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RE: [NMusers] DDEs in NONMEM

From: Krzyzanski, Wojciech <>
Date: Mon, 7 Mar 2016 16:55:04 +0000

Dear Jon,

Thera are two aspects of DDEs that make them different from ODEs: presence =
of delays states and need to define a past (history of the states). Implem=
entation of DDEs in software that does not have a DDE solver but has an ODE=
 one is (in general) not a trivial task, but it is possible. The idea is to=
 convert a system of DDEs to a system of ODEs. This can be done for any DDE=
 system with fine number of delays that needs to be solved on over a finite=
 time interval 0<t<tend. The technique to apply is methods of steps. The m=
ethods of steps is particularly efficient for category 2.5 DDEs examples of=
 which you found in the tutorial by Koch et al you cited. Bob Bauer implem=
ented the method of steps in S-ADAPT which allows this program to solve arb=
itrary DDEs with non-constant past (Bauer et al., Computer Methods and Prog=
rams in Biomedicine 111:715-734 (2013).doi: 10.1016/j.cmpb.2013.05.026). A =
brief introduction for solving of DDEs by the method of steps has been publ=
ished by Perez-Ruixo (J. Pharmacokin. Pharmacodyn. 32: 767-793 (2005)). The=
 methods of steps has one serious limitation (among others), the number of =
ODEs is roughly speaking determined by the number of steps needed to reach =
tend. This number (for a system with one delay Tdel) is the product of the =
number of DEs in your model and the ratio tend/Tdel. This generally introdu=
ces of hundreds of ODES even for small 3-4 compartment DDE models. Coding m=
anually this many equations provides a challenge. I believe the current ver=
sion of NONMEM allows to code for such large dimensional models. One will =
need also a large number of ALAGs. Because of these challenges, it takes an=
 experience NONMEM user to correctly apply the methods of steps, and I DO N=
OT RECOMMEND IT. NONMEM should have a DDE solver not to make NONMEM users s=
uffer if they want to apply DDEs.

Please contact me directly if you want to apply the methods of steps in NON=
MEM. I have done it for several lifespan based indirect response models.


From: [] On=
 Behalf Of Jonathan Moss
Sent: Monday, March 07, 2016 9:34 AM
Subject: [NMusers] DDEs in NONMEM

Dear all,

I have a problem regarding delay differential equations (DDEs) in NONMEM. S=
o far, I have been unable to find a way of successfully using DDEs in NONME=
M, due to there being no in-built DDE solver (as far as I know). To me, it =
seems that the problem is that there is no way of recalling the value of th=
e dependant variable at an earlier time point within the $DES block (u(t-T)=
, where T is some fixed value, possibly to be estimated). I think that the =
problem is not a simple one to solve as NONMEM uses an adaptive step size w=
hen performing the integration, so even if there was a table output of the =
past values of the dependant variable, the value at the exact time (u(t-T))=
 might not exist...
Has anybody been able to successfully implement DDEs in NONMEM? I would rea=
lly appreciate some help with this.

Note: I am talking about DDEs in a general sense, I know that certain speci=
fic cases of DDEs can be solved in NONMEM (ref: Modelling of delays in PKPD=
, classical approaches and a tutorial for delay differential equations, G K=
och, W. Krzyzanski, J. J. Perez-Ruixo, Johannes schropp, JPKPD).

Many thanks,

Jon Moss, PhD
BAST Inc Limited
Loughborough Innovation Centre
Charnwood Wing
Holywell Park
Ashby Road
Loughborough, LE11 3AQ, UK
Tel: +44 (0)1509 222908

Received on Mon Mar 07 2016 - 11:55:04 EST

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