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Solving matrix of differential equations

Question from a user during a discussion about tools available in fit curve and nonlinear platforms:

Can I give a matrix of differential equations to JMP along with

1. data and have JMP fit the equations to the data to provide the parameters K12, K21, and kel?
2. constants K12, K21, and Kel and have JMP do simulations?

The parameters above refer to the differential equation for plasma in the image (p = plasma, D-drug, tis=tissue), where the other diff eq characterizing the system is missing (that for tissue).  He commented that JMP was already using the integrated equation in Fit Curve.

Any thoughts & details in point/click or scripted are appreciated!

Re: Solving matrix of differential equations

Hi @christianstopp ,

Is the Fit Curve option Two Compartment IV Bolus Dose not what he is looking for?

Statistical Details for the Fit Curve Platform (jmp.com)

Re: Solving matrix of differential equations

My sense, so far @Chris_Kirchberg is no: I originally showed him the one-compartment model in Fit Curve, to which he said effectively "you're using the integrated equation for estimation, can JMP take a matrix of diff eqs as inputs instead?".  I assume the same is true for the Two Compartment which was just an example I used in my correspondence with him post-demo.

I think his broader question still holds as he was initially describing a more elaborate body system than just the two compartments. If memory serves me, he's using WinNonLin to some degree but whether it's for this I'm uncertain. 

Re: Solving matrix of differential equations

Well, given the original question, JMP does calculate the rate constants mentioned in item 1 for the two compartment IV Bolus model so what does he mean by he wants to enter a matrix of differential equations? a linear combination of a matrix of coefficients and a matrix of variables so JMP can differentiate each simultaneously? or one at a time? a separate formula for each tissue?

Something like in this example in Symbolab?

JMP's Nonlinear expects a single formula in a column to fit, not a matrix of formula's in a column. It can expand intermediate formulas that might be reference in other columns, but it is still solving for one formula at a time. Solving meaning it will take the derivative of the formula in the column specified in the X role., but only one formula can be specified, not a matrix of formulas, as far as I know.

Re: Solving matrix of differential equations

Thanks for sharing @Chris_Kirchberg. I had reached out to the user inquiring after your post to dig a little further and continue the discussion (with him and here), but it seems to not be a priority at this point, so my apologies for the delay. I interpreted the question as needing to work with a matrix of diff eqs, solving the system simultaneously; if I hear back with any further clarification, I'll follow up - but I appreciate the input!