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I try to copy the PBPK model by Peng in Berkely Madonna. The amount of drug is increasing in my
script.
Did anyone try this PBPK model? How to keep the total amount in ths system stable? Regards
hester
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Hester,
Shouldn’t happen. Please, check the equations and / or script.
Ivan
Ivan Nestorov, PhD
Sr. Director Pharmacometrics
BiogenIdec Inc.
10 Cambridge Center
Cambridge MA 02142
USA
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Which of the models by Peng do you have in mind?
Zvi
[This paper? Tissue Distribution and Physiologically Based Pharmacokinetics of Antisense
Phosphorothioate Oligonucleotide ISIS 1082 in Rat, B. Peng, J. Andrews, I. Nestorov, B. Brennan, P.
Nicklin, and M. Rowland, Antisense and Nucleic Acid Drug Development. February 2001, Vol. 11, No. 1:
15-27 - db]
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A small typo can do this in a PBPK model. If the flows leaving the plasma space are not calculated
it's possible to have less leaving the plasma than entering the tissue which can cause a buildup.
I've encountered literature models where this can be attributed to rounding when the final numbers
are placed in the parameter table. It can be very painful to debug.
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Hello - Check the flow rates into each organ - they should add up to the total cardiac output.
Sounds like you have a mass balance error. If you check the early PBPK models by the toxicologists
(Andersen, Clewell etc) you will notice that their models all have a mass balance equation - which
should equal numerical zero at each step of the output. It is your only indication that all is well
with your equations. The most common source of this is an imbalance in the flows.
Best of luck
Edmond
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Zvi, that is the paper that I try to write in BM
My script which is a current status to get it right (and I did not yet succeed)
METHOD RK4
STARTTIME = 0
STOPTIME=10
DT = 0.01
DTOUT = 0.5
DTMAX=0.5
;dose= 10 mg/kg
; BW=0.250 kg (L)
;volumes (CL) are in mL/h
; CO= 2670 ml/h=2.67 L/h
Init Aa=0
Init Av=Dose
;init Alu=0
;init Avlu=0
Init Al=0
init Avl=0
init Ak=0
Init Avk=0
Init Ast=0
Init Avst=0
init Asp=0
init Avsp=0
init Aint=0
init Avint=0
init Am=0
init Avm=0
init Aad=0
Init Avad=0
init Ask=0
init Avsk=0
init Abo=0
init Avbo=0
init Aht=0
init Avht=0
init Ath=0
init Avth=0
init Abr=0
init Avbr=0
init Ates=0
init Avtes=0
;init Avv=0
;init Ava=0
init CLK=0
; b;oodflows
CO=2670 ; mL/h
Qven=2670 ; l/h
Qlu=CO; ml/h check of hier het systeem klop. co uit de lung is ca
Qhep=0.0606*CO
Ql=Qhep+Qst+Qint+Qsp
Qk=0.2561*CO
Qst=0.025*CO
Qsp=0.014*CO
Qint=0.1686*CO
Qm=0.1528*CO
Qad=0.043*CO
Qsk=0.0988*CO
Qbo=0.0562*CO
Qht=0.0786*CO
Qth=0.00719*CO
Qbr=0.0292*CO
Qtes=2670-Qbr-Qth-Qht-Qbo-Qsk-Qad-Qm-Qint-Qsp-Qst-Qk-Qhep
;extravas volumes
BW=250 ; mg vol in ml
;Va=0.0238*BW
;Vvv=0.0472*BW
Vvlu=0.004931*BW
Vvl=0.00407*BW
Vvk=0.008609*BW
Vvst=0.0004012*BW
Vvsp=0.003886*BW
Vvint=0.0040537*BW
Vvm=0.497305*BW
Vvad=0.035731*BW
Vvsk=0.16381*BW
Vvbo=0.063521*BW
Vvht=0.004722*BW
