Fast T1 Mapping Determined Using Incomplete Inversion Recovery Look-Locker 3D Balanced SSFP Acquisition and A Simple Two Parameter Model Fit

Abstract

Purpose

To evaluate a fast T1 mapping technique using incomplete inversion recovery 3D balanced steady-state free precession acquisition along with a two parameter model fit.

Materials and Methods

Using Bloch simulations, we explore the two parameter model fit for data acquired using such an acquisition scheme. The parameter space over which the fit holds good is determined through simulations. A linear correction is derived for the R1* (1/T1*) values so determined. Two phantoms and six volunteers were scanned using the described technique. Comparison scans using full recovery as well as gold standard inversion recovery spin echo were also performed.

Results

The two parameter fit works exceedingly well over a large parameter space. T1 values in the phantoms showed an error of 4.9% and 39% before correction and 0.9% and 1.6% after correction. For the six volunteers, error in T1 value was 5.3% for white matter (WM) and 2.4% for gray matter (GM) after correction, while it was 11.2% and 18.2% before correction.

Conclusion

The work presented here allows for T1 map determination with higher resolution and shorter acquisition time than previously possible. The technique is especially well suited for GM/WM T1 mapping.

Introduction

T1 relaxation time can be estimated by fitting the recovery of longitudinal magnetization following an inversion pulse. This requires obtaining images at multiple different inversion times to adequately sample the inversion recovery curve. The gold standard is to obtain a single sample following each inversion, and to repeat the experiment for each inversion time sampled with full recovery of magnetization. Clearly, it is more efficient to obtain multiple samples following a single inversion pulse, which may be achieved using the Look-Locker method which continuously samples the inversion recovery curve to acquire images at each of several different inversion times. If sampling did not perturb the inversion recovery curve at all, computation of T1 relaxation would be straightforward and accurate. However, to acquire images, the Look-Locker method uses acquisition schemes, such as fast gradient echo or low angle shot (FLASH) (1,2) or balanced steady-state free precession (b-SSFP) imaging ((3), (4), (5)) which do perturb the recovery curve.

Because of this perturbation, the simple two parameter inversion recovery equation (M₀(1−2e^−t/T1)) does not adequately fit the data. To correct for this perturbation, a three parameter model (2) can fit the data as long as magnetization recovery is complete. However, this correction is sensitive to the inversion times and SNR of the acquired images (6). Furthermore, the correction factor increases with increasing perturbation of the recovery curve.

Recently, the MORTLL (MOdulated Repetition Time Look Locker) technique using 3D b-SSFP acquisition and modulated repetition times (7) to measure T1, was designed specifically to measure T1 in CSF and other tissues with relatively long T1 and T2 relaxation times. For such tissues, b-SSFP perturbs the inversion recovery curve minimally even for large flip angles and provides high SNR, even at relatively lower flip angles (3). For other brain tissues (including white matter and gray matter), simulations showed that using low flip angles (~10°) results in errors of only 2–5% from the ideal T1 values (7). This allows for the use of a simpler two parameter model and eschews application of any correction.

To-date, all methods for T1 determination using Look-Locker acquisition are based on the premise of full inversion recovery of magnetization. This results in substantially increased scan times for tissues with long T1 values. For example, accurate gray matter T1 determination would require a shot repetition time of around 6 s while CSF T1 determination would need TR_seq ≈ 22 s. (Each inversion pulse is followed by a train on b-SSFP acquisitions; TR_seq is defined as the time between inversion pulses, distinct from the repetition time of each b-SSFP acquisition, TR.)

