Transfer Functions on Biologic Data Sets

I have blast data from 3 different organisms. Two animals and one human set. I am looking to develop a transfer function to translate the data sets from animal set to the human data set. I also have the ambient pressure from outside of the body for normalization as well as weight, speed of the wave, and weight of the individual body parts. I only have acess to the following toolboxes:

MATLAB Version 9.8 (R2020a)

Curve Fitting Toolbox Version 3.5.11 (R2020a)

Deep Learning Toolbox Version 14.0 (R2020a)

GUI Layout Toolbox Version 2.3.6 (R2023a)

Signal Processing Toolbox Version 8.4 (R2020a)

Statistics and Machine Learning Toolbox Version 11.7 (R2020a)

I want to be able to set up some sort of optimizaiton funciton that would work between both of the animal models, independetly. Likely a second order model. I have attached the raw data of the pressures as a CSV. Each of the data sets are computed at 0.8Mhz and the data listed by row is an maximum individual test, not a continous data set.

I am looking for gudiance on how to start this.

>>

Answer 1

[Garmit Pant]

Hello Kyle,

To develop a transfer function to translate the blast data from animal models to the human dataset, you can use the tools available in the Curve Fitting Toolbox to perform the optimization and fitting. Given the nature of your question, I can demonstrate a general method to set up a second-order model and fit your data to such a model, rather than providing you with the exact optimizations.

Please follow the code snippet below to understand how to set up a second-degree model and fit your data to it:

% Step 1: Load the Data
% Load the data into ‘lunginset’ using the ‘Data Import Tool’ by double clicking on the file in the ‘Current Folder’ window
data = lunginset;

% Extract the relevant columns
ferret_incident = data.FerretIncident;
ferret_lung = data.FerretLungPressure;
human_incident = data.PMHSIncidentPressure;
human_lung = data.PMHSLungPressure;
nhp_incident = data.NHPIncident;
nhp_lung = data.NHPLungPressure;

% Step 2: Normalize the Lung Pressures using Incident Pressures
normalized_ferret_lung = ferret_lung ./ ferret_incident;
normalized_human_lung = human_lung ./ human_incident;
normalized_nhp_lung = nhp_lung ./ nhp_incident;

% Step 3: Define the Model (Second-order polynomial)
model = @(b, x) b(1) * x.^2 + b(2) * x + b(3);

% Step 4: Fit the Model to Ferret Data
opts = fitoptions('Method', 'NonlinearLeastSquares', 'StartPoint', [1, 1, 1]);
fitType = fittype('b1*x^2 + b2*x + b3', 'independent', 'x', 'coefficients', {'b1', 'b2', 'b3'});
[fitresult_ferret, gof_ferret] = fit(normalized_ferret_lung, normalized_human_lung, fitType, opts);

% Fit the Model to NHP Data
[fitresult_nhp, gof_nhp] = fit(normalized_nhp_lung, normalized_human_lung, fitType, opts);

% Step 5: Optimize the Parameters (if necessary)
% You can use additional optimization techniques if needed

% Step 6: Validate the Model
% Compare the fitted results with the human data
predicted_human_from_ferret = model(coeffvalues(fitresult_ferret), normalized_ferret_lung);
predicted_human_from_nhp = model(coeffvalues(fitresult_nhp), normalized_nhp_lung);

% Plot the results for validation
figure;
subplot(2,1,1);
plot(normalized_ferret_lung, normalized_human_lung, 'o', normalized_ferret_lung, predicted_human_from_ferret, '-');
title('Ferret to Human Data');
legend('Actual Human Data', 'Predicted Human Data');
xlabel('Normalized Ferret Lung Pressure');
ylabel('Normalized Human Lung Pressure');

subplot(2,1,2);
plot(normalized_nhp_lung, normalized_human_lung, 'o', normalized_nhp_lung, predicted_human_from_nhp, 'o');
title('NHP to Human Data');
legend('Actual Human Data', 'Predicted Human Data');
xlabel('Normalized NHP Lung Pressure');
ylabel('Normalized Human Lung Pressure');

On fitting the data on the first 30 rows, thereby avoiding missing data, I obtained the following results.

This should give you a starting point and a template to perform your task with the tools available in the toolboxes that you can access.

For further understanding, kindly refer to the following MathWorks documentation:

• Refer to the ‘Examples’ section to understand how to fit curves or surfaces to data: MathWorks Documentation.

I hope you find the above explanation and suggestions useful!

[Kyle]

And if I was to add other input conditions such as weight, or any constants that are derived from body conditions. Would those go into the function that you developed in step 3?

