Michiel Kleinnijenhuis1, Jeroen Mollink1, Errin E Johnson2, Vitaly L Galinsky3, Lawrence R Frank3, Saad Jbabdi1, and Karla L Miller1
1Oxford Centre for Functional MRI of the Brain, University of Oxford, Oxford, United Kingdom, 2Sir William Dunn School of Pathology, University of Oxford, Oxford, United Kingdom, 3Center for Scientific Computation in Imaging, University of California San Diego, La Jolla, CA, United States
Synopsis
The cylindrical models
often used in Monte Carlo diffusion simulations do not resemble the shape of
axons very well. In this work, a more realistic substrate derived from electron
microscopy data is used to investigate the influence of axon shape and
myelination on the diffusion signal. In the DifSim simulation environment, diffusion signals from EM-derived substrates are compared to those from cylindrical substrates matched for
volume fraction. Furthermore, the effect of removing
the impermeable myelin sheath from the substrate is assessed.Introduction
The application of
microstructure techniques in diffusion imaging, such as axon diameter1 and
membrane permeability estimation2, are often validated using
Monte Carlo simulations. The geometric substrates are usually highly simplified
cylindrical models that have a limited number of compartments. This work
investigates a more realistic substrate derived from electron microscopy data
and aims to showcase how the influence of shape and compartments on the
diffusion signal can be investigated.
Methods
Simulation substrates
To create a realistic substrate, a serial blockface electron microscopy dataset
(4000x4000x500; 29.2x29.2x25.0 μm) was acquired from the genu of the
corpus callosum of a mouse brain in sagittal sections. Acquisition used a Zeiss
Merlin Compact Scanning Electron Microscope with a Gatan 3View system. For the
present purpose, a single section was segmented by tracing cell membranes and
myelin sheaths manually (Figure1). Six compartments were distinguished: unmyelinated
axons (UA), myelinated axons (MM and MA), glial bodies (GB) and glial processes
(GP). Extracellular space (ECS) was enforced around all objects (no touching
fibres).
Two EM substrates were created to yield ECS volume fractions of 0.19 and
0.23 (EM1 and EM2) by eroding the fibres. Cylindrical substrates were
obtained by tightly packing circles with equivalent radii (CT1/CT2; ECS volume fraction 0.14). To create cylindrical substrates matching EM packing densities, the circle
centroids were shifted (CM1/CM2). A substrate without myelin was created from
EM1 by replacing myelinated with unmyelinated axons with the shape of the MM outer
boundary. Dilation of substrates by 0.0292 μm resulted in a container fitting
tightly around the substrate. Substrates had a z-dimension (10 μm) to meet
the 3D nature of the simulation environment, but diffusion was periodic and
free in the—constant—z-dimension.
Monte Carlo simulations
Monte Carlo simulations were performed with DifSim3 tracking
the phase of the particles and calculating the diffusion MR signal.
Diffusivities for ECS, intracellular compartments and myelin were set to
[2.0;0.75;0.03] μm2/ms and the base rate of 35 particles /um3 was
scaled by concentration factors [0.95;0.88;0.50]4. Simulation
step size was 1 μs.
The effect of cross-sectional axon shape and myelination on the
diffusion signal was assessed for a PGSE sequence using a range of diffusion
times (Δ=[2-160] ms), b-values (100-32000 s/mm2) and 30 diffusion gradient
directions in a semicircle in the xy-plane.
Two simulation experiments were conducted to assess the effect of
geometry and permeability. (i) Shape: For assessing the effect of shape and
volume fraction, substrates EM1, EM2, CT1, CT2, CM1 and CM2 were compared. In
this experiment, membranes were impermeable. (ii) Permeability: Myelination has
a profound effect on the exchange between axons and ECS, therefore permeability
was included for the comparison between the myelinated and unmyelinated
substrate.
Results
Shape
The diffusion signal averaged over directions is
similar for EM1/2 vs. CM1/2 substrates (Figure2). The main variation is due to volume
fraction, as also demonstrated by smaller attenuation for the CT substrates. The
ECS signal is different between the two CM substrates, indicating that unequal
spacing around objects interacts with volume fraction (arrow). Two regimes where
shape might become a relevant factor (Figure3:”ALL”): i) very short Δ, where lower
signal in EM1 appears driven by restricted (quasi-)cylindrical compartments (MA/UA);
ii) for the lower b-values across Δ’s where the ECS signal is dominant.
Myelination
With low permeability, no effect of myelination on the
aggregate diffusion signal is seen (Figure4:”o”). Higher permeabilities (“+”) induce
loss of signal in the unmyelinated vs. the myelinated substrate as there
is both less restriction in intracellular compartments as well as increased
diffusion across membranes.
Discussion
The EM-based substrate and simulation environment presented here has
been developed to provide researchers with a flexible tool for investigating
the role of a range of tissue features. Here, we present the two examples of
shape and permeability.
Considering the modest change in signal between EM-derived and
cylindrical substrates, our results suggest that the circular cross-sectional
shape is a valid approximation for white matter tissue, for example as deployed
for axon diameter mapping. On the other hand, the minor effect myelination had at low permeability suggests higher exchange rate estimates2 in grey
compared to white matter might be due to abundance of highly permeable glia,
rather than degree of myelination.
The EM-derived substrate is somewhat oversegmented as connections
between objects occuring outside the segmented section were ignored. Future 3D
tissue modeling efforts will address this shortcoming. Further
compartmentalisation and variations in compartment properties (e.g.
mitochondria and separate permeabilities of glia and neurons) will add to the
accuracy of this realistic model. Fortunately, these improvements are
incorporated in the DifSim environment in a straightforward manner.
Acknowledgements
We are thankful for the help of James Larkin in handling the animal.References
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