# Time-varying clearance

Related resources:

When treatments span over a long time with numerous repeated doses, the clearance can be observed to change over time, for instance due to a change in the disease status. One possible approach to handle this case is to define in a parametric way how the clearance changes over time. A common assumption is to use an Imax or Emax model. Below, we show how to implement such a model in the Mlxtran language.

Examples of time-varying clearances are for instance presented for PEGylated Asparaginase, and for mycophenolic acid here

### Mlxtran structural model

In the example below, we assume that the clearance is decreasing over time, with a sigmoidal shape. We consider a one-compartment model with first-order absorption. The Mlxtran code for the structural model reads:

```
[LONGITUDINAL]
input = {ka, V, Clini, Imax, gamma, T50}
PK:
depot(target=Ac, ka)
EQUATION:
t_0 = 0
Ac_0 = 0
Clapp = Clini * (1 - Imax * t^gamma/(t^gamma + T50^gamma))
ddt_Ac = - Clapp/V * Ac
Cc = Ac/V
OUTPUT:
output = {Cc}
```

The `Clini`

parameter described the initial clearance, `Imax`

the maximal reduction of clearance, `T50`

the time at which the clearance is reduced by half of the maximal reduction, and `gamma`

characterizes the sigmoidal shape.

The apparent clearance `Clapp`

is defined via an analytical formula depending on the time `t`

and is then used in the ODE system. The first-order absorption is directly defined using the depot macro, which here indicates that the doses of the data set must be applied to the target Ac via a first-order absorption with rate ka (ka is a reserved keyword).