Non linear mixed effects model - Fitting Time Activity Curve

Hello MATLAB users!

I'm facing some issues with fitting the data I have in a excel spreadsheet. The Excel table contains 16 columns and 150 rows, excluding the header. From left to right, the columns are Times, Kidneys_P1, Kidneys_P2, Kidneys_P3, Kidneys_P4, Kidneys_P5, Tumor_P1, Tumor_P2, Tumor_P3, Tumor_P4, Tumor_P5, Blood_P1, Blood_P2, Blood_P3, Blood_P4, Blood_P5. The values represent the administered activity (radioactive activity) in patients. I want to fit the curves using a non-linear mixed-effects model, using the following equation:

model = [A1*e^-(λ1+λ1_phys)*t] + [A2*e^-(λ_phys)*t] - [A3*e^-(λ_2+λ_phys)*t] - (A1+A2-A3)*e^-(λ_bc+λ_phys)*t

where A1, A2, and A3 are the coefficients of the respective exponential terms with values ≥ 0, λ1 and λ2 are biological rate constants with values ≥ 0, λ_bc is the rate of blood circulation approximated as λbc = ln(2)/1min, and λphys represents the radionuclide physical decay constant = ln(2)/6.7*24*60 = 7.18E-5 min-1.

Here is a piece of my MATLAB code:

% Import Excel Data
clc, clear all, format compact
TAC_data = readtable("CorrectedFile.xlsx");

% Extract the times and activity data for each organ and patient
times = TAC_data{:,1};
kidneys = TAC_data(:, 2:6);
tumor = TAC_data(:, 7:11);
blood = TAC_data(:, 12:16);

% Initial guess
initialGuess = [0.5, 0.5, 0.5, 0.1, 0.1, 7.18E-5, 0.30];

% Model function
model = @(params, times) (params(1) * exp(-(params(4) + params(6)) * times)) + ...
                      (params(2) * exp(-params(6) * times)) - ...
                      (params(3) * exp(-(params(5) + params(6)) * times)) - ...
                      (params(1) + params(2) - params(3)) * exp(-(params(7) + params(6)) * times);

% Iterate over each organ and perform the curve fitting for all patients within that organ
organs = {'Kidneys', 'Tumor', 'Blood'};
patients = {'P1', 'P2', 'P3', 'P4', 'P5'};
optimized_parameters = cell(length(organs), length(patients));

for i = 1:length(organs)
    organ = organs{i};
    
    % Select the data for the current organ
    organ_data = TAC_data(:, (i-1)*5 + 2 : i*5 + 1);
    
    % Stack the columns of organ data into a matrix
    stacked_organ_data = table2array(organ_data);
    
    % Perform curve fitting for each combination of organ and patient
    for j = 1:length(patients)
        % Select the activity data for the current patient
        activity = stacked_organ_data(:, j);
        
        % Create the grouping variable for this patient
        patient_group = repmat(j, size(activity)); % Repeat patient index
        
        % Perform curve fitting for the current organ and patient
        [optimized_params, ~, ~] = nlmefitsa(times, activity, patient_group, [], model, initialGuess);
        
        % Store the optimized parameters
        optimized_parameters{i, j} = optimized_params;
        
        % Print the optimized parameters
        fprintf('Optimized parameters for %s - %s:\n', organ, patients{j});
        disp(optimized_params);
    end
end

In the line "Perform curve fitting" I am using the nlmefitsa tool, however, I ran the code and got the following error. Sorry in advance, I don`t know how to put the error text in red.

Error using nlmefitsa>modelcaller
Model function has returned Inf or NaN values.
Error in nlmefitsa>@(p,x,v,e)modelcaller(fvc,vect,modelfun,IdM,transphi(p),x,v,e) (line 602)
structural_model = @(p,x,v,e) modelcaller(fvc,vect,modelfun,IdM,transphi(p),x,v,e);
Error in nlmefitsa>saem_randstep (line 2120)
[f,g] = structural_model(phiMc,XM,VM,errmod);
Error in nlmefitsa/onefit (line 692)
                [f,g,etaMc] = saem_randstep(ind_eta,eta0,vk2,myrandn,cholfact,...
Error in nlmefitsa (line 470)
        [stop,betas(:,jrep),Gj,statsj,b_hat(idxRandPerm,uId,jrep)] = onefit(beta0(:,jbeta));
Error in test (line 43)
        [optimized_params, ~, ~] = nlmefitsa(times, activity, patient_group, [], model, initialGuess);

I think the error can be related to the initial guess, but I don't know how to fix it.

Any help is welcome. I appreciate it if anyone can assist me!

[Kautuk Raj]

You can share CorrectedFile.xlsx for better understanding of the problem.

Answer 1

[Shivansh]

Hi Nicollas!

I understand that you are working on fitting a non-linear mixed effects model.

The error message you're encountering, "Model function has returned Inf or NaN values," typically occurs when the model function evaluates to Infinity (Inf) or Not-a-Number (NaN) for some input parameter values.

A few steps for debugging can be

1. Ensuring no NaNs or inf in data.
2. Experiment with initial guess values.
3. Implement Constraints to prevent out-of-bound values.

You can also add a code snippet on sample data to check the problematic values. You can refer to the below example for implementation.

problematicValues = [];

for aValue = testRange
    % Update A1 in the parameter list
    params = initialGuess;
    params(1) = aValue;  % Update A1
    
    % Evaluate the model with the updated parameters
    modelOutput = model(params, testTimes);
    
    % Check for NaN or Inf
    if any(isnan(modelOutput) | isinf(modelOutput))
        problematicValues = [problematicValues; aValue];
    end
end

If the problem persists, provide a sample data for reproduction of the issue at my end.

You can refer to the following documentation for more information about "nlmefitsa": https://www.mathworks.com/help/stats/nlmefitsa.html.

I hope it helps!