# Mathematical calculation required for how matlab simbiology performs local sensitivity analysis for a set of ODEs in simbiology model analyzer. (https://w​ww.mathwor​ks.com/hel​p/simbio/u​g/perform-​sensitivit​y-analysis​-for-tumor​-growth.ht​ml)

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Darshna Joshi on 3 Jan 2021
Commented: Darshna Joshi on 4 Jan 2021
Specifically how local derivatives are calculated if we have a constant value of parameter which is its initial condition. How to interpret the time Vs Sensitivity plot and bar plot created in simbiology LSA.? If parameters remains constant throughout. How local derivatives (Sensitivities) are calculated? It would be nice if anyone can provide the mathematical equations?

Florian Augustin on 3 Jan 2021
Hi Darshna,
Here is a link with some information for how to interpret the sensitivity (time/bar) plots. The reported values, and the mathematical expressions SimBiology uses to compute them, depend on the normalization you choose.
For constant parameters, the reported sensitivities are the derivatives of the sensitivity output with respect to the initial values of the parameters. Marking a parameter constant means that it will be constant over time, but its initial value can still be varied. Examining the sensitivity with respect to a constant parameter can be helpful, for example, to assess whether or not a particular model response would change (significantly) if one chose a slightly different initial value for this parameter.
SimBiology uses the SUNDIALS solver to compute the derivatives by solving auxiliary differential equations for the derivatives. It is very technical, but this document (section 2.2) describes all the details about those sensitivity equations.
I hope this helps.
Best,
-Florian
Darshna Joshi on 4 Jan 2021
This made it pretty more clear. Thanks!!