Effects of B₁⁺ Heterogeneity on Spin Echo-Based Liver Iron Estimates

Abstract

BACKGROUND:

Liver iron concentration (LIC) measured by MRI has become the clinical reference standard for managing iron overload in chronically transfused patients. Transverse relaxivity (R₂ or R₂*) measurements are converted to LIC units using empirically derived calibration curves.

HYPOTHESIS:

That flip angle (FA) error due to B₁⁺ spatial heterogeneity causes significant LIC quantitation error. B₁⁺ scale (b₁, [FA_actual/FA_specified]) variation is a major problem at 3T which could reduce the accuracy of transverse relaxivity measurements.

STUDY TYPE:

Prospective

POPULATION:

47 subjects with chronic transfusional iron overload undergoing clinically-indicated LIC assessment.

FIELD STRENGTH/SEQUENCE:

1.5T/3T dual-TR B₁⁺ mapping sequence

ASSESSMENT:

We quantified the average/standard deviation b₁ in the right and left lobes of the liver from B₁+ maps acquired at 1.5T and 3T. The impact of b₁ variation on spin-echo LIC estimates was determined using a Monte Carlo model.

STATISTICAL TESTS:

Mean, median, and standard deviation in whole liver and right and left lobes; two-sided t-test between whole-liver b₁ means.

RESULTS:

Average b₁ within the liver was 99.3%±12.3% at 1.5T versus 69.6%±14.6% at 3T and was independent of iron burden (p<0.05). Monte-Carlo simulations demonstrated that b₁ systematically increased R₂ estimates at lower LIC (<~25mg/g@1.5T, <~15mg/g@3T) but flattened or even inverted the R₂-LIC relationship at higher LIC (≥~25mg/g@1.5T, ≥~15mg/g@3T); changes in the R₂-LIC relationship were symmetric with respect to over and under excitation and were similar at 1.5T and 3T (for the same R₂ value). The R₂*-LIC relationship was independent of b₁.

CONCLUSION:

Spin echo R₂ measurement of LIC at 3T is error-prone without correction for b₁ errors. The impact of b₁ error on current 1.5T spin echo-based techniques for LIC quantification is large enough to introduce measurable inter-subject variability but the in-vivo effect size needs a dedicated validation study.

Introduction

Chronic anemias such as thalassemia and sickle cell disease represent the most common genetic disorders in the world¹. Transfusion therapy in these patients produces severe iron deposition in the liver and other organs, leading to cardiac and endocrine dysfunction and liver cirrhosis². Iron overload in transfusional siderosis cannot be treated with phlebotomy; instead, patients receive iron chelators that bind and remove iron with dosing specific to their tissue iron content, necessitating reliable iron quantitation techniques^3,4. Before 2005, needle biopsies were required to quantify liver iron, with their attendant risks⁵ and sampling error^6–8. Since then, MRI systems have become key tools for diagnosing and following iron overload disorders such as transfusional siderosis in sickle cell disease and thalassemia, hemochromatosis, liver disease, and a number of neurodegenerative disorders^9,10. Both transverse relaxivity and magnetic susceptibility measurements have been used to estimate tissue iron concentrations in the liver, heart, endocrine glands, and brain¹¹.

MRI-based iron quantification at 1.5 Tesla (T) is now standard of care¹² but quantification of liver iron using high-field scanners (3T and above) is limited by excessively rapid signal decay and susceptibility artifacts. When increasing field strengths from 1.5T to 3T, field-dependent enhancement causes the slope of the relationship between LIC and R₂* (1/T₂*) decay to double, leading to transverse decay below 0.5 ms in organs such as the liver, well below the range standard gradient-echo techniques can reliably quantify¹³. Spin echo-based R₂ (1/T₂) estimates, which do not enhance as dramatically with increased field strength, have the potential to overcome these limitations at 3T and already see widespread use at 1.5T¹¹. However, spin echo estimates are more susceptible to spatial variations in the radiofrequency transmit efficiency, B₁⁺ heterogeneity, leading to incorrect flip angles throughout the image, a well-characterized imaging problem in high field scanners^14,15. The ratio of the achieved flip angle to the target flip angle is known as the B₁⁺ scale and is represented in this manuscript as b₁. Quantifying and correcting for this heterogeneity could lead to more accurate liver iron concentration (LIC) estimates. Accordingly, this study aimed to measure b₁ heterogeneity at 1.5T and 3T in patients over a broad range of iron burdens and to simulate the estimated error in R₂-based LIC estimates at both field strengths using a Monte Carlo model.

