Quantitative Susceptibility Mapping Using a Multispectral Autoregressive Moving Average Model to Assess Hepatic Iron Overload

Abstract

Background:

R2*-MRI is clinically used to noninvasively assess hepatic iron content (HIC) to guide potential iron chelation therapy. However, coexisting pathologies, such as fibrosis and steatosis, affect R2* measurements and may thus confound HIC estimations.

Purpose:

To evaluate whether a multispectral auto regressive moving average (ARMA) model can be used in conjunction with quantitative susceptibility mapping (QSM) to measure magnetic susceptibility as a confounder-free predictor of HIC.

Study Type:

Phantom study and in vivo cohort.

Subjects:

9 iron phantoms covering clinically relevant R2* range (20 – 1200 s⁻¹) and 48 patients (22 male, 26 female, median age 18 years).

Field Strength/Sequence:

3D and 2D multi-echo GRE at 1.5T.

Assessment:

ARMA-QSM modeling was performed on the complex 3D GRE signal to estimate R2*, fat fraction (FF), and susceptibility measurements. R2*-based dry clinical HIC values were calculated from the 2D GRE acquisition using a published R2*-HIC calibration curve as reference standard.

Statistical Tests:

Linear regression analysis was performed to compare ARMA R2* and susceptibility-based estimates to iron concentrations and dry clinical HIC values in phantoms and patients, respectively.

Results:

In phantoms, the ARMA R2* and susceptibility values strongly correlated with iron concentrations (R²≥0.9). In patients, the ARMA R2* values highly correlated (R²=0.97) with clinical HIC values with slope=0.026, and the susceptibility values showed good correlation (R²=0.82) with clinical dry HIC values with slope=3.3 and produced a dry-to-wet HIC ratio of 4.8.

Data Conclusion:

This study shows the feasibility that ARMA-QSM can simultaneously estimate susceptibility-based wet HIC, R2*-based dry HIC and FFs from a single multi-echo GRE acquisition. Our results demonstrate that both, R2* and susceptibility-based wet HIC values estimated with ARMA-QSM showed good association with clinical dry HIC values with slopes similar to published R2*-biopsy HIC calibration and dry-to-wet tissue weight ratio, respectively. Hence, our study shows that ARMA-QSM can provide potentially confounder-free assessment of hepatic iron overload.

Introduction

Hepatic iron overload is a complication in hereditary hemochromatosis, transfusional hemosiderosis and is also common in some chronic hepatopathies (e.g., non-alcoholic fatty liver disease) (1). High hepatic iron levels may cause toxicity leading to progressive fibrosis, cirrhosis, and eventually liver failure, if it is not monitored and appropriately treated (2). Measuring hepatic iron content (HIC) is therefore important to guide iron removal therapy and avoid disease progression.

MRI has emerged as a noninvasive and longitudinal monitoring tool for diagnosis and monitoring of hepatic iron overload. Acquiring multi-echo gradient echo (GRE) images and fitting a mono-exponential signal model to calculate the effective transverse relaxation rate (R2*) is now widely accepted as a diagnostic and therapeutic monitoring tool to estimate HIC via established R2*–biopsy HIC calibration curves (3–7). However, coexisting pathologies, such as steatosis and fibrosis, affect R2* measurements and thereby may interfere with HIC estimations.(8,9)

Hepatic steatosis is an abnormal accumulation of fat in the liver, affecting 20%–30% of the US population due to the increasing frequency of obesity and metabolic syndromes (10). The co-occurrence of hepatic iron overload and steatosis is also increasingly recognized as a common manifestation of diffuse liver diseases, chronic hepatopathies, and cancer therapy (2,11,12). Recently, multispectral R2* signal modeling techniques that incorporate a multipeak fat–water model were proposed to simultaneously quantify R2* and fat fraction (FF) (13,14). One such approach uses an autoregressive moving average (ARMA) model that translates the temporal GRE signal evolution into a rational polynomial in the z-domain, and determines amplitudes, relative frequencies, and R2* rates specifically for water and lipid species. In further investigation, ARMA was validated for simultaneous quantification of hepatic iron overload and steatosis in iron–fat phantoms and patients by using biopsy measurements as a reference standard (14). However, multispectral fat–water models are still confounded by fibrosis, which is frequently present in patients with iron overload (5,15).

