PROGRAM: MODEL FOR LACTATIONAL TRANSFER ' ******* LACTMAN.CSL ******* ' ' ******* PART 1 0F 2 OF MODEL LACTMAN ******* ' '-------------------------------------------------------------------' 'PCE AND RISK ASSESSMENT ' 'PBPK MODEL FOR WOMAN WITH INFANT ' 'Originally posted at PBPK-L Source Code Listing, ' 'URL: http://www.navy.al.wpafb.af.mil/new.htm ' 'DISCLAIMER: By using this PBPK source code you, the user, ' ' implicitly agrees with the conditions and rules stated in this ' ' public domain source code disclaimer. If you have not read ' ' this yet, please read it now. If you do not agree with the ' ' conditions and rules stated in it, please dispose of all contents ' ' of the PBPK source file and all related files now in your ' ' possession. The PBPK computer modeling programs are placed here by' ' their authors for the convenience of others interested in PBPK ' ' modeling. No representation of their suitability or correctness is' ' implied. Please understand that PBPK models are complex entities ' ' whose value is minimal when taken out of context. With that ' ' understanding, you are welcome to use this code for teaching and ' ' further development of the ideas that they represent. The ' ' information and/or opinions presented here are those of the ' ' authors and are not endorsed by the US Air Force, US Navy, US ' ' Army, Tri-Service Toxicology Consortium, Department of Defense, or' ' the US Government. The US Air Force, US Navy, US Army, Tri-Service' ' Toxicology Consortium, Department of Defense, or the US Government' ' and the authors of this PBPK source code accept no responsibility ' ' for damages resulting from the use of the code and make no ' ' warranty or representation, either express or implied, including ' ' but not limited to, any implied warranty of merchantability or ' ' fitness for a particular purpose. PBPK source code is provided *as' ' is*, and you, its user, assume all risks when using it. ' ' Description of this program has been published: Byczkowski,J.Z., ' ' and Fisher,J.W. (1995) A computer program linking physiologically ' ' based pharmacokinetic model with cancer risk assessment for ' ' breast-fed infants. Computer Methods Progr. Biomed. 46, 155-163. ' ' Reprints of this article are indicated as AL/OE-TR-1995-0014 by ' ' Armstrong Aerospace Medical Research Laboratory, Wright Patterson ' ' Air Force Base, OH. ' ' Results of simulation have been published: Byczkowski,J.Z. (1996) ' ' A linked pharmacokinetic model and cancer risk assessment for ' ' breast-fed infants. Drug Information J. 30, 401-412. ' ' Reprints of this article are indicated as AL/OE-TR-1996-0007 by ' ' Armstrong Aerospace Medical Research Laboratory, Wright Patterson ' ' Air Force Base, OH. ' 'Key words: