin(\omega_{1}t)(1-e^{-\frac{TR}{T1}})}{1-\cos(\omega_{1}t)e^{-\frac{TR}{T1}}}$$and the slice profile, ρ(τ), is computed by numerical solution of the Bloch equations for the quadratic phase modulated RF pulse.

Thus, for excitation flip angles below the Ernst angle, the numerator of Eq [3] increases with increasing τ, but so does the denominator. At some value, τ_opt, the balance of these competing effects will result in a maximum SNR. For example, given typical clinical scan parameters of FOV=250x250x250 mm³, G = 10 mT/m, isotropic resolution=1 mm, TR = 10 ms, B₁ amplitude = 15 µT, and T1/T2 = 108/89 ms. Figure 1 shows plots of SNR vs τ including and not including the slice profile effects and correction. Data were simulated using a set of random magnetization values and the previously stated scan parameters to estimate the SNR for various pulse durations. The simulated SNR values were then compared to the analytically derived SNR values in Eq [3].

These results demonstrate a novel approach to optimizing SNR in ZTE imaging, under the common conditions where increasing RF excitation flip angle requires increasing RF pulse duration. The simulated optimization showed that a pulse duration of 31 µs provided the highest SNR given 3T parameters. The flip angle induced by this pulsewidth was 7.1° which was less than the predicted Ernst angle of 24.3°. This is expected because division by the profile in [3] reduces the increase in SNR with increasing pulse duration. In most applications of ZTE where the TE is much less than the T2 of the imaged tissue, T2 relaxation effects may be neglected in Eq [4]. If the TE is on the same order of magnitude as T2 the numerator of Eq [3] can be modified to include $$$e^{-\frac{TE}{T2}}$$$, where TE must increase with increasing τ.