Hello - I have a question regarding identifiability of my model parameters and I was looking for a little guidance. I am modeling an oral drug and its metabolite that are interconvertible with one another and the parent undergoes enterohepatic recirculation. Although I initially attempted to model the interconversion of parent and metabolite in the central compartment, I have found that the model that best describes the data is such that the parent and the metabolite share a peripheral compartment (thus allowing for interconversion). In the central compartment, therefore, I am making the assumption that the metabolite formation is dependent upon the clearance of the parent (that is, I am estimating Clm/Fm where Fm is the fraction of the parent converted to the metabolite). However, this leads me to question whether or not this model structure is valid, as this allows for formation of the metabolite via the peripheral compartment in addition to the (irreversible) formation from the central compartment. Hence, I'm unsure if the model parameters are properly identifiable. Any insight on this matter would be greatly appreciated; I have included my control file below for you information.
Thanks for your assistance - Al Berg $SUBROUTINES ADVAN6 TRANS1 TOL=9 $MODEL NCOMP=5 COMP=(ABSORB) COMP=(CENTRAL); parent drug central COMP=(MET); Metabolite central COMP=(EHR); Bile compartment COMP=(PERIPH); shared parent-metabolite peripheral compartment $PK IF(AMT.GT.0)PODO=AMT KA1=THETA(1)*EXP(ETA(1)) BIO=1 ;bioavailability fixed as 1 as this is the reference formulation MTT=THETA(2)*EXP(ETA(2));mean transit time to absorption compartment N=THETA(3)*EXP(ETA(3));number of transit compartments F1=0; Since estimating from BIO CL=THETA(4)*EXP(ETA(4)); clearance of parent V=THETA(5)*EXP(ETA(5)); volume of parent CL30=THETA(6)*EXP(ETA(6)); clearance of metabolite V3=THETA(7)*EXP(ETA(7)); volume of metabolite CL24=THETA(8)*EXP(ETA(8)); clearance from parent to EHR K41=THETA(9)*EXP(ETA(9)); release from EHR comp MTIME(1)=THETA(10)*EXP(ETA(10)); EHR start time MTIME(2)=MTIME(1)+THETA(11)*EXP(ETA(11)); EHR end time CL25=THETA(12)*EXP(ETA(12)); clearance from parent to peripheral comp CL35=THETA(13)*EXP(ETA(13)); clearance from metabolite to peripheral comp V5=THETA(14)*EXP(ETA(14)); volume of peripheral comp S2=V S3=V3 K12=KA1 K20=CL/V K24=CL24/V K25=CL25/V K30=CL30/V3 K35=CL35/V3 K53=CL35/V5 K52=CL25/V5 KTR=(N+1)/MTT LNFAC=LOG(2.5066)+(N+0.5)*LOG(N)-N ;log transformation of the stirling approximation $DES DL=1/100000 FLAG=MPAST(1)-MPAST(2) DADT(1)=EXP(LOG(BIO*PODO+DL)+LOG(KTR+DL)+N*LOG(KTR*T+DL)-KTR*T-LNFAC)-K1 2*A(1)+FLAG*K41*A(4) DADT(2)=K12*A(1)-(K25+K20+K24)*A(2)+K52*A(5); parent central DADT(3)=K20*A(2)-(K35+K30)*A(3)+K53*A(5); metabolite central DADT(4)=K24*A(2)-FLAG*(K41)*A(4); EHR back into absorption compartment DADT(5)=K25*A(2)+K35*A(3)-(K52+K53)*A(5); shared peripheral compartment $ERROR DEL=0 IF (F.LE.0.0001) DEL=1 IPRE=F W1= F W2= 1 IRES= DV-IPRE IWRE=IRES/(W1+W2) Y = F + W1*ERR(1) + W2*ERR(2) $THETA ;TRANSIT (0, .4) ; KA1 ;1/h (0, 1) ; MTT ; h (0, 10) ; N ; ;CENTRAL (0, 10) ; CL ; L/h (0, 5) ; V ; L ;SID (0, 1) ; CL30 ; L/h (0, 3) ; V3 ; L ;EHR_SID (0, 5) ; CL24 ; L/h (0, 1) ; K41 ; 1/h (2, 6, 12) ; MTIME1 ; h (0, .1, 5) ; DURATION ; h ;PERIPHERAL (0, 10) ; CL25 ;L/h (0, 40) ; CL35 ;L/h (0, 300) ; V5 ; L
