References
J.-R. Li, V.-D. Nguyen, T. N. Tran, J. Valdman, C.-B. Trang, K. V. Nguyen, D. T. Vu, H. A. Tran, H. T. Tran and T. M. Nguyen. SpinDoctor: A MATLAB toolbox for diffusion MRI simulation. NeuroImage 202, 116120 (2019).
H. Si. TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator. ACM Trans. Math. Softw. 41, 11:1–11:36 (2015).
D. V. Nguyen, J.-R. Li, D. Grebenkov and D. L. Bihan. A finite elements method to solve the Bloch–Torrey equation applied to diffusion magnetic resonance imaging. Journal of Computational Physics 263, 283–302 (2014).
S. D. Agdestein, T. N. Tran and J.-R. Li. Practical computation of the diffusion MRI signal based on Laplace eigenfunctions: permeable interfaces. NMR in Biomedicine, e4646 (2022), arXiv:https://analyticalsciencejournals.onlinelibrary.wiley.com/doi/pdf/10.1002/nbm.4646.
C. Fang, V.-D. Nguyen, D. Wassermann and J.-R. Li. Diffusion MRI simulation of realistic neurons with SpinDoctor and the Neuron Module. NeuroImage 222, 117198 (2020).
D. S. Grebenkov. Pulsed-gradient spin-echo monitoring of restricted diffusion in multilayered structures. Journal of Magnetic Resonance 205, 181–195 (2010).
G. A. Ascoli, D. E. Donohue and M. Halavi. NeuroMorpho.Org: A Central Resource for Neuronal Morphologies. Journal of Neuroscience 27, 9247–9251 (2007), arXiv:http://www.jneurosci.org/content/27/35/9247.full.pdf.
K. K. Watson, T. K. Jones and J. M. Allman. Dendritic architecture of the von Economo neurons. Neuroscience 141, 1107–1112 (2006).
H.-H. Lee, E. Fieremans and D. S. Novikov. Realistic Microstructure Simulator (RMS): Monte Carlo simulations of diffusion in three-dimensional cell segmentations of microscopy images. Journal of Neuroscience Methods 350, 109018 (2021).
E. O. Stejskal and J. E. Tanner. Spin Diffusion Measurements: Spin Echoes in the Presence of a Time-Dependent Field Gradient. The Journal of Chemical Physics 42, 288–292 (1965).
P. T. Callaghan and J. Stepianik. Frequency-Domain Analysis of Spin Motion Using Modulated-Gradient NMR. Journal of Magnetic Resonance, Series A 117, 118–122 (1995).
M. D. Does, E. C. Parsons and J. C. Gore. Oscillating gradient measurements of water diffusion in normal and globally ischemic rat brain. Magn. Reson. Med. 49, 206–215 (2003).
J. Xu, M. Does and J. Gore. Numerical study of water diffusion in biological tissues using an improved finite difference method. Physics in medicine and biology 52 (2007).
S. Schiavi, H. Haddar and J.-R. Li. A macroscopic model for the diffusion MRI signal accounting for time-dependent diffusivity. SIAM Journal on Applied Mathematics (2016). Accepted.
P. P. Mitra, P. N. Sen, L. M. Schwartz and P. Le Doussal. Diffusion propagator as a probe of the structure of porous media. Physical review letters 68, 3555–3558 (1992).
P. P. Mitra, P. N. Sen and L. M. Schwartz. Short-time behavior of the diffusion coefficient as a geometrical probe of porous media. Phys. Rev. B 47, 8565–8574 (1993).
P. Callaghan. A Simple Matrix Formalism for Spin Echo Analysis of Restricted Diffusion under Generalized Gradient Waveforms. Journal of Magnetic Resonance 129, 74–84 (1997).
A. V. Barzykin. Theory of spin echo in restricted geometries under a step-wise gradient pulse sequence. Journal of Magnetic Resonance 139, 342–353 (1999).
J. R. Shewchuk. Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator. In: Applied Computational Geometry: Towards Geometric Engineering, Vol. 1148 of Lecture Notes in Computer Science, edited by M. C. Lin and D. Manocha (Springer-Verlag, 1996); pp. 203–222. From the First ACM Workshop on Applied Computational Geometry.
T. Rahman and J. Valdman. Fast MATLAB assembly of FEM matrices in 2D and 3D: nodal elements. Applied Mathematics and Computation 219, 7151–7158 (2013).
J.-R. Li, T. Tran and V.-D. Nguyen. Practical computation of the diffusion MRI signal of realistic neurons based on Laplace eigenfunctions. NMR in Biomedicine 33 (2020).
D. Grebenkov. NMR survey of reflected Brownian motion. Reviews of Modern Physics 79, 1077–1137 (2007).