MRI-based quantitative susceptibility mapping (QSM) techniques were recently demonstrated to quantify magnetic susceptibility, which is an intrinsic tissue property that is linearly related to iron content and is unaffected by cellularity changes such as fibrosis (16). QSM techniques are well validated in brain applications for quantifying iron deposits (17). However, these techniques are challenging to implement in liver tissue because of physiologic motion, the presence of fat, and severe iron overload that may hinder the accurate estimation of field maps, which is important for generating reliable QSM maps. In the brain, signals are primarily generated from water species. In contrast, field map estimations in the abdomen must account for signals from multiple species (i.e., fat and water). The multispectral ARMA model also generates field maps in the process of simultaneous R2* and FF estimations, and these field maps can be used in conjunction with QSM techniques to assess hepatic iron overload. In this study, we evaluated whether ARMA-based QSM can be used as a comprehensive technique for confounder-free assessment of HIC by validating the approach in phantoms and patients with hepatic iron overload.

Materials and methods

Phantoms

Nine 1-L phantoms were made from 2% agar–water mixtures, doped with bionized nonferrite particles covering the following iron concentrations: 0.43, 0.86, 1.72, 3.44, 6.88, 13.75, 27.5, 55 and 110 μg/mL to obtain a wide range of R2* values. The phantoms were stacked and scanned on a 1.5T scanner (Magnetom Avanto, Siemens Healthineers, Malvern, PA) by using a 3D multi-echo GRE sequence with the following acquisition parameters: TR = 16 ms, TE₁ = 1.41 ms, ΔTE = 1.6 ms, 6 echoes, flip angle = 6°, 28 slices, slice thickness = 3.5 mm, FOV = 350 mm, and matrix = 320 × 280.

Subjects

This study was approved by the Institutional Review Board of St. Jude Children’s Research Hospital and informed consent was obtained from all participants prior to any research assessment. In vivo liver data were collected from 55 patients who received MRI scans for clinical monitoring of hepatic iron overload.

All patients were scanned on a 1.5T scanner (Magnetom Avanto, Siemens Healthineers, Malvern, PA) with 2D and 3D multi-echo GRE sequences. The 2D GRE images were acquired from a single transverse slice of the liver near the hepatic portal vein with the following acquisition parameters: TR = 200 ms, TE₁ = 1.1 ms, ΔTE = 0.82–0.92 ms (small variations due to software upgrades), 20 echoes, bipolar readout gradient, flip angle = 35°, bandwidth = 1950 Hz/px, slice thickness = 10 mm, FOV = 280–400 mm and matrix size = 128 × 104. The 3D GRE images were acquired from the entire liver with the following acquisition parameters: TR = 16 ms, TE₁ = 1.41 ms, ΔTE = 1.6 ms, 6 echoes, flip angle = 6°, 28 slices, slice thickness = 3.5 mm, FOV = 280–400 mm and matrix = 320 × 280. Each sequence was acquired in a single breath-hold of ∼16–21 s in patients who could perform the breath-hold maneuver. For sedated patients or those unable to suspend breathing, 3 to 6 averages were acquired to minimize respiratory motion artifacts.

Data analysis

Multispectral ARMA modeling was performed on the complex 3D GRE signals in phantoms and patients to calculate R2* and FF values and to estimate field maps via an iterative Stieglitz–McBride algorithm (see Supplement) (14). The estimated field maps were further processed with simultaneous phase unwrapping and removal of chemical shifts by using the graph cuts method to remove chemical shifts and produce fine field maps (18). The background fields were removed from the fine field maps to produce local field maps with the projection onto dipole fields method (19). Susceptibility maps were generated from the local field maps by using the morphology enabled dipole inversion algorithm (20).

The mean liver R2*, FF, and susceptibility values were calculated by drawing a circular region of interest (ROI) in the phantoms and in a homogeneous area on the central slices of the liver, which were devoid of blood vessels, in patients. In phantoms, the mean susceptibility values were calculated by considering the phantom with lowest iron concentration, which has a R2* value in the normal range of muscle tissue, as a reference. For liver susceptibility measurements in patients, additional ROIs were drawn in the paravertebral muscle at the level of the renal hilum, and the mean susceptibility values were calculated with reference to muscle tissue because it does not accumulate iron (9). The susceptibility values were converted to HIC in mg of Fe/g wet weight tissue by using a conversion factor of 1.45 ppm per mg/g Fe wet weight, as previously described (9).

