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iCAPs/packages/spm12/spm_dcm_fmri_nmm.m
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spm_dcm_fmri_nmm.m
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function [DCM] = spm_dcm_fmri_nmm(P)
% Estimates parameters of a DCM (neural mass model) for fMRI data
% FORMAT [DCM] = spm_dcm_estimate(DCM)
% DCM - DCM structure or its filename
%
% Expects
%--------------------------------------------------------------------------
% DCM.a % switch on endogenous connections
% DCM.b % switch on bilinear modulations
% DCM.c % switch on exogenous connections
% DCM.U % exogenous inputs
% DCM.Y.y % responses
% DCM.Y.X0 % confounds
% DCM.Y.Q % array of precision components
% DCM.n % number of regions
% DCM.v % number of scans
%
% Options
%--------------------------------------------------------------------------
% DCM.options.nmm % neural mass model
% DCM.options.centre % mean-centre inputs
% DCM.options.nograph % graphical display
% DCM.options.P % starting estimates for parameters
% DCM.options.hidden % indices of hidden regions
% DCM.options.maxnodes % maximum number of (effective) nodes
% DCM.options.maxit % maximum number of iterations
% DCM.options.hE % expected precision of the noise
% DCM.options.hC % variance of noise expectation
%
% Evaluates:
%--------------------------------------------------------------------------
% DCM.M % Model structure
% DCM.Ep % Condition means (parameter structure)
% DCM.Cp % Conditional covariances
% DCM.Vp % Conditional variances
% DCM.Pp % Conditional probabilities
% DCM.H1 % 1st order hemodynamic kernels
% DCM.H2 % 2nd order hemodynamic kernels
% DCM.K1 % 1st order neuronal kernels
% DCM.K2 % 2nd order neuronal kernels
% DCM.R % residuals
% DCM.y % predicted data
% DCM.T % Threshold for Posterior inference
% DCM.Ce % Error variance for each region
% DCM.F % Free-energy bound on log evidence
% DCM.ID % Data ID
% DCM.AIC % Akaike Information criterion
% DCM.BIC % Bayesian Information criterion
%
%__________________________________________________________________________
% Copyright (C) 2002-2012 Wellcome Trust Centre for Neuroimaging
% Karl Friston
% $Id: spm_dcm_fmri_nmm.m 6922 2016-11-02 17:28:23Z karl $
SVNid = '$Rev: 6922 $';
%-Load DCM structure
%--------------------------------------------------------------------------
if ~nargin
%-Display model details
%----------------------------------------------------------------------
Finter = spm_figure('GetWin','Interactive');
set(Finter,'name','Dynamic Causal Modelling')
%-Get DCM
%----------------------------------------------------------------------
[P, sts] = spm_select(1,'^DCM.*\.mat$','select DCM_???.mat');
if ~sts, DCM = []; return; end
spm('Pointer','Watch')
spm('FigName','Estimation in progress');
end
if isstruct(P)
DCM = P;
P = ['DCM-' date '.mat'];
else
load(P)
end
% check options
%==========================================================================
try, DCM.options.nmm; catch, DCM.options.nmm = 'TFM'; end
try, DCM.options.two_state; catch, DCM.options.two_state = 0; end
try, DCM.options.stochastic; catch, DCM.options.stochastic = 0; end
try, DCM.options.nonlinear; catch, DCM.options.nonlinear = 0; end
try, DCM.options.centre; catch, DCM.options.centre = 0; end
try, DCM.options.hidden; catch, DCM.options.hidden = []; end
try, DCM.options.hE; catch, DCM.options.hE = 6; end
try, DCM.options.hC; catch, DCM.options.hC = 1/128; end
try, DCM.options.maxit; catch, DCM.options.maxit = 32; end
try, DCM.options.maxnodes; catch, DCM.options.maxnodes = 16; end
try, DCM.n; catch, DCM.n = size(DCM.c,1); end
try, DCM.v; catch, DCM.v = size(DCM.Y.y,1); end
try, M.nograph = DCM.options.nograph; catch, M.nograph = spm('CmdLine'); end
try, M.Nmax = DCM.M.Nmax; catch, M.Nmax = DCM.options.maxit; end
% unpack
%--------------------------------------------------------------------------
U = DCM.U; % exogenous inputs
Y = DCM.Y; % responses
n = DCM.n; % number of regions
v = DCM.v; % number of scans
% detrend outputs (and inputs)
%--------------------------------------------------------------------------
Y.y = spm_detrend(Y.y);
if DCM.options.centre
U.u = spm_detrend(U.u);
end
% check scaling of Y (enforcing a maximum change of 4%)
%--------------------------------------------------------------------------
scale = max(max((Y.y))) - min(min((Y.y)));
scale = 4/max(scale,4);
Y.y = Y.y*scale;
Y.scale = scale;
% check confounds (add constant if necessary)
%--------------------------------------------------------------------------
if ~isfield(Y,'X0'),Y.X0 = ones(v,1); end
if ~size(Y.X0,2), Y.X0 = ones(v,1); end
% fMRI slice time sampling
