feComputeSignal

 Compute expected diffusion signal from tensor

  S = feComputeSignal(S0, bvals, bvecs, Q)

 This function implements the Stejskal Tanner equation prediction given a
 quadratic form.  There should also be a form of this equation that takes
 in the ADC values, rather than the quadratic form.

 This is a version of the Stejskal/Tanner equation for signal attenuation
 See: http://en.wikipedia.org/wiki/Diffusion_MRI#Diffusion_imaging

 We need a better description of the expected parameter format (BW).

 INPUTS
   S0    - The signal measured in the non-diffusion weighted scans (B0)  
   bvals - the b values
   bvecs - the b vectors
   Q     - The tensors (quadratic forms) (e.g. see fgTensors) corresponding
           to each node in a voxel. There are often several tensors.  

 OUTPUTS
   S     - The signal predicted according to this form of the Stejskal/Tanner eq: 
 
         S = S0 exp(-bval*(bvec*Q*bvec))

    There is a column of signals for each of the tensors.  So if there are
    30 directions and 4 tensors, then the returned signals is 30 x 4.

 Example:

 Copyright (2013-2014), Franco Pestilli, Stanford University, pestillifranco@gmail.com.

0001 function S = feComputeSignal(S0, bvecs, bvals, Q)
0002 % Compute expected diffusion signal from tensor
0003 %
0004 %  S = feComputeSignal(S0, bvals, bvecs, Q)
0005 %
0006 % This function implements the Stejskal Tanner equation prediction given a
0007 % quadratic form.  There should also be a form of this equation that takes
0008 % in the ADC values, rather than the quadratic form.
0009 %
0010 % This is a version of the Stejskal/Tanner equation for signal attenuation
0011 % See: http://en.wikipedia.org/wiki/Diffusion_MRI#Diffusion_imaging
0012 %
0013 % We need a better description of the expected parameter format (BW).
0014 %
0015 % INPUTS
0016 %   S0    - The signal measured in the non-diffusion weighted scans (B0)
0017 %   bvals - the b values
0018 %   bvecs - the b vectors
0019 %   Q     - The tensors (quadratic forms) (e.g. see fgTensors) corresponding
0020 %           to each node in a voxel. There are often several tensors.
0021 %
0022 % OUTPUTS
0023 %   S     - The signal predicted according to this form of the Stejskal/Tanner eq:
0024 %
0025 %         S = S0 exp(-bval*(bvec*Q*bvec))
0026 %
0027 %    There is a column of signals for each of the tensors.  So if there are
0028 %    30 directions and 4 tensors, then the returned signals is 30 x 4.
0029 %
0030 % Example:
0031 %
0032 % Copyright (2013-2014), Franco Pestilli, Stanford University, pestillifranco@gmail.com.
0033 
0034 % Converts the tensors and bvecs into ADC values.  If there are 80
0035 % directions and 4 tensors, the returned ADC is 80 x 4, with each column
0036 % representing the ADCs in all directions for one of the tensors.
0037 % ADC = dtiADC(Q, bvecs);
0038 %
0039 % We have a bval for each ADC:     S = S0 * exp(-bvals .* ADC);
0040 %
0041 % We repmat the bvals to have the same number of rows as Q.  Each row is a
0042 % tensor.  But bvals will have nDirs x nTensors after the repmat.
0043 % S = S0 * exp(- (repmat(bvals, 1, size(Q,1)) .* ADC));
0044 %
0045 S = S0 * exp(- (repmat(bvals, 1, size(Q,1)) .* dtiADC(Q, bvecs)));
0046 
0047 % end
0048 
0049 end