MR fingerprinting (MRF) is a promising technique for quantifying tissue characteristics including T₁, T₂ and M₀¹. However, system imperfection causes the acquired data to deviate from the signal model, which can lead to significant estimation error. This systematic imperfection typically comes from RF and gradient coil. The B₁ inhomogeneity effect has been dealt with previously². In addition, non-ideal slice profile from limited RF time and the k-space shift from gradient delay or eddy current can bring errors in parameter quantification. Here, we present how these two factors affect parameter estimation in MRF using simulation studies.

Slice profile simulation

To observe the effects of imperfect slice profile, two hamming windowed sinc RF pulses of time-bandwidth product (TBW) 4 and 8 with same RF duration (= 2 ms) were used. Signal evolutions across the slice direction (-5 mm to +5 mm with 0.2 mm interval, slice thickness = 5 mm) were generated based on Bloch simulation using hard pulse approximation. These signal evolutions from different slice locations were summed and matched to the predefined dictionary. The simulation was performed for different T₁ (500:100:2000ms), T₂ (50:10:150ms) and B₀ (0:5:50Hz). A gradient strength of 9.395 and 18.790 mT/m for each TBW corresponding to the 5 mm slice thickness were used based on 3T system.

Gradient delay simulation

A radial acquisition scheme was simulated to observe the effects of gradient delay. The gradient delay effects can be modeled as k-space center shift³. Here, we assumed that the amount of shift induced by x and y gradient delay are identical. Thus, the amount of shift in radial direction (shift_r) was varied from 0 to 1.5 points with spacing of 0.1 point. A 2D numerical phantom with different T₁ and T₂ values and B₀ distribution were generated (Fig. 1) with 128x128 matrix. K-space shift was applied to 16 radial spokes distributed with golden angle obtained by inverse gridding. For both simulations, fixed TR (= 6 ms) and sinusoidal FA pattern with 500 time points were used. The dictionary was designed to cover the range of simulated parameters.

Figure 2 shows the estimated T₁ with fixed T₂ = 100 ms and estimated T₂ with fixed T₁ = 1000 ms for TBW = 4 (a, b), 8 (c, d). The estimated values for different B₀ are also presented. T₁ was underestimated by about 3.5% and 1.7% for TBW = 4 and 8 respectively. T₂ was overestimated by more than 30% and 15% for each. It is noticeable that T₂ estimation was more sensitive to slice profile imperfection than T₁ estimation.

For the gradient imperfection study, the estimated T₁, T₂ and B₀ maps are shown in Fig. 3(a). The estimated parameter maps were severely contaminated due to geometric distortions in images induced by k-space shift. The geometric distortion pattern also varied with the amount of k-space shift. The relative estimation errors according to k-space shift are presented in Fig. 3(b, c). The overall estimation errors increased as k-space shift increased. The relative errors were not only affected by k-space shift but also T₁ or T₂ values. However, these changes depend on the geometric distortion that the imperfections cause.

In this study, we demonstrated the estimation error from slice profile and gradient delay. The results may vary depending on TR/FA pattern but in general, the effects were considerable. To correct the effect of imperfect slice profile, higher TBW RF pulse or Shinnar-Le Roux pulse should be used. Also, the dictionary design incorporating the effect of slice profile imperfection could be another solution.

According to the gradient simulation results, estimation error can range up to ~10% for shifts that are not noticeable visually (e.g. 0.5 k-space shift). These results should apply to other sampling trajectories such as spirals. Accurate calibration is necessary.