Nathalie Just1, Samo Lasič2,3, Ditte Bentsen Christensen4, Julien Valette5, Tim Dyrby2,6, Hartwig Siebner2, and Henrik Lundell2
1Danish Research Center for Magnetic Resonance, Copenhagen University Hospital - Amager and Hvidovre, Hvidovre, Denmark, 2Danish Research Center for Magnetic Resonance, Copenhagen University Hospital Amager and Hvidovre, Hvidovre, Denmark, 3Random Walk Imaging, Lund, Sweden, 4HYPERMAG, DTU, Copenhagen, Denmark, 5MIRCen, Commissariat à l' energie atomique et aux Energies Alternatives, Fontenay-aux-Roses, France, 6Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark
Synopsis
Metabolite diffusion provide the unique ability to study the intracellular environment of specific cell types of the brain. Multiple studies suggest that the diffusivity along dendrites and axons is time dependent due to variations in diameter. We explore the signal due to such effects in Monte Carlo simulations in settings feasible for preclinical PGSE measurements and find that time dependent kurtosis, but not diffusivity provide the most potent source of contrast to this effect. We observe similar effects of intraneuronal NAA diffusion in rat.
Introduction
Morphology is varying along axons and
dendrites, such as thickness (varicosities), and dispersedly located
mitochondria and spines (1, 2). Such features may occur on length scales of
1-10 µm and affect time dependent diffusion (TDD) in diffusion weighted MRI experiments (1, 2, 3, 4, 5). Diffusion-weighted MR spectroscopy (DW-MRS) is able to measure the
diffusion of endogenous metabolites such as N-Acetyl-Aspartate (NAA) providing a probe with a high specificity to the intra-neuronal
space (6). In experiments with longer diffusion times (>50 ms), the diffusivity of NAA corresponded well to disperse “sticks” defined by an axial diffusivity but a negligible transverse
diffusivity (7, 8).
However, at decreasing diffusion times, an increase in NAA diffusivity
suggests the influence of more complex morphologies (9) while towards the tortuosity limit, diffusivity may be affected by exchange across
fibrous branches of cells, as in astrocytes (8) . Understanding
their influence on diffusion could provide valuable biomarkers of disease
related changes.
In this study, we are focusing on maximizing
the contrast to noise in a PGSE DW-MRS experiments to demonstrate the effect where the amplitude or duration of transient effects are
expected to change. Identifying optimal experimental parameters and the related
feature on data is crucial for optimal sensitivity to underlying variations in
morphology. Using our minimal geometrical Monte Carlo
simulator of fibrous geometries (10), we show that the effects on time dependent
diffusivity from variations along thin fibers on length scales 1-10 µm is small
and attenuates quickly while transient kurtosis and higher order terms are long
lived and more measurable. For intermediate diffusion times in a rotationally
disperse region, we hypothesize that the signal will decay slower than that of a
“stick” model. Preliminary data collected in one rat suggest small effects of
time dependent Diffusivity or Kurtosis in the investigated range.
Materials and Methods
Monte Carlo
simulation: We performed Monte Carlo simulations using our recently proposed model (10). Briefly, a long tubular
structure with sinusoidally varying radius along its length was used. The substrate was
constructed from: 50 connected segments, internode distances varying between
5-10 µm and a constant ratio between radii for each segment. Simulations used the free diffusion coefficient set to 0.8 µm2/ms
similar to that of NAA (11), 106 walkers, a length step of 100 nm.
The diffusion process was simulated over 100 ms with a typical computation time
of 60 seconds. Time dependent diffusivity (D(t)) and Kurtosis (K(t)) where
calculated from stored trajectories. Signals from a PGSE experiment were computed for δ = 8 ms, Δ = 20,
30 and 40 ms and with gradient amplitude G= [0 0.6] T/m.
Signals were represented both as decays from a substrate aligned with the
diffusion encoding gradients and as uniformly distributed powder average.
Experimental : In-vivo experiments were conducted in a rat under Isoflurane (2.5% in air ) on a Bruker
Biospin 7T (Ettlingen, Germany) MR Scanner equipped with 0.66 T/m
gradients. The rat‘s head was secured in a stereotactic frame. Respiration and
temperature (37.5 ± 0.5 °C) were monitored.
Acquisitions were performed using a surface coil and a quadrature
volume coil (Bruker, Germany). T2-weighted
images for voxel positioning (Fig1.A) were used. DW-MRS was conducted using a modified PGSE version of a Spin-Echo (SE) LASER
sequence with the following parameters:
TR/TE-SE= 2000/50 ms; FOV = 30x30 mm2; VOI =6 x 6 x 6 mm3;
fixed δ = 8 ms; Δ = 20, 30 and 40 ms and b values ranging from 0.1 to 20 ms/µm2. 64 FIDs
were individually acquired (Spectral Width = 4000 Hz; 4096 points). With MAPSHIM, a water linewidth of 10.7 Hz was achieved. 64 FIDs were
individually acquired (Spectral Width = 4000 Hz; 4096 points) and processed with in-house Matlab routines. Averaged
spectra for different b and Δ values were subsequently realigned (Fig.1B). NAA maximum peak amplitudes
were recorded and used for subsequent analysis and fitting procedures. For
visualization a model of disperse sticks with Gaussian diffusion was fitted to
data individually for each Δ.Results and Discussion
A segment
of the simulated structure (Fig.2A) with computed D(t) and K(t) (Fig.2B) are
shown. While D(t) attenuates from free diffusion to the tortuosity level within
20 ms reflecting the partial restriction of each internodal space, the process remains
non-Gaussian over an extended range of diffusion times. Simulated signals from
a PGSE experiment are shown from measurements along the substrate (Fig.3.A) and
for a uniform distribution of the substrate (Fig.3.B). Signal attenuations for
mono-exponential decays are extrapolated from the initial slope of each curve
( dispersion in Fig.3.B) and are overlapping for the different Δ, while Kurtosis and
higher order terms provide a substantial contrast of >5% at large b-values
over the simulated range of Δ.
Fig.4.A
shows attenuation curves normalized to a fitted S(b=0). The measurements and
fits are strikingly consistent over the range of Δ, as previously concluded with longer diffusion times (7,8). However, for b=20
ms/µm2, datapoints diverge consistently above the gaussian model supporting the influence of additional non-gaussian effects. Various optimization strategies and evaluation of alternative
encoding strategies (9, 10) will be included. Since the
contrast is diluted by orientational dispersion (e.g in Fig.3A and B), higher
sensitivity may also be achieved for macroscopic alignment .Acknowledgements
SL, NJ and HL have received funding
from the European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme
(grant agreement No 804746).SL is supported also by Random Walk Imaging.References
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