Autoregressive moving average modeling for hepatic iron quantification in the presence of fat

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.

Simulation of a virtual liver iron overload model and R2 * estimation using multispectral fat-water models for GRE and UTE acquisitions at 1.5 T and 3 T

R2 *-MRI has emerged as a noninvasive alternative to liver biopsy for assessment of hepatic iron content (HIC). Multispectral fat-water R2 * modeling techniques such as the nonlinear least squares (NLSQ) fitting and autoregressive moving average (ARMA) models have been proposed for the accurate assessment of iron overload by also considering fat, which can otherwise confound R2 *-based HIC measurements in conditions of coexisting iron overload and steatosis. However, the R2 * estimation by these multispectral models has not been systematically investigated for various acquisition methods in iron overload only conditions and across the full clinically relevant range of HICs (0-40 mg Fe/g dry liver weight). The purpose of this study is to evaluate the R2 * accuracy and precision of multispectral models for various multiecho gradient echo (GRE) and ultrashort echo time (UTE) imaging acquisitions by constructing virtual iron overload models based on true histology and synthesizing MRI signals via Monte Carlo simulations at 1.5 T and 3 T, and comparing their results with monoexponential model and published in vivo R2 *-HIC calibrations. The signals were synthesized with TE1  = 1.0 ms for GRE and TE1  = 0.1 ms for UTE acquisition for varying echo spacing, ΔTE (0.1, 0.5, 1, 2 ms), and maximum echo time, TEmax (2, 4, 6, 10 ms). An iron-doped phantom study is also conducted to validate the simulation results in experimental GRE (TE1  = 1.2 ms, ΔTE  = 0.72 ms, TEmax  = 6.24 ms) and UTE (TE1  = 0.1 ms, ΔTE  = 0.5 ms, TEmax  = 6.1 ms) acquisitions. For GRE acquisitions, the multispectral ARMA and NLSQ models produced higher slopes (0.032-0.035) compared with the monoexponential model and published in vivo R2 *-HIC calibrations (0.025-0.028). However, for UTE acquisition for shorter echo spacing (≤0.5 ms) and longer maximum echo time, TEmax (≥6 ms), the multispectral and monoexponential signal models produced similar R2 *-HIC slopes (1.5 T, 0.028-0.032; 3 T, 0.014-0.016) and precision values (coefficient of variation < 25%) across the full clinical spectrum of HICs at both 1.5 T and 3 T. The phantom analysis also showed that all signal models demonstrated a significant improvement in R2 * estimation for UTE acquisition compared with GRE, confirming our simulation findings. Future work should investigate the performance of multispectral fat-water models by simulating liver models in coexisting conditions of iron overload and steatosis for accurate R2 * and fat quantification.

Quantitative MRI of diffuse liver diseases: techniques and tissue-mimicking phantoms

Quantitative magnetic resonance imaging (MRI) techniques are emerging as non-invasive alternatives to biopsy for assessment of diffuse liver diseases of iron overload, steatosis and fibrosis. For testing and validating the accuracy of these techniques, phantoms are often used as stand-ins to human tissue to mimic diffuse liver pathologies. However, currently, there is no standardization in the preparation of MRI-based liver phantoms for mimicking iron overload, steatosis, fibrosis or a combination of these pathologies as various sizes and types of materials are used to mimic the same liver disease. Liver phantoms that mimic specific MR features of diffuse liver diseases observed in vivo are important for testing and calibrating new MRI techniques and for evaluating signal models to accurately quantify these features. In this study, we review the liver morphology associated with these diffuse diseases, discuss the quantitative MR techniques for assessing these liver pathologies, and comprehensively examine published liver phantom studies and discuss their benefits and limitations.

Hepatic Iron Quantification Using a Free-Breathing 3D Radial Gradient Echo Technique and Validation With a 2D Biopsy-Calibrated R2* Relaxometry Method

BACKGROUND

Hepatic iron content (HIC) is an important parameter for the management of iron overload. Non-invasive HIC assessment is often performed using biopsy-calibrated two-dimensional breath-hold Cartesian gradient echo (2D BH GRE) R2* -MRI. However, breath-holding is not possible in most pediatric patients or those with respiratory problems, and three-dimensional free-breathing radial GRE (3D FB rGRE) has emerged as a viable alternative.

