Models and gradients

Units

SpinDoctor uses micrometers and microseconds:

Quantity	Unit	Example
Length	µm
Time	µs	PGSE(5000.0, 20000.0): 5 and 20 ms
Diffusion coefficient	µm²/µs	0.002 is 2 × 10⁻³ mm²/s (water)
b-value	µs/µm² (= s/mm²)	1000
Permeability, relaxivity	µm/µs (= m/s)	1e-5
Gradient amplitude	T/m
Gyromagnetic ratio	rad / (µs µm T/m)	2.67513e-4 for water protons

Model

A Model contains the mesh and the coefficients of each compartment (initial spin density rho, diffusion tensor D, relaxation time T2) and of each boundary (permeability or relaxivity kappa), and the gyromagnetic ratio gamma. coefficients distributes the coefficients of the layers and the ECS of a recipe over the compartments and boundaries:

coeffs = coefficients(
    setup;
    D = (; cell = [0.002 * I(3), 0.0005 * I(3)], ecs = 0.002 * I(3)),
    T2 = (; cell = [Inf, Inf], ecs = Inf),
    rho = (; cell = [1.0, 1.0], ecs = 1.0),
    kappa = (; cell_interfaces = [1e-5], cell_boundaries = [0, 0], cell_ecs = 1e-5, ecs = 0),
    gamma = 2.67513e-4,
)
model = Model(; mesh, coeffs...)
matrices = assemble_matrices(model)

The diffusion tensor of a compartment may also vary: a vector with one tensor per element of the compartment (e.g. from diffusion tensor imaging) replaces the constant tensor, in the same order as mesh.elements[i].

assemble_matrices assembles the finite element matrices, in parallel on all Julia threads (start Julia with --threads=auto). compartment_weights gives the contribution of each compartment to the signal without gradient.

Gradient sequences

A ScalarGradient has a fixed direction and a time profile:

• PGSE: two pulses of duration delta, separated by Delta;

• DoublePGSE: two PGSE sequences;

• CosOGSE and SinOGSE: oscillating gradients.

The amplitude is given directly, or by the b-value:

gradient = ScalarGradient([1.0, 0.0, 0.0], PGSE(5000.0, 20000.0); bvalue = 1000, gamma)
bvalue(gradient, gamma)

A GeneralGradient is any function of time, with a varying direction. Directions for high angular resolution imaging are given by unitcircle and unitsphere.