Statistical Analysis

Linear regression analyses were used to determine the associations between the obtained R2* and susceptibility values by using ARMA-QSM with the true iron concentrations in phantoms, and with the dry clinical HIC values calculated from the 2D GRE acquisitions and a previously published calibration curve in patients (5).

Results

A schematic view of the ARMA-QSM process is shown in Fig. 1. In phantoms, the R2* and susceptibility values estimated with the ARMA field maps showed a strong linear correlation (R² ≥ 0.9) with iron concentrations (Fig. 2). Of 55 cases (n = 55 patients), seven were discarded because of severe motion artifacts (n = 5) and technical failure in assessing the clinical HIC values (n = 2) because of massive iron overload (R2* > 1000 s^–1). The demographics for the remaining 48 patients are shown in Table 1.

Fig. 1.

Schematic view of the ARMA-QSM process. Multispectral ARMA modeling is first performed on the complex GRE signal (magnitude and phase) to calculate the R2*, FF, and field maps. The ARMA field maps are then processed with SPURS to produce fine field maps and projection onto dipole field (PDF) to remove the background fields and produce local field maps. The morphology-enabled dipole inversion (MEDI) is finally applied to the local field maps to generate susceptibility maps. The ARMA-QSM outputs consist of R2*, FF, and susceptibility maps.

Fig. 2.

Linear regression analysis between the mean R2* (a) and susceptibility (b) values obtained with ARMA-QSM and iron concentrations in phantoms doped with iron nanoparticles. Regression equations and correlation coefficients (R²) are shown in the respective plots.

Table 1.

Patient demographics

Characteristic	N (%)
Total MRI cases	55
Evaluable cases	48
Adults (> 18 years)	27 (56)
Pediatric patients	21 (44)
Age at first exam (years)
Median (range)	18 (3–43)
Sex
Male	22 (46)
Female	26 (54)
Diagnosis
Sickle cell disease	11 (23)
β-thalassemia	9 (19)
Cancer	23 (48)
Others (aplastic anemia, pyruvate kinase deficiency, myelodysplastic syndrome)	5 (10)

The mean and range of the clinical HIC values and ARMA-estimated R2*, susceptibility, and FF values are shown in Table 2. The R2* values ranged from 31 s^–1 to 682 s^–1 (mean = 219 ± 159 s^–1), and the susceptibility values ranged from –1.0 ppm to 4.3 ppm (mean = 1.5 ± 1.2 ppm). Representative examples of the ARMA-calculated R2*, susceptibility, and FF maps in mild, moderate, and severe cases of iron overload are shown in Fig. 3. The susceptibility difference between the liver and adjacent abdominal muscle tissue increased with increasing R2* values as shown in the displayed susceptibility values.

Table 2.

Clinical HIC values and R2*, susceptibility, and FF values obtained with the ARMA-QSM technique

	Clinical HIC (mg Fe/g)	ARMA-QSM
		R2* (1/s)	Susceptibility (ppm)	FF (%)
Mean ± SD	6.0 ± 4.2	219 ± 159	1.5 ± 1.2	3.0 ± 3.2
Range	0.6–16.6	31–682	–1.0–4.3	0.5–19.1

FF fat fraction, HIC hepatic iron content, ppm parts per million, SD standard deviation.

Fig. 3.

Magnitude images and R2*, FF, and QSM maps obtained with ARMA-QSM model in mild, moderate, and severe iron overload cases. The mean liver R2* and susceptibility measurements increased with clinical HIC values. The ARMA-QSM map for mild HIC cases exhibited similar contrast for liver tissue and the surrounding muscle, whereas the contrast between the liver parenchyma and surrounding tissues and hepatic vessels increased with increasing HIC.

The linear regression analyses between ARMA estimated R2*, susceptibility and susceptibility-based wet HIC values with clinical dry HIC values are shown in Fig. 4. The ARMA R2* values exhibited a high linear correlation (R² = 0.97) with the clinical HIC values (slope = 0.026). The susceptibility values also demonstrated a high linear correlation (R² = 0.82) with the clinical dry HIC values and the calibration curve produced a slope of 3.3 and an intercept of 0.99. The regression between clinical dry HIC values and susceptibility-based wet HIC values produced a dry-to-wet tissue weight ratio of 4.8.

Fig. 4.

Linear regression analysis between R2* values (a), susceptibility values (b) and susceptibility-based wet HIC measurements (c) obtained with ARMA-QSM and clinical dry HIC values in patients with iron overload. Regression equations and correlation coefficients (R²) are shown in the respective plots.

