Simbiology example expression in the Tumor growth model

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Anu
Anu 2023-1-16
评论： Anu 2023-1-18
I am trying to understand one of the case study models in simbiology, "tumor_growth_fitPKPD.sbproj", explained at https://www.mathworks.com/help/simbio/ug/calculate-NCA-and-estimate-PKPD-parameters.html. I am wondering about the expression used for the total tumor weight in this example. Changes in tumor weight has been expressed using a dedicated reaction with a custom reaction rate. How the expression for the reaction rate has been derived? I guess, the original publication used wt(t) = x1(t) + x2(t) + x3(t) + x4(t).

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Arthur Goldsipe
Arthur Goldsipe 2023-1-17
Hi,
We chose to model the tumor weight this way so that it would be possible to perform local sensitivity analysis using tumor weight as a sensitivity output. (Here's an example that does that.) This is basically due to a current technical limitation of SimBiology's local sensitivity analysis. If you don't care about local sensitivity analysis, then the more natural way to define tumor weight is probably to use a repeated assignment rule similar to what you wrote in your question.
-Arthur
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Arthur Goldsipe
Arthur Goldsipe 2023-1-18
It's not about continuity. SimBiology doesn't check the continuity of expressions. Today, you can attempt local sensitivity analysis on a model that has a discontinuous reaction rate, but you will likely encounter problems (for example, integration errors).
The last time I looked into this, my assessment was that doing this sensitivity analysis would require significant additions to our internal infrastructure. And the obvious way I would implement the functionality would likely slow down the calculations significiantly.
Here's a little more detail: The bulk of the sensitivity calculations are handled by the ODE solver itself. But the solver only calculates sensitivities of state variables. So repeated assignment rules need to be connected to these sensitivities. We had a similar challenge when we needed to take into account the affect of initial assignment rules on the sensitivity calculations. In that case, we only need to differentiate the rules at time=0. But for the case of repeated assignment rules as sensitivity outputs, we would need to differentiate the repeated assignment rules at every time reported in the simulation results.

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