Dual flip angle (2FA) IR-FLASH with spin history mapping for B1+-corrected T1 mapping: Application to T1 cardiovascular magnetic resonance Multitasking

Abstract

Purpose:

To develop a single-scan method for B₁⁺-corrected T₁ mapping and apply it for free breathing (FB) cardiac MR Multitasking without electrocardiogram (ECG) triggering.

Methods:

One dual-flip-angle (2FA) inversion recovery (IR)-FLASH scan provides two observations of $T_1^{*}$ (apparent T₁) corresponding to two distinct combinations of the nominal flip angle α and B₁⁺. Spatiotemporally co-registered T₁ and B₁⁺ spin history maps are obtained by fitting the 2FA signal model.

T₁ estimate accuracy and repeatability for single-flip-angle (1FA) and 2FA IR-FLASH sequence MR Multitasking were evaluated at 3 Tesla. A T₁ phantom was first imaged on the scanner table, then on two human subjects’ thoraxes in both breath-hold (BH) and free-breathing (FB) conditions. IR turbo spin echo (IR-TSE) static phantom T₁ measurements served as reference. In 10 healthy subjects, myocardial T₁ was evaluated with ECG-free, FB Multitasking sequences alongside ECG-triggered BH MOLLI.

Results:

For phantom-on-table T₁ estimates, 2FA agreed better with IR-TSE (ICC=0.996, mean error ±SD = −1.6%±1.9%) than did 1FA (ICC=0.922; mean error ±SD = −4.3%±12%). For phantom-on-thorax, 2FA was more repeatable and robust to respiration than 1FA (coefficient of variation [CoV]=1.2% 2FA, =11.3% 1FA). In-vivo, in intrasession T₁ repeatability, 2FA (septal CoV=2.4%, 6-segment CoV=4.4%) outperformed 1FA (septal CoV=3.1%, 6-segment CoV=5.5%). In six-segment T₁ homogeneity, 2FA (CoV=7.9%) also outperformed 1FA (CoV=11.1%).

Conclusion:

2FA IR-FLASH improves T₁ estimate accuracy and repeatability over 1FA IR-FLASH, and enables single-scan B₁⁺-corrected T₁ mapping without breath-holds or ECG when used with MR Multitasking.

1. INTRODUCTION

T₁ maps quantify longitudinal relaxation time T₁ on an absolute scale (typically using inversion recovery^1–3 or saturation recovery^1,4 sequences), enabling objective assessment of tissue status and statistical analysis in longitudinal and multi-center oncological⁵, neurological⁶, abdominal^7–8, cardiovascular^1,9–11 studies, and more. Mapping T₁ in moving organs, e.g., the heart, is challenging, although can be done with prospectively triggered strategies^2–4,12 or continuous-acquisition techniques which avoid triggering.^13–18 Continuous acquisition sequences like inversion recovery (IR)-FLASH with a short repetition time (TR) between excitation pulses allow for motion-resolved T₁ mapping in the heart.^13–18

IR-FLASH T₁ mapping is subject to the Look-Locker effect, which introduces T₁ estimate bias, dependent on the effective RF transmit field $B_1^{+}$.^19–20 This bias magnifies at B₀ ≥ 3T^{10, 19–21} due to the reduced wavelength and greater inhomogeneity of $B_1^{+}$ at the tissue. To correct for the bias, a separate pre-scan could in principle be used to map $B_1^{+}$.^22–24 However, this map is a snapshot of $B_1^{+}$ during a time separate from (and much shorter than) the typical IR period. On the other hand, the Look-Locker-induced bias depends not only on instantaneous $B_1^{+}$, but also the $B_1^{+}$ “spin history” (effective $B_1^{+}$ experienced by spins as they change location relative to the excitation volume) during the full IR period. A $B_1^{+}$ snapshot does not account for this history, which can vary substantially across tissue with motion and/or flow, e.g., with heartbeat, respiration, circulation, and perfusion. Incomplete correction for spin history reduces T₁ mapping reliability. A time-cumulative effective (or historical) $B_1^{+}$ map, spatiotemporally co-registered with the T₁ map and ideally obtained from the same scan data is therefore preferred.