The 3D b-SSFP acquisition has an effective scan time of one repetition (or shot) time per slice as one z (slice) encoding step is followed by a single shot acquisition of all phase encoding (y) steps. The scan time then increases with increasing number of acquired slices. To reduce scan time, TR_seq can be modulated from TR_min to TR_max from shot to shot using a predefined smooth function. Similar to the effective inversion time or an effective echo time being defined to the center of k_y space, an effective repetition time can be defined for the center of k_z space. Thus the center of 3D k-space sees a TR corresponding to full recovery of the inverted magnetization. Modulating the repetition time in this manner results in almost a two-fold reduction in scan time (7). However, the scanning time is still longer than warranted by the two parameter model. This is because unlike the three parameter model which dictates use of at least six to eight phases for a good fit, the two parameter model can work with just three phases. (A phase in this work is synonymous with an image obtained from a single-shot b-SSFP acquisition.) Even with a high spatial resolution of ~1 mm, acquiring three phases results in many seconds of dead time for brain tissues (to allow full recovery of the inverted magnetization). This would be particularly true if parallel imaging is employed since the number of phase encoding steps drops with increasing parallel imaging factor. Further reduction in scan time can be obtained by allowing only partial recovery of the longitudinal magnetization. This would result in an underestimation of T1 values which would need to be corrected to provide accurate final values for T1. Allowing for partial recovery can impact the SNR of the acquired images. To regain some of the reduction in SNR, a higher flip angle could be used compared with the case when full recovery and relatively low flip angles (~10°) are used (to eschew a correction).

A method to correct for the T1, resulting from flip angle perturbation and, more significantly, incomplete inversion recovery, with the two parameter model is described here. We first characterize the estimated T1 (T1*) resulting from such an acquisition through simulations. It is shown that a simple linear model can be designed to correct for T1 underestimation. Comparison between the two parameter and three parameter model is done to show adequacy of the two parameter model. Conditions under which the two parameter model provides a good fit to the inversion recovery curve, when recovery is incomplete or a higher flip angle is used, are analyzed. The parameter space over which the two parameter fit and hence the correction is valid is thereby characterized. We compare results obtained from phantom scanning and brain T1 mapping with results from other established techniques to show that the correction is accurate. Assumptions made and the various factors affecting the correction are also described.

Materials and Methods

First, we provide details on the simulations for the incomplete inversion recovery sequence with b-SSFP acquisition. This is followed by a discussion of the two and three parameter model fit. It is shown that both fits are equivalent at steady-state and hence a two parameter model suffices. Next, we perform simulations to show that the two parameter model does indeed provide a good fit over most of the practically relevant parameter space. This is followed by a description of the correction needed to obtain the correct T1 from the estimated value obtained by the two parameter fit.

Theory

Simulations

To study the effect of incomplete inversion recovery on the estimated value of T1 (T1*), simulations based on Bloch equations were performed. Magnetization evolution under continuous b-SSFP acquisition was implemented using a numerical solution as proposed in (8):

$$\mathbf{M}(\mathrm{n}+1)=\mathbf{A}•\mathbf{M}(\mathrm{n})+\mathbf{B}$$

where A = P₁C₁R_αP₂C₂ and B = P₁C₁R_αD₂ + D₁. P, C and R are the precession, relaxation and rotation matrices, respectively. M(n+1) refers to the magnetization vector at the (n+1)th step; P₁ = P(TE) relates to the precession of spins from the beginning of the b-SSFP sequence till the echo time while P₂ = P(TR−TE) relates to precession from TE to the end of TR; similarly, C₁ matrix calculates the (T1,T2) relaxation till TE; R_α corresponds to rotation of magnetization by flip angle. D₁ = D₂ = (I − C)[0 0 1]^T where I is the identity matrix. n refers to the n^th RF pulse (or b-SSFP acquisition). For the Look-Locker acquisition, the starting magnetization will be M(0) = [0 0 −1]^T.

First we explore the relationship between the two and three parameter models. Formulation of the two parameter and the three parameter model allows for comparison of the fitted parameters from the two models.

Three parameter model

The three parameter model is described as

$$M_z(t)=A-B\text{exp}(-{R1}^{*}.t)$$

where A, B and R1* are constants determined by fitting the model to acquired phases. R1* is an estimate of the relaxivity. T1 is then determined using T1 = (B/A −1)T1* where T1* = 1/R1*.

