Re: Enterohepatic Recirculation Model

From: alison@c255.ucsf.EDU (ABoeckmann) Subject: Re: Enterohepatic Recirculation Model Date: Fri, 9 Oct 1998 14:00:07 -0700 (PDT) Rik de Greef writes ... > Recently, I have made an attempt to model the PK of a compound which showed a > clear enterohepatic recirculation pattern. You'll find the control stream I > used below; I included it solely to stimulate some discussion on this subject - > the code is definitely not THE answer to the problem.... etc. I'll copy his complete email below, after my remarks. In recent NONMEM Intermediate Level workshops, Stuart Beal has talked about a "change-point" model. This is a pont in time where a state vector or its derivative is discontinuous. A differential equation solver may not integrate properly over a discontinuity. The $DES block should not make discontinous changes in the DADT's based on the value of T. Instead, the discontinuities should ONLY happen at event times and/or at nonevent (i.e., lagged) dose times. Also, the only way that an eta derivative associated with time T (which would arise if there were an eta in the model for TENT) can be computed correctly is if the value of TENT corresponds to a change-point. We would like to find a nice way that change-points can be modelled in PREDPP. Maybe this will be part of NONMEM someday. Till then, Stuart says: An absorption lag time with a dose is an example of a change-point. With this change-point, PREDPP knows to use the solver to integrate up to the lag time, to "reset the solver" at the lag time, and then to continue using the solver to integrate beyond the lag time. We can fool PREDPP into thinking that a change-point is an absorption lag time by placing a unit dose into a dummy compartment at time 0 and setting an absorption lag equal for this compartment to the change-point. Based on these ideas, here's how I would modify Rik's code. The change also provides for the termination of EHC. If you want to let EHC continue indefinitely, delete compartment 6 and its dose, and the code involving ALAG6. 1) Add 2 more compartments to $MODEL: $MODEL NCOMPARTMENTS=6 COMP=(DEPOT, DEFDOSE) COMP=(CENTRAL, DEFOBS) COMP=(PERI) COMP=(ENT) ; 'bile compartment' COMP=(DUMMY1) COMP=(DUMMY2) 2) Add to the data "dummy" doses to "dummy" compartments 5 and 6. TIME AMT CMT 0 1 5 0 1 6 2) Tell PREDPP to call PK ("evaluate $PK") when the lag times occur and give a model for the lag times: $PK CALLFL=-2 ; with NONMEM V, the above can be coded ; $PK (LAGGED) ... ALAG5=THETA(7) ; time gall bladder emptying starts ALAG6=ALAG5+THETA(8) ; time gall bladder emptying stops Make sure that the lower bound for theta(8) is 0. 3) Define EHYN in $PK, not $DES: $PK ... IF (NEWIND.LT.2) THEN EHYN=0 ; indicator variable; is gall bladder emptying? OLDTIM=0 ENDIF IF (OLDTIM.EQ.ALAG5) EHYN=1 ; if time later than start of gall bladder emptying IF (OLDTIM.EQ.ALAG6) EHYN=0 ; if time later than stop of gall bladder emptying OLDTIM=DOSTIM In Guide VIII, PROCM2, we say: DOSTIM>0: this call to PK occurs at a non-event dose time DOSTIM, i.e., at the time of an additional or lagged dose. OLDTIM saves the value of DOSTIM from the previous call to PK EHYN is set to 1 when PREDPP is advancing beyond the first lagged dummy dose. EHYN stays 1 until PREDPP is advancing beyond the second lagged dummy dose. 4) In $DES, eliminate the IF statements. Add d.e.'s for the dummy compartments. Because the statements are getting too long, I define the intermediate variable EHC to save space. $DES EHC=EHYN*K42*A(4) DADT(1)=-K12*A(1) DADT(2)=K12*A(1)-(1-FENT)*K20*A(2)-K23*A(2)+K32*A(3)-FENT*K24*A(2)+EHC DADT(3)=K23*A(2)-K32*A(3) DADT(4)=FENT*K24*A(2)-EHC DADT(5)=0 DADT(6)=0 -- Alison Boeckmann =============== Here is Rik's complete email. ============== Recently, I have made an attempt to model the PK of a compound which showed a clear enterohepatic recirculation pattern. You'll find the control stream I used below; I included it solely to stimulate some discussion on this subject - the code is definitely not THE answer to the problem. The code is based on several assumptions/restrictions: a. the fraction of drug that is excreted into the bile (CMT 4 in the model) is kept there until the gall bladder is emptied (at t=TENT) b. the drug that returns into the intestine in this way is absorbed at the same rate as it was directly after administration (however, in the model it does not return in CMT 1 (the depot) - after t=TENT it is allowed to return to the central compartment (CMT 2) with k=ka) c. elimination into the bile occurs at the same speed as the 'other elimination' (e.g. the metabolism) d. the model does not allow for a second (third, fourth...) recirculation (if someone has any idea how to deal with that...?) So, the parameters concerning the enterohepatic circulation which are estimated are: (1) fraction of drug following this route and (2) time of gal bladder emptying. Thus, the model looks like (etas have been chosen quite arbitrarily): $PROB enterohepatic recirculation $INPUT ID TIME AMT DV $DATA ..... IGNORE='#' $SUBROUTINE ADVAN6 TOL=5 $MODEL NCOMPARTMENTS=4 COMP=(DEPOT, DEFDOSE) COMP=(CENTRAL, DEFOBS) COMP=(PERI) COMP=(ENT) ; 'bile compartment' $PK K12=THETA(1) ; absorption constant K20=THETA(2)*EXP(ETA(1)); elimination constant VC=THETA(3)*EXP(ETA(2)) ; central volume VP=THETA(4) ; peripheral volume Q=THETA(5) ; intercompartmental Cl K23=Q/VC ; rate constant to Vp K32=Q/VP ; rate constant from Vp FENT=THETA(6) ; fraction excreted (unchanged) in bile TENT=THETA(7) ; time of gall bladder emptying K24=K20 ; elimination rate into bile equals other elimination rate(s) K42=K12 ; absorption rate from 'bile compartment' equals absorption rate from depot S2=VC $DES EHYN=0 ; indicator variable; has gall bladder emptying already taken place? No IF (T.GT.TENT) EHYN=1 ; if time later than time of gall bladder emptying: Yes DADT(1)=-K12*A(1) DADT(2)=K12*A(1) - (1-FENT)*K20*A(2) - K23*A(2) + K32*A(3) - FENT*K24*A(2) + EHYN*K42*A(4) DADT(3)=K23*A(2)-K32*A(3) DADT(4)=FENT*K24*A(2)-EHYN*K42*A(4) $ERROR Y =F+F*ERR(1)+ERR(2) IPRED=F $THETA .... $OMEGA .... $SIGMA .... $EST .... $TABLE .... I am curious whether someone has already developed some more advanced code for problems like these. Rik de Greef Pharmacokinetics Section Department of Drug Metabolism and Kinetics N.V. Organon