Polyacrylamide Gel Calibration Phantoms for Quantification in Sodium MRI

Abstract

Quantitative sodium (²³Na) MRI utilises a signal calibration approach to derive maps of total sodium concentration (TSC). Agarose gel vials are often used as calibration phantoms, but as a naturally occurring substance, agarose may exhibit unfavourable qualities relating to instabilities, inconsistencies and heterogeneity. To contribute towards standardisation and methods harmonisation of quantitative ²³Na MRI, the objective of this study was to develop and test a novel, standardisable synthetic polymer calibration phantom for in vivo quantitative ²³Na MRI. Seven crosslinked polyacrylamide gel (PAG) samples were prepared, doped with sodium chloride (NaCl) at nominal concentrations of 10-150 mM. The sodium concentrations of all samples were estimated by volumetrics using high-precision mass measurements. Relaxation time constants ( $T_1,T_2^{*}$ ) of all samples were measured at 3 T with a non-localised pulse-acquire sequence. $T_2^{*}$ was measured longitudinally over 14 months to assess stability. Finally, in vivo TSC quantification with PAG phantoms was demonstrated in the human brain and calf muscle on different systems, with different imaging sequences. The measured sodium concentrations of phantoms were on average 5% lower than nominal ones, owing to the unknown volumetric contribution of the solid fraction. Hence, they were reported as apparent sodium concentrations, and the apparent TSC (aTSC) was quantified in vivo. Mean relaxation time constants of ²³Na in PAG were in the following ranges: $T_1$ = 27-39 ms, $T_{2s}^{*}$ = 4.8-7.1 ms, $T_{2l}^{*}$ = 16.8-18.8 ms, short fraction $f$ = 0.64-0.77. Over 14 months, relaxation time constants were stable within 10% (above sodium concentrations of 25 mM). In vivo aTSC measurements were in the expected ranges. PAG phantoms are well suited for quantification and standardisation in ²³Na MRI, offering tissue-matched relaxation time constants and the intrinsic benefits of a synthetic material.

Keywords: phantoms; polyacrylamide gel; relaxometry; sodium MRI; standardisation; x‐nuclei.

FIGURE 1

An overview of the phantom preparation procedure. Before polymerisation, (a) shows the three essential ingredients, comprising a monomer solution, to which small volumes of ion solution and polymerisation initiator are added (TEMED is tetramethylethylenediamine). After polymerisation, (b) shows estimation of the set gel volume by measuring the mass of mineral oil added to fill the vial to the brim. A photograph of the final, polymerised gel phantom is shown in (c).

FIGURE 2

Schematic chemical diagrams of the monomer compounds acrylamide and N,N′‐methylenebisacrylamide (bis‐acrylamide, the cross‐linker). Unlike simple linear polyacrylamide, which forms in conventional polymer chains, cross‐linked polyacrylamide forms into so‐called polymer networks by conjoining acrylamide chains via bis‐acrylamide cross‐linkers. Their placement is irregular and random, such that cross‐linked polyacrylamide cannot be represented by a repeated polymer unit, unlike linear polyacrylamide.

FIGURE 3

An overview of the processing of complex FID data. In (a), magnitude, real and imaginary parts of the FID are displayed as acquired. The phase is shown in (c) and (d), before and after unwrapping, respectively. The fitted zero‐phase line in (d) is used to derive a complex conjugate exponential term to multiply the complex signal in (a) with, giving rise to the phased FID in (b). During signal decay, the real component closely follows the magnitude; once the signal has decayed, the real part oscillates across the x‐axis, whereas the magnitude oscillates across a positive, non‐zero noise floor, as shown in the zoomed inset. The imaginary part only contains noise.

FIGURE 4

Nine different slices (XZ plane) of five polyacrylamide gel (PAG) phantom vials (samples 2–6, nominal [NaCl] of 25–125 mM and [NiCl₂] of 0.75–3.75 mM) acquired with a proton density (PD) weighted ¹H MRI scan to ascertain structural homogeneity. Phantoms are in a holder containing potassium chloride solution. Signal in the phantoms appears uniform, with no evidence of bubbles, macroscopic compartmentalisation or other unexpected patterns in image intensity. Diffuse Nyquist ghosting of the potassium chloride solution is visible in the rightmost phantoms, vanishing in the first two slices where the vials protrude from the holder.

FIGURE 5

Relaxometry data and fitted curves for samples 2 (a–c) and 5 (e–f), giving examples at both low and high sodium concentration regimes. Plots (a) and (d) show data (grey points) and fitted biexponential relationships (black line, Equation 1) of the FID signal to measure the ${\mathbf{T}}_{\mathbf{2}}^{\mathit{*}}$ of phantoms. Plots (b) and (e) show the corresponding spectra of fitted ${\mathbf{T}}_{\mathbf{2}}^{\mathit{*}}$ values ($\mathit{g}\left(\mathit{\tau }\right)$ in Equation 2). The two peaks of the spectra clearly indicate a biexponential decay mode. Plots (c) and (f) show data (grey points) and fits of Equation (3) (black line) for an inversion recovery experiment to measure the ${\mathbf{T}}_{\mathbf{1}}$.

FIGURE 6

Results of in vivo ²³Na MRI of the human brain. The raw intensity image with calibration phantoms is shown in (a). A conventional quantification procedure with calibration curve and resulting aTSC map is shown in (e) and (f). A bootstrap quantification procedure with 1000 iterations, along with the resulting mean and standard deviation aTSC map, is shown in (b), (c) and (d). Finally, (g) shows the difference between (f) and (c). Note different intensity scales in (d) and (g).

FIGURE 7

Results of in vivo ²³Na MRI of human calf muscle. The raw intensity image with calibration phantoms is shown in (a). A conventional quantification procedure with calibration curve and resulting aTSC map is shown in (e) and (f). A bootstrap quantification procedure with 1000 iterations, along with the resulting mean and standard deviation aTSC map, is shown in (b), (c) and (d). Finally, (g) shows the difference between (f) and (c).