A new method for long-T2 suppression in a prepared steady-state 3D-UTE sequence is introduced. The method is based on long-T2 signal behavior in steady-state as the diffusion-inducing spoiling gradients are modified, giving a theoretical signal cancellation using appropriate coherence combinations. At the same time, short-T2 signal quantity is optimized, offering a positive contrast over this component. Imaging experiments over a Lego brick soaked in doped water show an excellent agreement with theoretical predictions.
The pulse sequence employed (fig. 1) consists in a long (≫Tshort2) rectangular saturation pulse followed by a short one (α2≤ 90°), whose flip angle will be computed to maximize the short-T2 signal. It’s very similar to the Actual Flip Angle sequence7, except that α1≠α2. Gradient spoiling, RF spoiling and delays are optimized to ensure a steady-state of the long-T2 component to be suppressed, and a minimal impact of potential static gradients (e.g. B0 inhomogeneities)8.
First, the short-T2 transverse magnetization can be tracked using the Bloch equations in steady-state:
Mxy=M0(1−Es)+Es(1−Ew)fz11−fz1fz2EsEwfxy,
with Es=e−TR1/T1,Ew=e−TR2/T1,
fxy=e−τ2/2T2α2sinc(√α22−(τ2/2T2)2),
fzi=e−τi/2T2[cos(√α2i−(τi/2T2)2)+τi/2T2sinc(√α2i−(τi/2T2)2)] (τi pulse duration) as described in [9]. These quantities account for the signal loss during a RF pulse caused by T2 relaxation.
The short-T2 signal can therefore be maximized with respect to α2 (given a first flip angle α1 = 90°) with ^α2=argminα2(M0−Mxy(Es,Ew,fz1,fz2,fxy)).
Then, with α2 set, we take advantage of the steady-state to suppress the water signal. Using the expression of configuration states in [5], the signal to be suppressed can be written:
F+0=cos(α2/2)2F−0+e2iΦsin(α2/2)2F−∗0−ieiΦsin(α2)Z−0,
with F0 and Z0 being functions of α1,α2, RF-phase Φ,n=TR2/TR1,TR2,TR1,Tlong1,Tlong2 and diffusion coefficient D. In this case, having |F+0|=0 would imply a complete long-T2 suppression. Since no trivial analytical expression exists for the F−0 and Z−0 states in steady-state, we numerically explored the tissues and sequence parameters space in order to assess whether the diffusion effect induced by the spoiling gradients would combine the F−0 and Z−0 states in order to satisfy |F+0|=0. Using the EPG formalism, we have shown that this condition can be met for sets of parameters and RF-phase increment Φ0=k×360/(n+1) (k∈N) (fig. 2), offering a signal falling to 0 (referred hereafter to as “signal pit”).
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