README.Rmd

---
title: 'Reversible Metabolism'
author: 'Sungpil Han'
date: '`r Sys.Date()`'
bibliography: ['bib/bib.bib', 'bib/books.bib']
---

# Reversible Metabolism

[<img src="assets/logo.jpg" style="max-width:15%;float:right;">](assets/logo.jpg)

# Abstract

**Keywords**  
Reversible metabolism, cisplatin, monohydrate, multiple compartment

# Introduction

본 모델링의 목적은 가역적 대사 (reversible metabolism, 혹은 가역적 상호전환, reversible interconversion)을 기술하는 미분방정식을 고안하여 모델링하고 이를 통한 시뮬레이션을 도출하는 것이다.

The aim of this exercise is to demonstrate how to implement a system of differential equations describing reversible metabolism. 
Data were taken from thε li〔eraturε on cisplatin kinetics (Andersson (1995]) and used [ O generate synthetic concentr따ion-time values for cisplatin p and its monohydrate m. 
This information was then used to obtain initial parameter estimates for a model of reversible metabolism. 
This exercise demonstrates how to implement the equations for this model into a program. 
In an infusion solution of cisplatin, equilibrium is established berween cisplatin and its monohydratε complex. 
Thus, the input rate can be split into cisplatin infusion ratε Iη and monohydra[ e infusion rate In,,
We have also chosen to describe thε εquilibrium process in vivo berween cisplatin and its monohydrate complex by means of rwo clearance rates.

# Materials and Methods

Objectives {@andersson1995stability}

- To implement a set of differential equations mimicking reversible metabolism
- To estimate the disposition and interconversion parameters of the two compounds

Pharmacokinetic and Pharmacodynamic Data Analysis PK34


Clpd and Cl,,,d. The exper
that takes account of such a split inf] ut rate and clearance are shown in 「
Figure 34.1. See also Section 2.4.
638

6 Input, lnputm
5
/.
등 4
3-
C
];I 2
Eliminat,。n Eliminati 。n
ct, Cl.,
0
0 20 40 60 80 100 120 140 160 180
Time (min)
The equation for C뼈latin (p) is
dC
V - --ι= J.η - Cl · C - Cl J • C + Cl , · C dt p p P a P “ (341)
Where VP' CP' Iη/μ Clp and Clpd are the volume, concentration, input rate,
clearance and interthe
concentration of [ he monohydratε. The conversion of cisplatin to the
monohydrate occurs with a rate constant derived according to Equation
34:2
k12,pd = Cl pd . VP (34:2)
The reversal rate for conversion of the monohydrate to cisplatin is
k21 씨 = Cl111d · κ” (34 3)
The equation for the monohydr따E (m) is
dC
V· -」뜨 = In111 -Cl111 · C” - Cl111r1 · C'" + Clpc1 · Cp (34:4)
dt

# Results

Where κ,,, ζ’” Iη”” C/111 and Cl111d arε the volume, ζoncentration, input rate,
clearance and inter-conversion clearancε of the monohydrate respectively.
ζ” is the concentration of the monohydrate.
Pharmac。kinetic Applications
Figure 34.1 Left: 

Left: Observed (symbols) and predicted (solid lines) concentration time data of cisplatin and its monohydrate.
The symbols correspond to cisplatin (upper curve) and the monohydrate (bottom curve) after infusion of cisplatin which also contains the monohydrate, 
and cisplalin (second from bottom) and monohydrate (second from top) after monohydrate infusion.
Right: A two compaπment model mimicking reversible metabolism was used to model the data.


·‘ E」-- ·• ‘•·"'￥‘;-. -’--· ' - }T ~
Pharmac。kinetic and Pharmacodynamic Data Analys is ‘ ;」
Parameter
κ(니
Clm (L·min·')
ι,(μg·L· ')
GIP (L· min-1)
k12(min-1)
k21 (min-1)
WRSS
640
Initial parameter estimates
Procedures involved in obtaining initial parameter estimates, AUC, MRT,
and so on for a system of revεrsible processes are covered in depth in Ebling
and Jusko [1986] . The initial parameter estimates selected diffcεred a little
from the values used to gener따C the data.
Interpretation of results and conclusions
The observed and model-predicted plasma concentrations, and the final
parameter estimates are shown in Figure 34.1 and Table 34. 1, respectively.
WRSS in Table 34.1 denotes the weighted residual sum of squares.
Table 34.1 Paramete「estimates of the micro-constant and interconversion clearance models
Microconstant model Interconversion clearance model
Estimate CV% Parameter Estimate CV%
14.1 3 κ(니 14.1 3
0.0085 22 C/m (L·min-1) 0.0084 22
2.96 2 Vm (μg·L-1) 2.97 2
0.446 2 GIP (L·min 1) 0.445 2
0.00021 34 Clpd (min-1) 0.0031 33
0.021 3 C/md (min-1) 0.063 5
0.0089 WRSS 0.0089


# Discussion

```{r code = readLines('PK34.R')}
```

# Acknowledgement

Edison Ack

# Appendix

## NONMEM control stream 

```{r code = readLines('nm/PK34.CTL'), eval = FALSE}
```

## NONMEM output

```{r code = readLines('nm/PK34.OUT'), eval = FALSE}
```

# References