Expanding upon the authors’ recent conference work,²⁵ this paper describes a method aimed at improving the accuracy and repeatability of T₁ mapping with IR-FLASH, especially under free breathing conditions. The method comprises a dual-flip-angle (2FA) pulse sequence and complementary fitting algorithm for joint T₁/spin-history mapping. The 2FA IR-FLASH sequence removes the ambiguity in the signal between $B_1^{+}$ and T₁; the fitting algorithm produces spatiotemporally co-registered spin history and T₁ maps. We evaluate the accuracy and precision of this 2FA IR-FLASH method within the MR Multitasking framework^13,16, imaging a static phantom, the phantom on the thoraxes of free-breathing volunteers, and 10 healthy volunteers with cardiac scans.

2. THEORY

Assuming complete gradient spoiling and final approach to steady-state, the IR-FLASH signal equation for the nth readout with excitation repetition time TR and nominal flip angle (FA) α is

$$S\left[n\right]=A\text{ sin }\alpha \frac{1-e^{-TR/T_1}}{1-e^{-TR/T_1}\text{ cos }\alpha }\left[1-\left(1-\Pi \right){\left(e^{-TR/T_1}\text{ cos }\alpha \right)}^{n-1}\right],$$ (1)

where Π accounts for inversion preparation efficiency (Π = −1 for perfect inversion), and the amplitude A absorbs proton density, $T_2^{*}$ decay, and receive coil sensitivity. The Look–Locker effect results in a shorter apparent recovery time constant $T_1^{*}<T_1$.¹⁹ In principle, with perfect prior knowledge of α, for the voxel at position r, T₁(r) could be calculated by correcting $T_1^{*}\left(\text{r}\right)$:

$$\frac{1}{T_1\left(\text{r}\right)}=\frac{1}{T_1^{*}\left(\text{r}\right)}+\frac{\text{ln cos }\alpha }{TR}.$$ (2)

In practice, however, the true α depends on the typically-inhomogeneous $B_1^{+}$ amplitude, whose unknown spatial pattern impacts the correction in Equation (2). For small FA <30°,²⁶ the actual (true) FA map α_true(r) is

$${\alpha }_{\text{true}}\left(\text{r}\right)=\beta \left(\text{r}\right)\cdot \alpha ,$$ (3)

where the dimensionless parameter β(r) is the normalized B₁⁺ relative to the nominally prescribed FA, such that the true flip angle matches the nominal flip angle wherever β(r) = 1. Equation (2) then updates to

$$\frac{1}{T_1\left(\text{r}\right)}=\frac{1}{T_1^{*}\left(\text{r}\right)}+\frac{\text{ln cos}\left[\beta \left(\text{r}\right)\cdot \alpha \right]}{TR},$$ (4)

which now has two unknowns: T₁(r) and β(r). This ambiguity can be resolved by either: 1) assuming β(r) = 1, which introduces bias and error into T₁ mapping; 2) mapping β(r) from a separate pre-scan, which is inefficient; or 3) assuming that FLASH excitation pulse $B_1^{+}$ efficiency equals inversion pulse $B_1^{+}$ efficiency¹⁴, i.e., (β = acos(Π)/π), although the inversion pulse violates the small FA approximation, and may have different properties (e.g., non-selective inversion vs. slice-selective excitation).

Furthermore, none of these strategies addresses the effects of inflow and through-plane respiratory motion on the effective $B_1^{+}$ experienced by spins in the excited slice. Spins within the excited slice (e.g., myocardial tissue) experience the full set of slice-selective excitation pulses during the recovery period, whereas spins that flow through the slice (e.g., blood) see fewer excitation pulses, experiencing a reduced Look–Locker effect (lower effective $B_1^{+}$). Additionally, through-plane respiratory motion dynamically shifts the slice excitation profile as seen in the reference frame of the spins, further reducing the effective $B_1^{+}$ during T₁ recovery. A $B_1^{+}$ map reflecting physiological dynamics and the time-cumulative nature of the Look–Locker effect during T₁ relaxation is, then, better suited for correcting the error in $T_1^{*}$, improving the fidelity of the resulting T₁ estimate.

A straightforward way to resolve the ambiguity of having two unknowns in Equation (4) would be to repeat the acquisition with a second TR or a second nominal FA, obtaining two different measurements of $T_1^{*}$ from which to extract the two unknowns: T₁(r), β(r). For fast sequences such as used in cardiac MR, TR is typically very short, near the limits of gradient switching and physiological stimulation, so a second TR must necessarily be longer, incurring a time penalty and loss of temporal resolution. Introducing a second nominal excitation FA α₂ is therefore more attractive.