PURPOSE

To evaluate the performance of a 3D FB rGRE and validate its R2* and fat fraction (FF) quantification with 3D breath-hold Cartesian GRE (3D BH cGRE) and biopsy-calibrated 2D BH GRE across a wide range of HICs.

STUDY TYPE

Retrospective.

SUBJECTS

Twenty-nine patients with hepatic iron overload (22 females, median age: 15 [5-25] years).

FIELD STRENGTH/SEQUENCE

Three-dimensional radial and 2D and 3D Cartesian multi-echo GRE at 1.5 T.

ASSESSMENT

R2* and FF maps were computed for 3D GREs using a multi-spectral fat model and 2D GRE R2* maps were calculated using a mono-exponential model. Mean R2* and FF values were calculated via whole-liver contouring and T2* -thresholding by three operators.

STATISTICAL TESTS

Inter- and intra-observer reproducibility was assessed using Bland-Altman and intraclass correlation coefficient (ICC). Linear regression and Bland-Altman analysis were performed to compare R2* and FF values among the three acquisitions. One-way repeated-measures ANOVA and Wilcoxon signed-rank tests, respectively, were used to test for significant differences between R2* and FF values obtained with different acquisitions. Statistical significance was assumed at P < 0.05.

RESULTS

The mean biases and ICC for inter- and intra-observer reproducibility were close to 0% and >0.99, respectively for both R2* and FF. The 3D FB rGRE R2* and FF values were not significantly different (P > 0.44) and highly correlated (R2  ≥ 0.98) with breath-hold Cartesian GREs, with mean biases ≤ ±2.5% and slopes 0.90-1.12. In non-breath-holding patients, Cartesian GREs showed motion artifacts, whereas 3D FB rGRE exhibited only minimal streaking artifacts.

DATA CONCLUSION

Free-breathing 3D radial GRE is a viable alternative in non-breath-hold patients for accurate HIC estimation.

LEVEL OF EVIDENCE

3 TECHNICAL EFFICACY: Stage 2.

Accuracy versus reliability-based modelling approaches for medical decision making

Forecasting in the medical domain is critical to the quality of decisions made by physicians, patients, and health planners. Modeling is one of the most important components of decision support systems, which are frequently used to simulate and analyze under-studied systems in order to make more appropriate decisions in medical science. In the medical modeling literature, various approaches with varying structures and characteristics have been proposed to cover a wide range of application categories and domains. Regardless of the differences between modeling approaches, all of them aim to maximize the accuracy or reliability of the results in order to achieve the most generalizable model and, as a result, a higher level of profitability decisions. Despite the theoretical significance and practical impact of reliability on generalizability, particularly in high-risk decisions and applications, a significant number of models in the fields of medical forecasting, classification, and time series prediction have been developed to maximize accuracy in mind. In other words, given the volatility of medical variables, it is also necessary to have stable and reliable forecasts in order to make sound decisions. The quality of medical decisions resulting from accuracy and reliability-based intelligent and statistical modeling approaches is compared and evaluated in this paper in order to determine the relative importance of accuracy and reliability on the quality of made decisions in decision support systems. For this purpose, 33 different case studies from the UCI in three categories of supervised modeling, namely causal forecasting, time series prediction, and classification, were considered. These cases were chosen from various domains, such as disease diagnosis (obesity, Parkinson's disease, diabetes, hepatitis, stenosis of arteries, orthopedic disease, autism) and cancer (lung, breast, cervical), experiments, therapy (immunotherapy, cryotherapy), fertility prediction, and predicting the number of patients in the emergency room and ICU. According to empirical findings, the reliability-based strategy outperformed the accuracy-based strategy in causal forecasting cases by 2.26%, classification cases by 13.49%, and time series prediction cases by 3.08%. Furthermore, compared to similar accuracy-based models, the reliability-based models can generate a 6.28% improvement. As a result, they can be considered an appropriate alternative to traditional accuracy-based models for medical decision support systems modeling purposes.

