# Two compartment beaker model

### Objective and introduction

# Objectives

- To observe the time course of drug concentration in the centrl and peripheral compartments of a two-compartment system.
- To compare the time course after 3 types of input.
- Single Bolus Dose
- Single Bolus Dose and Constant Rate Infusion
- Single Bolus Dose plus First-Order and Constant Rate Infusion

# Introduction

This is a practical session held in a laboratory. For health and safety reasons it is important to wear a lab coat and closed shoes.

Bring a printed copy of the lab instructions and read through them before you arrive at the lab.

### Overview and assignment

# Overview

- Use the data in the beka_assay_calibration.xlsx to define the relationship between absorbance and amaranth concentration
- Construct a standard curve relating absorbance to amaranth dye concentrations on three occasions.
- Use one of the provided data sets with absorbance measurementts in the central compartment (DVID=1) and the tissue compartment (DVID=2).
- bo----_ABS is a bolus dose of 10 mg into the central compartment;
- bo--zo_ABS is a bolus dose of 10 mg into the central compartment, constant infusion of 1 mg/min
- bofozo_ABS is a bolus dose of 10 mg into the central compartment, first-order infusion with a bolus dose of 40 mg in the burette and constant infusion of 1 mg/min
- Add a concentration column to the data set with absorbance measurements using the slope and intercept from the first calibration curve.
- Save the concentration data set with columns #ID, TIME, DVID, ABS and CONC in a csv file with a name such as bo----_CONC.csv
- Use either Monolix and the beka_mlxt model (Figure 1) or NONMEM and the beka.ctl model (Figure 2) to estimate the parameters of the two compartment system with the data set of concentrations.
- You will need to change the constants in the Monolix or NM-TRAN code defining the 3 kinds of input in order to match the kinds of input you used for your experiment.

$PROBLEM BEKA two compartment model with bolus, zero-order and
first-order input

$MODEL

COMP=(AMTC) ; central

COMP=(AMTT) ; tissue

COMP=(AMTB) ; burette

$PSI

cl vc clic vt ; PK parameters

$PK

; Check these values match the experimental design

bolus=10 ; 10 mg bolus dose into central compartment

infrate=1 ; 1 mg/min infusion into burette

burdose=40 ; 40 mg bolus dose into burette

burvol=0.1 ; 0.1 L burette volume

burflow=0.01 ; 0.01 L/min burette flow

tk0=120 ; 120 min infusion from burette

$ODE

AMTC_0 = bolus

AMTT_0 = 0

AMTB_0 = infrate/burflow*burvol+burdose

CC=AMTC/vc

CT=AMTT/vt

CB=AMTB/burvol

;'t' is the name used by Monolix to

; refer to the data item defined as TIME.

if (t<tk0) then

ratein=burflow*CB

else

ratein=0

endif

DDT_AMTC = ratein + clic*CT - (cl+clic)*CC

DDT_AMTT = clic*(CC - CT)

DDT_AMTB = infrate - ratein

$OUTPUT

OUTPUT1 = AMTC/vc

OUTPUT2 = AMTT/vt

Figure 1. Code for beka_mlxt.txt

$INPUT ID TIME DVID ABS DV

$DATA bo----_CONC.csv

$EST METHOD=COND INTER

MAX=9990 NSIG=3 SIGL=9 NOABORT PRINT=1

$THETA

(0,0.1,) ; CL

(0,1,) ; VC

(0,0.4,) ; CLIC

(0,4,) ; VT

$OMEGA 0 FIX ; PPV_CL

$SIGMA

1 ; RUVC_SD

1 ; RUVT_SD

$SUBR ADVAN13 TOL=9

$MODEL

COMP=(AMTC) ; central

COMP=(AMTT) ; tissue

COMP=(AMTB) ; burette

$PK

bolus=10 ; 10 mg bolus dose into central compartment

infrate=1 ; 1 mg/min infusion into burette

burdose=40 ; 40 mg bolus dose into burette

burvol=0.1 ; 0.1 L burette volume

burflow=0.01 ; 0.01 L/min burette flow

tk0=120 ; minutes of infusion from burette

cl=CL*EXP(PPV_CL)

A_0(1) = bolus

A_0(2) = 0

A_0(3) = infrate/burflow*burvol+burdose

$DES

CC=A(1)/vc

CT=A(2)/vt

CB=A(3)/burvol

; T is time used by differential equation solver

if (T<tk0) then

ratein=burflow*CB

else

ratein=0

endif

DADT(1) = ratein + clic*CT - (cl+clic)*CC

DADT(2) = clic*(CC - CT)

DADT(3) = infrate - ratein

$ERROR

CCONC = A(1)/vc

TCONC = A(2)/vt

if (dvid.eq.1) then

y=CCONC + RUVC_SD

else

y=TCONC + RUVT_SD

endif

$TABLE ID TIME Y dvid

NOPRINT ONEHEADER FILE=beka.fit

Figure 1. Code for beka.ctl