To this end, our proposed 2FA IR-FLASH sequence (Figure 1B) alternates between different nominal FAs α₁ and α₂ during successive IR periods. This interleaved FA pattern is preferred to a non-interleaved pattern (a half-length scan at α₁ followed by a half-length scan at α₂), which would share the same temporal co-registration shortcomings as performing a separate $B_1^{+}$ pre-scan. Furthermore, the interleaved FA strategy benefits high-dimensional motion-resolved frameworks, e.g., Multitasking, ensuring for example that each respiratory bin has data from both FAs even with respiratory drift present.

FIGURE 1.

Pulse sequence and simulated T₁ recovery curves for 1FA (A, C) and 2FA (B, D) IR-FLASH. In 2FA IR-FLASH, an inversion pulse is followed by a first train of FLASH readout pulses with the repetition time TR at the first small flip angle (FA) α₁, then immediately by another inversion pulse and the second train of FLASH pulses at the second small FA α₂ at the same TR (B) before repeating. T₁ recovery curves for T₁ = 1000ms, B₁⁺ = 1.00 and for T₁ = 1750ms, B₁⁺ = 1.183 are nearly superimposed in 1FA IR-FLASH (C), but resolved in 2FA IR-FLASH (D). In this simulation, for 1FA IR-FLASH, α = 5° , and for 2FA IR-FLASH, α₁ = 3°, α₂ = 10°, the same values that were used in all experiments. Note that in the experiments, 1FA and 2FA scans were of the same duration.

The 2FA IR-FLASH signal equation at the kth IR period can be obtained by updating Equation (1) as

$$S_k\left[n\right]=A\text{ sin}\left(\check{\beta }{\alpha }_k\right)\frac{1-e^{-TR/T_1}}{1-e^{-TR/T_1}\text{cos}\left(\beta {\alpha }_k\right)}\left[1-\left(1-\Pi Q_k\right){\left(e^{-TR/T_1}\text{cos}\left(\beta {\alpha }_k\right)\right)}^{n-1}\right]$$ (5)

where Q absorbs the effects of having inverted the magnetization from the previous FA’s steady-state. Assuming steady-state established at the final FLASH readout at each FA, Q would be expressed as

$$Q_k= \frac{1-e^{-TR/T_1}\text{cos}\left(\beta {\alpha }_k\right)}{1-e^{-TR/T_1}\text{cos}\left(\beta {\alpha }_{k-1}\right)}.$$ (6)

Both cosine terms in Equation (5) depend on spin history, and thus include the time-cumulative effective $B_1^{+}$ parameter, β. However, the sine term depends instead on the instantaneous $B_1^{+}$, denoted by the dimensionless parameter $\check{\beta }$ (also normalized relative to the nominal FA). This difference is inconsequential for estimating T₁, because for small FA, the $\check{\beta }$ in $\text{sin}\left(\check{\beta }{\alpha }_k\right)$ can be absorbed into an apparent amplitude A*; i.e., $A\text{ sin}\left(\check{\beta }{\alpha }_k\right)\approx A\check{\beta }\text{ sin }{\alpha }_k\equiv A^{*}\text{ sin }{\alpha }_k$. The revised signal equation is then

$$S_k\left[n\right]=A^{*}\text{ sin }{\alpha }_k\frac{1-e^{-TR/T_1}}{1-e^{-TR/T_1}\text{cos}\left(\beta {\alpha }_k\right)}\left[1-\left(1-\Pi \cdot Q_k\right){\left(e^{-TR/T_1}\text{cos}\left(\beta {\alpha }_k\right)\right)}^{n-1}\right].$$ (7)

To illustrate the advantage of 2FA over 1FA IR-FLASH for T₁ mapping, IR curves simulated from Equations (1) and (5) for two different combinations of T₁ and β are shown in Figures 1C–D. The two curves are superimposed for 1FA but separated for 2FA. Furthermore, we hypothesize that because Equation (7) encodes a cumulative history of spins in the excited slice, 2FA is not only more robust than 1FA to $B_1^{+}$ inhomogeneity, but also to through-plane motion, e.g., with respiration and flow.

