Measurement of Intraneurite Sodium Concentration from NODDI-based Partial Volume Correction of in vivo 23Na MRI
Iris Asllani1,2, Guillaume Madelin3, Marco Bozzali1,4, and Mara Cercignani1,4

1Neuroscience, Brighton and Sussex Medical School, Brighton, United Kingdom, 2Biomedical Engineering, Rochester Institute of Technology, Rochester, NY, United States, 3Radiology, New York University School of Medicine, New York, NY, United States, 4Neuroimaging, Santa Lucia Foundation, Rome, Italy


The sodium ion plays a crucial role in maintaining healthy brain function and metabolism. Changes in sodium concentration measured with 23Na MRI have been implicated in several diseases in the brain and other organs. However, due to SNR and scanning time requirements, 23Na MRI remains a low resolution technique hampered by partial volume effects. Here, we combined a partial volume correction (PVC) algorithm, previously used in Arterial Spin Labeling perfusion MRI, with Neurite Orientation Dispersion and Density Imaging (NODDI) to extract sodium concentration values from intra- and extra-neurite compartments in the brain in vivo using 23Na MRI at 3T.


Measurement of intracellular sodium concentration in the brain is the holy grail of 23Na MRI. Sodium plays a vital role in maintaining healthy brain function because of its direct involvement in processes such as conduction of action potentials and regulation of osmotic pressure. Any disruption in the 23Na balance among different cellular compartments could lead to dysfunction and eventually apoptosis. Recent advances in hardware and readout schemes have resulted in a surge of 23Na MRI studies investigating the link between sodium imbalance and specific pathologies, such as Alzheimer’s disease, stroke, and multiple sclerosis1. Nevertheless, because 23Na MRI is a low spatial-resolution technique, it suffers from partial volume effects, i.e., mixing of the 23Na signals originating from different compartments within a voxel. Due to these effects, measurement of 23Na at the intracellular level has proven challenging. To this end, we combined a partial volume correction (PVC) algorithm, initially developed for Arterial Spin Labeling (ASL) MRI2, with a multi-compartment DWI model, referred to as NODDI3, to measure intraneurite 23Na in vivo at 3T. Intraneurite 23Na represents sodium restricted within axons and dendrites and as such its measurement could be key to studying disease mechanisms at the microstructural level.


Theory: At any given voxel, the total sodium concentration, NaT, is given as:

Eq.1: NaT = VFinNaIn + VFEnNaEn + VFIsoNaIso

where VFIn, VFEn, VFIso represent, respectively, the intraneurite (axons and dendrites), extraneurite (soma, glial cells, etc.), and non-tissue compartments3. The goal is to solve for Na in each compartment, which is not possible with Eq.1 alone. By assuming, however, that for each compartment (j), Na is constant over a region (‘kernel’) surrounding the voxel, Eq.1 can be re-written in vectorial form to include each voxel at position ri within the kernel, as detailed in Asllani et al.2:

Eq.2: NaT(ri) = VFj(ri)·Naj(ri)

Each Naj can now be computed as per Eq.3: Naj = [VFT·VF]-1·VFT·NaT

MRI protocol: The following images were acquired on 5 participants (age 35±7y, 3F) on a Siemens 3T scanner: MPRAGE, voxel size 1mm3; 1H NODDI DWI as following the protocol in Cercignani et al.4, with voxel size 2.14mm3; 23Na MRI using FLORET5 with TE=0.2ms, TR=100ms, and voxel size 4 mm3. For calibration purposes, two agar phantoms, 65mM and 155mM NaCl, were placed in the coil. To test the robustness of the PVC algorithm, Na images were acquired with and without an inversion recovery pulse aimed at modulating the CSF signal.

Processing & Analysis: The 23Na image and the GM, WM, and CSF tissue-volume maps (obtained from the segmentation of MPRAGE) were coregistered to the VFIn image using SPM12. The images were calibrated and corrected for tissue relaxation times1. A cubic regression kernel (size = 9 voxels) was used for PVC2. A threshold of 0.75% was used to make GM, WM, and CSF masks.


Images from a single subject are showing in Fig. 1. Results are summarized in Table 1. The highest NaEn concentration was found in GM whereas WM contained the highest NaIn concentration, which bodes well with our hypothesis that NaIn reflects axonal Na. As hypothesized, the inversion recovery (IR) did not have an observable effect on the estimation of NaIn and NaEn; only NaIso was affected.


Combining NODDI with the PVC algorithm previously used in ASL3, we resolved the intracellular Na signal into intra- and extra-neurite sodium concentrations. While NODDI has been previously used to estimate NaIn, the computation was based on assuming fixed values for NaEn and NaIso and without accounting for the mixing of the signals4. Ours is the first study to estimate NaIn and NaEn independently, which makes comparison with data from literature difficult. However, when computed at the tissue level (see Table 1), the Na concentrations obtained from our method were within the range of published values for GM and WM1. Regarding PVC, Niesporek et al. have used the geometric transfer matrix method to estimate the PSF of the sodium signal from different compartments using a phantom at 7T6. Future work is needed to compare (and perhaps combine) the two methods and to test their sensitivity in detecting changes in sodium concentrations in vivo. Further investigation is also needed to assess the potential effect on the Na quantification of the difference in T2 relaxation between the intra- and extra-neurite compartments, for each tissue. Here, no such distinction was made and global tissue values were used1.


No acknowledgement found.


1G Madelin et al. JMRI 2013; 2I Asllani et al. MRM 2009; 3B Solanky et al. Proc ISMRM 2015; 4M Cercignani et al. Neurob. Aging 2017; 5J G Pipe et al. MRM 2011; 6S C Niesporek et al. NeuroImage 2015


Figure 1: NaIn and NaEn images obtained from the PVC algorithm were conjoined with the GM and WM masks to yield tissue specific intra- and extra-neurite Na images. For each tissue, NaT was computed as per Eq.1.

Table 1

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)