# Two Compartment Model

Table of Contents

- 1 Description
- 2 Usage
- 3 Arguments
- 4 Return value
- 5 Note

## 1 Description

Function `pmx_solve_twocpt`

solves a two-compartment PK
model (Figure /Torsten/function/one-cpt/). The model obtains the mass \((y_1, y_2, y_3)\) in each compartment
by solving the ODEs

\begin{align} \label{eq:twocpt}
y_1' &= -k_a y_1 \\\

y_2' &= k_a y_1 - \left(\frac{CL}{V_2} + \frac{Q}{V_2}\right) y_2 + \frac{Q}{V_3} y_3 \\\

y_3' &= \frac{Q}{V_2} y_2 - \frac{Q}{V_3} y_3
\end{align}

The plasma concentrations of parent drug in the central compartment can then be calculated as \(c=y_2/V_2\).

## 2 Usage

```
matrix = pmx_solve_twocpt(time, amt, rate, ii, evid, cmt, addl, ss, theta [, biovar, tlag ] )
```

## 3 Arguments

See Tables in Section Events specification.

## 4 Return value

An `ncmt`

-by-`nt`

matrix, where `nt`

is the number of time steps and `ncmt=3`

is the number of compartments.

## 5 Note

- ODE Parameters
`theta`

consists of \(CL\), \(Q\), \(V_2\), \(V_3\), \(k_a\). `biovar`

and`tlag`

are optional, so that the following are allowed:

```
pmx_solve_twocpt(..., theta);
pmx_solve_twocpt(..., theta, biovar);
pmx_solve_twocpt(..., theta, biovar, tlag);
```

- Setting \(k_a = 0\) eliminates the first-order absorption.