## Algorithm (geometric progression) [Design Issues]

Dear Eduardo,

the ‘classical’ algorithm uses a geometric progression in order to calculate sampling points based on:

I prepared a little example based on following PK data:

Now you have to adapt these time points for practicability (

In the example you see another problem which may arise from mean curves (very often the only ones being published). The sampling scheme works fine for the ‘average’ subjects, and also for the ‘fastest’ ones, but the elimination phase may be insufficiently described for 'slow' subjects.

Therefore whenever possible try to get some

Another problem are enteric coated formulations, which show a large variability in lag-times due to variability in gastric emptying.

The example to the right used PK parameters from the ‘fast’ subject with additonal lag-times of 0.5 and 1.5 h. The algorithm will simply fail if you are applying data from a mean curve only.

In such a case you will have to ‘pack’ as much time points as possible within the first 3 hours or so, in order to define the absorption phase and the peak properly; you should use the algorithm only for the elimination phase (with

Also note that the example is just illustrative; with ‘real world’ enteric coated formulations the t

Conclusion: A simple algorithm may only serve you as an entry point; thorough knowledge of the drug’s (and formulation’s) PK is a prerequisite in study planning.

the ‘classical’ algorithm uses a geometric progression in order to calculate sampling points based on:

- the number of samples

- the time points of the first and last sample

*t _{i}* =

*t*

_{i-1}× (

*t*/

_{n}*t*

_{1})

^{1/(n–1)}

*i*index of the respective time points (2, 3, …,*n*),*n*number of time points,*t*calculated time point at_{i}*i*,*t*_{i–1}previous time point,*t*_{1}first time point, and*t*last time point._{n}I prepared a little example based on following PK data:

- 1 compartment open model, no lag time

- F = 1

- Dose = 100 Units

- V = 10 L

- k
_{el}= 0.25 h^{-1}

- k
_{a}= 4 h^{-1}(‘fastest’ subject), 0.4 h^{-1}(‘slowest subject’)

*t*_{1}= 5 min (0.083 h),*t*= 12 h and 15 sampling points we get: 0.0833, 0.1188, 0.1695, 0.2417, 0.3447, 0.4917, 0.7012, 1.0000, 1.4262, 2.0339, 2.9007, 4.1369, 5.8999, 8.4142, and 12.0000._{n}Now you have to adapt these time points for practicability (

*e.g.*, sampling at 0.25 h instead of at 0.2417 h).In the example you see another problem which may arise from mean curves (very often the only ones being published). The sampling scheme works fine for the ‘average’ subjects, and also for the ‘fastest’ ones, but the elimination phase may be insufficiently described for 'slow' subjects.

Therefore whenever possible try to get some

*‘Spaghetti-Plots’*(overlays of all subjects in a previous study) in the planning phase.Another problem are enteric coated formulations, which show a large variability in lag-times due to variability in gastric emptying.

The example to the right used PK parameters from the ‘fast’ subject with additonal lag-times of 0.5 and 1.5 h. The algorithm will simply fail if you are applying data from a mean curve only.

In such a case you will have to ‘pack’ as much time points as possible within the first 3 hours or so, in order to define the absorption phase and the peak properly; you should use the algorithm only for the elimination phase (with

*t*_{1}= 3 and*t*= 12)._{n}Also note that the example is just illustrative; with ‘real world’ enteric coated formulations the t

_{max}may be at 12 hours – or even later…Conclusion: A simple algorithm may only serve you as an entry point; thorough knowledge of the drug’s (and formulation’s) PK is a prerequisite in study planning.

—

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

*Dif-tor heh smusma*🖖Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

### Complete thread:

- How to Define Sampling Interval eduardojmorales 2006-10-05 21:11 [Design Issues]
- How to Define Sampling Interval eduardojmorales 2006-10-05 23:16
- Soliloquy? H_Rotter 2006-10-06 13:27
- Soliloquy? eduardojmorales 2006-10-10 18:09

- Algorithm (geometric progression)Helmut 2006-10-07 21:48
- Algorithm (geometric progression) eduardojmorales 2006-10-10 18:23
- Algorithm (geometric progression) Helmut 2006-10-10 19:05

- Algorithm (geometric progression) intuitivepharma 2013-02-28 08:10
- Geometric progression in Excel Helmut 2013-02-28 13:56
- Sampling (optimization?) Helmut 2013-02-28 16:50
- Sampling (optimization?) intuitivepharma 2013-03-01 07:42
- Sampling (optimization?) SDavis 2013-03-07 10:40
- VIFs? Helmut 2013-03-07 15:50
- Sampling (optimization?) intuitivepharma 2013-03-08 12:39

- Sampling (optimization?) SDavis 2013-03-07 10:40

- Sampling (optimization?) intuitivepharma 2013-03-01 07:42

- Algorithm (geometric progression) eduardojmorales 2006-10-10 18:23

- Soliloquy? H_Rotter 2006-10-06 13:27

- How to Define Sampling Interval eduardojmorales 2006-10-05 23:16