Physiologically based pharmacokinetic model, PBPK, ' ' Tetrachloroethylene, PERC, PCE, Cancer risk assessment, ' ' Breast-fed infant, Toxicology. ' ' Please send comments to the authors E-mail address: ' ' JANUSZ.BYCZKOWSKI@USA.NET ' '^^^^^^^^^^^^^^^Please do not delete this message^^^^^^^^^^^^^^^^^^^' '-------------------------------------------------------------------' INITIAL '* Physiological parameters ' CONSTANT BWA = 60. $'INITIAL BODY WT [KG] ' CONSTANT BWC = 1. $'MATERNAL BODY WT GAIN [RATIO] ' CONSTANT BWPI = 7.2 $'INITIAL BODY WT INFANT [KG] ' CONSTANT QLC = 0.25 $'FRACTIONAL BLOOD FLOW TO LIVER ' CONSTANT QFC = 0.05 $'FRACTIONAL BLOOD FLOW TO FAT ' CONSTANT QPC = 19.7 $'ALVEOLAR VENTILATION RATE [L/HR/KG] ' CONSTANT QPCP = 25.2 $'ALVEOLAR VENTILATION RATE INFANT [L/HR] ' CONSTANT QCC = 18.0 $'CARDIAC OUTPUT [L/HR] ' CONSTANT QCCP = 22.0 $'CARDIAC OUTPUT INFANT [L/HR] ' CONSTANT QMTC = 0.1 $'BLOOD FLOW TO MAMMARY TISSUE [L/HR] ' CONSTANT VFC = 0.2 $'VOLUME OF FAT [L/L BW] ' CONSTANT VMATC= 0.05 $'VOLUME MAMMARY TISSUE ' CONSTANT VLC = 0.04 $'FRACTION LIVER TISSUE ' CONSTANT PB = 19.8 $'BLOOD/AIR PARTITION COEFFICIENT, PCE ' CONSTANT PPB = 8.0 $'PART. COEFF.INF BLOOD/AIR, PCE ' CONSTANT PL = 6.83 $'LIVER/BLOOD PARTITION COEFFICIENT, PCE ' CONSTANT PF =159.03 $'FAT/BLOOD PARTITION COEFFICIENT, PCE ' CONSTANT PS = 7.77 $'SLOWLY PERFUSED TISSUE/BLOOD PART.COEFF.,PCE' CONSTANT PR = 6.83 $'RICHLY PERFUSED TISSUE/BLOOD PART.COEFF.,PCE' CONSTANT PPt = 6.596 $'TISSUE INF/BLOOD PC, PCE ' CONSTANT VtCP = 0.9 $'FRACTION INF TISSUE [based on 75ml blood/kg]' CONSTANT PNO = 1. $'NO. OF INFANTS ' CONSTANT PMILK = 2.8 $'MILK BLOOD PC FOR PCE ' CONSTANT VMILK = 0.02917 $'VOLUME OF MILK [L] ' CONSTANT OUTI = 0.02917 $'MILK YIELD [L/HR] ' CONSTANT VGI = 0.0836 $'FRACTION GI TRACT, INFANT ' '* Toxicant ' CONSTANT MW = 166. $'MOLECULAR WEIGHT [G/MOL] ' CONSTANT KM = 0.315 $'MICHAELIS-MENTEN CONSTANT [MG/L] ' CONSTANT KFC = 0. $'FIRST ORDER METABOLISM RATE CONSTANT[/HR-1KG]' '* Exposure ' CONSTANT PDOSE = 0.0 $'ORAL DOSE [MG/KG] ' CONSTANT VMAXC = 0.151 $'MAXIMAL VELOCITY METABOLISM,PCE [MG/KG/HR]' CONSTANT KA = 0.00 $'ORAL UPTAKE RATE [/HR] ' CONSTANT KAP = 0.50 $'ORAL UPTAKE, INF [/HR] ' CONSTANT IVDOSE = 0.00 $'IV DOSE [MG/KG] ' CONSTANT CONC = 50. $'INHALED CONCENTRATION [PPM] ' CONSTANT BCK = 0.0041$'BACKGROUND INHALATION EXPOSURE [PPM] ' CONSTANT INFEX = 0. $'INFANT NOT EXPOSED TO BCK (if so INFEX=1) ' CONSTANT Y = 1. $'YEARS OF EXPOSURE TO PCE [YEARS] ' IF (PDOSE.EQ.0.) KA = 0. '* Timing commands ' CONSTANT WDAYS=5.,WEDAYS=2.,DAYS=27. CONSTANT PDAYS=0. INTEGER DAY TSTOP = (DAYS+PDAYS)*24. $'LENGTH OF SIMULATION [HRS] ' CONSTANT TCHNG = 8.0 $'LENGTH OF INHALATION EXPOSURE [HRS] ' CONSTANT TINF = 0.01 $'LENGTH OF IV INFUSION [HRS] ' CONSTANT CINT = 0.1 $'COMMUNICATION INTERVAL ' DAY=-1 $'TO START ON MONDAY -1, TUES 0, WEDN 1, ETC. ' END $'END OF INITIAL ' '-------------------------------------------------------------------' DYNAMIC '* Discrete schedule for CI and OUTX ' ' CI = CONCENTRATION IN INHALED AIR (MG/L) ' ' OUTX = SUCKLING MILK ' DISCRETE CAT1 INTERVAL CAT = 24. $'EXECUTE CAT1 EVERY 24 HR ' DAY=DAY+1 IF(MOD(DAY,7).GE.5) GOTO OUT CI = CONC*MW/24450. $'START INHAL. EXPOSURE [MG/L] ' OUTX = 0 $'NOT FEEDING INFANT ' SCHEDULE CAT2 .AT. T + TCHNG $'SCHEDULE END OF EXPOSURE ' OUT.. CONTINUE END $'END OF CAT1 ' DISCRETE CAT2 CI = BCK*MW/24450 $'BACKGROUND INHALATION EXPOSURE ' OUTX = OUTI $'KEEP FEEDING INFANT ' END $'END OF CAT2 ' '-------------------------------------------------------------------' ALGORITHM IALG = 2 $ 'GEAR METHOD FOR STIFF SYSTEMS ' DERIVATIVE '* Scaled parameters ' VL = VLC*BW $ 'VOLUME LIVER [L] ' VS = 0.79*BW-VF-VMAT $ 'VOLUME SLOWLY PERF. TISSUE [L] ' VR = 0.12*BW-VL $ 'VOLUME RAPIDLY PERFUSED TISSUE [L] ' QL = QLC*QC $ 'BLOOD FLOW TO LIVER [L/HR] ' QS = 0.24*QC-QF $ 'BLOOD FLOW TO SLOWLY PERF.TISS.[L/HR]' QR = 0.76*QC-QL-QMT $ 'BLOOD FLOW TO RAPIDLY PERF.TISS[L/HR]' QF = QFC*QC $ 'BlOOD FLOW TO FAT [L/HR] ' VMAX = VMAXC*BW**.74 $ 'Vmax FOR PCE [MG/HR] ' KF = KFC/BW**0.3 $ 'FIRST ORDER METABOL. RATE PCE [/HR] ' DOSE = PDOSE*BW $ 'ORAL DOSE, MOTHER [MG] ' IVR = IVDOSE*BW/TINF $ 'RATE INTRAVENOUS DOSING [MG/HR] ' BW=BWC*BWA $ 'BODY WEIGHT [KG] ' QMT=QMTC*QC $ 'MAMMARY BLOOD FLOW [L/HR] ' VF=VFC*BW $ 'FAT VOLUME [L] ' VMAT=VMATC*BW $ 'MAMMARY VOLUME [L] ' QC=QCC*BW**0.74 $ 'CARDIAC OUTPUT [L/HR] ' QP=QPC*BW**0.74 $ 'ALVEOLAR VENTILATION RATE [L/HR] ' '* Scaled parameters for infant ' BWP = BWPI*PNO $ 'TOTAL BODY WEIGHT OF ALL INFs [KG] ' QCP = QCCP*BWP**0.74 $ 'CARDIAC OUTPUT INFANT [L/HR] ' QPP = QPCP*BWP**0.74 $ 'ALVEOLAR VENTILATION RATE INF. [L/HR]' VtP = VTCP*BWP $ 'VOLUME SOLID TISSUE INFANT [L] ' GIW = VGI*BWP $ 'GASTROINTESTINAL TRACT WEIGHT INF[KG]' INF = BCK*MW/24450. $ 'CONCENTR.INFANT BREATHING ZONE [MG/L]' '-------------------------------------------------------------------' '* CA = CONCENTRATION IN ARTERIAL BLOOD [MG/L] ' CA=(QC*CV+QP*CI)/(QC+(QP/PB)) AUCB=INTEG(CA,0.) '* AX = AMOUNT EXHALED [MG] ' CX=CA/PB CXPPM=(0.79*CX+0.21*CI)*24450./MW RAX=QP*CX AX=INTEG(RAX, 0.) CEXP=(0.79*CX+0.21*CI) '* AS = AMOUNT IN SLOWLY PERFUSED TISSUES [MG] ' RAS=QS*(CA-CVS) AS=INTEG(RAS,0.) CVS=AS/(VS*PS) CS=AS/VS '* AR = AMOUNT IN RAPIDLY PERFUSED TISSUES [MG] ' RAR=QR*(CA-CVR) AR=INTEG(RAR,0.) CVR=AR/(VR*PR) CR=AR/VR '* AF = AMOUNT IN FAT TISSUE [MG] ' RAF=QF*(CA-CVF) AF=INTEG(RAF,0.) CVF=AF/(VF*PF) CF=AF/VF '* AL = AMOUNT IN LIVER TISSUE [MG] ' RAL=QL*(CA-CVL)-RAM AL=INTEG(RAL,0.) CVL=AL/(VL*PL) CL=AL/VL '* AM = AMOUNT METABOLIZED [MG] ' RAM=(VMAX*CVL)/(KM+CVL) + KF*CVL*VL AM=INTEG(RAM,0.) '* IV = INTRAVENOUS INFUSION RATE [MG/HR] ' IV=IVR*(1.