Answer 2

[Star Strider]

The data do not appear to have anything in common, and several are missing. (The plots here are sorted by the independent variables, that I have termed the ‘Incident’ variables.)

The idea of a ‘transfer function’ implies a frequency-based expression of however I am not certain what tthe inputs and outputs are in this instance. This is complicated by the nature of the data. That would also require that the data be regularly sampled in order to calculate their Fourier transforms, and they are so disparate that would not be appropriate.

What sort of relation do you want between the data? One option would simply be to interpolate (thhere are several funcitons to do this, for example interp1), however with respect to some of the data, this would involve an extrapolation, and extrrapolations of the ‘Ferret’ or ‘NHP’ data to the ‘PMHS’ data would be extreme, since they have very little in common. There is no reason to assume that those extrapolations would be at all accurate, much less reliable. A regression would have the same problems.

T1 = readtable('lunginset.csv', 'VariableNamingRule','preserve');
disp(T1)

    Ferret Incident    Ferret Lung Pressure    PMHS Incident Pressure    PMHS   Lung Pressure    NHP Incident    NHP Lung Pressure
    _______________    ____________________    ______________________    ____________________    ____________    _________________

        7.3006                6.0947                   11.153                   5.8322              4.8064            2.9359      
        12.419                13.591                    11.08                   5.6407              5.7547            2.9158      
        13.502                 18.15                   26.627                   15.517              10.468            6.0277      
        18.217                23.503                   27.433                    18.92              11.056            6.0318      
         5.907                6.0416                   43.627                    31.36              18.505            11.275      
        17.357                18.197                   25.827                   27.654              13.671            10.235      
        19.365                17.227                   11.843                   6.8671               23.32            15.092      
         7.186                5.7315                   12.155                   7.7653              18.544            14.691      
        12.187                7.9471                   26.976                    29.87              4.2681            3.0381      
        15.769                13.543                   40.443                   42.264               10.57            6.5558      
        23.596                17.491                   11.208                   4.7718              18.198            11.519      
        11.445                13.078                   9.4587                   3.5979              17.719            14.462      
        14.613                16.109                   26.624                   12.628              4.5954            3.0979      
        18.229                20.284                   26.333                   16.436              4.8551            3.1622      
        6.3318                5.4459                   41.253                    40.04              5.0341            3.9259      
        12.873                 15.17                   11.153                   6.3304              10.577            7.9241      
        10.207                10.746                    11.08                   6.1432              8.4851            9.2707      
        14.455                14.338                   26.627                   21.383              8.2862            7.7484      
        23.961                 17.88                   27.433                   20.334              13.556            15.538      
        6.4588                 5.245                   43.627                   29.096              14.151            16.605      
        11.754                11.058                   25.827                   24.657              14.673            22.423      
        13.489                13.857                   11.843                   5.8246              26.287            20.845      
         6.047                5.1856                   12.155                    6.222              26.913            29.695      
        7.1909                5.9545                   26.976                   30.319              18.466            27.364      
        12.793                9.9787                   40.443                   44.628              13.874            15.762      
        13.277                13.215                   11.208                    4.832              14.657            16.729      
        24.987                16.388                   9.4587                   3.7285              14.183            16.847      
        17.623                17.336                   26.624                   15.262              18.651            16.567      
        6.8857                8.1118                   26.333                    15.33              12.681            16.655      
        11.118                15.012                   41.253                   24.554              24.935            23.576      
        6.0598                8.2016                      NaN                      NaN              14.421            16.725      
        13.107                17.106                      NaN                      NaN              4.6786            3.7845      
        19.299                 22.15                      NaN                      NaN              3.9222            2.6399      
        23.503                   NaN                      NaN                      NaN              7.9823             7.536      
        6.6339                5.6176                      NaN                      NaN              8.7042            5.6448      
         12.23                10.996                      NaN                      NaN              3.4596            3.7787      
        13.696                16.639                      NaN                      NaN              9.7698            8.7789      
        7.1356                5.4598                      NaN                      NaN              11.877            17.314      
        14.691                16.834                      NaN                      NaN              17.778            24.907      
        14.361                15.867                      NaN                      NaN              4.9075            4.3363      
        15.084                16.026                      NaN                      NaN              8.2721             8.946      
           NaN                   NaN                      NaN                      NaN              17.328            19.415      
           NaN                   NaN                      NaN                      NaN              13.513            12.434      
           NaN                   NaN                      NaN                      NaN              22.244            17.448      