Vvth=0.002842*BW
Vvbr=0.006854*BW
Vvtes=BW*0.88687-Vvbr-Vvth-Vvht-Vvbo-Vvsk-Vvad-Vvm-Vvint-Vvsp-Vvst-Vvk-Vvl-Vvlu
;vascular volume
Va=0.02382*BW
Vv=0.047223*BW
Vlu=0.001755*BW
Vl=0.005307*BW
Vk=0.001003*BW
Vst=0.000627*BW
Vsp=0.001546*BW
Vint=0.005433*BW
Vm=0.013415*BW
Vad=0.00606*BW
Vsk=0.003176*BW
Vbo=0.002716*BW
Vht=0.000627*BW
Vth=0.0000836*BW
Vbr=0.000251*BW
Vtes=(BW*0.11313)-Vbr-Vth-Vht-Vbo-Vsk-Vad-Vm-Vint-Vsp-Vst-Vk-Vl-Vlu-Va-Vv
;PS*fubl
Plu=0.26
Pl=10.1
Pk=4.69
Pst=0.25
Psp=0.49
Pint=3.34
Pm=7.16
Pad=0.67
Psk=9.15
Pbo=17.1
Pht=0.31
Pth=1.37
Pbr=0.03
Ptes=0.18
CLuk=2.11 ;ml/h
; KP
KPlu=2.77
KPl=12.7
KPk=38.8
KPst=1.41
KPsp=6.04
KPint=2.4
KPm=0.94
KPad=0.66
KPsk=0.97
KPbo=2.63
KPht=1.28
KPth=0.86
KPbr=0.89
KPtes=1.68
Ca=Aa/Va
Cv=Av/Vv
Clu=Alu/Vlu
Cl=Al/Vl
Ck=Ak/Vk
Cst=Ast/Vst
Csp=Asp/Vsp
Cint=Aint/Vint
Cm=Am/Vm
Cad=Aad/Vad
Csk=Ask/Vsk
Cbo=Abo/Vbo
Cht=Aht/Vht
Cth=Ath/Vth
Cbr=Abr/Vbr
Ctes=Ates/Vtes
;Cva=Ava/Vva
;Cvv=Avv/Vvv
Cvlu=Avlu/Vvlu
Cvl=Avl/Vvl
Cvk=Avk/Vvk
Cvst=Avst/Vvst
Cvsp=Avsp/Vvsp
Cvint=Avint/Vvint
Cvm=Avm/Vvm
Cvad=Avad/Vvad
Cvsk=Avsk/Vvsk
Cvbo=Avbo/Vvbo
Cvht=Avht/Vvht
Cvth=Avth/Vvth
Cvbr=Avbr/Vvbr
Cvtes=Avtes/Vvtes
Inplu=CO*Cv
Inpl=Qhep*Ca+Qst*Cst+Qsp*Csp+Qint*Cint
Inpk=Qk*Ca
Inpst=Qst*Ca
Inpsp=Qsp*Ca
Inpint=Qint*Ca
Inpm=Qm*Ca
Inpad=Qad*Ca
Inpsk=Qsk*Ca
Inpbo=Qbo*Ca
Inpht=Qht*Ca
Inpth=Qth*Ca
Inpbr=Qbr*Ca
Inptes=Qtes*Ca
qtot=Qtes+Qbr+qth+qht+qbo+qsk+qad+qm+qint+qsp+qst+qk+qhep
Qtot=CO
fubl=0.03
d/dt (Al)=-(Ql+fubl*(Pl))*Cl+(Pl/KPl)*Cvl+Inpl
d/dt(Avl)=fubl*Pl*Cl-(Pl/KPl)*Cvl
d/dt (Alu)=-(Qlu+fubl*(Plu))*Clu+(Plu/KPlu)*Cvlu+Inplu
d/dt(Avlu)=fubl*Plu*Clu-(Plu/KPlu)*Cvlu
d/dt (Ak)=-(Qk+fubl*(PSk+CLuk))*Ck+(Pk/Kpk)*Cvk+Inpk
d/dt(Avk)=fubl*Pk*Ck-(Pk/KPk)*Cvk
d/dt(CLK)=fubl*CLuK*Ck
d/dt (Ast)=-(Qst+fubl*(Pst))*Cst+(Pst/KPst)*Cvst+Inpst
d/dt(Avst)=fubl*Pst*Cst-(Pst/KPst)*Cvst
d/dt (Asp)=-(Qsp+fubl*(Psp))*Csp+(Psp/KPsp)*Cvsp+Inpsp
d/dt(Avsp)=fubl*Psp*Csp-(Psp/KPsp)*Cvsp
d/dt (Aint)=-(Qint+fubl*(Pint))*Cint+(Pint/KPint)*Cvint+Inpint
d/dt(Avint)=fubl*Pint*Cint-(Pint/KPint)*Cvint
d/dt (Am)=-(Qm+fubl*(Pm))*Cvm+(Pm/KPm)*Cvm+Inpm
d/dt(Avm)=fubl*Pm*Cm-(Pm/KPm)*Cvm
d/dt (Aad)=-(Qad+fubl*(Pad))*Cad+(Pad/KPad)*Cvad+Inpad
d/dt(Avad)=fubl*Pad*Cad-(Pad/KPad)*Cvad
d/dt (Ask)=-(Qsk+fubl*(Psk))*Csk+(Psk/KPsk)*Cvsk+Inpsk
d/dt(Avsk)=fubl*Psk*Csk-(Psk/KPsk)*Cvsk
d/dt (Abo)=-(Qbo+fubl*(Pbo))*Cbo+(Pbo/KPbo)*Cvbo+Inpbo
d/dt(Avbo)=fubl*Pbo*Cbo-(Pbo/KPbo)*Cvbo
d/dt (Aht)=-(Qht+fubl*(Pht))*Cht+(Pht/KPht)*Cvht+Inpht
d/dt(Avht)=fubl*Pht*Cht-(Pht/KPht)*Cvht
d/dt (Ath)=-(Qth+fubl*(Pth))*Cth+(Pth/KPth)*Cvth+Inpth
d/dt(Avth)=fubl*Pth*Cth-(Pth/KPth)*Cvth
d/dt (Abr)=-(Qbr+fubl*(Pbr))*Cbr+(Pbr/KPbr)*Cvbr+Inpbr
d/dt(Avbr)=fubl*Pbr*Cbr-(Pbr/KPbr)*Cvbr
d/dt (Ates)=-(Qtes+fubl*(Ptes))*Ctes+(Ptes/KPtes)*Cvtes+Inptes
d/dt(Avtes)=fubl*Ptes*Ctes-(Ptes/KPtes)*Cvtes
;Ca1=(Av-Alu)
;Ca=Ca1/Va
d/dt(Aa)=-(Ql*Cl+Qk*Ck+Qm*Cm+Qsk*Csk+Qad*Cad+Qbo*Cbo+Qht*Cht+Qth*Cth+Qbr*Cbr+Qtes*Ctes)+CO*Cv
d/dt (Av)=-CO*Cv+Ql*Cl+Qk*Ck+Qm*Cm+Qsk*Csk+Qad*Cad+Qbo*Cbo+Qht*Cht+Qth*Cth+Qbr*Cbr+Qtes*Ctes
Dose=(10*BW) ; mg
Tmass=Av+Aa+Al+Ak+Ast+Asp+Aint+Aad+Am+Aht+Ask+Ath+Abr+Abo+Avl+Avk+Avst+Avsp+Avint+Avm+Ask+Avad+Avbo+
Avbr+Avbr+Avth+Avht+Ates+Avtes+CLK
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