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

Abstract

Purpose: To investigate the effect of particle size on liver $R_2^{*}$ 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 predicting $R_2^{*}$ , 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. $R_2^{*}$ measurements in the phantom were made at both 1.5 T and 3.0 T. Finally, differences in $R_2^{*}$ predictions or measurements were evaluated across varying particle sizes.

Results: In the simulation study, strong linear and positively correlated relationships were observed between $R_2^{*}$ predictions and particle concentrations across varying particle sizes and magnetic field strengths ( $r\ge 0.988$ ). The relationships were affected by iron sphere size ( ), where smaller iron sphere size yielded higher predicted $R_2^{*}$ , whereas fat droplet size had no effect on $R_2^{*}$ predictions ( $p\ge 0.617$ ) for constant total fat concentration. Similarly, the phantom study showed that $R_2^{*}$ measurements were relatively sensitive to iron sphere size ( $p\le 0.004$ ) unlike fat droplet size ( $p\ge 0.223$ ).

Conclusion: Liver $R_2^{*}$ 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 of $R_2^{*}$ relaxometry in vivo, and enable improved quantitative MRI phantom design.

Keywords: Monte Carlo simulations; fat droplet; iron; liver R2*; particle size; phantom.

Figure 1.

Examples of virtual liver models and their corresponding sections for liver iron overload (A-F) and hepatic steatosis (G-L). For a given LIC of 15 mg/g, three virtual liver models were developed with dimensions of 80×80×80 μm³, and iron sphere sizes were 0.2 μm (A), 0.4 μm (B) and 0.6 μm (C). For a given FF of 15%, three virtual liver models were developed with dimensions of 480×480×480 μm³, and fat droplet sizes were 5 μm (G), 10 μm (H) and 15 μm (I). Note that the blue dots represent iron spheres or fat droplets, and 2D sections are with thickness of 5 μm.

Figure 2.

Effect of iron sphere size on simulated signals (A-B) and ${\mathrm{R}}_2^{\mathrm{*}}$ predictions (C-D) in the simulation study at 1.5T and 3.0T. For LIC of 15 mg/g, signals at varying TEs (0.5 μs, 1 ms, 1.5 ms, 2.0 ms, …, 29.5 ms, 30 ms) were plotted, and analyzed without the signals at 0.5 μs. Positive linear relationships between ${\mathrm{R}}_2^{\mathrm{*}}$ predictions and LICs were demonstrated across different iron sphere sizes ($r\ge 0.996,\mathrm{ }p<0.01$), and the slopes decreased as iron sphere size increased.

Figure 3.

Effect of fat droplet size on PDFF (A-B) and ${\mathrm{R}}_2^{\mathrm{*}}$ (C-D) predictions in the simulation study at 1.5T and 3.0T. PDFF predictions were highly linear with true FFs across different fat droplet sizes ($r\ge 0.999,\mathrm{ }p<0.01$), and almost identical to true FFs. Positive linear relationships between ${\mathrm{R}}_2^{\mathrm{*}}$ and PDFF predictions were demonstrated across different fat droplet sizes ($r\ge 0.988,\mathrm{ }p<0.01$), and the slopes remained approximately constant.

Figure 4.

${\mathrm{R}}_2^{\mathrm{*}}$ maps of the iron-water phantom at 1.5T (A) and 3.0T (B). In the iron-water phantom, vials were manufactured with combinations of iron concentrations (20 μg/mL, 40 μg/mL, 60 μg/mL, 80 μg/mL and 100 μg/mL) and iron sphere sizes (0.1~0.2 μm, 0.3~0.4 μm and 0.5~0.6 μm). For vials with the same iron concentration, ${\mathrm{R}}_2^{\mathrm{*}}$ decreased visually as iron sphere size increased.

Figure 5.

Effect of iron sphere size on ${\mathrm{R}}_2^{\mathrm{*}}$ measurements of the iron-water phantom at 1.5T (A) and 3.0T (B). Positive linear relationships between ${\mathrm{R}}_2^{\mathrm{*}}$ measurements and iron concentrations were demonstrated across different iron sphere sizes ($r\ge 0.973,p<0.01$), and the slopes decreased as iron sphere size increased.

Figure 6.

Micrographs of three vials with same FF (20%) and different fat droplet sizes. Fat droplet sizes in each vial were respectively controlled using homogenous emulsifier at rotational speed of 15000 rpm (A, D) and 8000 rpm (B, E), as well as using magnetic stirring apparatus at rotational speed of 1000 rpm (C, F). Note that FFs of the above micrographs may not be exactly equal to 20% due to sampling. These micrographs are mainly used to illustrate the difference in fat droplet size.

Figure 7.

PDFF (A-B) and ${\mathrm{R}}_2^{\mathrm{*}}$ (C-D) maps of the fat-water phantom at 1.5T and 3.0T. In the fat-water phantom, vials were with combinations of true FFs (10%, 20%, 30%, 40% and 50%) and fat droplet sizes (small size, medium size and large size). For vials with the same FF, PDFF and ${\mathrm{R}}_2^{\mathrm{*}}$ remained visually unaffected by fat droplet size.

Figure 8.

Effect of fat droplet size on PDFF (A-B) and ${\mathrm{R}}_2^{\mathrm{*}}$ (C-D) measurements of the fat-water phantom at 1.5T and 3.0T. PDFF measurements were highly linear with true FFs across different fat droplet sizes ($r\ge 0.999,p<0.01$), and approximate to true FFs. Positive linear relationships between ${\mathrm{R}}_2^{\mathrm{*}}$ and PDFF measurements were demonstrated across different fat droplet sizes ($r\ge 0.976,p<0.01$), and the slopes remained approximately constant.