arterio-venous modeling

From: lewis@c255.ucsf.EDU (LSheiner) Subject: arterio-venous modeling Date: 26 Sep 1997 18:48:07 -0400 Rik - A further remark on the AV difference and proteresis: The paper in which we worked out a semi-parametric approach to this problem is Verotta, Beal, & Sheiner, Am J Physiol 256 (Reg Integ Comp Physiol 25) R1005-R1010, 1989. The idea, as you correcly surmise, is to model an unobserved arterial compartment which drives both the venous compartment and the effect compartments, and in your case the venous compartment will be "shalower" than the effect compartment. We put forward a method that is semiparametric and involves (constrained) deconvolution ... this is not going to be easy (possible?) using NONMEM. So, a more parametric version of our model might proceed as follows: DADT(1) = KVO*A(3) - KVO*A(1) ; Venous Conc, Cv DADT(2) = KEO*A(3) - KEO*A(2) ; Ce DADT(3) = K43*A(4) - (K30+K34)*A(3) ; Arterial Conc, Ca DADT(4) = -K43*A(4) + K34*A(3) ; "Tissue" Conc The above models Ca as biexponential. Note that it has no loss from A(3) to A(1) or A(2) - they are both "hypothetical" even tho Cv is observed (that is, A(4) is supposed to take care of the kinetics being non-first-order) For identifiability, S1 should be fixed to 1 (we observe Cv), and S4 should be estimated (the model requires SS Cv = SS Ce = SS Ca). Note: 1) In principle, you have to fit the PK and PD simultaneously - you can't do the PK first and fix on it since it takes the PD proteresis to define the Ca kinetics. HOWEVER, you can ASSUME a value for KVO from knowledge of the perfusion of the site from which the venous drainage is sampled. It doesn't matter very much if this is right or not, since all it has to be is sufficienlty "slow" so that the estimated arterial kinetics "get ahead" of the effect (i.e., they have to be such that estimated Ca vs effect exhibits no proteresis; it can, of course, exhibit hysteresis, which will be taken care of in the PD fit by KEO. 2) If you fit simultaneoulsy, it is likely that KEO -> infinity, in which case, as you suggested, Ce cannot be distinguished from Ca, and the model requires one less parameter. It will be unidentifiable as I have written it. Therefore, if yotu want to do a simultaneous fit, you might start with fixing KEO to a very large value, and then, once you have a fit, seeing if you can let it go free. Good luck.