Tissue Compartments

Compartment Type is an abstract type that includes the Cylinder, Stick, Zeppelin, Sphere and Iso type. A Compartment Type object contains relevant tissue parameters that affect the MRI signals. Each type of compartment contain a t2 field for combined-diffusion-T2 imaging. When your data supports only T2-weighted compartment modelling, i.e. acquired with single-TE, set the t2 field to zero for conventional dMRI modelling.

Cylinder(
    da::Float64, 
    dpara::Float64, 
    d0::Float64, 
    t2::Float64
    )

Return a Cylinder Type object with the cylinder diameter da, parallel diffusivity dpara, the intrinsic diffusivity d0 and the T2 relaxation time t2.

Examples

julia> Cylinder(da = 3.0e-6, dpara = 1.8e-9, d0 = 1.7e-9, t2 = 90e-3)
Cylinder(3.0e-6, 1.8e-9, 1.7e-9, 0.09)

Stick(dpara::Float64, t2::Float64)

Return a Stick Type object with parallel diffusivity dpara and T2 relaxation time t2. The perpendicular diffusivity of a Stick model is zero.

Examples

julia> Stick(dpara = 1.7e-6, t2 = 60e-3)
Stick(1.7e-6, 0.06)

Zeppelin(
    dpara::Float64, 
    dperp_frac::Float64, 
    t2::Float64
    )

Return a Zeppelin Type object with parallel diffusivity dpara, axially symmetric perpendicular diffusivity represented as a fraction of the parallel diffusivity dperp_frac, and the T2 relaxation time t2.

Examples

julia> Zeppelin(dpara = 1.7e-6, dperp_frac = 0.5, t2 = 0.0)
Zeppelin(1.7e-6, 0.5, 0.0)

Sphere(
    diff::Float64, 
    size::Float64, 
    t2::Float64
    )

Return a Sphere Type object with diffusivity within sphere diff, spherical radius size, and T2 relaxation time t2.

Examples

julia> Sphere(diff = 3.0e-9, size = 8.0e-6, t2 = 45e-3)
Sphere(3.0e-9, 8.0e-6, 0.045)

Iso(diff::Float64, t2=Float64)

Return an isotropic tensor with diffusivity diff and T2 relaxation time t2. This compartment can be used to represent CSF (diff = free water) or dot compartment (diff = 0). The latter is for immobile water typically seen in ex vivo tissue. This compartment can also represent an isotropic extra-cellular environment with diffusivity diff slower than free water.

Examples

julia> Iso(diff = 3.0e-9,t2 = 2000.0e-3)
Iso(3.0e-9, 2.0)

julia> Iso(diff = 0.0)
Iso(0.0, 0.0)

compartment_signals(model::Compartment,protocol::Protocol)

Return compartment signals given a compartment object model and a imaging protocol. model can be the Cylinder/Zeppelin/Stick/Sphere/Iso Type. When t2 in compartment model is set as default (0), relaxation-weightings are not considered in the signal equation.

References

If you use these compartments to build models, please cite the recommended references.

For using any compartment in current release, please cite the following references for expressions of spherical mean/power averaging:

Callaghan, P.T., Jolley, K.W., Lelievre, J., 1979. Diffusion of water in the endosperm tissue of wheat grains as studied by pulsed field gradient nuclear magnetic resonance. Biophys J 28, 133. https://doi.org/10.1016/S0006-3495(79)85164-4

Kroenke, C.D., Ackerman, J.J.H., Yablonskiy, D.A., 2004. On the nature of the NAA diffusion attenuated MR signal in the central nervous system. Magn Reson Med 52, 1052–1059. https://doi.org/10.1002/MRM.20260

Kaden, E., Kruggel, F., Alexander, D.C., 2016. Quantitative mapping of the per-axon diffusion coefficients in brain white matter. Magn Reson Med 75, 1752–1763. https://doi.org/10.1002/MRM.25734

Consider the following reference for overview of all tissue compartments:

Panagiotaki, E., Schneider, T., Siow, B., Hall, M.G., Lythgoe, M.F., Alexander, D.C., 2012. Compartment models of the diffusion MR signal in brain white matter: A taxonomy and comparison. Neuroimage 59, 2241–2254.

Cylinder compartment:

Van Gelderen, P., Des Pres, D., Van Zijl, P.C.M., Moonen, C.T.W., 1994. Evaluation of Restricted Diffusion in Cylinders. Phosphocreatine in Rabbit Leg Muscle. J Magn Reson B 103, 255–260. https://doi.org/10.1006/JMRB.1994.1038

Alexander, D.C., Hubbard, P.L., Hall, M.G., Moore, E.A., Ptito, M., Parker, G.J.M., Dyrby, T.B., 2010. Orientationally invariant indices of axon diameter and density from diffusion MRI. Neuroimage 52, 1374–1389. https://doi.org/10.1016/j.neuroimage.2010.05.043

Fan, Q., Nummenmaa, A., Witzel, T., Ohringer, N., Tian, Q., Setsompop, K., Klawiter, E.C., Rosen, B.R., Wald, L.L., Huang, S.Y., 2020. Axon diameter index estimation independent of fiber orientation distribution using high-gradient diffusion MRI. Neuroimage 222.