Two parameter model

Now consider the case of the two parameter model. For the moment, we assume that such a model perfectly fits the data from b-SSFP acquisition with incomplete inversion recovery. Accordingly,

$$M_z(t)=M_0^{*}[1-2\text{exp}(-\beta .t)]$$

In the above equation, $M_0^{*}$ (< 1) corresponds to the steady-state magnetization at t = 0 and β (an estimate of R1) need to be determined. Figure 1 shows the longitudinal magnetization at the end of each inversion recovery interval immediately preceding the next inversion pulse (b-SSFP acquisition). It can be seen that M_z(t) reaches steady-state within n = 4–5 shots (TR_seq). When M_z(t) is in steady-state, M_z(nTR_seq) = M_z((n−1)TR_seq). In which case, B = 2A and the three parameter model reduces to the two parameter model. Comparing the two models, we get A = B/2 = M₀* and β = R1*.

Figure 1.

Longitudinal magnetization (prior to application of the inversion pulse) as a function of the number of times the inversion pulse is applied. Each inversion pulse is followed by b-SSFP acquisition with TR/TE = 4/2 ms, α as indicated in the legend and two different echo train lengths. Shorter etl (270) allows for some dead time between end of acquisition and the inversion pulse. TR_seq = 2000 ms is the time between inversion pulses. Initial M_z = 1 (prior to first inversion pulse) while T1/T2 = 1500/60 ms.

Model Correlation

Next we test the validity of the relationships over a range of scan parameters through simulations. TR_seq was varied to approximately correspond to the range of sequence TRs seen in our MR experiments for 1 mm³ resolution. T1 time was varied over a range that included the T1 value for gray matter. The correlation between the two parameter model and the three parameter model was tested using the following parameters: Inversion recovery TR_seq time = 2 s, b-SSFP acquisition: α = 30°, TR/TE = 4/2 ms, T1 = [400, 600, 800, 1000] ms and T2 = 60 ms while inversion times TI were assumed to be [100 200 400 500 700 850] ms. TI (as per definition) is the time from the inversion pulse isocenter to the center of k-space for a phase (image). The shot time (TR_seq) was changed from 2000 ms to 3000 ms in steps of 200 ms (constant T1 = 800 ms). The excitation angle was also changed from 30° to 60° while keeping other parameters the same as above. For the simulations above, we assumed T2 to be constant. The effect of changing T2 and off-resonance will be analyzed later. Note that the longitudinal magnetization will reach a steady-state after ~ 5T1. If the longest T1 under consideration is GM, this would be < 7 s. For example, if TR_seq is assumed greater than 1.5 s, steady-state would be reached by the fifth z-encoding acquisition. For linear 3D slice encoding as used here, the longitudinal magnetization would be in steady-state by the time the center of k_z space is sampled when number of prescribed slices is greater than 12 (if one assumes no oversampling). With 3D oversampling as is usually done, the total number of prescribed slices needed for the steady-state assumption to hold true would be reduced even further.

Parameter Space

Next, the relevance of the two parameter model to incomplete IR-BSSFP with different MR scan combinations is shown. Two scan parameter sets similar to the ones used for MR experiments were considered for goodness of fit of the two parameter model. Parameters used for the first plot were: TR/TE = 3.6/1.8 ms, total number of echoes in echo train length (etl) = 495, TR_seq = 3 s, TI = [100 200 400 500 700 850] ms. In order to derive reliable statistical values, six sampling points were chosen instead of three used in the MR acquisitions. Two measures of goodness of fit were considered. The first was the Pearson goodness-of-fit (χ² test) while the other measured the Pearson correlation between measured and fitted data values. The second parameter set corresponded to images acquired using parallel imaging factor of 2 along y and z. Parameters used for the simulation were: TR/TE = 4/2 ms, total etl = 270, TR_seq = 1.5 s, TI = [173 535 897] ms. T1 ranged from 750 ms to 1500 ms.

Note that while the three parameter model provides an accurate fit to the inversion recovery curve resulting from incomplete recovery and acquisition perturbation, correcting the resulting T1* using (B/A −1) as a correction factor will not return the original T1. With incomplete inversion recovery, the calculated R1* or β is overvalued.