VN = T1.Properties.VariableNames;

figure
hold on
for k = 1:2:size(T1,2)
    DN = extractBefore(VN{k},' ');
    [~,idx] = sort(T1{:,k});
    plot(T1{idx,k}, T1{idx,k+1}, '.-', 'DisplayName',DN)
end
hold off
grid
xlabel('Incident')
ylabel('Lung Pressure')
title('Sorted Data')
legend('Location','best')

for k = 1:2:size(T1,2)
    TA = [T1{:,k} T1{:,k+1}];
    TA = rmmissing(TA);
    x = TA(:,1);
    y = TA(:,2);
    B(:,k) = [x.^2 x ones(size(x))] \ y;
end
B = B(:,1:2:end);
DN = cellfun(@(x)extractBefore(x,' '), VN(1:2:size(VN,2)), 'Unif',0);
Parameters = array2table(B, 'VariableNames',DN, 'RowNames',{'x^2','x','Intercept'})

Parameters = 3x3 table
                  Ferret         PMHS          NHP   
                 _________    __________    _________

    x^2          -0.055544    -0.0043134    -0.020394
    x               2.4247        1.1762       1.5468
    Intercept      -7.7462       -7.0648      -3.4791

RGB = 'rgb';

figure
hold on
for k = 1:2:size(T1,2)
    TA = [T1{:,k} T1{:,k+1}];
    TA = rmmissing(TA);
    DN = extractBefore(VN{k},' ');
    [~,idx] = sort(TA(:,1));
    x = TA(idx,1);
    yfit = [x.^2 x ones(size(x))] * B(:,ceil(k/2));
    hs1 = scatter(TA(idx,1), TA(idx,2), 15, RGB(ceil(k/2)), 'o', 'filled', 'DisplayName',DN);
    plot(x, yfit, '-', 'Color',RGB(ceil(k/2)), 'LineWidth',2, 'DisplayName','Regression')
end
hold off
grid
xlabel('Incident')
ylabel('Lung Pressure')
title('Data & Regression')
legend('Location','best')

.

[Kyle]

These data sets are not continous. There are curves associated with these data points that I have selected a maximum from as in literature this has been found to be the most impactful point of the data set. The incident pressure is a continous scale by proxy of it being an ambinet response to the test condition. All other data points are responses to the test condition. So there are not "missing points" per say as all of these were tested indiviudally and then post proccessed to get here. What I am referencing as a goal is what in papers is refered to as a transfer function - (which i understand the implications of but in this feild they use it for to mean something slightly different). A function that is able to take the biologics data from one species and mapping those data points with the use of inputs of weight, wave speed, size, pressure and a few constants to a secondary species and have that overall funciton be applicable to any species given the correct input conditions.

Fully following this is a bigger question than what the matlab forums is able to provide however, I was trying to determine if with the tools I have availible, if something like this was even possible to attempt toward, developing some optimization code or something similar for this globalizing function concept.

[Star Strider]

You seem to be requesting a multiple regression (linear or nonlinear regression using multiple independent variables to get one or more results). That is certainly possible and relatively straightforward, once you know the sort of relation you want. That means that you will first need to decide on the sort of linear or nonlinear model you want to use, and then calculate the parameters to fit it, similar to what I did with the quadratic linear regression here. (I sorted tthe data to create the plots. The regression itself cares not one whit if the data are sorted.)

So you first need to devise a reasonable model (‘reasonable’ meaning that it makes sense both mathematically and physiologically). Providing that there are more data to fit than there are parameters in the model, the fitting process itself should then be relatively straightforward. (If there are fewer data than parameters, the process is doomed from the start, since no unique estimations of the parameters are possible.)

[Sam Chak]

Hi @Kyle

I don't think that the deteministic input-output mathematical function of this form

or this form

can be extracted from the data.

Is there a direct correlation between the number or incidents and the lung pressure?

[Kyle]

It is less that relationship and more I have a fit from NHP and I want that fit to match up with the PMHS with inputs of weight, wave speed, size, pressure and a few constants to a secondary species such that the Blue line lays over the green line after some fiddling and inputted constants.

[Star Strider]

@Kyle — If you provide those values and an appropriate mathematical relationship (model) that can be used to fit the data (estimate the relevant parameters), that might be an option for at least part of the ‘Incident’ range of ‘PMHS’. (I have no idea what you are doing or what that model would include.) However since the ‘Incident’ ranges of ‘NHP’ and ‘PMHS’ definitely overlap only in a limited range of ‘Incident’, only part of those values can be approximated.

I would fit them only over the ranges of values that they have in common, completely avoiding extrapolation. That would also allow you to compare the estimated parameters of the models for each group.