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Berkeley Madonna: Dose Calculations for Pharmacokinetics and Pharmacodynamics, Study notes of Medical statistics

The Berkeley Madonna code for calculating single and steady-state doses of a drug based on its pharmacokinetic (PK) and pharmacodynamic (PD) properties. The code includes parameters for dosing, saturable bioavailability, PK values, PD potency, and threshold values for drug holiday calculations. It also includes definitions for sliders and batch runs for parameter selection and execution.

Typology: Study notes

2021/2022

Uploaded on 09/12/2022

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BERKELEY MADONNA CODE - FOR SINGLE DOSE CASE
;Single Dose - ICp=Cmax only
METHOD RK4
STARTTIME = 0
STOPTIME=24
DT = 0.05
;Enter dosing parameters
TAU=24 ;inter-dose interval
TABMG=1 ;tablet size available (mg)
;Enter saturable bioavailability parameters
D50=90 ; (mg) will only be used if saturable bioavailability selected
MaxS=0.9 ;maximum saturation of bioavailability
;Enter PK values and PD potency
Ka=0.367 ;1/h
CL=5.0 ;L/h
Vc =46.0 ;L
IC50=0.01 ;mcg/mL
;define the threshold to use for drug holiday calculations (number or formula)
THLD=15*IC50/85
;dosetype - Cmax only
;bioavailability type 1 is F=1 and 2 is saturable
biotype=1
;-----------------CODE BEGINS---------------------------
;initial value of inhibition
P=10
;calculate ICx based upon IC50
ICP=P*IC50/(100-P)
;Single-Dose PK
Ke=CL/Vc
diff=Ka-Ke
;compute single-dose Tmax
tmax=LOGN(Ka/Ke)/diff
;-------------------exact dose calculations f=1-------------------
bio=1
fedose=ICP*Vc/(bio*exp(-Ke*tmax))
;-------------------exact dose calculations f=1-------------------
;-------------------exact dose calculations F=1- MaxS*D/(D50+D)-------------------
A=(1-MaxS)*exp(-Ke*tmax)
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BERKELEY MADONNA CODE - FOR SINGLE DOSE CASE

;Single Dose - ICp=Cmax only METHOD RK STARTTIME = 0 STOPTIME= DT = 0.

;Enter dosing parameters TAU=24 ;inter-dose interval TABMG=1 ;tablet size available (mg)

;Enter saturable bioavailability parameters D50=90 ; (mg) will only be used if saturable bioavailability selected MaxS=0.9 ;maximum saturation of bioavailability

;Enter PK values and PD potency Ka=0.367 ;1/h CL=5.0 ;L/h Vc =46.0 ;L IC50=0.01 ;mcg/mL ;define the threshold to use for drug holiday calculations (number or formula) THLD=15*IC50/

;dosetype - Cmax only

;bioavailability type 1 is F=1 and 2 is saturable biotype=

;-----------------CODE BEGINS--------------------------- ;initial value of inhibition P=

;calculate ICx based upon IC ICP=P*IC50/(100-P)

;Single-Dose PK Ke=CL/Vc diff=Ka-Ke

;compute single-dose Tmax tmax=LOGN(Ka/Ke)/diff

;-------------------exact dose calculations f=1------------------- bio= fedose=ICPVc/(bioexp(-Ke*tmax)) ;-------------------exact dose calculations f=1-------------------

;-------------------exact dose calculations F=1- MaxSD/(D50+D)------------------- A=(1-MaxS)exp(-Ke*tmax)

B=D50exp(-Ketmax)-ICPVc C=-1ICPD50Vc

sedose=( -1B + SQRT(B2-4AC))/(2A) ;-------------------exact dose calculations F=1-MaxS*D/(D50+D)-------------------

;select the final exact dose based upon bioavailability type edose= if (biotype=1) then fedose else sedose

;compute doses that can be administered dose=INT(edose/TABMG)*TABMG

; ignore available table size for QC ;dose=edose

;compute relative bioavailability of administered dose F= if (biotype=2) then 1-MaxS*dose/(D50+dose) else 1

;compute model-predicted Cmax, Ctau, AUC(0-tau), Cavg for administered single-doses Co=(KaF)/(Vcdiff) AF1=(1-exp(-1KeTAU))/Ke AF2=(1-exp(-1KaTAU))/Ka

Cmax=Codose(exp(-1Ketmax)-exp(-1Katmax)); Ctau=Codose(exp(-1KeTAU)-exp(-1KaTAU)) auctau=Codose(AF1-AF2) Cavg=AUCtau/TAU

;compute the concentration and PD effect - time values Cp=Codose(exp(-1KeTIME) - exp(-1KaTIME)) PD=100-100*(Cp/(IC50+Cp))

;compute the avgerage PD effect d/dt (PDAUC) = PD init PDAUC = 0 AvgPD=if TIME >= TAU-0.0001 then PDAUC/TAU else -

;compute drug holiday HOL = IF (Cp >= THLD) THEN 1 ELSE 0 d/dt (DHOL) = HOL init DHOL = 0 DrugHol = if TIME >= TAU-0.0001 then (TAU-DHOL) else 0

BERKELEY MADONNA CODE - FOR STEADY-STATE DOSE CASE

;Steady-State METHOD RK STARTTIME = 0 STOPTIME= DT = 0.