Materials and Methods

Patient Population

Study participants were selected from a population of patients undergoing clinical treatment for iron overload primarily resulting from transfusional treatment of sickle cell disease, thalassemia, and other rare anemia syndromes. Participants were recruited and provided informed consent to participate in an IRB-approved study (CCI-14–00034). Each participant received a clinically indicated MRI assessment for iron overload via R₂* on the 1.5T scanner; a similar research protocol was completed at 3T. All images were acquired on single-RF-transmit 1.5T and 3T Philips Achieva magnets (v3.2.2, Best, Netherlands) using 16-element SENSE-XL torso coils.

Patient Assessment

Imaging was performed on in 47 representative subjects (19M, 28F, 20.1±11.6 years of age, 19 β-Thalassemia, 21 Sickle Cell, 7 other rare anemia, LIC=0.5–41.5 mg FE/g liver tissue). Liver iron estimates were obtained at 1.5T using a 3-slice gradient echo acquisition with the following parameters: 16 linearly spaced echoes with TE/TR=0.96–11.47/50ms, FA=30°, matrix/voxel=72×67/1.25×1.25×10mm, BW=4409Hz/px. R₂* estimates were made in hand-segmented regions of interest (ROI) in the liver, excluding major hilar vessels, and fit using an exponential+constant model to the data using a constrained Levenburg-Marquadt algorithm in custom MATLAB (Mathworks, Natick, MA) code; R₂* values were converted to LIC estimates using a R₂*-LIC calibration curve derived from biopsy¹⁶.

B₁⁺ scale maps were obtained at 1.5T and 3T in a single slice using a dual repetition time (TR) b₁ mapping sequence¹⁷ with TE/TR1/TR₂=3ms/20ms/120ms, bandwidth of 2894Hz/px, voxel size of 4.2×4.2×8 mm, and one signal average. A second set of b₁ maps were obtained at both fields using an echo time of one millisecond to ensure that we could sample severely iron loaded patients who demonstrate particularly rapid T₂* decay. b₁ maps were validated in a phantom (0–24 mM MnCl₂ vials in a 0.5 mM MnCl₂ bath) with transverse decay rates as low as 0.4 ms to ensure that the b₁ maps had sufficient dynamic range to reliably map the patient population.

The maps were manually segmented by a biomedical engineering doctoral student (ED) with 5 years of experience to quantify the b₁ heterogeneity found in this iron overloaded patient population. B₁⁺ scale maps were assessed for dependence on patient size and clinical iron-load. Patient b₁ maps were averaged after non-rigidly warping individual maps to a canonical liver shape to generate an aggregate b₁ map. Because of imperfect registration, some pixels in the canonical liver shape received contributions from fewer than 5 patients and were excluded; each pixel was weighted according to the number of contributing patients. The warped b₁ maps were used to estimate spatial statistics in the right and left lobe.

Simulation

An internally developed simulation framework written in MATLAB was used to create physiologically realistic liver iron geometries in-silico over a range of 1–50 mg/g (mg iron/g dry tissue weight, iron loads of=1,[5:5:50]mg/g). The framework was validated in human subjects at 1.5T and 3T¹³. Detailed descriptions of these models may be found in previous reports^18–20. Briefly, liver tissue was modeled as 80 μm cubes of liver tissue containing 64 cuboidal hepatocytes and 18 cylindrical sinusoid regions¹⁸. Iron overload was modeled by distributing spheres of iron in the hepatocytes using Gamma distributions describing size and shape. From the iron distributions, magnetic field disturbances were calculated based on the field strength and magnetic susceptibility of iron¹⁹. Simulated protons were then diffused through the geometries using a random walk simulation obeying cell boundaries. The previous version of the simulation framework assumed perfect excitation and refocusing, ignored pulse bandwidth, and did not model longitudinal magnetization or T₁ decay.

To model b₁ heterogeneities, we implemented a full Bloch simulator to calculate the 3D magnetization of each proton at every time step. The simulations calculated rotations from instantaneous excitation and inversion pulses, realistic iron-free T₂/T₁ relaxation rates of 42ms/812ms at 3T and 50ms/576ms at 1.5T²¹, and the iron-based phase accrual from the proton’s random walk at each 0.05 μs time step. Iron-based T₁ changes were ignored due to minimal longitudinal recovery over the duration of the echo trains simulated and lack of multiple TRs. Excitations and inversions were modeled as instantaneous pulses and achieved angles were scaled by b₁ amplitude for each simulation. For example, a 90_x-180_y single spin echo sequence with 90% excitation efficiency would be simulated with an excitation pulse of 81° about x and inversion of 162° about y. Signals from 2500 separate spin cohorts were superposed to form a transverse signal for each combination of iron load and b₁.

