modeling fast and slow absorption

From MAJ_Ralf_Brueckner@wrsmtp-ccmail.army.mil Mon May 8 15:10:52 1995 Subject: modeling fast and slow absorption Dear fellow NONMEM users: I am trying to model a drug where absorption from the IM depot appears to be rapid for the first 2 hours, and then slow for the remaining time. (DV includes actual drug amounts extracted/measured from IM site). I tried to switch from rapid KA to slow as follows: ********************************************************** $INPUT ID TIME AMT DV WT CMT EVID $DATA data.csv IGNORE=C $SUBROUTINE ADVAN6 TOL=3 $MODEL NCOMP=1 ; add other COMPs later COMP=(DEPOT) ; COMP=(CENTRAL) $PK KA1 = THETA(1) ; rapid KA2 = THETA(2) ; slow tka=2.5 ; or THETA(3) temp=0 IF (TIME.LT.tka) temp=1 KA=KA1*temp + KA2*(1-temp) S1=1/1000000 ; DV in ng, AMT in mg ; S2=V/1000 ; DV in ng/ml, AMT in mg $DES DADT(1) = -KA*A(1) ; DADT(2) = KA*A(1) - KEL*A(2) ********************************************************** Before TIME=tka, NONMEM/PREDPP (correctly) calculates predicted drug amount in COMP 1 (PRED) using rapid KA. But at TIME=tka, NONMEM/PREDPP suddenly starts calculating PRED as if slow KA had been used *since time=0*. Am I doing something wrong, or is there a way to get the model to take into accout that less drug is left at the depot site when slow KA starts taking effect. Thank you for your help. Ralf Brueckner

From jaap@leland.stanford.edu Mon May 8 16:02:46 1995 Subject: RE: modeling fast and slow absorption The follwoing control stream should work for what you want. At least for a 1-compartment model. However, everything is easily adapted for a multi-compartment model. You will have to delete the part for the oral solution and keep the controlled release part Jaap Mandema $PROB controlled release ; simultaneous fit to immediate release (IR) oral solution (CR=0) and ; controlled release tablet (CR=1). The controlled release product ; is characterized by a biphasic absorption profile, with an initial fast rate ; followed by a slower rate $INPUT ID TIME DV MDV CR $ABBREV DERIV2=NO $DATA $PRED CL=THETA(1)*EXP(ETA(1)) ; clearance V=THETA(2)*EXP(ETA(2)) ; volume of distribution KA=THETA(3)*EXP(ETA(3)) ; ka for solution KB1=THETA(5)*EXP(ETA(5)) ; fast absorption component for CR KB2=THETA(6)*EXP(ETA(6)) ; slow absorption component for CR FABS=THETA(4)*EXP(ETA(4)) ; relative availability CR versus IR FKA=THETA(7)*EXP(ETA(7)) ; fraction of dose absorped via fast component TLA1=THETA(8)*EXP(ETA(8)) ; lag time A1=1/V AL1=CL/V T1=TIME-TLA1 T1S=1 IF (T1.LT.0.0) T1S=0.0 FF1=EXP(-AL1*T1*T1S)-EXP(-KA*T1*T1S) F1=A1*FF1*KA/(KA-AL1) FF2=EXP(-AL1*T1*T1S)-EXP(-KB1*T1*T1S) F2=A1*FF2*KB1/(KB1-AL1) FF3=EXP(-AL1*T1*T1S)-EXP(-KB2*T1*T1S) F3=A1*FF3*KB2/(KB2-AL1) F4=FKA*F2+(1-FKA)*F3 CT=20.0*F1*(1-CR)+20.0*FABS*F4*CR Y=LOG(CT)+EPS(1) $THETA (0,2) (0,0.2) (0,5) (0,1.0) (0,2.0) (0,0.1) (0,0.5,1) (0,0.1) $OMEGA BLOCK(2) 0.1 0.01 0.1 $OMEGA 0.1 0.1 0.1 0.1 0.1 0.1 $SIGMA 0.2 $EST NOABORT SIG=3 MAX=3000 PRINT=10 $COVARIANCE $TABLE ID TIME DV MDV CR NOHEADER NOPRINT FILE= **** From alison Mon May 8 17:40:53 1995 In response to Ralf Brueckner's posting: Jaap Mandema sent mail that appears to have solved the differential equations. This is great if you can use it (e.g., if your dosing scheme is appropriate) because a $PRED is so much faster than using PREDPP. I think that Brueckner's problem may lie partly in his data file. If he has only event records at time 0 (the dose) and time > tka, the $PK block computes KA ONLY at time > tka, and so this value of KA is in effect for the entire integration. If tka is known and fixed, he could include an event record having TIME=tka-.0001 (or some other very small value.) This event record has EVID=2. It causes PK to compute a value of KA appropriate for the time interval (0, tka-.0001) which is used for the first part of the integration. Any event record having TIME > tka will provide a value of KA appropriate to the time interval (tka-.0001, TIME). (It is also unnecessary in this case to use ADVAN6, since ADVAN2 can be used in this case.) However, this won't work when tka is modelled as a theta, because he won't know what time to use. Instead, for a general solution, with the "switching time" a parameter, it would be better to compute KA within the $DES block. Within $DES, the variable T represents "continuous" valued time, as opposed to the discrete values of TIME in $PK. E.g., $PK KA1 = THETA(1) ; rapid KA2 = THETA(2) ; slow tka=2.5 ; or THETA(3) S1=1/1000000 ; DV in ng, AMT in mg ; S2=V/1000 ; DV in ng/ml, AMT in mg $DES temp=0 IF (T.LT.tka) temp=1 KA=KA1*temp + KA2*(1-temp) DADT(1) = -KA*A(1) Ralf, let me know if this solves your problem. Alison

