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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. This means that time-activity curves (TACs) are generated by calculating mean activity from a user-defined ROI at each time point in a dynamic image data set. 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 pixel-by-pixel method. This approach may generate several parametric images, and pixels value in each parametric image represents the value of a kinetic parameter. 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. This example demonstrates how the MATLAB Distributed Computing Server (MDCS) can be used to reduce the time required for parameter estimation.
Setting Matlab Distributed Computing Server (MDCS)
To start the parallel computing, user should install MDCS as described in this 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. Users could use funciton 'addpath' to add pathway for COMKAT folders.
Example of Parallel Computing using MDCS for COMKAT
After finishing the setting of MDCS, users could increase the number of workers to reduce the computational time of parameter estimation for a large number of data. The maximum worker is the product of the number of computers and the number of CPUs per computer. To compare the computational time under different numbers of workers, we perform a pixel-wise estimation of FDG rate constants (k1~k4) for 128 x 128 pixels x 29 time frames. All data are generated from the FDG model (Step 1 and Step 2). There are six different tests: 1, 2, 4, 8, 16 and 32 workers. In each test, we run five trials to calculate mean computational time.
Step 1. This part is to create a 18F-FDG model by using COMKAT commands. The basic commands can be found in the user manual and the overview of the 18F-FDG model can be found in the example.
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)
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
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 sensitivities
% _____________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.;];
Step 2. Generate 128x128 noisy TACs by adding noise to noise-free TACs.
noise_level = 0.1;
for i=1:128*128
noisy_data(:,i) = [addNoiseDefault(data,noise_level,scant)];
end
Step 3. This part is to perform parameter estimation for 128x128 TACs with parallel computing. For each test, the number of trials is 5 (test_idx). Before fitting the noisy TACs, users must use the Matlab function 'matlabpool' to start parallel language worker pool. This indicates that the number of workers is used in the test. To use parallel computing for fitting all TACs , the 'for' loop is replaced by the 'parfor' loop. Note: users should use 'command matlabpool close' to close matlabpool after each test.
for pool_idx =1:6
% run the computation using 32 workers, then 16 workers,..., then 1 worker
mat_pool_n = [32 16 8 4 2 1];
% run 5 trials for each test
for test_idx = 1:5
% specify the number of workers to use in this test
matlabpool(mat_pool_n(pool_idx));
% add all required COMKAT m-files into the pathway
addpath('D:\COMKAT_R3.1');
addpath('D:\COMKAT_R3.1\utilities');
addpath('D:\COMKAT_R3.1\validation');
t0 = clock;
for_times = 128*128;
% use 'parfor' to perform parallel computing for 128x128 noisy data
parfor i=1:for_times
% set the data, which will be fitted and use COMKAT's function 'fit' to fit the data
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
for i=1:6
% calculate mean computational time of 5 trials for each test and convert time from second to minute
mean_time(i)=mean(time_consumed_parfor(i,:))/60;
end
bar(mean_time);
set(gca,'XTickLabel',[1 2 4 8 16 32]);
xlabel('# of workers');
ylabel('Computational time (minute)');
Results: The below figure is the computational time (minute) versus the number of workers. As we expected, the computational time reduces with the increase of the number of workers.