3. METHODS

All scans were performed on a 3.0T scanner (MAGNETOM Vida, Siemens Healthcare, Erlangen, Germany). Informed Consent was obtained for all human subjects in accordance with an Institutional Review Board protocol.

3.1. MR Multitasking

We evaluated 2FA IR-FLASH T1 mapping using MR Multitasking^13,16, a non-ECG free-breathing framework for continuous-acquisition parameter mapping. Multitasking sequences using 1FA and 2FA IR-FLASH sequences were implemented. A low-rank tensor^27–28 model was used for undersampled reconstruction of an image array with multiple temporal dimensions, here chronicling T₁ relaxation, respiration, and cardiac motion. Additional detail is available in the Supporting Information and cited references.^13,16

3.2. In-vitro Methods

We assessed T₁ measurement agreement of 1FA (with and without a pre-scan-derived B₁⁺ correction) and 2FA IR-FLASH Multitasking sequences with an IR-turbo spin echo (IR-TSE) reference sequence, by imaging on the scanner table a static phantom consisting of 13 vials of gadolinium-doped water surrounded by an undoped water matrix. Within-vial T₁ standard deviations (SDs) measured 1FA and 2FA precision difference. We also assessed the impact of respiration on 1FA and 2FA measurements by placing the same phantom on the thoraxes of two subjects, scanning it under both breath-hold (BH) and free-breathing (FB) conditions. For the first volunteer, both scans were performed twice to further assess repeatability.

Sequence parameters for both IR-FLASH scans were: non-selective inversion pulse; IR recovery period=2.5s; TR=3.6ms; T_E=1.6ms; FOV=270mm×270mm; matrix size=160×160; spatial resolution=1.7mm×1.7mm; slice thickness=8mm. For 1FA scans, α=5°; for 2FA scans, α₁=3°, α₂=10°, chosen to minimize the Cramér-Rao bound on myocardial T₁ variance. For both 1FA and 2FA, acquisition time=60s for static and FB scans, and 17s for BH scans. IR-TSE sequence parameters were: TR=8s; Echo spacing=9.8ms; TurboFactor=8; T_E=9.8ms; TI=25, 250, 750, 1000, 1250, 1500, 1750, 2000, 3000, and 4000ms; FOV=225mm×225mm; matrix size=256×256; spatial resolution=0.9mm×0.9mm; slice thickness=8mm; total acquisition time=26 minutes (156s per TI). To compare the overall trend of B₁⁺ inhomogeneity, a separate B₁⁺ map was also obtained for the static scan with a pre-saturation-based B₁⁺ pre-scan provided by the scanner manufacturer.²⁹

IR-FLASH images were reconstructed with the MR Multitasking framework, with only a T₁ recovery time dimension for the static and BH cases, and with an additional respiratory dimension (6 bins) for the FB cases; the number of spatial basis functions (spatial rank) was 7 for in-vitro scans. For 1FA, three-parameter non-linear least-squares (NLLS) fitting of T₁, A, and Π, to Equation (1) assumed fixed nominal FA. For 2FA, four-parameter NLLS fitting of two concatenated instances of Equation (7) (k=1, 2) was performed, fitting T₁, β, A*, and Π. Q was re-derived symbolically to additionally account for incomplete steady-state. Both fitting procedures included slice profile correction with 5 sub-slices.³⁰

3.3. In-vivo Methods

To assess in-vivo performance of myocardial T₁ mapping, we imaged n=10 healthy adult subjects, scanned with MOLLI, followed by 60s 1FA and 60s 2FA IR-FLASH Multitasking scans. A short-axis mid-ventricular slice was scanned twice with each protocol in 9 subjects and, time constrained, once in a 10^th. MOLLI reference maps were acquired at an end-expiration BH at end-diastole. MOLLI scan parameters: FOV=306mm×360mm, matrix size=218×256; spatial resolution=1.4mm×1.4mm; slice thickness=8mm.