From 73532.1742@compuserve.com Tue May 9 08:28:58 1995 Subject: fast and slow absorption Hi, This is my response to the original mail by Ralf Brueckner and to the proposals by Jaap Mandema and Alison Boeckmann. I think there is yet another way to model a fast absorption which is followed by a slow absorption: I used ADVAN5 with 2 Depot compartments linked by first-order rate constants to the Central compartment (Compartment 3). It is assumed that DEPOT1 has availability F1 and that DEPOT2 has availability F2=1-F1. Furthermore, both Depot compartments have different lag times (ALAG1 and ALAG2) and different absorption rate constants (K13 and K23). When all these parameters are modelled simultaneously, one can have two types of absorption occur at the same time or one can restrict the difference between ALAG1 and ALAG2. It seems to me that this model offers maximal flexibility to describe any kind of controlled release formulation. Joachim Grevel **** From lewis Tue May 9 10:02:29 1995 This is anopther way of viewing absorption at 2 different rates, but does not correspond to Ralf's model. Ralf's model states that drug comes in first at one rate and then at another. Joachim's models states (when both lag times are equal) that a fraction of total drug enters at one rate, and the remainder at another; simultaneously. Ralf's model gives rise to an absorption rate curve that follows first one exponential and then another; i.e., it is an exponential "spline" with one break-point at the rate-transition time. Joachim's model gives rise to a sum of 2 exponentials. Each modeler will have to decide, based on the physiology of the system he is modeling, which model he prefers.

From MAJ_Ralf_Brueckner@wrsmtp-ccmail.army.mil Thu May 11 09:50:46 1995 Subject: re: fast and slow absorption Many thanks to the NONMEM users who responded to my question regarding modeling fast and slow absorption. In response to Dr. Sheiner's question, here is a representation of what I based my "problem" on. >Before TIME=tka, NONMEM/PREDPP (correctly) calculates predicted drug >amount in COMP 1 (PRED) using rapid KA. But at TIME=tka, >NONMEM/PREDPP suddenly starts calculating PRED as if slow KA had been >used *since time=0*. |* |* A |* + x = DV m | * + + = PRED o | * + * = overlapping u | * + (DV=PRED) n | x x + t | xxx + | xxxx + | xxxxxxx | + xxxxxxx | ++++ | +++++++ ---------------------------------- ^ time | tka Dr. Sheiner and Alison Boeckmann were correct when they suggested that the problem was in the data (I should have known better!). The data was obtained from a rat study using destructive sampling. And as suggested by Alison, >I think that Brueckner's problem may lie partly in his data file. If >he has only event records at time 0 (the dose) and time > tka, the >$PK block computes KA ONLY at time > tka, and so this value of KA is >in effect for the entire integration. That was what had happened. When I reanalyzed the data using the pooled data approach, the "problem" went away and I was able to estimate both KA's. Thanks also to Dr.s Mandema, Grevel and Sheiner for useful models and discussion re: modeling absorption processes. I am most appreciative of this NONMEM Users Network! Ralf Brueckner