Correction

Assuming that the two parameter model provides an excellent fit over some parameter space of interest (in GM/WM imaging), we investigate β as a function of R1. For the simple case of complete inversion recovery, the observation of a linear relationship is trivial since β(R1) = mR1 where m = ((B−A)/A). When recovery is incomplete, magnetization and corresponding derived relaxation parameters can be described using Bloch equations as discussed above. Simulations using a numerical solution for Bloch equations show that β(R1) = mR1 + c. β(R1) varies with sequence acquisition parameters (TR/TE of b-SSFP acquisition, flip angle α, TR_seq, echo train length). The algorithm then consists of three steps: (a) Simulate the recovery curve using acquisition parameters from the imaging experiment and using two to four values of T1 (say [800 1400] ms) over the range of interest. (b) Perform the two parameter fit to the recovery curve in (a) for each of the R1=1/T1 used in the simulation. This gives us R1* for the corresponding R1 used. (c) Now find m and c by fitting the values of R1 to R1*. This linear fit then provides the correction for any value of calculated R1* for the chosen parameter set. The parameter set used for model comparison was used to simulate correction curves with three different flip angles.

MRI Experiments

T1 measurements in phantoms and volunteers were carried out under an IRB approved protocol using a 3T Philips Achieva scanner (release 2.5.3). Scan parameters for phantom and volunteer scanning were TI_1,2,3 ≈ [180, 800, 1420] ms; TR_seq= 3 s, 3D b-SSFP acquisition TR/TE=3.6/1.8ms, resolution=0.9×1×1 mm, α=10°, 25 slices, scan time: 1:36. T2 values for the two phantoms were determined using a multi-echo spin echo sequence (TR = 15 s, six echoes with ΔTE = 15 ms).

Six healthy volunteers were also imaged under an IRB approved protocol. In addition, accurate T1 mapping was also done with TR_seq = 10s (allowing for full recovery in WM/GM) (7) with other parameters similar to the short TR_seq scan. GM T1 values were obtained by measuring in the caudate nucleus. Gold standard IR-SE scans were done for two of the volunteers. An accelerated protocol with scan time ~ 1 s per slice was obtained in some volunteers using the following modifications of the scan parameters: α = 30°, parallel imaging factor = 2 along k_y and k_z, 27 slices, TR_seq = 1500 ms, scan time: 26 s.

Results

Model Correlation

Figure 2 shows the simulated longitudinal magnetization curve along with fits obtained with the two and three parameter model for α = 45° and TR_seq = 2.5 s. For the study looking at the correlation between two and three parameter models, when α = 30° and TR_seq = 3 s, the difference between β and R1* is just 3.1% while it is 7.3% for α = 60° and TR_seq = 3 s. With different inversion sampling times (TI), the values will differ slightly. One observation from the above parameter variation experiment is that the percent error between the two models increases as the excitation angle increases and decreases slightly as TR_seq increases over the range described. Note that the above values are true only when the entire recovery curve is sampled with a b-SSFP acquisition with no dead time between b-SSFP acquisitions.

Figure 2.

Shows the two parameter and three parameter fit for inversion recovery b-SSFP (in steady-state) with TR/TE = 4/2 ms, TR_seq = 2.5 ms, α = 45° and continuous sampling along the recovery curve. T1/T2 were assumed to be 800/60 ms for the simulation. Every 50^th sampled point is shown for clarity. M_z shown is in the steady-state.

Figure 3a shows the correlation between M₀* from the two parameter model and A from the three parameter model. Figure 3b similarly shows correlation between β and R1*. The slope in Figure 3a is 0.974 while it is 1.025 in Figure 3b indicating excellent correspondence between the two sets of values.

Figure 3.

(A) Relationship between M₀* (two parameter model) and A (three parameter model) and (B) between β (two parameter model) and R1* (three parameter model) for a selected scan parameter set. R1 values used for the simulation correspond to T1 = [400 600 800 1000] ms.