Multitasking reconstruction of IR-FLASH images used a T₁ recovery time dimension, a respiratory dimension (6 bins), and a cardiac dimension (20 cardiac phases); the spatial rank was 40. A wavelet denoising parameter was determined by visual inspection on a representative subject, and then used for all subjects (Supporting Information Figure S4). Unlike MOLLI, fitted 1FA and 2FA T₁ maps were cardiac- and respiratory-resolved, so the end-expiration, end-diastolic phases were extracted for comparison. Measurements from six mid-ventricular myocardial segments were taken from conservative ROIs to avoid partial volume effects.

3.4. Statistical Analysis

Intraclass correlation coefficient (ICC) was computed according to Watson.³¹ Coefficient of variation (CoV) for one pair of T₁ values is the SD divided by the mean. For a group of pairs (aggregate CoV), it is the root mean square of pairwise CoVs. In-vitro, we calculated BH-FB CoV (variation of pairwise BH-FB measurements) to measure the impact of free-breathing, and total CoV (variation across all 6 phantom-on-thorax scans) as a measure of reproducibility. In-vivo, we calculated intrasession CoV (variation of measurements from two scans) in each myocardial segment as a measurement of repeatability, and left ventricular (LV) intersegment CoV (variation of segmental means) as a measure of spatial inhomogeneity. Bias and limits of agreement were, respectively, the mean of differences and ±1.96 times the SD of differences. Statistics reporting follows guidelines in Cole.³²

3.5. Statement on Code Availability

MATLAB (The MathWorks Inc. Natick, MA) reconstruction and fitting P-code is available from the corresponding author upon reasonable request.

4. RESULTS

4.1. In-vitro Results

For the phantom-on-table experiment, 1FA T₁ estimates for the water matrix surrounding the vials decreases from the periphery to the center, Figure 2B. This pattern is mirrored in the reference $B_1^{+}$ map, Figure 2D, where $B_1^{+}$ increases from the periphery to the center, suggesting $B_1^{+}$ inhomogeneity as the source of 1FA T₁ mapping error. Similarly, 1FA substantially underestimates T₁ in the center three vials (IR-TSE T₁=1486ms, 1563ms, 1780ms), accounting for most of the disagreement between 1FA and IR-TSE estimates seen in Figure 3. In contrast, the 2FA water matrix T₁ is relatively uniform in Figure 2C. It is instead the 2FA spin history β map, Figure 2F, which mimics the $B_1^{+}$ pre-scan pattern, as desired. The Bland–Altman and scatter plots in Figure 3 confirm that 2FA agreed better with IR-TSE (ICC=0.996, bias ± limits of agreement= −1.6%±1.9% or −21±10ms) than did 1FA (ICC=0.922, bias ± limits of agreement= −4.3%±11.6% or −63±57ms). Although agreement between 1FA and IR-TSE improved with pre-scan-derived B₁⁺ correction (Supporting Information, Figure S1), 2FA values agreement remained better. Within-vial SDs showed no significant difference between 1FA and 2FA (p=0.87), but difference in SDs was correlated with β such that 2FA was more precise when β<1.04 (Supporting Information, Figure S2).

FIGURE 2.

Maps of T₁ and normalized B₁⁺ from static T₁ phantom experiments. The cylindrical phantom was approximately 13.6cm diameter, fully captured in the images. IR-TSE T₁ (A), 1FA IR-FLASH T₁ (B), 2FA IR-FLASH T₁ (C), scanner-produced B₁⁺ (D), simulated uniform B₁⁺ (=1) for 1FA IR-FLASH (E), and 2FA IR-FLASH β (F) (see Theory section). In the water matrix surrounding the 13 vials, gradual decrease of T₁ values from the perimeter towards the center is present only in the 1FA T₁ map (B), absent in the 2FA T₁ map (C) and in the IR-TSE T₁ map (A). The mirror of this pattern is visible in the 2FA β map (F): gradual increase of β values from the perimeter towards the center. By fitting concurrently from the same data for T₁ and β, 2FA absorbs the artifactual T₁ variation seen in the 1FA T₁ map into the 2FA β map, thus producing a T₁ map (C) closer to the reference T₁ map of the IR-TSE scan (A), including in-vial T₁ estimates (see text, and also Figure 3).

FIGURE 3.

