Help with ODEs for a time varying clearance
Dear nmusers,
I'm working on the pharmacokinetics of an antiCD20 mAb; I suspect the
clearance of this mAb should be time dependent as rituximab’s clearance do.
I tried to model this behavior but I’m not sure if the ODEs are correct.
Please can you help? I share part of the code.
$SUBROUTINE ADVAN13 TOL=9
$MODEL COMP=(CENTRAL) COMP=(PERIPH1)
$PK
;---- STRUCTURAL PARAMETERS ------
TVCL1 = THETA(2) ; system-nonspecific clearance
TVV1 = THETA(3)
TVQ = THETA(4)
TVV2 = THETA(5)
TVKDES = THETA(6) ; rate constant of the specific clearance decay
TVCL2 = THETA(7) ; time varying clearance at time zero
;---- MU_TRANSFORMATION ------
MU_1 = LOG(TVCL1)
MU_2 = LOG(TVV1)
MU_3 = LOG(TVQ)
MU_4 = LOG(TVV2)
MU_5 = LOG(TVKDES)
MU_6 = LOG(TVCL2)
;---- INDIVIDUAL PARAMETERS ------
CL1 = EXP(MU_1+ETA(1))
V1 = EXP(MU_2+ETA(2))
Q = EXP(MU_3+ETA(3))
V2 = EXP(MU_4+ETA(4))
KDES = EXP(MU_5+ETA(5))
CL2 = EXP(MU_6+ETA(6))
S1 = V1
;---- INITIAL CONDITIONS ------
A_0(1) = 0
A_0(2) = 0
CL2_TIME = CL2*EXP((-KDES)*(TIME))
CL_TOTAL = CL2_TIME + CL1 ; total clearance
;---- DES ------
$DES
CONC = A(1)/V1
DADT(1) =-(CL_TOTAL/V1)*A(1)-(Q/V1)*A(1)+(Q/V2)*A(2)
DADT(2) = (Q/V1)*A(1)-(Q/V2)*A(2)
;----$ERROR ------
CONC1 = A(1)/V1
IPRED=-3
IF(CONC1.GT.0) IPRED=LOG(CONC1)
W = THETA(1)
Y = IPRED+W*EPS(1)
IRES=DV-IPRED
IWRES=IRES/W
Thank you,
Niurys
MSc Niurys de Castro Suárez
Assistant Professor of Pharmacometrics
Assistant Research
Pharmacy Department
Institute of Pharmacy and Food,
University of Havana
Cuba