-STEP(TINF)) '* CV = MIXED VENOUS BLOOD CONCENTRATION [MG/L] ' CV=(QF*CVF+ QL*CVL+ QS*CVS+ QR*CVR+QMT*CVMT)/QC AUCCV=INTEG(CV,0.) AVEN=INTEG(CV*QC,0.) '* PCEMAS = MASS BALANCE IN MOTHER [MG] ' PCEMAS=AF+AL+AS+AR+AM+AX+AMAT+APUP AINH=INTEG(CI*QP,0.) INHBAL=PCEMAS-AINH '* AMAT = AMT OF PCE IN MILK [MG] ' RMAT=QMT*(CA-CVMT)-RPUP AMAT=INTEG(RMAT,0.) CVMT=AMAT/(VMILK*PMILK) CMAT=AMAT/VMILK AUCMAT=INTEG(CMAT,0.) '* ELIM. RATE FOR TCE FROM MILK TO INF [MG/HR] ' RPUP=OUTX*CMAT APUP=INTEG(RPUP,0.) DOSEP=APUP/BWP $'DOSE RECEIVED BY INF [MG/KG] ' '-------------------------------------------------------------------' PROCEDURAL IF (T.GE.24.) MOMID=(AINH*24)/(BW*T) IF (T.GE.24.) IDM=(DOSEP*24)/T IF (T.GE.24.) IDI=(AINF*24)/(BWP*T) END $'END OF PROCEDURAL, MOMID,IDM,IDI [MG/KG/DAY] ' '* AMOUNT REMAINING IN GI. TRACT, INFANT [MG] ' MR=INTEG(RMR,0.) RMR=RPUP-RAP $'RATE OF GI. LOADING,INFANT [MG/HR] ' RAP=MR*KAP $'RATE OF GI.ABSORPTION, INFANT [MG/HR] ' AAP=INTEG(RAP,0.) $'AMOUNT ABSORBED, INFANT [MG] ' CGIT=MR/GIW $'CONCENTRATION IN GI.TRACT, INFANT [MG/KG] ' GIBAL=APUP-(MR+AAP) '* CAP = CONCENTRATION IN ARTERIAL BLOOD INFANT [MG/L] ' CAP=(QCP*CVP+QPP*INF*INFEX)/(QCP+(QPP/PPB)) AUCBP=INTEG(CAP,0.) AINF=INTEG(INF*INFEX*QPP,0.) $'AMOUNT INHALED FROM BCK,INF.[MG]' '* AXP = AMOUNT EXHALED INFANT [MG] ' CXP=CAP/PPB CXPPMP=(0.7*CXP)*24450./MW RAXP=QPP*CXP AXP=INTEG(RAXP,0.) '* ATP = AMOUNT IN SOLID TISSUES EXCEPT GI. TRACT, INFANT [MG] ' RATP=QCP*(CAP-CVP)+RAP ATP=INTEG(RATP,0.) CTP=ATP/VTP '* CPUPT = CONCENTRATION IN A WHOLE INFANT [MG/KG] ' CPUPT=(MR+ATP)/VTP '* CVP = CONCENTRATION IN VENOUS BLOOD INFANT [MG/L] ' CVP=ATP/(VTP*PPT) '* TMASSP = MASS BALANCE INFANT [MG] ' TOTINF=IDM+IDI $'TOTAL INFANT DOSE [MG/KG/DAY] ' TMASSP=AtP+AXP PUPBAL=TMASSP-AAP $'BALANCE IN TISSUES EXCEPT GI. TRACT, INF. ' TOTP=TMASSP+MR TTBALP=TOTP-(APUP+AINF) $'BALANCE IN A WHOLE INFANT ' '-------------------------------------------------------------------' '* Risk assessment: ECRI - FROM PCE IN MILK, INFANT ' ' TCRI - FROM BOTH INGESTED AND INHALED, INFANT ' ECRI = 0.051*IDM*Y/70 $'1 YEAR OVER LIFESPAN OF 70' TCRI = 0.051*TOTINF*Y/70 $'1 YEAR OVER LIFESPAN OF 70' '-------------------------------------------------------------------' '* CONDITION FOR TERMINATION OF RUN TO PREVENT JUMPING OVER TSTOP ' TERMT(T.GE.TSTOP) END $'END OF DERIVATIVE ' END $'END OF DYNAMIC ' '-------------------------------------------------------------------' END $'END OF PROGRAM LACTMAN.CSL ' 'CUT HERE>----------------------------------------------------------' ' ***** END OF PART 1 0F 2 OF MODEL LACTMAN***** '