Agreement of IR-FLASH with IR-TSE in static phantom experiments. 1FA and 2FA IR-FLASH T₁ estimates for 13 phantom vials seen in Figure 2, and linear regressions (dashed sloped lines) of the scatters; also, IR-FLASH and IR-TSE intraclass correlation coefficients (ICCs) (A). Bland-Altman plot of data in A: T₁ estimate difference (1FA IR-FLASH T₁ minus IR-TSE T₁ and 2FA IR-FLASH T₁ minus IR-TSE T₁) reported as percentage of two-method (1F IR-FLASH and IR-TSE, or 2F IR-FLASH and IR-TSE) mean T₁ values, with bias or mean difference (solid horizontal lines; −63ms, P = 0.035 for 1FA; −21ms, P < 0.001 for 2FA), and ± 95% confidence intervals (mean ± 1.96 × SD) denoting limits of agreement (dashed horizontal lines; ± 57ms for 1FA; ± 10ms for 2FA) (B).

For the phantom-on-thorax experiments, IR-FLASH agreement with IR-TSE is depicted in Figures 4A–B for 6 scans each: 2 BH and 2 FB in the same session (Subject 1), and another 1 BH and 1 FB in a separate session (Subject 2). Comparing FB to BH scans in Figures 4C–D, agreement was better in 2FA (the 3 paired BH and FB ICCs ranged 0.988–0.996) than in 1FA (paired BH and FB ICCs ranged 0.40–0.96). In both overall (6-scan) repeatability and in paired BH-to-FB comparisons, 2FA repeatability outperformed 1FA (total CoV=11.3% 1FA, =1.2% 2FA; BH-FB CoV range =2.7%–13.8% 1FA, =1%–1.5% 2FA), showing 2FA was more robust to respiratory motion, as hypothesized.

FIGURE 4.

Phantom-on-thorax breath-hold (BH) and free-breathing (FB) T₁ estimates in 2 subjects. Subject 1 was scanned twice with each protocol in the same session; subject 2 was scanned once with each protocol. The phantom had 13 vials (see Figure 2). Each of three colors represents a pair of scans: an FB scan and its counterpart BH scan; there were two such pairs for subject 1, and one pair for subject 2. Panels A and B show scatter plots of T₁ estimates from 1FA (A) and 2FA (B) IR-FLASH phantom-on-thorax scans vs. IR-TSE (phantom on scanner table scan) for 13 vials, as well as ICCs for each pair of BH-FB values. BH-FB CoVs were 11.3% for 1FA IR-FLASH and 1.2% for 2FA IR-FLASH. Panels C and D are Bland-Altman plots comparing FB to BH T₁ estimates for 1FA IR-FLASH (C) and 2FA IR-FLASH (D) scans, showing FB vs. BH biases (mean deviation; solid line) and 95% limits of agreement around the mean (dashed line); they also include BH-FB CoVs, and p-values for FB vs. BH bias.

4.2. In vivo Results

For subject 3, Figures 5A–D, the 2FA T₁ map identifies right ventricular myocardium better than the 1FA map. For subject 4, Figures 5E–H, the 2FA T₁ map is more homogeneous in LV myocardium than the 1FA map, with inhomogeneity absorbed into the β map instead. This is especially pronounced in the anterolateral LV myocardium (where there is typically an abrupt susceptibility change due to the heart-lung interface). Both subjects’ 2FA β maps are darker in the blood pool than in myocardium, reflecting reduced time-cumulative $B_1^{+}$ experienced by inflowing blood.

FIGURE 5.

Representative maps from 2D scans of mid-ventricular cardiac slices in end diastole in free-breathing in subject 3 (A-D) and subject 4 (E-H). MOLLI T₁ (A, E), 1FA IR-FLASH T₁ (B, F), 2FA IR-FLASH T₁ (C, G), and 2FA IR-FLASH β (normalized B₁⁺) spin history (D, H). In the blood pool, T₁ estimate improved in 2FA over 1FA, and β had lower values than in the myocardium. Differences in β reflect the different spin histories (i.e., the number of excitation pulses experienced) of the blood, which flows through the slice and thus experiences fewer FLASH excitation pulses, versus of the myocardium, which, despite in-plane motion, is expected to largely remain in the slice, thus experiencing most if not nearly all the FLASH excitation pulses. For subject 4, in the anterolateral region of the myocardium, β records larger B₁⁺ experienced by spins (arrow in H), possibly from abrupt susceptibility difference across the myocardium/lung boundary. 1FA underestimates T₁ in this region (arrow in F) relative to the rest of the myocardium, an artefact which is absent in 2FA T₁ (G) and MOLLI T₁ (E) maps. In this region, 2FA has absorbed this regional difference into the spin history (β) map, correcting the 1FA T₁ error.