Andersson, M., Pizzolato, M., Kjer, H.M., Skodborg, K.F., Lundell, H., Dyrby, T.B., 2022. Does powder averaging remove dispersion bias in diffusion MRI diameter estimates within real 3D axonal architectures? Neuroimage 248.

Sphere compartment:

Neuman, C.H., 1974. Spin echo of spins diffusing in a bounded medium. J Chem Phys 4508–4511. https://doi.org/10.1063/1.1680931

Balinov, B., Jönsson, B., Linse, P., Söderman, O., 1993. The NMR Self-Diffusion Method Applied to Restricted Diffusion. Simulation of Echo Attenuation from Molecules in Spheres and between Planes. J Magn Reson A 104, 17–25. https://doi.org/10.1006/JMRA.1993.1184

Stick compartment:

Behrens, T.E.J., Woolrich, M.W., Jenkinson, M., Johansen-Berg, H., Nunes, R.G., Clare, S., Matthews, P.M., Brady, J.M., Smith, S.M., 2003. Characterization and Propagation of Uncertainty in Diffusion-Weighted MR Imaging. Magn Reson Med 50, 1077–1088. https://doi.org/10.1002/MRM.10609

Panagiotaki, E., Schneider, T., Siow, B., Hall, M.G., Lythgoe, M.F., Alexander, D.C., 2012. Compartment models of the diffusion MR signal in brain white matter: A taxonomy and comparison. Neuroimage 59, 2241–2254.

Zhang, H., Schneider, T., Wheeler-Kingshott, C.A., Alexander, D.C., 2012. NODDI: Practical in vivo neurite orientation dispersion and density imaging of the human brain. Neuroimage 61, 1000–1016. https://doi.org/10.1016/j.neuroimage.2012.03.072

Zeppelin & Iso:

Alexander, D.C., 2008. A General Framework for Experiment Design in Diffusion MRI and Its Application in Measuring Direct Tissue-Microstructure Features. Magn Reson Med 60, 439–448. https://doi.org/10.1002/mrm.21646

Panagiotaki, E., Schneider, T., Siow, B., Hall, M.G., Lythgoe, M.F., Alexander, D.C., 2012. Compartment models of the diffusion MR signal in brain white matter: A taxonomy and comparison. Neuroimage 59, 2241–2254.

Zhang, H., Schneider, T., Wheeler-Kingshott, C.A., Alexander, D.C., 2012. NODDI: Practical in vivo neurite orientation dispersion and density imaging of the human brain. Neuroimage 61, 1000–1016. https://doi.org/10.1016/j.neuroimage.2012.03.072

Compartmental T2-weighting:

Veraart, J., Novikov, D.S., Fieremans, E., 2017. TE dependent Diffusion Imaging (TEdDI) distinguishes between compartmental T2 relaxation times. https://doi.org/10.1016/j.neuroimage.2017.09.030

Lampinen, B., Szczepankiewicz, F., Novén, M., van Westen, D., Hansson, O., Englund, E., Mårtensson, J., Westin, C.F., Nilsson, M., 2019. Searching for the neurite density with diffusion MRI: Challenges for biophysical modeling. Hum Brain Mapp 40, 2529–2545. https://doi.org/10.1002/hbm.24542

Gong, T., Tong, Q., He, H., Sun, Y., Zhong, J., Zhang, H., 2020. MTE-NODDI: Multi-TE NODDI for disentangling non-T2-weighted signal fractions from compartment-specific T2 relaxation times. Neuroimage 217. https://doi.org/10.1016/j.neuroimage.2020.116906

Gong, T., Tax, C.M., Mancini, M., Jones, D.K., Zhang, H., Palombo, M., 2023. Multi-TE SANDI: Quantifying compartmental T2 relaxation times in the grey matter. Toronto.

Kernel functions of the Zeppelin/Stick/Iso compartments are also included for standard model imaging using higher order rotational invariants:

Novikov, D.S., Veraart, J., Jelescu, I.O. and Fieremans, E., 2018. Rotationally-invariant mapping of scalar and orientational metrics of neuronal microstructure with diffusion MRI. NeuroImage, 174, pp.518-538.

Novikov, D.S., Fieremans, E., Jespersen, S.N. and Kiselev, V.G., 2019. Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation. NMR in Biomedicine, 32(4), p.e3998.

Coelho, S., Baete, S.H., Lemberskiy, G., Ades-Aron, B., Barrol, G., Veraart, J., Novikov, D.S. and Fieremans, E., 2022. Reproducibility of the standard model of diffusion in white matter on clinical MRI systems. NeuroImage, 257, p.119290.