Discussion

This study shows that ARMA is a comprehensive technique for simultaneously quantifying R2*, FF, and field maps from a single multi-echo GRE acquisition. ARMA R2* maps produce dry HIC estimations and ARMA-generated field maps when used in conjunction with QSM, provide susceptibility-based wet HIC measurements. Both, the R2* and susceptibility-based wet HIC measurements estimated by ARMA-QSM highly correlated with the clinical HIC values, demonstrating the potential of ARMA-QSM for confounder-free assessment of hepatic iron overload.

In phantoms, both, the R2* and susceptibility measurements highly correlated with iron concentrations. However, the correlation for the susceptibility measurements was inferior to that of the R2* values. We believe this is due to suboptimal measurement conditions for QSM in phantoms, because air gaps are present between the phantoms as they are stacked and scanned. Further, uncertainties during removal of the background field at air–phantom boundaries can corrupt the QSM map estimations.

In patients, the ARMA R2* measurements highly correlated with the clinical HIC measurements. The clinical HIC measurements were estimated by acquiring a 2D single-slice bipolar multi-echo GRE acquisition, fitting a mono-exponential signal decay with noise subtraction, and using a published R2*–HIC calibration curve (5). In contrast, ARMA modeling was performed with 3D monopolar GRE acquisitions by using a multipeak fat–water model. The slope of the regression equation between the ARMA R2* and clinical HIC values was similar to previously published R2*–biopsy HIC calibration curves (4–6). The agreement between the clinical HIC values and R2* values estimated by ARMA signifies the robustness of the multispectral ARMA model for accurately estimating dry HIC values, similar to that of biopsy-validated, magnitude-based mono-exponential models.

Without requiring additional scans or processing, ARMA also generates field maps, which by applying QSM techniques can produce susceptibility-based wet HIC measurements. The ARMA-QSM susceptibility measurements highly correlated with the dry clinical HIC values, consistent with previous studies that correlated susceptibility measurements with R2* values and R2-based Ferriscan HIC measurements (8,21,22). However, it is reported in a recent study that there might be large discrepancies between R2- and R2*-based HIC values, and therefore, both cannot be used interchangeably. Our study brings value, as it correlated susceptibility measurements directly with R2*-based HIC measurements (slope: 3.3) that are acquired from the same GRE sequence, hence avoiding any biases due to differences in R2 and R2* based acquisitions. Because there were no prior studies that compared QSM-based liver susceptibility measurements to R2*-based HIC values, we have converted susceptibility values to wet HIC values and correlated them to R2*-based clinical dry HIC values so as to directly compare and validate our slope of 4.8 with the previously published dry-to-wet weight ratio of 4.1 (23). Our results are also in agreement with other studies that have estimated liver susceptibility values using different MRI acquisition and analysis methods and other techniques such as biomagnetic liver susceptometry (24,25), hence underscoring the potential of ARMA-QSM in providing confounder-free wet HIC assessments. However, in cases of mild to moderate iron overload, the wet HIC measurements from ARMA-QSM exhibited more scattering, similar to other published work, (8,22,26) which may be due to the interfering effects of fibrosis on R2* that are more substantial in this range than is the iron contribution, thereby biasing the clinical R2*-based HIC measurements but not the susceptibility (8). However, neither of the prior studies, nor ours included biopsies or other imaging techniques to assess fibrosis in patients. Therefore, prospective studies are needed for further investigation.

In addition to dry and wet HIC estimates, the ARMA model produces simultaneous FF maps that can be used to assess steatosis. A previous study demonstrated that ARMA FF values agreed with the true FFs in phantoms and with histopathologic steatosis grading in patients (27). The ARMA estimated FF values were < 10% in our cohort, except for one patient who had a FF of 19%. Our cohort predominantly consisted of patients with hepatic iron overload due to receiving chronic blood transfusions for managing hematologic diseases and cancer. These patients typically present with low BMI; therefore, steatosis was not commonly observed. Moreover, because of limited subcutaneous adipose tissue in our cohort, liver susceptibility measurements were made with reference to muscle tissue rather than adipose tissue, as reported in previous studies (22,28). However, using either muscle or subcutaneous adipose tissue as a reference was shown to produce similar correlations with the Ferriscan HIC measurements (21,22). Of note, paravertebral muscles may sometimes be infiltrated with fat in older adults and patients with obesity and metabolic syndromes and this can introduce inaccuracies in liver susceptibility measurements. As our study cohort consisted primarily of pediatric and young adolescent transfusional iron overloaded patients (42/48 < 30 yrs) with low BMI, we expect that fatty infiltration in the muscle to be unlikely.