;Enter dosing parameters TAU=24 ;inter-dose interval TABMG=1 ;tablet size available (mg)

;Enter saturable bioavailability parameters D50=90 ; (mg) will only be used if saturable bioavailability selected MaxS=0.9 ;maximum saturation of bioavailability

;Enter PK values and PD potency Ka=0.367 ;1/h CL=5.0 ;L/h Vc =46.0 ;L IC50=0.01 ;mcg/mL ;define the threshold to use for drug holiday calculations (number or formula) THLD=15*IC50/

;dosetype 1=ctau, 2=cavg, 3=cmax dosetype=

;bioavailability type 1 is F=1 and 2 is saturable biotype=

;-----------------CODE BEGINS---------------------------

;initial value of inhibition P= ;calculate ICx based upon IC ICP=P*IC50/(100-P)

;Steady-State PK values needed for calculations Ke=CL/Vc diff=Ka-Ke tKedif=1-exp(-1KeTAU) tKadif=1-exp(-1KaTAU)

;compute steady-state Tmax tmax=(1/diff)LOGN(KatKedif/(Ke*tKadif))

;-------------------begin exact dose calculations f=1------------------- bio= fracss1=exp(-1keTAU)/tKedif fracss2=exp(-1kaTAU)/tKadif

fracss3=exp(-1ketmax)/tKedif fracss4=exp(-1katmax)/tKadif

fedosetau=(ICpVcdiff)/(Kabio(fracss1-fracss2)) ;exact dose for Ctau=ICp fedoseavg=ICpCLTAU/bio ;exact dose for Cavg=ICp fedosemax=(ICpVcdiff)/(Kabio(fracss3-fracss4)) ;exact dose for Cmax=ICp

;select the exact dose for the type of interest fedose = if (dosetype=1) then fedosetau else (if (dosetype=2) then fedoseavg else fedosemax) ;-------------------end exact dose calculations f=1-------------------

;-------------------begin exact dose calculations F=1 - MaxSD/(D50+D)------------------- A1dtau=exp(-KeTAU) A2dtau=exp(-KaTAU) A3dtau=1-A1dtau A4dtau=1-A2dtau Adtau=Ka(1-MaxS)(A1dtauA4dtau-A2dtauA3dtau) Bdtau=KaD50(A1dtauA4dtau-A2dtauA3dtau)-ICPVc(Ka-Ke)A4dtauA3dtau Cdtau=-1ICPD50Vc(Ka-Ke)A4dtau*A3dtau

A1dmax=exp(-Ketmax) A2dmax=exp(-Katmax) A3dmax=exp(-KeTAU) A4dmax=exp(-KaTAU) A5dmax=1-A3dmax ;(1-ketau) A6dmax=1-A4dmax ;1-katau Admax=Ka(1-MaxS)(A1dmaxA6dmax-A2dmaxA5dmax) Bdmax=KaD50(A1dmaxA6dmax-A2dmaxA5dmax)-ICPVc(Ka-Ke)A5dmaxA6dmax Cdmax=-1ICPD50Vc(Ka-Ke)A5dmaxA6dmax

Adavg=1-MaxS Bdavg=D50-1ICPCLTAU Cdavg=-1ICPCLTAU*D

sedosetau=( -1Bdtau + SQRT(Bdtau2-4AdtauCdtau))/(2Adtau) ;exact dose for Ctau=ICp sedoseavg=( -1Bdavg + SQRT(Bdavg2-4AdavgCdavg))/(2Adavg) ;exact dose for Cavg=ICp sedosemax=( -1Bdmax + SQRT(Bdmax2-4AdmaxCdmax))/(2Admax) ;exact dose for Cmax=ICp

;select the saturable edose for the type of interest sedose = if (dosetype=1) then sedosetau else (if (dosetype=2) then sedoseavg else sedosemax) ;-------------------end exact dose calculations F=1 - MaxS*D/(D50+D)-------------------

;select the final exact dose based upon bioavailability type edose= if (biotype=1) then fedose else sedose

;compute doses that can be administered dose=INT(edose/TABMG)*TABMG