Quantification correction for free-breathing myocardial T1ρ mapping in mice using a recursively derived description of a T1ρ* relaxation pathway

Abstract

Background: Fast and accurate T_1ρ mapping in myocardium is still a major challenge, particularly in small animal models. The complex sequence design owing to electrocardiogram and respiratory gating leads to quantification errors in in vivo experiments, due to variations of the T_1ρ relaxation pathway. In this study, we present an improved quantification method for T_1ρ using a newly derived formalism of a T_1ρ* relaxation pathway.

Methods: The new signal equation was derived by solving a recursion problem for spin-lock prepared fast gradient echo readouts. Based on Bloch simulations, we compared quantification errors using the common monoexponential model and our corrected model. The method was validated in phantom experiments and tested in vivo for myocardial T_1ρ mapping in mice. Here, the impact of the breath dependent spin recovery time T_rec on the quantification results was examined in detail.

Results: Simulations indicate that a correction is necessary, since systematically underestimated values are measured under in vivo conditions. In the phantom study, the mean quantification error could be reduced from - 7.4% to - 0.97%. In vivo, a correlation of uncorrected T_1ρ with the respiratory cycle was observed. Using the newly derived correction method, this correlation was significantly reduced from r = 0.708 (p < 0.001) to r = 0.204 and the standard deviation of left ventricular T_1ρ values in different animals was reduced by at least 39%.

Conclusion: The suggested quantification formalism enables fast and precise myocardial T_1ρ quantification for small animals during free breathing and can improve the comparability of study results. Our new technique offers a reasonable tool for assessing myocardial diseases, since pathologies that cause a change in heart or breathing rates do not lead to systematic misinterpretations. Besides, the derived signal equation can be used for sequence optimization or for subsequent correction of prior study results.

Keywords: Cardiac; Correction; Mapping; Quantitative MRI; Radial; Spin-lock; T1rho; T1ρ.

Fig. 1

Sequence design for myocardial T_1ρ mapping in small animals. The high heart and respiratory rates require the use of prospective triggering in combination with breath gating. Usually a trigger on the R-wave and dynamic trigger delays are applied before the spin-lock (SL) preparation. The acquisition window in diastole is very short (≈20–30 ms), so that several readouts can only be carried out by using fast gradient echoes. To acquire a single T_1ρ weighted image, the experiment has to be repeated several times (N_I). For T_1ρ mapping, imaging has to be repeated with different SL times (N_D). The sequence parameters of the readout (T_rec, TR, NR, α) have a decisive impact on the relaxation pathway of T_1ρ. This is explained in Fig. 2 by considering the signal S₁

Fig. 2

Simulation results of the investigation of quantification errors. The signal of the first acquisition S₁ was calculated using Bloch simulations for realistic in vivo parameters (A). An individual steady state ${\mathrm{S}}_1^{\mathrm{SS}}$ is reached for each SL time. When using small flip angles, more repetitions are required for this. In B the values were fitted with the common monoexponential model. The relaxation time T_1ρ* calculated in this way is systematically below the true T_1ρ value. The relationship between the systematic underestimation and the two parameters T₁ and T_rec is shown in C. From this it can be seen that an incomplete spin recovery is the decisive point. A systematic error of − 2% to − 16% is to be expected in vivo. If the corrected fit is used (novel signal equation), errors only arise if incorrect sequence parameters are assumed (D). The error propagation is moderate here, since ± 5% estimation errors in the sequence parameters only lead to ± 1.447% errors in T_1ρ

Fig. 3

Results of the phantom experiments. In A, calculated relaxation time maps using the monoexponential model and the corrected model are compared. The increase in T_1ρ* with T_rec can be seen visually. The measured T_1ρ* values agree well with theoretically predicted values (B). The mean deviation from the prediction for the phantoms with increasing BSA concentration was 0.47%, 0.84% and 1.38%. The corrected fit, on the other hand, delivers nearly constant results. This is confirmed in the ROI based evaluation in B and C. The highest deviations arise in the phantom with the longest T₁ relaxation time. Corrected fitting reduced the quantification error averaged over all measurements from -7.4% to -0.97%. The errors in the corrected fit could result from incorrect values of T₁, T_rec, or α. The R² values are generally higher for the corrected fit (> 0.999). However, for monoexponential fitting, R² values > 0.996 were achieved despite high quantification errors

