This work investigates the validity of the stick model used in diffusion-weighted MRI for modelling cellular projections in brain tissue. We hypothesize that the model will fail to describe the signals from grey matter due to an abundance of cell bodies. Using high b-value (≥3 ms/µm ) data from rat and human brain, we show that the assumption fails for grey matter. Using diffusion simulation in realistic digital models of neurons/glia, we demonstrate the breakdown of the assumption can be explained by the presence of cell bodies. Our findings suggest that high b-value data may be used to probe cell bodies

Alexander, D.

Ianus, A.

Palombo, M.

Shemesh, N.

Zhang, H.

Online Research @ Cardiff

07/11/2017, 23)32Page 1 of 4https://submissions.mirasmart.com/ISMRM2018/ViewSubmission.aspx?sbmID=6170Abundance of cell bodies can explain the stick model’s failure in grey matter at high b-valueMarco Palombo , Noam Shemesh , Andrada Ianus , Daniel C. Alexander , and Hui ZhangComputer Science Department and Centre for Medical Imaging Computing, University College London, London, United Kingdom, ChampalimaudNeuroscience Programme, Champalimaud Centre for the Unknown, Lisbon, PortugalSynopsisThis work investigates the validity of the stick model used in diffusion-weighted MRI for modelling cellular projections in brain tissue. Wehypothesize that the model will fail to describe the signals from grey matter due to an abundance of cell bodies. Using high b-value (≥3 ms/µm ) data from rat and human brain, we show that the assumption fails for grey matter. Using diffusion simulation in realistic digital modelsof neurons/glia, we demonstrate the breakdown of the assumption can be explained by the presence of cell bodies. Our findings suggestthat high b-value data may be used to probe cell bodies.IntroductionWe examine the validity of a standard assumption in modelling the relationship between brain tissue microstructure and diffusion-weighted MRI (DW-MRI) data. Specifically, from the water diffusion standpoint, it has been conjectured that the neuronal and glial projections (neurites) can be modelledas sticks . If this stick model is valid, then the decay of the direction-averaged normalized signal, S, at high b values (b≥3 ms/µm ) is expected tofollow the distinctive behaviour :, with α=-1/2 and β,γ≥0 (1)where f  and D  are the intra-neurites volume fraction and (axial) diffusivity, respectively, β f /(D )  and γ fraction of fully restricted water.The extra-neurites contribution is assumed to decay exponentially faster than the intra-neurites one, and can be neglected for large b . Testing thevalidity of the power-law (1) is challenging, because high b values over a few orders of magnitude are required. While recent studies  suggested thatrelation (1) may hold in white matter (WM), a distinctively faster decay in grey matter (GM) was observed, with α<-1/2 and/or γ<0. We hypothesise thatcell bodies, namely soma, may be responsible for this observed violation. We assess the role of size/density of soma in these experimental findingsusing numerical simulations and a comparison with experimental data from rat and human brain.MethodsNumerical simulations. Diffusion simulation in realistic digital models of dendritic structures were first conducted to investigate the influence of somasize/density (r /f ) in a controlled fashion. Detailed three-dimensional geometries were constructed to mimic realistically connected neurites, indifferent (r ,f ) conditions (Fig.1). The DW-MRI signals, as measured by a Pulsed-field-Gradients Spin-Echo (PGSE) sequence, were computedin CAMINO  for 10  b-values from 0 to 100 ms/µm  and 60 directions, uniformly distributed over the sphere. The direction-averaged signal as afunction of b was then computed (Fig.2). Gradient-pulse duration/separation: δ/Δ=10/20 ms were chosen to be compatible with the experimentaldatasets. Note that here we focus on intracellular