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Confidence Maps for Reliable Proton Density Fat-Fraction and R2* Estimation

Daiki Tamada¹, Rianne A Van der Heijden¹, Diego Hernando^1,2,3,4, and Scott B Reeder^1,2,4,5,6
¹Radiology, University of Wisconsin-Madison, Madison, WI, United States, ²Medical Physics, University of Wisconsin-Madison, Madison, WI, United States, ³Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, WI, United States, ⁴Biomedical Engineering, University of Wisconsin-Madison, Madison, WI, United States, ⁵Medicine, University of Wisconsin-Madison, Madison, WI, United States, ⁶Emergency, University of Wisconsin-Madison, Madison, WI, United States

Synopsis

Keywords: Data Processing, Artifacts, CSE-MRI

In this work we develop a confidence map algorithm to identify reliable estimates of PDFF and R2* for CSE-MRI in the liver. Reliability of estimates is evaluated based on a normalized root-mean-square-error (NRMSE) between measured and model signals. Threshold values of the NRMSE are determined by using the Cramér–Rao Lower Bound. Monte-Carlo simulations and clinical CSE-MRI successfully validate the proposed method.

Introduction

Proton density fat-fraction(PDFF) and transverse relaxivity rate(R2*) acquired using quantitative chemical shift-encoded MRI(CSE-MRI)^1,2 are well-established biomarkers of diffuse liver disease. Unbiased estimation of PDFF and R2* is essential for accurate diagnosis, staging and treatment monitoring.
However, reliable PDFF and R2* estimation remains challenging due to confounding factors such as low SNR^3,4, high iron(high R2*)⁵, inhomogeneous magnetic field(B0) and phase errors^6-8. In addition, water-fat swaps⁹ commonly occur in water- or fat-dominant pixels. Further, severe magnetic field inhomogeneities can lead to focally elevated and unreliable R2* estimates.
A reconstructed quantitative PDFF/R2* map may not clearly show the regions with inadequate or corrupted measurements, and there is a lack of guidance in current CSE-MRI methods, for objective identification of invalid regions of the maps.
In this study, we aim to develop an automated algorithm to generate confidence maps that automatically identify regions on PDFF/R2* maps that are valid for analysis.

Theory

CSE-MRI
Multi-echo spoiled gradient echo imaging with signal modeling provides simultaneous estimation of PDFF and R2*. In this study, we adopt the multi-peak model by Yu that includes multiple fat peaks as well as R2* decay^2,10.
Confidence Map
We consider 6 possible scenarios that can lead to inaccurate estimation of PDFF/R2* as summarized in Figure 1(a-f). To address and exclude these scenarios, we introduce a confidence map approach.
The reliability of PDFF/R2* can be evaluated based on the normalized root-mean-square-error(NRMSE) between measured and fitting signals of CSE-MRI. The calculated NRMSE provide a confidence threshold which is determined using a Cramér–Rao Lower Bound(CRLB)¹¹. A measurement lower than the threshold is regarded as reliable.
The estimation of PDFF/R2* may be biased due to incorrect estimation of the field map, leading to water-fat swapping. To identify the swapping, a set of calculations of water-fat separation with fixed off-resonance shifts of +3.3/-3.3ppm relative to the estimated frequency is performed. Areas with the swapping have larger NRMSE compared to that with fixed off-resonance shifts⁹.
Strong off-resonance effects often result from susceptibility effects, resulting in additional R2* signal decay. To detect R2* decay, a point spread function approach¹² can be used. Areas with a high B0 gradient can then be excluded.
Cramér–Rao Lower Bound (CRLB)
The CRLB^5,11, derived from the equation for CSE-MRI², is used to determine lower theoretical bounds on PDFF/R2* variance. For PDFF/R2* measurements, the minimum SNR to achieve certain standard errors (SE) (1% of PDFF, and either 3% of R2* or 5 1/s whichever is larger, determined based on known variable coefficients^13,14) is calculated. Maximum NRMSE can be estimated from SNR by using a relationship between them derived from Monte-Carlo simulations as shown in Figure 2.

Methods

NRMSE thresholds for PDFF/R2* measurements with variable first TE(TE0), echo spacing(ΔTE), PDFF, and R2* were calculated for 1.5 and 3.0T using the CRLB. The following experiments were conducted.
Monte-Carlo
SimulationsMonte-Carlo simulations using the signal model were performed to validate thresholds calculated using CRLB. Physiologically reasonable ranges of R2*(50-1500 1/s), PDFF(0-50%), TE0(0.9-1.7 ms), ΔTE(0.59-2.1 ms), and SNR(2-50) were used.
In-vivo Experiments
An IRB-approved prospective study included 59 consecutive patients who underwent PDFF/R2* mapping in the liver on 1.5/3.0T MR systems(GE Healthcare, Waukesha, WI) between May-September 2022. A nonlinear optimization¹⁵ was used for reconstruction.
A board-certified radiologist delineated ROIs for each 9 liver segments, blinded to the confidence maps. We calculated the percent area of the ROIs in inappropriate areas that were identified by the confidence map. In this way, we aimed to determine the impact of confidence maps on clinical analysis.