Fig. 4

Results of the in vivo measurements at high T_rec variability. The recovery times recorded during the data acquisition are shown in A. The different colored curves show the individual T_rec times for 10 repetitions of the T_1ρ mapping sequence in animal I. In B the calculated relaxation time maps (short axis view, isotropic resolution 250 µm) for the monoexponential fit (left) and the corrected fit (right) are shown. 5 repetitions with different T_rec times are exemplary shown. The mean T₁ value 1391 ± 34 ms in myocardial tissue was obtained by an inversion recovery snapshot flash (IRSF) sequence and used to calculate the corrected maps. The maps show distinct artifact formation, which is primarily due to the unsteady breathing. The region-of-interest (ROI) based correlation analysis with T_rec is shown in Fig. 6A

Fig. 5

Results of the in vivo measurements at low T_rec variability. The recovery times recorded during the data acquisition are shown in A. The different colored curves show the individual T_rec times for 10 repetitions of the T_1ρ mapping sequence in animal II. In B the calculated relaxation time maps (short axis view, isotropic resolution 250 µm) for the monoexponential fit (left) and the corrected fit (right) are shown. 5 repetitions with different T_rec times are exemplary shown. The mean T₁ value 1342 ± 44 ms in myocardial tissue was obtained by an IRSF sequence and used to calculate the corrected maps. A high image quality and less streaking is perceptible due to reduced motion issues. The ROI based correlation analysis with T_rec is shown in Fig. 6B

Fig. 6

Correlation analysis of the measured relaxation times with T_rec. The T_1ρ and T_1ρ* values are the mean values within the left ventricular ROIs (Figs. 4B, 5B). The T_rec values correspond to the averaged recovery times during the corresponding individual measurements (Figs. 4A, 5A). A Shows the results with high and (B) shows the results with low T_rec variability. In both cases there is a significant positive correlation (r = 0.684, r = 0.709, p < 0.05) for uncorrected monoexponential fitting and no significant correlation (r = 0.373, r = 0.272) for corrected fitting. The plots also show the 95% confidence intervals (light red/blue areas) and the respective mean values and standard deviations as error bars in both cases

Fig. 7

Correlation analysis of the measured relaxation times with T_rec for n = 14 different animals and N = 44 individual measurements. The recovery times recorded during the data acquisition are shown in A for the remaining animals. The evaluation was carried out analogously to animal I and animal II (Figs. 4, 5, 6). Here, corrections were made for all animals with the T₁ estimate of 1400 ms. In B a significant positive correlation for uncorrected fitting (r = 0.708, p < 0.001) and no significant correlation (r = 0.204) for corrected fitting was identified. The plots also show the 95% confidence intervals (light red/blue areas) and the respective mean values and standard deviations as error bars in both cases. Since comparisons were made between different animals, the variation in relaxation times is higher here than, for example, in the single study of animal II

Fig. 8

Simulation of in vivo experiments for the detectability of diseased tissue. The gray areas illustrate the true T_1ρ values for healthy (light gray) and diseased tissue (dark gray). A natural variation of ± 1% was assumed in the simulation for the N = 1000 random experiments. The uncorrected fit results (red) and the corrected fit results (blue) were compared. In A, the impact of radiofrequency (RF) flip angle choice (α = 10–40°) on quantification accuracy and significance levels at 5% increased T_1ρ in diseased tissue was investigated. In B the sensitivity of detectability for increased T_1ρ in the range 1–4% was investigated for α = 40°. The corrected fit provides consistent results for all simulated RF flip angles (p < 0.001) and improved detection sensitivity for increased T_1ρ (p < 0.05 for + 2%)

Fig. 9

Simulation of in vivo experiments for the detectability of diseased tissue. The gray areas illustrate the true T_1ρ values for healthy (light gray) and diseased tissue (dark gray). A natural variation of ± 1% was assumed in the simulation for the N = 1000 random experiments. For the RF flip angle α = 40° was used. The impact of varying T₁ values in diseased tissue on T_1ρ quantification and detectability was investigated. A 5% increased T_1ρ in diseased tissue was considered. In A, the uncorrected fit results (red) and the corrected fit results (blue) were compared. Here, the correction was performed using the baseline T₁ value (1400 ms) for both healthy and diseased tissue. In (B), the corrected fit using the true T₁ values of healthy and diseased tissue was supplemented. The results show significantly improved detectability based on the corrected fit (A). Using true T₁ values instead of baseline values, the quantification accuracy can be slightly increased (B)