Changing the repetition time from 2000 ms to 3000 ms in steps of 200 ms (when T1 = 800 ms) results in β = 2.362 ± 0.017 s⁻¹ (R1* from the three parameter model is 2.282 s⁻¹) while the ratio of M₀*/A = 0.991 ± 0.004 while 2M₀*/B = 1.017 ± 0.0003. Similarly, changing the excitation angle from 30° to 60° results in a correlation of 1 between β and R1*; however, the slope is 0.87. In both cases, T1 estimated by the two parameter model is slightly lower than the T1 estimated by the three parameter model. The correlation between them, however, is perfect. (A different slope implies that for the case of incomplete inversion recovery, the correction would be different for the two cases.) From the above, it is clear that there is a range of parameters over which a two parameter model provides an accurate fit without the need for a three parameter solution.

Parameter Space for Two Parameter Model

Over a T1 range of 750 ms to 2000 ms, the two parameter fit is extremely good by both measures (chi-square test and Pearson correlation). Figure 4A shows only small localized regions of T1/TR for excitation angles greater than 50° that exhibit relatively poor fits for the first parameter set (TR/TE = 3.6/1.8 ms, total etl = 495, TR_seq = 3 s). In the second case (TR/TE = 4/2 ms, total etl = 270, TR_seq = 1.5 s), the two parameter fit works relatively better than the first case except for a localized area around α = 32° and for T1 = 1300 ms (see Figure 4B). Note that χ² = 9.48 and Pearson r = 0.81 for a level of significance α = 0.05 for the case of six phases (TI times). A similar analysis using just three sampled points on the curve (instead of six) provides a similar result although the (T1, α) values at which the fit is poor are different.

Figure 4.

(A) Chi-square test and (C) Pearson correlation for parameter space when TR/TE = 3.6/1.8 ms, total etl = 495, TR_seq = 3 s (Rx1) while (B) and (C) are the corresponding tests for a different parameter space where TR/TE = 4/2 ms, total etl = 270, TR_seq = 1.5 s. (Note that χ² = 9.48 and r = 0.81 for a level of significance α = 0.05.) This shows that the two parameter model provides an excellent fit over most of the parameter space.

Correction

Typical linear fit used for correction in a volunteer scan is shown in Figure 5. T1 varies from 800 ms to 1400 ms in steps of 200 ms. The plots show data and fit for three different values of the excitation angle. In all cases, a linear fit provides excellent correspondence between the uncorrected and corrected T1 values.

Figure 5.

Shows the linear correspondence between the calculated R1* value for a two parameter fit and the true R1 value (T1 = 400, 600, 800 and 1000 ms) for three different flip angles. Other scan parameters are TR_seq = 2 s, b-SSFP acquisition: TR/TE = 4/2 ms.

MRI Experiments

T2 values were determined to be 520 ms (phantom 1) and 270 ms (phantom 2). Since the T2s are considerably different, different corrections were applied to the two phantoms. Measurement were made by placing circular ROIs in each phantom. T1 values determined from inversion recovery spin-echo were 2625±21.6 ms and 915±1.9 ms while full recovery IR-BSSFP gave values of 2624±84.1 ms and 907±23.2 ms for the two phantoms. T1 values for the two phantoms obtained with incomplete inversion recovery were 862±24.9 ms and 1607±69.8 ms. As mentioned above, different correction was applied to the two phantoms because of their grossly different T2s. Correction applied for phantom 1 was R1 = 1.1938×R1* − 0.00029186 while correction for the second phantom was R1 = 1.5247×R1* − 0.00055906. The values after correction were 921±178.9 and 2584±185 ms. Figure 6 shows a bar plot of T1 values for the two phantoms obtained prior to and after correction and the values from a full recovery scan. Standard deviations within the ROIs are shown as error bars. Error is 4.9% and 39% before correction and is 0.9% and 1.6% after correction. (Note the large difference in errors prior to correction is a result of the very different T1 relaxation times of the two phantoms.)

Figure 6.