Previous liver QSM studies used either T2*-IDEAL or nonlinear least squares fitting (NLSQ) for performing multispectral fat–water modeling and estimating field maps for QSM processing (8,21,22). These multispectral techniques are constrained by assuming certain relative chemical shifts between water and multiple lipid species and the relative amplitudes for multiple lipid peaks, with respect to the primary lipid peak. Nevertheless, the chemical shift of water can change because of the iron content (9), which may also affect the assumed relative lipid chemical shifts and lead to inaccurate HIC and FF estimations, especially in cases of severe iron overload (27). Furthermore, these techniques fit only a single R2* value for both water and fat peaks to reduce model complexity, although water and fat may have different R2* decay rates, especially in the presence of both iron overload and steatosis (29). Any inaccurate assumptions in the signal model will corrupt the field map estimations and thereby the QSM maps. In contrast, ARMA does not require prior information about the relative amplitudes and frequencies of the lipid peaks and provides separate R2* values for water and fat species (14,30). However, additional studies are still needed to investigate whether high HIC affects lipid chemical shifts and R2* decay rates differently for water and fat species and causes bias in R2*, FF, and field map estimations. Lastly, T2*-IDEAL or NLSQ fitting techniques need good initialization parameters, otherwise they are computationally expensive. A recent paper demonstrated that using in-phase echoes has provided rapid initialization for T2*-IDEAL and improved the computation speed by ∼5.5 times, making QSM feasible for clinical use (31). On the other hand, ARMA does not need initialization parameters, yet it provides faster computation times (∼3.2 times faster) compared to fitting techniques,(30) and hence, may facilitate ARMA-based QSM for routine clinical use.

LIMITATIONS

A particular limitation of our study included the acquisition parameters of the 3D GRE monopolar sequence, which were optimized for fat–water imaging rather than for reliable field map and QSM estimations. Bipolar acquisitions offer reduced echo spacing and improved signal-to-noise ratio efficiency, which are essential for capturing the rapid signal decay in cases of moderate to high iron overload and may produce robust field map estimates. However, bipolar acquisitions induce inconsistent phase errors between odd and even echoes, and these errors must be corrected before generating the field maps. A systematic investigation of such acquisition parameters will promote robust estimation of the susceptibility maps, which we plan to perform in future studies. Some cases were excluded as failed fit likely due to severe iron overload, which causes the signal to decay rapidly before the first possible TE ∼ 1 ms is achieved with our conventional GRE sequence. For these severe iron cases, ultrashort echo time (UTE) sequences (TE₁ ∼ 0.1 ms) can be a viable alternative for accurate HIC determination as demonstrated via simulations, phantoms, and patient data.(32) Further, some recent studies have demonstrated implementing QSM with UTE in iron phantoms,(33,34) however studies in patients and in the presence of fat need further investigation.

Another limitation of our study is, that biopsies were not performed, so we could not directly correlate our data with biopsy iron concentrations, especially in cases of coexisting fibrosis, which can bias R2*-based HIC estimates. Also, there was only one patient with steatosis in our study cohort, so ARMA-QSM still needs to be systematically validated in patients with concomitant steatosis. Future prospective studies that include patient biopsy data are needed to evaluate the potential value of ARMA-QSM for providing confounder-free assessments of hepatic iron overload in patients with concomitant fibrosis and steatosis, and derive a QSM-biopsy HIC calibration.

CONCLUSION

The co-existence of liver fibrosis and steatosis can confound R2*-based HIC measurements. This feasibility study shows that ARMA-QSM comprehensively estimates susceptibility-based wet HIC measurements in addition to R2*-based dry HIC and FF measurements from a single multi-echo GRE acquisition and therefore, provides potentially confounder-free assessments of hepatic iron overload.

Abbreviations and acronyms:

ARMA

Auto regressive moving average

FF

Fat fraction

FOV

Field of view

GRE

Gradient echo

HIC

Hepatic iron content

MEDI

Morphology enabled dipole inversion

PDF

Projection onto dipole fields

QSM

Quantitative susceptibility mapping

ROI

Region of interest

SPURS

Simultaneous phase unwrapping and removal of chemical shifts