Morphological characterization of hepatic steatosis and Monte Carlo modeling of MRI signal for accurate quantification of fat fraction and relaxivity

Chemical-shift-based fat-water MRI signal models with single- or dual-R₂ * correction have been proposed for quantification of fat fraction (FF) and assessment of hepatic steatosis. However, there is a void in our understanding of which model truly mimics the underlying biophysical mechanism of steatosis on MRI signal relaxation. The purpose of this study is to morphologically characterize and build realistic steatosis models from histology and synthesize MRI signal using Monte Carlo simulations to investigate the accuracy of single- and dual-R₂ * models in quantifying FF and R₂ *. Fat morphology was characterized by performing automatic segmentation on 16 mouse liver histology images and extracting the radius, nearest neighbor (NN) distance, and regional anisotropy of fat droplets. A gamma distribution function (GDF) was used to generalize extracted features, and regression analysis was performed to derive relationships between FF and GDF parameters. Virtual steatosis models were created based on derived morphological and statistical descriptors, and the MRI signal was synthesized at 1.5 T and 3 T. R₂ * and FF values were calculated using single- and dual-R₂ * models and compared with in vivo R₂ *-FF calibrations and simulated FFs. The steatosis models generated with regional anisotropy and NN distribution closely mimicked the true in vivo fat morphology. For both R₂ * models, predicted R₂ * values showed positive correlation with FFs, with slopes similar to those of the in vivo calibrations (P > 0.05), and predicted FFs showed excellent agreement with true FFs (R²  > 0.99), with slopes close to unity. Our study, hence, demonstrates the proof of concept for generating steatosis models from histologic data and synthesizing MRI signal to show the expected signal relaxation under conditions of steatosis. Our results suggest that a single R₂ * is sufficient to accurately estimate R₂ * and FF values for lower FFs, which agrees with in vivo studies. Future work involves characterizing and building steatosis models at higher FFs and testing single- and dual-R₂ * models for accurate assessment of steatosis.

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

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

Nine iron phantoms covering clinically relevant R2* range (20-1200/second) and 48 patients (22 male, 26 female, median age 18 years).

FIELD STRENGTH/SEQUENCE

Three-dimensional (3D) and two-dimensional (2D) multi-echo gradient echo (GRE) at 1.5 T.

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.

LEVEL OF EVIDENCE

3 TECHNICAL EFFICACY: Stage 2.

Predictive study of tuberculosis incidence by time series method and Elman neural network in Kashgar, China

OBJECTIVES

Kashgar, located in Xinjiang, China has a high incidence of tuberculosis (TB) making prevention and control extremely difficult. In addition, there have been very few prediction studies on TB incidence here. We; therefore, considered it a high priority to do prediction analysis of TB incidence in Kashgar, and so provide a scientific reference for eventual prevention and control.

DESIGN

Time series study.

SETTING KASHGAR, CHINA

Kashgar, China.

METHODS

We used a single Box-Jenkins method and a Box-Jenkins and Elman neural network (ElmanNN) hybrid method to do prediction analysis of TB incidence in Kashgar. Root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) were used to measure the prediction accuracy.

RESULTS

After careful analysis, the single autoregression (AR) (1, 2, 8) model and the AR (1, 2, 8)-ElmanNN (AR-Elman) hybrid model were established, and the optimal neurons value of the AR-Elman hybrid model is 6. In the fitting dataset, the RMSE, MAE and MAPE were 6.15, 4.33 and 0.2858, respectively, for the AR (1, 2, 8) model, and 3.78, 3.38 and 0.1837, respectively, for the AR-Elman hybrid model. In the forecasting dataset, the RMSE, MAE and MAPE were 10.88, 8.75 and 0.2029, respectively, for the AR (1, 2, 8) model, and 8.86, 7.29 and 0.2006, respectively, for the AR-Elman hybrid model.

CONCLUSIONS

Both the single AR (1, 2, 8) model and the AR-Elman model could be used to predict the TB incidence in Kashgar, but the modelling and validation scale-dependent measures (RMSE, MAE and MAPE) in the AR (1, 2, 8) model were inferior to those in the AR-Elman hybrid model, which indicated that the AR-Elman hybrid model was better than the AR (1, 2, 8) model. The Box-Jenkins and ElmanNN hybrid method therefore can be highlighted in predicting the temporal trends of TB incidence in Kashgar, which may act as the potential for far-reaching implications for prevention and control of TB.