Simulate ODE models described in Excel

I have an ODE system described in an Excel spreadsheet, and I want to simulate it with Matlab. The attached spreadsheet has an example set up and runs fine with the code below:

function Solver

%Import and format data (xlsread or whatever)
%End up with the following variables:

Rates = {'k1f*A' , 'k2f*B - k2r*C'};

Constants = struct('k1f',1,'k2f',2,'k2r',0.5);

Rate_Matrix = [-1 0 ; 1 -1; 0 1];

Initial = {'A',1;'B',2;'C',3};

%The method of storing the information is somewhat arbitrary

%Begin Setting up the ODE solver
    %Time Span to run simulation
    t0 = [0, 10];
    %Species being solved for
    Species = Initial(:,1);
    %Initial Amounts
    x0 = [Initial{:,2}];

      %Run the simulation, passing additional needed variables
      [t,x]=ode45(@Model,t0,x0,[],Rates,Constants,Rate_Matrix);

      %plot the results
      plot(t,x)
      legend(Species)

      function dx = Model(t,x,Rates,Constants,Rate_Matrix)

          %Unpack species vector and Constants
          A = x(1);
          B = x(2);
          C = x(3);

          k1f = Constants.k1f;
          k2f = Constants.k2f;
          k2r = Constants.k2r;

       %Evaluate Rates at current values
          rates = cellfun(@eval,Rates);

      %Calculate the change in each species
          dx = Rate_Matrix * rates';       

      end
  end

The code works, but I don't want to have to hard-code anything into the solver/Model function like "k1f = Constants.k1f;" because the excel file might change. I might add another rate equation or change a constant value. I also would like to avoid using the cellfun(@eval,...) construct because it's slow and not recommended for use.

I've been having a lot of trouble with static work-spaces and passing variables through the ODE function, so any help would be appreciated.

Answer 1

[Rajesh Balagam]

You can create all the rate constants from Excel sheet as shown below.

[~,~,raw] = xlsread('Model_Summary.xls','Rates','C3:D5') % remove empty rows in Excel sheet
for i = 1:size(raw,1)
eval(sprintf('%s = %d',raw{i,1},raw{i,2})); 
end

or create a structure dynamically as below

for i=1:size(raw,1)
    const.(raw{i,1}) = raw{i,2};
end

For alternative approaches to "eval" you can look at the following documentation page.

https://www.mathworks.com/help/matlab/matlab_prog/string-evaluation.html

However, here rate expressions are interpreted as strings from Excel, we cannot eliminate usage of eval.

You can use eval function once, to create rate expressions as function handles and pass the cell array of function handles to the Model function

 rate_expr{2} = eval(sprintf('@(k1f, k2f, k2r, A, B, C) %s', 'k2f*B - k2r*C')) % rate expression comes from Excel sheet

But you need to pass all the variables as parameters to each function handle as we do not know which parameters being used in the rate expression.