water diffusion only, because, with this model, the effects of extracellular diffusion and membranepermeability were shown to be negligible at high b-values  and short diffusion times .Experimental Data. Our numerical results were compared with data from healthy rat andhuman brain. An ex-vivo rat brain was scanned using a PGSE sequence on a 16.4T(Bruker/Aeon), with: TE/TR=18/8000 ms; δ/Δ=4/7 ms; 16 b-values from 0 to 15 ms/µm , 10uniformly distributed diffusion-encoding directions per b value. One subject (age=25-29) fromthe MGH Adult Diffusion Dataset (https://www.humanconnectome.org) was analysed. Thedataset  was acquired at 3T (Siemens/Connectom) with b=1,3,5,10 ms/µm  and respectively64, 64, 128 and 256 uniformly distributed diffusion-encoding directions; five b=0;TE/TR=57/8800 ms; δ/Δ=13/22 ms. Both datasets were corrected for motion and eddy-currents using FSL (https://fsl.fmrib.ox.ac.uk/fsl), and the direction-averaged DW-MRI signalcomputed.Data analysis. To investigate the validity of the stick model for different controlled (r ,f )conditions, relation (1) was fitted to simulated signals (for 3≤b≤15 ms/µm ), using the twoapproaches shown to provide the best performance : (i) fixing α=-1/2 and fitting β and γ; (ii)fixing γ=0 and fitting α and β (insets in Fig.2-a,b). The stick model is considered valid if1 2 1,2 1 11 221-4 24,5S(b) ≈ ( erf [(b ] + γ ≈ β + γfintra π4bDintra )1/2 Dintra )1/2 bαintra intra ∝ intra intra 1/25,65,6soma somasoma soma7 3 25 829 2soma soma2507/11/2017, 23)32Page 2 of 4https://submissions.mirasmart.com/ISMRM2018/ViewSubmission.aspx?sbmID=6170α=-0.50±0.05 and γ≥-0.025 (assuming an experimental uncertainty of 10%). The sameapproach was used to analyse the two experimental datasets, from which α, β and γ mapswere obtained (Fig.3). To verify the validity of the stick model in WM and GM, a region-of-interest based statistical analysis of α and γ values was performed (Fig.4).ResultsOur results show that, within the experimentally accessible window for human studies, relation (1) fails in the case of non-negligible soma presence(f >0.2), independently of the fitting approach used (Fig.2-c,d). Indeed, both the approaches (i) and (ii) perform equally well for r ≤10 µm andf 0.6 (inset Fig.2-a,b). The estimated α and γ values seem to be consistently biased by the presence of soma (Fig.2-c,d). The bias predicted bysimulations is confirmed by experimental results reported in Fig.3,4, where the estimated γ and α values in GM and WM with approach (i) and (ii) areγ ≤γ ≥-0.025 and α ≤α ≈-0.50±0.05.Discussion and ConclusionThis work suggests that, in the region 3≤b≤15 ms/µm , the direction-averaged DW-MRI signal may contain useful information about the soma sizeand density. We show that 1) the stick model fails for GM, known to be comprised of mostly soma and non-myelinated neurites; 2) the failure can bedue to the presence of soma, although we cannot exclude other factors like neurites' curvature and branching.This study provides insights for interpreting the direction-averaged DW-MRI of the centralnervous system, aiding in acquisition strategy design and improved biophysical models forbrain microstructure estimation.AcknowledgementsThis work was supported by EPSRC (EP/G007748, EP/I027084/01, EP/L022680/1, EP/M020533/1, N018702), EPSRC EP/M507970/1 and ERC underthe European Union’s Horizon 2020 research and innovation programme (Starting Grant, agreement No. 679058). We like to acknowledge Dr.Ekaterina Vinnik for ex-vivo data acquisition.References Zhang H, et al. NODDI: practical in vivo neurite orientation dispersion and density imaging of the human brain. Neuroimage 2012; 61 (4): 1000-1016. Jespersen S N, Kroenke C D, Østergaard L, Ackerman J J, Yablonskiy D A. Modeling dendrite density from magnetic resonance diffusionmeasurements. Neuroimage 2007; 34(4): 1473-1486. Assaf Y, Freidlin R Z, Rohde G K, Basser P J. New modeling and experimental