Simulations varied b₁ from 53% to 127% in single echo and Carr-Purcell-Meiboom-Gill (CPMG) multiecho spin echo experiments with 90° excitations and 180° inversions; spin echo and CPMG echo times were [1.70, 2.56, 3.86, 5.82, 8.76, 13.2, 19.9, 30.0] ms and [2.0, 4.0, 6.0, 8.0, 10, 12, 14, 16, 18, 20] ms, respectively; the simulated b₁ range was chosen empirically based on the range demonstrated by subject b₁ maps. Complex signals were fit using a complex signal model with a non-negativity constraint to estimate the R₂ relaxation rate of each sample. R₂ as a function of LIC was determined for each simulated b₁ by fitting individual results to a 3^rd order polynomial. R₂* was calculated from the simulation framework by fitting the envelope of the FID to a simple monoexponential.

Post-study investigation

Following the conclusion of study in patients and initial data analysis, we assessed the feasibility of overcoming issues identified at 3T using tools available on many clinical MRI systems. Following completion of the patient studies and the initial data analyses, b₁ maps were obtained in 5 healthy volunteers using the same pulse sequences on a Philips 3T Ingenia platform with dual transmit capability. We attempted to correct the underexcitation by manually increasing the RF transmit gain proportional to the demonstrated underexcitation (gain_new = gain_original * 1/b₁). We then tested adaptive RF shimming to determine if spatial variability could be improved.

Data availability

Code and data relating to this work is available in the following git repo:

https://<CCI-14-00034>/gitlab/res/B1-SE-LIC

Statistical Analysis

Mean B1 from acquired B1 maps was assessed for dependence on LIC and subject weight via linear regression. There was no significant dependence on LIC at either field strength. Mean B1 at 3T demonstrated a modest but significant dependence on weight; the relationship was insignificant at 1.5T.

LIC vs B1 regression

1.5T: B1mean = 0.087*LIC + 99.4 (p =0.143)

3T: B1mean = −0.178*LIC + 75.9 (p = 0.127)

Weight vs B1 regression

1.5T B1mean = 0.086*weight + 98.7 (p = 0.66)

3T B1mean = −0.24*weight + 86.5 (p < 0.05)

A two-sided t-test comparing 1.5T and 3T mean B1 values rejected the null hypothesis that the means were the same (p<0.05).

Results

Figure 1 demonstrates b₁ heterogeneity in the liver at 1.5T and 3T. At 3T, mean b₁ was low and the standard deviation was high (69.6%±14.6%). Excitation efficiency was higher in the right lobe than the left lobe (left mean=62.1%±12.8%, right mean=73.6%±13.9%) but there was considerable inter-subject variability. B₁⁺ scale heterogeneity was independent of liver iron burden. Both the spatial homogeneity and the mean achieved b₁ (99.3%±12.3%) were better at 1.5T compared to 3T; right and left lobe means were 103.3% and 92.0% respectively.

Figure 1-.

B₁⁺ scale heterogeneity maps in patients demonstrate significantly different behavior at 1.5T and 3T. 1.5T maps demonstrate largely uniform excitation patterns and consistently complete excitation. 3T maps demonstrate significant spatial variation in b₁ as well as a mean achieved b₁ of only 69.6%.

Simulations results demonstrating the effects of varying b₁ on multiple single echo R₂ estimates and CPMG multiecho R₂ estimates are shown in Figure 2 and Figure 3, respectively. The R₂* iron calibration was robust to b₁ errors at both 1.5T and 3T (not shown); no change in R₂*-LIC calibration was detectable. Spin echo simulations demonstrated that calibration error increased noticeably with b₁ error. At 1.5 T, b₁ error caused single echo R₂ to rise more quickly with iron concentration than the true calibration curve but then to flatten and even decrease at higher iron levels. The impact of b₁ error was relatively symmetric about 100%, i.e. overexcitation and underexcitation produced similar changes to the R₂-LIC relationship. When underexcitation was severe (b₁ < 67%), increases in iron load greater 25 mg/g caused R₂ estimates to decline.

Figure 2-.

Single echo simulations over a wide range of iron loads and b₁ values demonstrates that R2, and therefore iron concentration, is overestimated in the presence of b₁ at 1.5T. Further, inaccuracies increase with iron load for a given b₁ value. Although at 1.5T R₂ estimates tend to increase with b₁ values, 3T maps show the opposite effect for LIC>~15mg/g due the combination of fast initial decay and shortened T₁ resulting in artificially flat signal decay curves which are interpreted as having slow T₂ decay when fitting is performed in the absence of additional constraints³¹.