T1 values before and after correction for two different T1 phantoms are compared with the T1 value obtained from a full magnetization recovery study. Note the substantial improvement in accuracy for the long T1 phantom after correction.

Figure 7 shows in-vivo images obtained with (A) full recovery (accurate T1 mapping) and those obtained with partial inversion recovery before (B) and after correction (C). Figure 8 shows the bar plot for uncorrected and corrected T1 values from incomplete inversion recovery protocol, and from the full recovery scan protocol, for the six volunteers. Standard deviation in the measured mean T1 values across the six volunteers is shown as an error bar. When compared with the accurate full recovery scheme, average error across six volunteers was 5.3±1.3% for WM and 2.4±0.91% for GM after correction, while it is 11.2 ± 0.65% and 18.2 ± 2.4% before correction. With the scan using higher flip angle and parallel imaging along the y- and z-axis, error was 1.1±0.9% for WM and 6.5±0.9% for GM after correction while it was 41.5±0.6% and 57.2±1.6% prior to correction. For two volunteers, corrected T1 values (obtained with partial recovery TR_seq = 3s) were found to differ by an average of 2.7% in WM and 4.7% in GM when compared with IR-SE T1 values. Prior to correction the mean error was 7% and 13.7% in WM and GM, respectively.

Figure 7.

(A) Uncorrected and corrected (B) T1 maps of the brain compared to a map obtained with (C) full inversion recovery (TR_seq = 10 s) for gray and white matter. Inset (D) shows the corresponding M₀* map with B1 inhomogeneity.

Figure 8.

T1 values for white and gray matter prior to and after correction across six volunteers compared to values obtained with full recovery. Bars denote the mean values obtained for the six volunteers while the error bars denote the standard deviation of the mean values for the six volunteers.

Figure 9 shows images obtained with the accelerated protocol before and after applying the correction.

Figure 9.

Rapid high resolution T1 imaging (0.9×0.9×1 mm) with short TR (TR_seq = 1.5 s) and SENSE along slice and phase encoding directions (SENSE factor = 2). Uncorrected (A) and corrected (B) images on the same gray scale depict the improvement in T1 contrast between gray and white matter after correction. 27 slices were obtained in 26 s for this acquisition. When compared with full recovery IR-BSSFP, error was 41% and 56% in WM and GM, respectively, while after correction it was 1.7% and 5.8% after correction.

Discussion

We described a way to obtain correct T1 values for the case when inversion recovery is incomplete and for relatively large flip angles with 3D b-SSFP acquisition.

The correction algorithm described here is accurate for T2 values that do not show much variation between tissues of interest. Voxels containing two tissue types with one or both T2s very different from the assumed T2 will show greater deviation from the true T1 value even after correction. For example, the correction will not be as effective in lesions with a very different T2 from GM/WM. Here, T2 was assumed to be 60 ms for all simulations. The error in T1 resulting from a different T2 (since GM/WM T2 values reported in literature vary between 50–90 ms) of say 100 ms is 1.25% for WM and 1.12% for GM compared with values obtained assuming T2 = 60 ms. Therefore, moderate variations in T2 value have little effect on the accuracy of the correction.

Correspondingly, the correction will not hold for tissues or fluids exhibiting very different T2s than those of white and gray matter. So values obtained in CSF after correction, using the same correction as for WM/GM, are overvalued. In such a case, it might be possible to apply a separate correction to CSF by first segmenting out regions of CSF from WM/GM. Although only a limited number of different scan prescriptions were considered in the simulations and experiments, the parameter space over which the two parameter model and correction hold encompasses almost all practical parameter combinations. (T1, α) values over which a certain combination for TR/TE, echo train length gives a poor fit to the two parameter model can be identified through simulations as described earlier.