Across 19 scans of 10 volunteers, septal T₁ mean±SD was 1240±37ms for MOLLI, 1633±167ms for 1FA IR-FLASH, and 1610±135ms for 2FA IR-FLASH. For the 9 volunteers scanned twice, intrasession CoVs (septal, 6-segment aggregate) were (0.56%, 1.4%) for MOLLI, (3.1%, 5.5%) for 1FA, and (2.4%, 4.4%) for 2FA. Across the 19 scans, intersegment CoVs were 2.8% for MOLLI, 11.1% for 1FA IR-FLASH and 7.9% for 2FA IR-FLASH. Supporting Information Figure S3 shows statistics for each segment.

5. DISCUSSION

Regardless of phantom experiment type (static, BH, FB) 2FA IR-FLASH T₁ estimates agreed with reference IR-TSE better than 1FA estimates did. In phantom-on-thorax (BH, FB) and in vivo scans, 2FA estimated T₁ more repeatably and homogeneously than 1FA.

Recent parallel conference work³³ implemented two separate three-parameter fits to obtain two estimates $T_{1,1}^{*}$ and $T_{1,2}^{*}$ from signals at FAs α₁ and α₂, and computed T₁ and B₁⁺ from two instances of Equation (4). In that work, the two different FA scans were performed sequentially in contrast to the interleaved FA scheme performed here and motivated in the Theory section. Direct comparison of these approaches may be warranted in future studies.

5.1. Static Phantom

By fitting concurrently for T₁ and β from the same scan data, 2FA IR-FLASH removes the artefactual variation seen in the 1FA T₁ map and absorbs it into the β map, thus compensating the Look–Locker error due to nonuniform B₁⁺ and producing T₁ estimates closer to the IR-TSE estimates.

5.2. Phantom on Thorax

T₁ estimates from 2FA exhibited less variability with respect to respiratory patterns and conditions than estimates from 1FA, as evidenced by the lower CoVs. Furthermore, when directly comparing paired BH-vs.-FB T₁ estimates, 2FA produced higher ICC values, lower biases, and tighter limits of agreement. Overall, these results indicate that 2FA improves robustness to FB conditions, reducing the measurement variability that comes in-part with different subject’s respiration patterns and breath holding instruction compliance.

5.3. In vivo Cardiac

Septal T₁ estimates obtained with 2FA IR-FLASH (1610±135ms) were higher than with MOLLI (1240±37ms), which is known to underestimate T₁,¹⁰ but were closer to values reported at 3T for SAPPHIRE (1578±42ms) and SASHA (1523±46ms),³⁴ which are considered more accurate than MOLLI. Septal T₁ estimates obtained with 1FA (1633±167ms) were higher than in previous 1FA IR-FLASH literature¹⁶ that did not include slice profile correction, but were also close to the SAPPHIRE and SASHA ranges. A direct comparison of 2FA IR-FLASH to SAPPHIRE and/or SASHA is warranted as a subject of future study.

The Look–Locker effect scales with the number of experienced excitation pulses. Stationary isochromats experience more excitation pulses, thus reaching steady-state faster than moving isochromats that experience fewer excitations. In 2D scans, transient blood flowing through the slice experiences fewer excitation pulses than the myocardium resident in the slice, therefore leading to a lower cumulative $B_1^{+}$. The 2FA cardiac β maps reflect this feature; the blood pool has lower β than the surrounding myocardium. Accordingly, 2FA’s T₁ estimate of the blood pool is closer to the published range than 1FA’s. Since β is influenced by flow, there is a potential for physiological information to be embedded in this map that we are not currently using, but which future studies may explore, including time-dependent modeling of β to include the expected flow velocities in systole and diastole.

