Monte Carlo modeling of hepatic steatosis based on stereology and spatial distribution of fat droplets

Prediction of MRI R 2 * $$ {\mathrm{R}}_2^{\ast } $$ relaxometry in the presence of hepatic steatosis by Monte Carlo simulations

To develop Monte Carlo simulations to predict the relationship ofR 2 * $$ {\mathrm{R}}_2^{\ast } $$ with liver fat content at 1.5 T and 3.0 T. For various fat fractions (FFs) from 1% to 25%, four types of virtual liver models were developed by incorporating the size and spatial distribution of fat droplets. Magnetic fields were then generated under different fat susceptibilities at 1.5 T and 3.0 T, and proton movement was simulated for phase accrual and MRI signal synthesis. The synthesized signal was fit to single-peak and multi-peak fat signal models forR 2 * $$ {\mathrm{R}}_2^{\ast } $$ and proton density fat fraction (PDFF) predictions. In addition, the relationships betweenR 2 * $$ {\mathrm{R}}_2^{\ast } $$ and PDFF predictions were compared with in vivo calibrations and Bland-Altman analysis was performed to quantitatively evaluate the effects of these components (type of virtual liver model, fat susceptibility, and fat signal model) onR 2 * $$ {\mathrm{R}}_2^{\ast } $$ predictions. A virtual liver model with realistic morphology of fat droplets was demonstrated, andR 2 * $$ {\mathrm{R}}_2^{\ast } $$ and PDFF values were predicted by Monte Carlo simulations at 1.5 T and 3.0 T.R 2 * $$ {\mathrm{R}}_2^{\ast } $$ predictions were linearly correlated with PDFF, while the slope was unaffected by the type of virtual liver model and increased as fat susceptibility increased. Compared with in vivo calibrations, the multi-peak fat signal model showed superior performance to the single-peak fat signal model, which yielded an underestimation of liver fat. TheR 2 * $$ {\mathrm{R}}_2^{\ast } $$ -PDFF relationships by simulations with fat susceptibility of 0.6 ppm and the multi-peak fat signal model wereR 2 * = 0.490 × PDFF + 28.0 $$ {\mathrm{R}}_2^{\ast }=0.490\times \mathrm{PDFF}+28.0 $$ (R 2 = 0.967 $$ {R}^2=0.967 $$ ,p < 0.01 $$ p<0.01 $$ ) at 1.5 T andR 2 * = 0.928 × PDFF + 39.4 $$ {\mathrm{R}}_2^{\ast }=0.928\times \mathrm{PDFF}+39.4 $$ (R 2 = 0.972 $$ {R}^2=0.972 $$ ,p < 0.01 $$ p<0.01 $$ ) at 3.0 T. Monte Carlo simulations provide a new means forR 2 * $$ {\mathrm{R}}_2^{\ast } $$ -PDFF prediction, which is primarily determined by fat susceptibility, fat signal model, and magnetic field strength. AccurateR 2 * $$ {\mathrm{R}}_2^{\ast } $$ -PDFF calibration has the potential to correct the effect of fat onR 2 * $$ {\mathrm{R}}_2^{\ast } $$ quantification, and may be helpful for accurateR 2 * $$ {\mathrm{R}}_2^{\ast } $$ measurements in liver iron overload. In this study, a Monte Carlo simulation of hepatic steatosis was developed to predict the relationship betweenR 2 * $$ {\mathrm{R}}_2^{\ast } $$ and PDFF. Furthermore, the effects of fat droplet morphology, fat susceptibility, fat signal model, and magnetic field strength were evaluated for theR 2 * $$ {\mathrm{R}}_2^{\ast } $$ -PDFF calibration. Our results suggest that Monte Carlo simulations provide a new means forR 2 * $$ {\mathrm{R}}_2^{\ast } $$ -PDFF prediction and this means can be easily generated for various regimes, such as simulations with higher fields and different echo times, as well as correction of magnetic susceptibility measurements for liver iron quantification.

Potential of Raman-Reflectance Combination in Quantifying Liver Steatosis and Fat Droplet Size: Evidence From Monte Carlo Simulations and Phantom Studies

This study explores a combined strategy of Raman and reflectance spectroscopy for quantifying liver fat content and fat droplet size, crucial in assessing donor livers. By using Monte Carlo simulations and experimental setups with oil-in-water phantoms, our findings indicate that Raman scattering can solely differentiate between varying fat contents. At the same time, reflectance intensity is influenced by both fat content and oil droplet size, with a more pronounced sensitivity to fat droplet size. This study demonstrates the efficacy of combined Raman and reflectance spectroscopy in assessing liver steatosis and fat droplet size, potentially aiding in assessing donor livers for transplantation.

Effect of particle size on liver MRI R 2 * relaxometry: Monte Carlo simulation and phantom studies

PURPOSE

To investigate the effect of particle size on liverR 2 * $$ {\mathrm{R}}_2^{\ast } $$ by Monte Carlo simulation and phantom studies at both 1.5 T and 3.0 T.

