; Model code of semi-mechanistic population PBPK model for coproporphyrin I (CPI)
; The control file including indiviudal's clinical data for CPI and rifampicin (ControlFile.csv) are not provided due to confidentiality.

$SIZES LVR=60
$PROBLEM CP1 PBPK
$DATA ControlFile.csv IGNORE=@
$INPUT ID TIME TAD DV AMT MDV CMT OCC EVID DAY TYPE TRT KA CL V MTT N RS GEN STID SEX
$SUBROUTINE ADVAN13 TOL9

$MODEL
	; NUM/ DESCRIPTION
	COMP=(DEPO)    	    				; 1 DEPO
	COMP=(RIF)    	    				; 2 RIF (PLAS)
	COMP=(CP1PL)    				; 3 CP1, BLOOD (Central)
	COMP=(CP1LV)    				; 4 CP1, LIV VASCULAR
	COMP=(CP1LT)    				; 5 CP1, LIV VASCULAR
	COMP=(CP12 INITIALOFF NODOSE)    		; 6 CP1, URINE
	COMP=(BILE)    					; 7 CP1, BILE
	
$PK
	CALLFL=-1
	MXSTEP=500000
	
; .....................FIXED PARAMETERS
	CLPASS 	= 0.76           	; ul/min/million cells
	VL	= 1.6			; L
	QH	= 92.7			; L/hr
	FUP	= 0.069			; no inits 
	VLT	= VL*(1-0.115)		; L                   
	VLB	= VL*0.115		; L
	FULT	= 0.19			; based on human fucell
	BP	= 0.63			; Yoshikado et al. (2018)
	FUB	= FUP/BP			
	NHEPS	= VLT*1000*120		; number of hepatocytes per mL of liver
	UC	= 1/1000000*60		; unit conversion ƒÊL/min to L/h
	
;   IOV 
    OCC1=0
    OCC2=0
    OCC3=0

    IF (OCC.EQ.1) OCC1=1
    IF (OCC.EQ.2) OCC2=1
    IF (OCC.EQ.3) OCC3=1
	IOV_CLB   =OCC1*ETA(5)+OCC2*ETA(6)+OCC3*ETA(7)
	
; Ethnicity effect
	RACE=1
	IF (STID.EQ.2) RACE=0
	
; Sex effect	
	GENDER=0
	IF (SEX.EQ.0) GENDER=1	
;................................................................................	
	
	IF(AMT.GT.0.AND.CMT.EQ.1)PODO=AMT 	; rifamcpiin oral dose
	
; ---------PARAMETERS TO BE ESTIMATED-------------------------------------------------
	KTR 	= (N+1)/MTT 										
	KSYN	= THETA(1)*EXP(ETA(1))*(1-GENDER*THETA(13))							
	CLB	= THETA(2)*EXP(ETA(2) + IOV_CLB)
    	CLR	= THETA(3)*EXP(ETA(3))	
	VCP  	= THETA(4)*EXP(ETA(4))							
	KI	= THETA(5)
	CLACT   = THETA(6)*(1-RACE*THETA(8))

; Genetic effect
	CLFRAX  = THETA(7)
	CLFRA   = 1/(1+CLFRAX)
	CLUP    = CLACT*(1-RS*CLFRA)
	
	NFAC = SQRT(2*3.1415)*N**(N+0.5)*EXP(-N) 	; Stirling approximation to n! included for completeness

;---------------- SCALE THE VOLUMES ( NO SCALING) ----------------------------------------------
S1 = 1
S2 = V
S3 = BP
S4 = 1
S5 = 1
S6 = 1

; THIS IS IMPORTANT
F1 = 0    
;---------------- DIFFERENTIAL EQUATIONS -------------------------------------------------------
$DES	
	; (1) RIF - DEPO (AMT)
	DADT(1)= PODO*KTR*(KTR*TAD)**N*EXP(-KTR*TAD)/NFAC - KA*A(1)