Figure 3-.

CPMG simulations over a wide range of iron loads and b₁ heterogeneities demonstrate that R2, and therefore iron concentration, is overestimated for all b₁ values except with low iron loads at high b₁ values. Further, inaccuracies increase with iron load for a given b₁ value.

Single echo R₂-LIC calibrations at 3T demonstrate a similar appearance with b₁ error, but the effects were amplified. Inverse relationships between R₂ and iron burden were observed at lower b₁ (<80%) and higher iron burdens (>15 mg/g) (ie R₂ estimates decreased as LIC increased). Using the b₁ estimates derived from patient data (69.6%±14.6%), more than half of liver voxels corresponded to calibration curves that do not have a unique relationship between R₂ and liver iron at 3T.

Multi-echo calibrations at 1.5T were qualitatively similar to single echo results, except for the expected blunting of R₂ relaxation across all iron loads²². Multi-echo calibrations were more stable over b₁ ranges of ±20% but demonstrated a larger proportional b₁ effect than the single echo calibration for larger b₁ values. At 3T, multi-echo R₂ exhibited a more linear relationship with liver iron concentration. Spatial heterogeneities in b₁ primarily changed the intercept of the R₂-LIC relationships. R₂ retained a 1:1 relationship with LIC until b₁ was < 60%.

Supplemental Figure 1 demonstrates b₁ mapping performed on a health volunteer at 3T with (bottom panel) and without (middle panel) adaptive RF shimming from dual RF transmission. The mean liver b₁ was 76.2% ± 9.2% without dual transmit, similar to the average b₁ values in our study. B₁⁺ shimming corrected the systematic under-excitation but did not lower the spatial variability (102.2%±10.2%).

Supplementary Figure 2 restates the results from Figure 1 and Figure 2 as percent error of R2 versus LIC. The figure helps to demonstrate that as B1+ error increases, SE R2 is overestimated for lower iron loads and underestimated for higher iron loads. CPMG R2 estimates on the other hand always demonstrate an overestimate of R2 with B1+ error, though the error decreases with increasing LIC.

Supplementary Figure 3 demonstrates the long and short TE B1+ mapping sequences in a manganese chloride phantom. The images demonstrate that both sequences have sufficient dynamic range to perform B1+ mapping across the physiologically relevant range of liver iron.

Discussion

This study examined the magnitude of b₁ error in the liver and its potential impact on clinical liver iron estimates. Iron chelation therapy is tuned based on LIC estimates and patient motivation to continue using chelating drugs is heavily motivated by their LIC estimates demonstrating efficacy over time. Thus, the accuracy of iron estimates is important for both clinicians and patients. This work has demonstrated that B₁⁺ heterogeneity presents a quantitative challenge at 3T and, more surprisingly, that spatial flip angle variation at 1.5T may be sufficient to cause meaningful quantitative changes.

At 1.5T, the average excitation achieved in the liver was complete (ie matched the flip angle requested) but there was variation between the right and left lobes. Substantially larger spatial variations in b₁ were observed in the liver at 3T. We had postulated a potential iron effect because B₀ and B₁⁺ heterogeneities can interact²³. Because off-resonance from liver iron can exceed 1000 Hz for extreme clinical iron loads²⁴, we expected the excitation bandwidth for standard b₁ mapping sequences would to be too narrow, although the phantom study demonstrated a sufficiently short TE. Further, off-resonance can cause slice misplacement or distrotion²⁵. In spite of this, excitation efficiency was uncorrelated with liver iron and manual visual evaluation of the images did not indicate that slices were meaningfully shifted.

At 3T, we observed a systematic underexcitation in the liver, averaging just ~70% of our specified flip angle in whole-liver ROIs. The effect was not observed at 1.5T. The underexcitation was observed both in patients and in healthy controls. Manual increases of the transmit gain improved whole-ROI average to near 100% at 3T, although the observed spatial heterogeneity remained, suggesting that the under-excitation may have been an unintended consequence of SAR modeling. We do not have access to abdominal 3T b₁ maps from other imaging platforms to determine whether the observed underexcitation was vendor-specific, although this has been demonstrated across multiple vendors at 3T²⁶. Further, a recent study of liver B1 inhomogeneity by Roberts, et.al noted similar spatial variation and average b1 scale at both 1.5T and 3T in a larger patient cohort²⁷. Of note, adaptive RF shimming improved the systematic underestimation but did not lower the spatial variability in our small post-study investigation; however, Roberts et.al demonstrated underexcitation at 3T even with dual-transmit enabled on a different vendor.

