Multinuclear MRI to disentangle intracellular sodium concentration and extracellular volume fraction in breast cancer

Abstract

The purpose of this work was to develop a novel method to disentangle the intra- and extracellular components of the total sodium concentration (TSC) in breast cancer from a combination of proton ([Formula: see text]H) and sodium ([Formula: see text]) magnetic resonance imaging (MRI) measurements. To do so, TSC is expressed as function of the intracellular sodium concentration ([Formula: see text]), extracellular volume fraction (ECV) and the water fraction (WF) based on a three-compartment model of the tissue. TSC is measured from [Formula: see text] MRI, ECV is calculated from baseline and post-contrast [Formula: see text]H [Formula: see text] maps, while WF is measured with a [Formula: see text]H chemical shift technique. [Formula: see text] is then extrapolated from the model. Proof-of-concept was demonstrated in three healthy subjects and two patients with triple negative breast cancer. In both patients, TSC was two to threefold higher in the tumor than in normal tissue. This alteration mainly resulted from increased [Formula: see text] ([Formula: see text] 30 mM), which was [Formula: see text] 130% greater than in healthy conditions (10-15 mM) while the ECV was within the expected range of physiological values (0.2-0.25). Multinuclear MRI shows promise for disentangling [Formula: see text] and ECV by taking advantage of complementary [Formula: see text]H and [Formula: see text] measurements.

Figure 1

Three compartment model of an imaging voxel. Each voxel is constituted by water (blue) and fat (yellow) in different proportions. Within the water portion we identify an intracellular (IC) and an extracellular (EC) compartments. In our study we assume the extracellular sodium concentration (${\text{C}}_{\text{EC}}$) to be fixed to 140 mM, which simplifies the calculation of intracellular sodium concentration (${\text{C}}_{\text{IC}}$). TSC, total sodium concentration; ${\text{C}}_{\text{fat}}$, fat sodium concentration; ECV, extracellular volume fraction; ICV, intracellular volume fraction; WF, water fraction; ${\text{V}}_{\text{TOT}}$, total voxel volume.

Figure 2

Quantification pipeline: a combination of ${}^{23}\text{Na}$ and ${}^1$H imaging modalities are employed to isolate the intracellular component of the total sodium signal. From left to right: four GRE images with incremental TE’s, a ${}^{23}\text{Na}$ FLORET image and two ${}^1$H ${\text{T}}_1$ measurements (pre and post contrast) are independently elaborated to generate, respectively, WF, TSC and ECV. Ultimately, these three maps are combined (Eq. 1) to calculate ${\text{C}}_{\text{IC}}$ and ICV.

Figure 3

Total sodium concentration (TSC) calibration and validation in phantoms. (A) Calibration phantoms with ten 3% agar gels with sodium concentration ranging from 25 to 125 mM with 25 mM step. The FLORET dataset was corrected to account for ${\text{B}}_1$ profile and gels relaxation times. (B) Calibration curve, ${\text{R}}^2$ = 0.980. Each point in the plot corresponds to the average signal intensity of two bilateral gels with same sodium concentration. (C) Schematic of validation phantoms consisting of ten gels with agar concentrations between 0 and 8%, which are overlaid for each gel. The true sodium concentrations are color coded and ranged between 25 and 140 mM. (D) TSC map (mM) measured in validation phantoms shows good agreement with ground truth with < 7% error. Specifically, the mean TSC calculated in the 0%, 4% and 8% agar gels (true concentration: 140 mM) were, respectively, $141.9\pm 18.4$ mM, $137.9\pm 9.7$ mM and $150.0\pm 12.0$ mM. In the 3% agar gels (true concentrations: 25, 50, 75, 100, 125 mM) the mean TSC were: $26.5\pm 2.9$ mM, $47.3\pm 3.8$ mM, $78.3\pm 6.3$ mM, 95.5 ± 7.6 mM and $125.4\pm 10.0$ mM. The relaxation times of the 0%, 3%, 4% and 8% agar gels are reported in Supplementary Table S1.

Figure 4

MRI images in 51-year-old patient with triple negative breast cancer. (A) Proton ${\text{T}}_1$w fat suppressed (FS) anatomical image. The area in red is the ROI containing the lesion. (B) Different slice of the same volume showing the control ROI (blue region) in the contralateral breast. (C) Dynamic ${}^1$H signal enhancement shows high uptake of contrast agent (CA) in a 645-voxel-ROI that includes the tumor (red ROI in panel A) compared to a 100-voxel control ROI in contralateral healthy fibroglandular tissue (blue region in panel B) (D) Sodium image, corresponding to the ${}^1$H ${\text{T}}_1$w in panel A, acquired with a FLORET sequence showing hyperintensity in the tumor. (E) Sodium image in which healthy contralateral tissue is visible, co-registered with the ${}^1$H ${\text{T}}_1$w image in (B). (F) Boxplot showing the distribution of ${}^{23}\text{Na}$ signal within the tumor and in the contralateral healthy fibroglandular tissue (control). Sodium signal intensity in the lesion is 2-fold higher than in the control.

Figure 5

Quantitative maps in a post-menopausal 51-years-old patient with triple negative breast cancer (Patient 1) and in a post-menopausal 58-years-old patient with triple negative breast cancer (Patient 2). In patient 1: average ECV and ICV in the lesion were respectively $0.28\pm 0.12$ and $0.55\pm 0.15.$ TSC in the lesion was 47.0 ± 11.1 mM, which was approximately double the TSC measured in contralateral healthy glandular tissue ($23.0\pm 7.6$ mM, not visible in the figure) in accordance with previous findings. ${\text{C}}_{\text{IC}}$ in the lesion was $29.6\pm 17.9$ mM. In patient 2: average ECV and ICV in the lesion were respectively $0.14\pm 0.05$ and 0.69 ± 0.10. TSC in the lesion was $39.2\pm 15.2$ mM, which was three times higher than in contralateral healthy tissue ($13.5\pm 7.5$ mM). ${\text{C}}_{\text{IC}}$ in the lesion was $27.2\pm 21.1$ mM. ECV, extracellular volume fraction; ISC, intracellular volume fraction; TSC, total sodium concentration; ${\text{C}}_{\text{IC}}$, intracellular sodium concentration.

Figure 6

Baseline ${\text{T}}_1$, post contrast ${\text{T}}_1$ and ECV in two healthy controls and a patient. In control 1 (top row) poor CA uptake with only 6% ${\text{T}}_1$ decrease and consequently extremely low average ECV (0.06 ± 0.10) were observed. In control 2 (center row) the average ${\text{T}}_1$ decrease in the fibrograndular tissue was 42% but with a non-uniform pattern, resulting in regions with higher ECV of 0.29 ± 0.24 (white arrows) where the uptake was greater, and regions with lower ECV of $0.03\pm 0.03$ in regions with lower uptake. The ${\text{T}}_1$ decrease in the lesion of a 51-years-old triple negative breast cancer patient (bottom row) was 67% which resulted into mean ECV in the lesion of $0.28\pm 0.12.$