NEXI

Neurite EXchange Imaging based on diffusion MRI (dMRI).

gpuNEXI

NEXI with askAdam solver.

Usage

obj = gpuNEXI(bval, BDELTA);
out = obj.estimate(dwi, mask, extradata, fitting);

Model parameters

% fa        : Neurite volume fraction
% Da        : longitudinal diffusivity of neurite [ms/us^2]
% De        : diffusivity of extracellular water [ms/us^2]
% ra        : exchange rate from neurite to extracellular space [1/s]
% p2        : non-linear neurite dispersion index
model_params    = {'fa','Da','De','ra','p2'};
ub              = [   1,   3,   3,   1,  1];
lb              = [ eps, eps, eps,1/250, eps];
startpoint      = [ 0.4,   2,   1, 0.05, 0.2];

I/O overview

obj = gpuNEXI(bval, BDELTA);

Input	Description
bval	1xNshell b-values vector [ms/um2]
BDELTA	1xNshell diffusion time, same size as ‘bval’ [ms]

out = obj.estimate(dwi, mask, extradata, fitting);

Input	Description
dwi	4D dMRI data, can be either full acquisition or SMT signal [x,y,z,diffusion]
mask	3D mask, [x,y,z]
extradata	Structure array with additional data (Optional)
extradata.bval	1D b-values [1xdiffusion], same order as ‘dwi’ [ms/um2] (Optional, only if ‘dwi’ is full acquisition)
extradata.bvec	2D b-vector [3xdiffusion], same order as ‘dwi’ (Optional, only if ‘dwi’ is full acquisition)
extradata.ldelta	1D gradient duration [1xdiffusion], same order as ‘dwi’ [ms] (Optional, only if ‘dwi’ is full acquisition)
extradata.BDELTA	1D diffusion time [1xdiffusion], same order as ‘dwi’ [ms] (Optional, only if ‘dwi’ is full acquisition)
fitting	Structure array for model parameter estimation
fitting.optimiser	Algorithm for parameter update, ‘adam’ (default) | ‘sgdm’ | ‘rmsprop’
fitting.isdisplay	boolean, display optimisation process in graphic plot
fitting.convergenceValue	tolerance in loss gradient to stop the optimisation
fitting.convergenceWindow	# of elements in which ‘convergenceValue’ is computed
fitting.iteration	maximum # of optimisation iterations
fitting.initialLearnRate	initial learn rate of Adam optimiser
fitting.tol	tolerance in loss
fitting.lambda	regularisation parameter(s)
fitting.regmap	model parameter(s) in which regularisation is applied, ‘fa’|’ra’|’Da’|’De’
fitting.TVmode	Mode for total variation (TV) regularisation, ‘2D’|’3D’
fitting.lossFunction	loss function, ‘L1’|’L2’|’huber’|’mse’
fitting.lmax	Maximum order of rotational invariant, 0|2, default = 0
fitting.isPrior	Starting point estimated based on likelihood method instead of fix/random location

Output	Description
out	structure contains optimisation result
out.final	output structure at final iteration
out.final.loss	total loss = loss_fidelity + loss_reg
out.final.loss_fidelity	loss of data consistency term
out.final.loss_reg	loss of regularisation term
out.final.(model_params{k})	estimated model parameter(s)
out.min	output structure at loss is minimum

See example here.

gpuNEXImcmc

NEXI with MCMC solver.

Usage

obj = gpuNEXImcmc(bval, BDELTA);
out = obj.estimate(dwi, mask, extradata, fitting);

Model parameters

% fa        : Intraneurite volume fraction
% Da        : Intraneurite diffusivity (um2/ms)
% De        : Extraneurite diffusivity (um2/ms)
% ra        : exchange rate from intra- to extra-neurite compartment
% p2        : dispersion index (if fitting.lmax=2)
% default model parameters and estimation boundary
model_params    = { 'fa';   'Da';   'De';   'ra';'p2'; 'noise'};
ub              = [    1;      3;      3;      1;   1;     0.1];
lb              = [    0;  0.002;  0.001;  1/250;   0;    0.01];
step            = [  0.05;  0.15;   0.15;  0.005;0.05;   0.005];
startpoint      = [  0.2;      2;    0.5;   0.05; 0.2;    0.05];

I/O overview

obj = gpuNEXImcmc(bval, BDELTA);

Input	Description
bval	1xNshell unique b-values vector [ms/um2]
BDELTA	1xNshell diffusion time, same size as ‘bval’ [ms]

out = obj.estimate(dwi, mask, extradata, fitting);

Input	Description
dwi	4D dMRI data, can be either full acquisition or SMT signal [x,y,z,diffusion]
mask	3D mask, [x,y,z]
extradata	Structure array with additional data (Optional)
extradata.bval	1D b-values [1xdiffusion], same order as ‘dwi’ [ms/um2] (Optional, only if ‘dwi’ is full acquisition)
extradata.bvec	2D b-vector [3xdiffusion], same order as ‘dwi’ (Optional, only if ‘dwi’ is full acquisition)
extradata.ldelta	1D gradient duration [1xdiffusion], same order as ‘dwi’ [ms] (Optional, only if ‘dwi’ is full acquisition)
extradata.BDELTA	1D diffusion time [1xdiffusion], same order as ‘dwi’ [ms] (Optional, only if ‘dwi’ is full acquisition)
fitting	Structure array for model parameter estimation
fitting.algorithm	MCMC algorithm, ‘MH’ (Metropolis-Hastings)|’GW’ (Affline-invariant ensemble)
fitting.iteration	# MCMC iterations
fitting.repetition	# repetition of MCMC proposal
fitting.thinning	sampling interval between iterations
fitting.burnin	iterations to be discarded at the beginning, if >1, the exact number will be used; else iteration*burnin
fitting.xStepSize	step size of model parameter in MCMC proposal, same size and order as ‘model_params’ (‘MH’ only)
fitting.StepSize	step size for ‘GW’ in MCMC proposal (‘GW’ only)
fitting.Nwalker	# random walkers (‘GW’ only)
fitting.metric	cell variable, metric(s) derived from posterior distribution, ‘mean’|’std’|’median’|’iqr’ (can be multiple)
fitting.start	Starting point methods, ‘likelihood’|’default’|1xM parameters array

Output	Description
out	structure contains optimisation result
out.posterior	structure contains MCMC posterior samples
out.posterior.(model_params{k})	Model parameter MCMC posterior samples, masked and unshaped for memory preservation
out.{metric}.(model_params{k})	Posterior statistics chosen in fitting.metric

See example here.