Results

Plots of maximum NRMSE with PDFF of 0% as a function of TE1and ΔTE are shown in Figure 3. The results indicated that required NRMSE values vary depending on PDFF, R2*, TE1and ΔTE.
Figure 4 shows plots of SEs as a function of NRMSE and R2* for PDFF of 0, 10, and 20% calculated using Monte-Carlo simulations for typical TE1and ΔTE at 1.5 and 3.0T. The estimated NRMSE thresholds roughly agreed with those suggested by the confidence maps.
Figure 5 shows examples of PDFF/R2* and corresponding confidence maps. Failure of PDFF measurement due to high R2* can be successfully detected as shown in Figure 5(a). Regions containing metal artifact(Figure 5(b)) and fat-water swapping(Figure 5(c)) were also removed. ROI analysis revealed that 4% and 21% of the ROIs in PDFF and R2* maps were placed inside unreliable areas identified by confidence maps.

Discussion

We have successfully developed an algorithm for generating confidence maps for PDFF and R2* estimation based on NRMSE. Thresholds for NRMSE were determined using CRLB. Monte-Carlo simulations and in vivo experiments demonstrated the validity of the proposed algorithm.
Automation of quantitative map analysis has become increasingly important in recent years. For MR elastography in the liver region, several automated algorithms^16-19 have been proposed. Automated analysis can avoid costly “call-backs” by ensuring quality measurements while the patient is still present²⁰. While this work doesn't provide automated segmentation, confidence maps will be essential for automated segmentation algorithms to exclude invalid pixels.
There are limitations to this study. Reconstruction algorithms and acquisition parameters may impact the threshold values, and the proposed method is currently computationally expensive.
In conclusion, a confidence map algorithm, which provides reliable areas of PDFF/R2* measurement, was successfully developed.

Acknowledgements

We appreciate the helpful suggestions and source code for confidence map graphics provided by Dr. Roger C. Grimm from the Mayo Clinic, Rochester, MN. We acknowledge support from the NIH (R01EB031886). We wish to acknowledge support from Bracco Diagnostics who provide research support to the University of Wisconsin.

References

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Figures

Figure 1 Simulated PDFF/R2* maps with possible measurement errors (a-e) and the corresponding measured and fitted signals are plotted. The confidence map is developed to identify 5 scenarios, which include (a)low SNR, (b)moderate/(c)high iron overload, (d)water-fat swapping, and (e)extraneous phase errors. Low SNR causes signal fitting to fail, leading to high variance. Water fat swapping and extraneous phase errors induce highly biased PDFF/R2*. Metallic implants (f) induce significant R2* decay and off-resonance effects, which lead severe estimation errors of PDFF/R2*.

Figure 2 There is straightforward relationship between NRMSE and SNR as shown in the plots, which shows NRMSE versus SNR for PDFF of 0, 10, and 20% at (a)1.5 and (b)3.0T derived from Monte-Carlo simulation. SNR in low- to mid-R2* values decreases monotonically with increasing NRMSE whereas NRMSE in high-R2* has a tendency to decline in low SNR regions. Also, the relationship has less dependency on PDFF compared to R2*. The plotted datasets are fitted with polynomial regression to estimate NRMSE threshold values from SNR required for reliable PDFF/R2* measurements calculated by CRLB.

Figure 3 NRMSE is used to determine measurement reliability in this study. These plots provide maximum NRMSEs, which are threshold values for the confidence map, calculated in relation to TE1 and ΔTE for (a) 1.5T and (b) 3.0T, using the CRLB approach. Measurements made with NRMSEs higher than threshold values are regarded as unreliable. As shown in the figures, PDFF and R2* measurements have different thresholds, which depend on TE1, ΔTE, PDFF, and R2*.

Figure 4 Monte-Carlo (MC) simulations validated thresholds of NRMSE estimated by CRLB approach (proposed method). The plots show distributions of standard error of R2*/PDFF measurements with varying R2* and RMSE calculated by using MC simulations at (a) 1.5T and (b) 3.0T. Black solid and white dotted lines show acceptable NRMSE thresholds estimated from MC simulations and the CRLB. Although there are moderate differences between them in high-R2*, threshold values calculated using the proposed method roughly agree with MC simulations.

Figure 5 Examples of PDFF/R2* maps and corresponding overlaying confidence maps. The hashed-out regions in the confidence maps are regions identified as unreliable PDFF/R2* estimates. (a) PDFF measurement fails due to moderate iron overload while R2* is appropriately measured. (b) A metallic implant produces susceptibility artifacts, which cause additional R2* decay. (c) Fat-water swapping at the hepatic dome is correctly identified (red arrow). Confidence maps successfully excluded these unreliable areas. An in-vivo study acquisition table is shown at the bottom-right.

Proc. Intl. Soc. Mag. Reson. Med. 31 (2023)

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DOI: https://doi.org/10.58530/2023/0076