framework to characterize hindered and restricted water diffusion inbrain white matter. Mag. Reson. Med. 2004; 52(5): 965-978. Kaden E, Kruggel F, Alexander D C. Quantitative mapping of the per‐axon diffusion coefficients in brain white matter. Mag. Reson. Med. 2016; 75(4):1752-1763. Veraart J, Fieremans E, Novikov D S. Universal power-law scaling of water diffusion in human brain defines what we see with MRI. arXiv preprint2016; arXiv:1609.09145. McKinnon E T, Jensen J H, Glenn G R, Helpern J A. Dependence on b-value of the direction-averaged diffusion-weighted imaging signal in brain.Mag. Reson. Imag. 2017; 36: 121-127. Cook P A, Bai Y, Nedjati-Gilani S K K S, Seunarine K K, Hall M G, Parker G J, Alexander D C. Camino: open-source diffusion-MRI reconstructionand processing. In 14th scientific meeting of the international society for magnetic resonance in medicine 2004 (Vol. 2759). Seattle WA, USA. Yang D M, Huettner J E, Bretthorst G L, Neil J J, Garbow J R, Ackerman J J H. Intracellular water preexchange lifetime in neurons and astrocytes.Magn. Reson. Med. 2017; doi:10.1002/mrm.26781 Setsompop K, Kimmlingen R, Eberlein E, Witzel T, Cohen-Adad J, McNab JA, et al. Pushing the limits of in vivo diffusion MRI for the humanconnectome project. NeuroImage 2013; 80: 220–33.soma somasoma≤GM WM GM WM2123456789Figures07/11/2017, 23)32Page 3 of 4https://submissions.mirasmart.com/ISMRM2018/ViewSubmission.aspx?sbmID=6170Fig.1 Three-dimensional mesh of intracellular compartment at different rsegment, rsoma and corresponding fsoma conditions. Many randomlyoriented cylindrical segments of radius r =0.25-0.80 µm and 200 µm long (neurites) were projected from a spherical compartment (soma) ofradius r =3-10 µm (zoomed inset), leading to a fraction of the total cell volume occupied by the soma, f =0-0.9. The diffusion of 5x10  non-interacting spins was simulated within each synthetic geometry with the bulk diffusivity 1 µm /ms in CAMINO . From the resulting spins’ trajectories,the DW-MRI signals, as measured by a PGSE sequence, were computed (δ/Δ=10/20 ms, b=0-100 ms/µm ).Fig.2 Normalized signal attenuation as a function of b  for different f  (a) and r  (b) conditions (with r =0.50 µm). The shaded boxdefines the high b-value range currently accessible in human studies and used to fit relation (1) using approaches (i) and (ii). In the inset, an exampleof relation (1) fitted to the simulated signals using approaches (i) and (ii). Fitted parameters values are reported in each plot. c-d) Fitted parameters αand γ, for different (r ,f ) conditions. The size and color of the points in the plot corresponds to 2r , as indicated by the colorbar.Fig.3 Parametric maps of α, β and γ obtained by fitting voxel-wise the relation (1) to experimental data (ex-vivo rat brain on the left; in-vivo humanbrain on the right) using approach (i) (top row) and (ii) (bottom row), for 3≤b≤15 ms/µm . Note the strong contrast between WM and GM in both α andγ maps, with overall α and γ values lower in GM compared to WM.segmentsoma soma 52 72-1/2 soma soma segmentsoma soma soma207/11/2017, 23)32Page 4 of 4https://submissions.mirasmart.com/ISMRM2018/ViewSubmission.aspx?sbmID=6170Fig.4 Region-of-interest (ROI) average values (error bars stand for standard deviation) of fitted γ, with approach (i), and α, with approach (ii) for the ex-vivo rat brain and the in-vivo human brain in GM (gray bars) and WM (white bars). Note the much lower α and γ values in GM compared to WM ROIs(***: p<0.001). Labels of each ROI: Hip=Hippocampus; Thal=Thalamus; Put=Putamen; Cor=Cortex; Cer=Cerebellum; CC=Corpus Callosum; IC=Internal Capsule.

Abundance of cell bodies can explain the stick model’s failure in grey matter at high bvalue

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Abundance of cell bodies can explain the stick model’s failure in grey matter at high bvalue

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