METHODS

Two kinds of particles (i.e., iron sphere and fat droplet) with varying sizes were considered separately in simulation and phantom studies. MRI signals were synthesized and analyzed for predictingR 2 * $$ {\mathrm{R}}_2^{\ast } $$ , based on simulations by incorporating virtual liver model, particle distribution, magnetic field generation, and proton movement into phase accrual. In the phantom study, iron-water and fat-water phantoms were constructed, and each phantom contained 15 separate vials with combinations of five particle concentrations and three particle sizes.R 2 * $$ {\mathrm{R}}_2^{\ast } $$ measurements in the phantom were made at both 1.5 T and 3.0 T. Finally, differences inR 2 * $$ {\mathrm{R}}_2^{\ast } $$ predictions or measurements were evaluated across varying particle sizes.

RESULTS

In the simulation study, strong linear and positively correlated relationships were observed betweenR 2 * $$ {\mathrm{R}}_2^{\ast } $$ predictions and particle concentrations across varying particle sizes and magnetic field strengths (r ≥ 0.988 $$ r\ge 0.988 $$ ). The relationships were affected by iron sphere size (p < 0.001 $$ p<0.001 $$ ), where smaller iron sphere size yielded higher predictedR 2 * $$ {\mathrm{R}}_2^{\ast } $$ , whereas fat droplet size had no effect onR 2 * $$ {\mathrm{R}}_2^{\ast } $$ predictions (p ≥ 0.617 $$ p\ge 0.617 $$ ) for constant total fat concentration. Similarly, the phantom study showed thatR 2 * $$ {\mathrm{R}}_2^{\ast } $$ measurements were relatively sensitive to iron sphere size (p ≤ 0.004 $$ p\le 0.004 $$ ) unlike fat droplet size (p ≥ 0.223 $$ p\ge 0.223 $$ ).

CONCLUSION

LiverR 2 * $$ {\mathrm{R}}_2^{\ast } $$ is affected by iron sphere size, but is relatively unaffected by fat droplet size. These findings may lead to an improved understanding of the underlying mechanisms ofR 2 * $$ {\mathrm{R}}_2^{\ast } $$ relaxometry in vivo, and enable improved quantitative MRI phantom design.

Hepatic steatosis modeling and MRI signal simulations for comparison of single- and dual-R2* models and estimation of fat fraction at 1.5T and 3T

BACKGROUND AND OBJECTIVE

Magnetic resonance imaging (MRI) has emerged as a noninvasive clinical tool for assessment of hepatic steatosis. Multi-spectral fat-water MRI models, incorporating single or dual transverse relaxation decay rate(s) (R2*) have been proposed for accurate fat fraction (FF) estimation. However, it is still unclear whether single- or dual-R2* model accurately mimics in vivo signal decay for precise FF estimation and the impact of signal-to-noise ratio (SNR) on each model performance. Hence, this study aims to construct virtual steatosis models and synthesize MRI signals with different SNRs to systematically evaluate the accuracy of single- and dual-R2* models for FF and R2* estimations at 1.5T and 3.0T.

METHODS

Realistic hepatic steatosis models encompassing clinical FF range (0-60 %) were created using morphological features of fat droplets (FDs) extracted from human liver biopsy samples. MRI signals were synthesized using Monte Carlo simulations for noise-free (SNRideal) and varying SNR conditions (5-100). Fat-water phantoms were scanned with different SNRs to validate simulation results. Fat water toolbox was used to calculate R2* and FF for both single- and dual-R2* models. The model accuracies in R2* and FF estimates were analyzed using linear regression, bias plot and heatmap analysis.

RESULTS

The virtual steatosis model closely mimicked in vivo fat morphology and Monte Carlo simulation produced realistic MRI signals. For SNRideal and moderate-high SNRs, water R2* (R2*W) by dual-R2* and common R2* (R2*com) by single-R2* model showed an excellent agreement with slope close to unity (0.95-1.01) and R2 > 0.98 at both 1.5T and 3.0T. In simulations, the R2*com-FF and R2*W-FF relationships exhibited slopes similar to in vivo calibrations, confirming the accuracy of our virtual models. For SNRideal, fat R2* (R2*F) was similar to R2*W and dual-R2* model showed slightly higher accuracy in FF estimation. However, in the presence of noise, dual-R2* produced higher FF bias with decreasing SNR, while leading to only marginal improvement for high SNRs and in regions dominated by fat and water. In contrast, single-R2* model was robust and produced accurate FF estimations in simulations and phantom scans with clinical SNRs.

CONCLUSION

Our study demonstrates the feasibility of creating virtual steatosis models and generating MRI signals that mimic in vivo morphology and signal behavior. The single-R2* model consistently produced lower FF bias for clinical SNRs across entire FF range compared to dual-R2* model, hence signifying that single-R2* model is optimal for assessing hepatic steatosis.