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Estimation of Parametric Image using Matlab Distributed Computing Server (MDCS)

Overview

Generally, the estimation of kinetic parameters is performed by a ROI (region-of-interest)-based method. It means that time-activity curves (TACs) are generated by calculating mean activity from a user-defined ROI at each dynamic image data. This method is simple and robust. However, it cannot represent physiological properties of the tissue, which is heterogeneous. For example, drawing a ROI in a tumor may include different tissue types, which have different biological properties. Therefore, a ROI-based method may fail to represent some significant characteristics of the tumor. One solution is to estimate kinetic parameters by a pixel-by-pixel method. It generates several parametric images, and pixel value in each parametric image represents a kinetic parameter. However, the generation of parametric images is time-consuming and the accuracy of parameter estimation is easily affected by image noise. To reduce the computational time, one alternate approach is to use parallel computing, which speeds up process of parameter estimation by using several computers or multiple CPUs. Here, we propose an example to reduce the computational load of parameter estimation (the pixel-by-pixel method) by Matlab Distributed Computing Server (MDCS).

Setting Matlab Distributed Computing Server (MDCS)

To start the parallel computing, user should install MDCS followed by the document. Note: In order to use MDCS for COMKAT, users must have COMKAT folders with the same pathway in both the client and the cluster.

Example of Parallel Computing using MDCS for COMKAT

Generally, the image size of a PET image is 128x128. Instead of performing parameter estimation for a PET image, we use the ¹⁸F-FDG model to generate 128x128 noise-free TACs and then estimate kinetic parameters using MDCS. To compare the reduction of computational time at differernt numbers of workers, the number of workers is changed from 1, 2, 4, 8,16 and 32. Also, there are 5 noise trials for each test.

cm = compartmentModel;  % start with a new, empty model

%        k1     k2      k3     k4
ktrueA=[0.1 ;  0.13 ; 0.06 ; 0.0068];
 
% define the parameters
cm = addParameter(cm, 'sa',    1);                 % specific activity of injection, kBq/pmol
cm = addParameter(cm, 'dk',    log(2)/109.8); % radioactive decay
cm = addParameter(cm, 'PV',    1);                 % (none)
 
% region A
cm = addParameter(cm, 'k1',    0.1);        % 1/min
cm = addParameter(cm, 'k2',    0.13);      % 1/min
cm = addParameter(cm, 'k3',    0.06);      % ml/(pmol*min)
cm = addParameter(cm, 'k4',    0.0068);   % 1/min
 
% define input function parameter vector
cm = addParameter(cm, 'pin', [28; 0.75; 0.70; 4.134; 0.1191; 0.01043]);

% define compartments
cm = addCompartment(cm, 'Junk');
cm = addCompartment(cm, 'Ce' );
cm = addCompartment(cm, 'Cm' );

% define plasma input function
% specifying function as refCp with parameters pin
cm = addInput(cm, 'Cp', 'sa', 'dk', 'refCp', 'pin'); % plamsa pmol/ml

% connect inputs and compartments
% region A
cm = addLink(cm, 'L', 'Cp',  'Ce', 'k1');
cm = addLink(cm, 'K', 'Ce', 'Junk','k2');
cm = addLink(cm, 'K', 'Ce', 'Cm', 'k3');
cm = addLink(cm, 'K', 'Cm', 'Ce', 'k4');
 
% specify scan begin and end times
ttt=[ ones(6,1)*5/60; ...    %  6 frames x  5   sec
      ones(2,1)*15/60; ...   %  2 frames x 15   sec
      ones(6,1)*0.5;...      %  6 frames x  0.5 min
      ones(3,1)*2;...        %  3 frames x  2   min
      ones(2,1)*5;...        %  2 frames x  5   min
      ones(10,1)*10];        % 10 frames x 10   min

scant = [[0;cumsum(ttt(1:(length(ttt)-1)))] cumsum(ttt)];
cm = set(cm, 'ScanTime', scant);

% define an outputs, one for each region
cm = addOutput(cm, 'RegA', {'Ce', 'PV'; 'Cm', 'PV'}, {});
 
% solve model and generate example output
[PET, PETindex]=solve(cm);

data = PET(:,3);  % data will have 3 columns, one for each region
 
% specify parameters to be adjusted in fitting
cm = addSensitivity(cm, 'pin', 'k1', 'k2', 'k3', 'k4');
 
% set parameter values initial guess, lower and upper bounds.  values are in same order as ensitivities
%        _____________pin_________________  ______Reg______    
pinit = [ 10; 0.4;  0.4;  3;  0.05; 0.01;   0.1;  0.1; 0.05; 0.001; ];
plb =   [ 10; 0.1;  0.1;  1;  0.05; 0.001;  1e-3; 1e-3; 1e-3 ; 1e-5];
pub =   [100; 2. ;  2. ; 10;  1.  ; 0.05;   1.;   1.;   1.;    1.;];

noise_level = 0.1;
for i=1:128*128
    noisy_data(:,i) = [addNoiseDefault(data,noise_level,scant)];
end

for pool_idx =1
    
    mat_pool_n = [31 16 8 4 2 1];
    
    for test_idx = 1:5
        
        matlabpool(mat_pool_n(pool_idx));
        
        t0 = clock;
        for_times = 128*128;

        parfor i=1:for_times

            cm2 = set(cm, 'ExperimentalData', noisy_data(:,i));

            pfit(:,i) = fit(cm2, pinit, plb, pub);

        end

        time_consumed_parfor(pool_idx,test_idx) = etime(clock,t0);

        matlabpool close;

    end
end