	; (2) RIF - PLAS (AMT)
	DADT(2)= KA*A(1) - (CL/V)*A(2) 
	
	; (3) CP1 - Blood, central (CONC)
	DADT(3) = KSYN/VCP - CLR*A(3)/VCP + QH*A(4)/VCP - QH*A(3)/VCP 
	
	; (4) CP1 - LIVER BLOOD (CONC)
	DADT(4) = QH*A(3)/VLB - QH*A(4)/VLB + CLPASS*NHEPS*UC*A(5)*FULT/VLB - CLPASS/VLB*NHEPS*UC*A(4)*FUB - ((1-TRT)*CLUP*NHEPS*UC*A(4)*FUB)/VLB - (TRT*CLUP*NHEPS*UC*A(4)*FUB/(1+((A(2)/V)/KI)))/VLB
	
	; (5) CP1 - LIVER TISSUE (CONC)
	DADT(5) = CLPASS*NHEPS*UC*A(4)*FUB/VLT - CLPASS*NHEPS*UC*A(5)*FULT/VLT + ((1-TRT)*CLUP*NHEPS*UC*A(4)*FUB)/VLT + (TRT*CLUP*NHEPS*UC*A(4)*FUB/(1+((A(2)/V)/KI)))/VLT - CLB*A(5)*FULT/VLT 

	; (6) CP1 - URINE (AMT))
	DADT(6)= CLR*A(3)
	
	; (7) CP1 - BILE  (AMT)
    	DADT(7)= CLB*FULT*A(5)
	
$ERROR
	IPRE = F
	IF(CMT.EQ.3)   W = (F*F*THETA(9)**2 + THETA(10)**2)**0.5    	; CP1 - BLOOD
	IF(CMT.EQ.-6)  W = (F*F*THETA(11)**2 + THETA(12)**2)**0.5    	; CP1 - URINE

	IF(W.EQ.0) W = 1
	IRES  = IPRE-DV
	IWRES = IRES/W

	Y = F + W*EPS(1)

$THETA
(0, 20) 		; (1) KSYN
(0, 5) 		        ; (2) CLB 
(0, 1.68) 		; (3) CLR
(0, 6.59) 		; (4) VCP
(0  1.15)  		; (5) KI
(0, 100) 		; (6) CLACT
(0, 0.34)  		; (7) CLFRAX
(0.4) 		        ; (8) COV - CLACT
(0, 0.126) 		; (9) PROP - CP1 BLOOD 	
(0.001) FIX             ; (10) ADD - CP1 BLOOD
(0, 0.354) 		; (11) PROP - CP1 URINE	
(0, 2.19) 		; (12) ADD - CP1 URINE	
(0.25) 		        ; (13) COV - KSYN

$OMEGA BLOCK(1) 0.01 		; (1) KSYN
$OMEGA BLOCK(1) 0.1 		; (2) CLB 	
$OMEGA BLOCK(1) 0.01 		; (3) CLR
$OMEGA BLOCK(1) 0.1 	        ; (4) VCP
$OMEGA BLOCK(1) 0.1 	        ; (5) IOV_CLB
$OMEGA BLOCK(1) SAME     	; (6) IOV_CLB
$OMEGA BLOCK(1) SAME    	; (7) IOV_CLB

$SIGMA 1 FIX 

$ESTIMATION MAXEVALS=999999 SIGL=4 NSIG=2 PRINT=10 NOABORT METHOD=1 INTERACTION
$COVAR UNCONDITIONAL
$TABLE ID TIME TAD DV AMT MDV CMT OCC EVID DAY TYPE TRT KA CL V MTT N RS GEN STID IPRE IRES IWRES CWRES KA CL V MTT N KSYN CLB CLR VCP KI CLACT
ONEHEADER NOPRINT APPEND FORMAT=,1PE15.8 FILE=PE_result.tab