Separately, in Figure 5, β maps are smoother than their 2FA T₁ complements. This is presumably because β values are time-cumulative (historical) measures of the excitation pulses (>8000 in a 1-minute scan) experienced at the corresponding voxels during multiple repetitions of consecutive T₁ recovery periods, each alone longer than a mapped cardiac phase. Also β, a measure of a magnetic field strength, may be expected to vary smoothly absent abrupt, large susceptibility variations across tissue. Notably, the β map records larger B₁⁺ experienced by spins in the anterolateral region of the myocardium (arrow in Figure 5H), possibly from abrupt susceptibility change across the myocardium/lung boundary. 1FA T₁ map underestimates T₁ in this region (arrow in Figure 5F). This artefact is absent in 2FA T₁ and MOLLI T₁ maps. As with the phantom, 2FA has absorbed the error in the 1FA T₁ estimate into the β map, rendering T₁ more uniform across the myocardium. Regional analyses confirmed 2FA outperformed 1FA in T₁ measurement homogeneity in healthy volunteers, especially the variation between anterior and lateral segments versus septal segments (Supporting Information Figure S3B).

We evaluated 2FA IR-FLASH using the Multitasking framework. Other continuous-acquisition T₁ mapping frameworks, e.g., TOPAZ¹⁴ and those by Becker et al.^15,18 have used short 1FA IR-FLASH breath-hold scans, avoiding respiratory-related B₁⁺/spin-history effects. However, they adjusted for other B₁⁺/spin-history effects by assuming the same B₁⁺ correction factor for the IR pulse and FLASH pulses¹⁴ or fitting the FA while assuming perfect inversion¹⁸. The basic 2FA concept is compatible with these frameworks and others, and may therefore benefit their future implementations.

CONCLUSIONS

The 2FA IR-FLASH method eliminates the need for a separate scan to obtain a B₁⁺ map, and produces a B₁⁺ spin history map spatially and temporally co-registered with the T₁ map from the same scan data. This spin history mapping compensates for T₁ estimation errors from inhomogeneous RF pulses and the Look–Locker effect, and reduces T₁ estimate variability from respiration-induced through-plane motion. As a result, T₁ mapping with 2FA IR-FLASH is more accurate and repeatable than with 1FA IR-FLASH.

Supplementary Material

supinfo

SUPPORTING FIGURE S1. Effect of B₁⁺ correction on 1FA IR-FLASH T₁ estimates using a scanner-generated B₁⁺ map pre-scan, and comparison with 2FA IR-FLASH. Although the pre-scan-derived B₁⁺ correction improves agreement between 1FA IR-FLASH and IR-TSE T₁ estimates, 2FA IR-FLASH shows even higher agreement with IR-TSE.

SUPPORTING FIGURE S2. Scatter plot of the difference between 2FA and 1FA within-vial standard deviations against spin history parameter β. The precision difference is strongly correlated (R²=0.8879; p<0.001) with β. T₁ estimates are more precise from 1FA than from 2FA for the 3 vials nearer to the phantom center (Figures 2B,C), where is β largest (Figure 2F); these vials are represented by the cluster of 3 data points in the present figure for which β > 1.10. For the three vials with the smallest β (≤ 0.98), 2FA estimates are slightly more precise. Overall, there was no significant difference between 1FA and 2FA within-vial SDs (p=0.87).

SUPPORTING FIGURE S3. Mid left ventricular diastolic segmental T₁ estimates and statistics. Mean T₁ (ms) ± SD (ms) for MOLLI (A), 1FA IR-FLASH (B), and 2FA-IR-FLASH (C), and intrasession coefficient of variation (CoV) aggregated across 9 subjects for MOLLI (D), 1FA IR-FLASH (E), and 2FA-IR-FLASH (F). Note that, for each method (1FA IR-FLASH, 2FA IR-FLASH, and MOLLI), the septal CoV values reported in the main text were computed from the combined ROI of both septal segments, and are distinct from two individual septal sub-region CoVs depicted here.

SUPPORTING FIGURE S4. Effect of wavelet denoising parameter value on T₁ (A-C) and B₁⁺ (D-F) mapping. The Multitasking image reconstruction framework uses a wavelet denoising algorithm whose noise thresholding parameter λ is adjustable. To illustrate the effect of λ on the quality of the maps, the T₁ and β maps in this figure were created from λ values ten times smaller (A, D) and ten times larger (C, F) than the value used throughout the remainder of the in-vivo study (1.25 × 10⁻¹⁰; B, E). Lower λ values result in noisier maps with reduced precision, whereas higher λ values blur the images, potentially compromising accuracy due to partial volume effects.