%--------------------------------------------------------------------------
try, M.delays = DCM.delays; catch, M.delays = ones(n,1); end
try, M.TE = DCM.TE; end
% create priors
%==========================================================================
% priors (and initial states) - neuronal
%--------------------------------------------------------------------------
[nE,nC] = spm_dcm_neural_priors(DCM.a,DCM.b,DCM.c,DCM.options.nmm);
[xn,fn] = spm_dcm_x_neural(nE,DCM.options.nmm);
% fix some neuronal (neural mass) parameters
%--------------------------------------------------------------------------
p = {'T','D','R','G'};
for i = 1:numel(p)
try
nC.(p{i}) = spm_zeros(nC.(p{i}));
end
end
pE.N = rmfield(nE,{'M','N','E','F'});
pC.N = rmfield(nC,{'M','N','E','F'});
% add neurovascular parameters
%--------------------------------------------------------------------------
pE.J = sparse(4,3); pC.J = sparse(4,3) + 1/16;
% and hemodynamic priors
%--------------------------------------------------------------------------
bE.transit = sparse(n,1); bC.transit = sparse(n,1) + 1/256;
bE.decay = sparse(n,1); bC.decay = sparse(n,1) + 1/256;
bE.epsilon = sparse(1,1); bC.epsilon = sparse(1,1) + 1/256;
x.x = xn;
x.h = sparse(n,4);
pE.H = bE;
pC.H = bC;
% Using specified priors
%--------------------------------------------------------------------------
str = 'Using specified priors';
try, M.P = DCM.options.P; end % initial parameters
try, pE = DCM.options.pE; fprintf(str); end % prior expectation
try, pC = DCM.options.pC; fprintf(str); end % prior covariance
% hyperpriors over precision - expectation and covariance
%--------------------------------------------------------------------------
hE = sparse(n,1) + DCM.options.hE;
hC = speye(n,n) * DCM.options.hC;
i = DCM.options.hidden;
hE(i) = -4;
hC(i,i) = exp(-16);
% complete model specification
%--------------------------------------------------------------------------
M.IS = @spm_gen_fmri; % integration scheme
M.fn = fn; % neuronal equations of motion
M.x = x; % initial condition (states)
M.pE = pE; % prior expectation (parameters)
M.pC = pC; % prior covariance (parameters)
M.hE = hE; % prior expectation (precisions)
M.hC = hC; % prior covariance (precisions)
M.m = size(U.u,2);
M.n = size(spm_vec(x),1);
M.l = n;
M.ns = v;
% nonlinear system identification (Variational Laplace)
%==========================================================================
[Ep,Cp,Eh,F] = spm_nlsi_GN(M,U,Y);
% predicted responses (y) and residuals (R)
%--------------------------------------------------------------------------
y = feval(M.IS,Ep,M,U);
R = Y.y - y;
R = R - Y.X0*spm_inv(Y.X0'*Y.X0)*(Y.X0'*R);
Ce = exp(-Eh);
% Bilinear representation and first-order hemodynamic kernel
%--------------------------------------------------------------------------
H.f = @spm_fx_hdm;
H.g = @spm_gx_hdm;
H.x = M.x.h;
H.m = M.m;
[H0,H1] = spm_kernels(H,Ep.H,64,1/2);
% and neuronal kernels
%--------------------------------------------------------------------------
N.f = M.fn;
N.x = M.x.x;
N.m = M.m;
[K0,K1] = spm_kernels(N,Ep.N,64,8/1000);
% Bayesian inference and variance
%--------------------------------------------------------------------------
T = full(spm_vec(pE));
sw = warning('off','SPM:negativeVariance');
Pp = spm_unvec(1 - spm_Ncdf(T,abs(spm_vec(Ep)),diag(Cp)),Ep);
Vp = spm_unvec(full(diag(Cp)),Ep);
warning(sw);
try, M = rmfield(M,'nograph'); end
% Store parameter estimates
%--------------------------------------------------------------------------
DCM.M = M;
DCM.Y = Y;
DCM.U = U;
DCM.Ce = Ce;
DCM.Ep = Ep;
DCM.Cp = Cp;
DCM.Pp = Pp;
DCM.Vp = Vp;
DCM.H1 = H1;
DCM.K1 = K1;
DCM.R = R;
DCM.y = y;
DCM.T = 0;
% Data ID and log-evidence
%==========================================================================
if isfield(M,'FS')
try
ID = spm_data_id(feval(M.FS,Y.y,M));
catch
ID = spm_data_id(feval(M.FS,Y.y));
end
else
ID = spm_data_id(Y.y);
end
% Save approximations to model evidence: negative free energy, AIC, BIC
%--------------------------------------------------------------------------
evidence = spm_dcm_evidence(DCM);
DCM.F = F;
DCM.ID = ID;
DCM.AIC = evidence.aic_overall;
DCM.BIC = evidence.bic_overall;
% Save SPM version and revision number of code used
%--------------------------------------------------------------------------
[DCM.version.SPM.version, DCM.version.SPM.revision] = spm('Ver');
DCM.version.DCM.version = spm_dcm_ui('Version');
DCM.version.DCM.revision = SVNid;
%-Save DCM
%--------------------------------------------------------------------------
if ~isstruct(P)
save(P,'DCM','F','Ep','Cp', spm_get_defaults('mat.format'));
end
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