No correction for B1 inhomogeneity is needed since RF inhomogeneity gets reflected as a multiplicative field in M₀* (9). This can be seen from Figure 7D which shows the M₀* map corresponding to the T1 maps in Figure 7A,B. The resulting correction then is only a function of the nominal flip angle used to derive β(T1^est). Accordingly, if the gross flip angle (which is assumed to be the nominal flip angle for correction) is 5° instead of 10°, values for WM would be higher by 2.5% and GM by 3%. B1 inhomogeneity would result in small errors in the gross accuracy of T1 values but not in regional variation. The inversion pulse is assumed to be 180° throughout the study. If the inversion pulse cannot achieve complete inversion, T1 values will be underestimated. For both parameter sets used with volunteers, the error in T1 (for T1=800 ms) is 3.5% with an inversion efficiency of 0.93 (10) (M_z = −0.976 after inversion) while the error is 3.1 – 3.3% when T1 = 1400 ms for the two scan prescriptions. In short, the sources of error discussed above result in minor variations in T1 values for WM/GM mapping. The correction will increase signal variation in the image as it can be seen as a stretching function.

Note that noise has not been considered in the simulation. The effect of noise on the value of corrected T1 can be easily simulated. If simulations are done (1000 iterations) with Gaussian noise (mean = M_z(TI), σ = 0.05 × M_z(TI)) added to the longitudinal magnetization at each TI, the corrected value of T1 shows σ = 7.2 ms when T1 = 800 ms for the first imaging protocol. The correction shows some variation with the sampling times TI. When noise is not considered, there’s negligible difference (< 0.6%) between the case when six TIs are considered (as in the simulations) and when three TIs corresponding to the first MR volunteer protocol are used. For example, when noise is considered with three TIs as used in the MR experiment, σ = 9.1 ms instead of 7.2 ms. The RF excitation in the simulations is considered instantaneous. The effect of a finite RF pulse in the context of b-SSFP sequence has been described recently (11). A finite RF duration leads to an underestimation of the b-SSFP signal. This effect can be quantified through a different $\widetilde{T2}>T2$. The time-bandwidth product (TBW) for our Gaussian filtered sinc excitation pulse was 7.12 for the first volunteer imaging parameter set. This results in an approximate value of $\widetilde{T2}=61.1\text{ms}$. For the second parameter set, TBW was 5.64 resulting in an effective $\widetilde{T2}=61.8\text{ms}$. As discussed earlier, such a small change in T2 would result in a negligible effect on the corrected T1 value.

MT effects have also been ignored. Magnetization transfer effects can significantly reduce the signal in GM/WM (12), particularly at relatively higher flip angles. If the signal reduction multiple is the same at each sampled time point (TI), the corrected value for T1 shows no change. For the two volunteer scans done with a higher flip angle (α = 30°), we did not see any significant errors over the results obtained for the protocol with α = 10°, thereby indirectly supporting our argument that MT scales all time points equally.

Note that the Pearson goodness of fit measure depends on the magnitude of data values used. Data values used in the simulations were of the same order of magnitude as those obtained from MR studies. Only on-resonant behavior was considered to derive the correction. Simulations were done to quantify off-resonance response of the correction. For example, spins at 25Hz off-resonance would result in an underestimation of the T1 value by 4.3% when T1 = 800 ms. We have also shown that high resolution T1 maps can be obtained efficiently at about one image per second when parallel imaging is used along two directions (slice and phase). Using parallel imaging along slice encoding direction currently requires the choice of a restricted preferred direction (coronal or sagittal) with a multi-channel head receive coil. The correction presented here is particularly suited for tissues with similar T2 ≪ T1. This is true in gray matter – white matter T1 mapping. When T2 ~ T1, the two parameter model does not provide a good fit.

Conclusion

Typical Look-Locker imaging uses a three parameter model along with full inversion recovery for accurate determination of T1 values. The two restrictions reduce image resolution and increase scan time. In this work, we show that a simple two parameter model along with incomplete inversion recovery b-SSFP acquisition allows for increased image resolution (due to reduced number of images needed for a two parameter model) and substantially reduced scan times. Accurate T1 mapping can still be achieved by applying a straightforward correction determined for the range of T1 values selected and the MRI parameter space. The technique is especially well suited for GM/WM T1 mapping.