In single echo simulations, the estimated error appeared to be primarily dependent on decay rate rather than field strength. The overestimation of liver R₂ occurs up to 200–250 s⁻¹ in both 1.5T and 3T simulation, representing approximate LIC burdens of 30 and 15 mg/g respectively. Note that the echo-sampling scheme (logarithmically spaced from 1.7 to 30 ms) should have been sufficient to capture rapid early signal decay. The increase in apparent R₂ decay with b₁ error arises from non-exponential signal loss in later echoes that prematurely collapses the decay curve. At decay rates over 250 s⁻¹, the amplitude of the early echoes is significantly reduced as well, flattening the decay curve and lowering the R₂ estimate. As iron load and b₁ error increase, it becomes impossible to uniquely determine LIC from measured R₂ values. Of note, the quantitative effects are symmetric for absolute b₁ error due to the fact that spin echo signals are maximized when a 90° excitation and 180° inversion are achieved; both over-excitation and under-excitation lead to the same apparent signal for both single echo and CPMG sequences.

For CPMG simulation estimates, the phase cycling of the echo pulses leads to “sawtoothing” that envelopes the true decay curve: the odd echoes have lower amplitudes than subsequent even echoes. For smaller errors in b₁, the error is mostly self-correcting. As b₁ becomes large, a significant portion of the longitudinal magnetization remains after the excitation pulse and is recovered into the transverse plane when subsequent echo pulses are applied; similarly, transverse magnetization is stored in the longitudinal plane when incomplete echo pulses are applied. The sawtoothing eventually increases to the point that the first echo amplitude is smaller than all of the even echoes, even for very high LIC burdens; the resulting fits show reduced R₂ estimates. The differing behavior of the 1.5T and 3T calibration curves in the presence of b₁ error over ~25% is primarily a T₁ effect. The longer T₁ at 3T compared to 1.5T results in less longitudinal magnetization recovery, leading to a less pronounced addition of transverse signal over the course of the echo train. Later echoes at 3T therefore demonstrate more realistic decay than 1.5T echoes in the presence of large b₁ error. Nonetheless, the inclusion of longitudinal magnetization and diminished first echo intensity lead to the apparent reduction of R₂ for high iron loads in the presence of large b₁ error.

At 1.5T, our study showed no systematic underexcitation, however the 95% confidence intervals were large enough to potentially impact signal quantification for clinical R₂ imaging^16,28. For a patient with true LIC of 10 mg/g, a b₁ error of +/−10% will increase the predicted LIC by 30%. This level of error may not change the dosing of chelation therapy, but such variation could lead to incorrect assumptions about the efficacy of a particular course of chelation therapy. Inter-subject variation in b₁ heterogeneity produces “noise” in R₂-based LIC estimates while having no effect on R₂*-based LIC estimates, contributing to disagreement between these methods^29,30. B₁⁺ variation could also contribute to the observed curvilinearity in the R₂-LIC calibration curve²⁸. With perfect excitation, the R₂-LIC relationship is relatively linear over a wide range of LICs but even mild b₁ errors introduce marked concavity to the calibration curve. B₁⁺ scale heterogeneity could also potentially confound techniques that rely on proton-density estimators to stabilize LIC measurements at high iron concentrations²⁸. Carefully controlled studies are warranted to determine whether B₁⁺ correction could improve R₂-based LIC measurements at 1.5T.

In contrast, correcting for b₁ error, especially whole-liver underexcitation, is an absolute necessity for R₂-based iron estimation at 3T. Our post-study investigations suggest that RF shimming using dual transmit RF systems can eliminate systematic underexcitation at 3T, without significantly impacting spatial variability, and should be considered a prerequisite for spin echo quantitation at 3T. Alternatively, one could limit R₂ analysis only to those voxels having b₁ of 90–110%, accepting the sampling limitations that this would impose.

Limitations

First, the B₁⁺ mapping was performed only on Philips MR systems. Although the simulation has been well-validated, R₂ estimates in patients were not performed. The simulation framework ignored iron-mediated T1 shortening and slice profile effects were not considered. Finally, the echo times chosen in the simulation are relatively fast and most clinical magnets may not be able to achieve such short TEs.

Conclusions

We observed clinically relevant b₁ variability at both 1.5T and 3T as well as large global underexcitation at 3T. Simulation results demonstrated that even a modest amount of error in b₁ leads to systematic LIC estimation error with spin echo protocols. Spin echo liver iron quantification cannot be performed reliably at 3T without RF shimming. Further work is necessary to validate the impact of b₁ heterogeneity on current FDA-approved approaches for LIC quantification at 1.5T and to evaluate the performance of other models and vendors of MRI scanners.