Prediction of MRI R2*$$ {\mathrm{R}}_2^{\ast } $$ relaxometry in the presence of hepatic steatosis by Monte Carlo simulations

To develop Monte Carlo simulations to predict the relationship of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> <mml:annotation>$$ {\mathrm{R}}_2^{\ast } $$</mml:annotation></mml:semantics> </mml:math> 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 for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> <mml:annotation>$$ {\mathrm{R}}_2^{\ast } $$</mml:annotation></mml:semantics> </mml:math> and proton density fat fraction (PDFF) predictions. In addition, the relationships between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> <mml:annotation>$$ {\mathrm{R}}_2^{\ast } $$</mml:annotation></mml:semantics> </mml:math> 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) on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> <mml:annotation>$$ {\mathrm{R}}_2^{\ast } $$</mml:annotation></mml:semantics> </mml:math> predictions. A virtual liver model with realistic morphology of fat droplets was demonstrated, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> <mml:annotation>$$ {\mathrm{R}}_2^{\ast } $$</mml:annotation></mml:semantics> </mml:math> and PDFF values were predicted by Monte Carlo simulations at 1.5 T and 3.0 T. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> <mml:annotation>$$ {\mathrm{R}}_2^{\ast } $$</mml:annotation></mml:semantics> </mml:math> 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. The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> <mml:annotation>$$ {\mathrm{R}}_2^{\ast } $$</mml:annotation></mml:semantics> </mml:math> -PDFF relationships by simulations with fat susceptibility of 0.6 ppm and the multi-peak fat signal model were <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> <mml:mo>=</mml:mo> <mml:mn>0.490</mml:mn> <mml:mo>×</mml:mo> <mml:mtext>PDFF</mml:mtext> <mml:mo>+</mml:mo> <mml:mn>28.0</mml:mn></mml:mrow> <mml:annotation>$$ {\mathrm{R}}_2^{\ast }=0.490\times \mathrm{PDFF}+28.0 $$</mml:annotation></mml:semantics> </mml:math> ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn></mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.967</mml:mn></mml:mrow> <mml:annotation>$$ {R}^2=0.967 $$</mml:annotation></mml:semantics> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>p</mml:mi> <mml:mo><</mml:mo> <mml:mn>0.01</mml:mn></mml:mrow> <mml:annotation>$$ p<0.01 $$</mml:annotation></mml:semantics> </mml:math> ) at 1.5 T and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> <mml:mo>=</mml:mo> <mml:mn>0.928</mml:mn> <mml:mo>×</mml:mo> <mml:mtext>PDFF</mml:mtext> <mml:mo>+</mml:mo> <mml:mn>39.4</mml:mn></mml:mrow> <mml:annotation>$$ {\mathrm{R}}_2^{\ast }=0.928\times \mathrm{PDFF}+39.4 $$</mml:annotation></mml:semantics> </mml:math> ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn></mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.972</mml:mn></mml:mrow> <mml:annotation>$$ {R}^2=0.972 $$</mml:annotation></mml:semantics> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>p</mml:mi> <mml:mo><</mml:mo> <mml:mn>0.01</mml:mn></mml:mrow> <mml:annotation>$$ p<0.01 $$</mml:annotation></mml:semantics> </mml:math> ) at 3.0 T. Monte Carlo simulations provide a new means for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> <mml:annotation>$$ {\mathrm{R}}_2^{\ast } $$</mml:annotation></mml:semantics> </mml:math> -PDFF prediction, which is primarily determined by fat susceptibility, fat signal model, and magnetic field strength. Accurate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> <mml:annotation>$$ {\mathrm{R}}_2^{\ast } $$</mml:annotation></mml:semantics> </mml:math> -PDFF calibration has the potential to correct the effect of fat on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> <mml:annotation>$$ {\mathrm{R}}_2^{\ast } $$</mml:annotation></mml:semantics> </mml:math> quantification, and may be helpful for accurate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msubsup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn> <mml:mo>*</mml:mo></mml:msubsup> </mml:mrow> <mml:annotation>$$ {\mathrm{R}}_2^{\ast } $$</mml:annotation></mml:semantics> </mml:math> measurements in liver iron overload.