Hello all modelers, I would like to link the pk to pd. The pd endpoint is a tumor growth volume and I would like to link them with the PK using AUCs as the PD driver. Below is my model. Since the tumor volume is measured by day, so the time point is by day (2-3 days interval). I just wonder how to do it in the ODE equations. What I wish to achieve is to use daily AUC to drive the K1, instead of concentration. I comment out the line where I think it might look like but need to change to cover all the experiment time course which is 14 day or more. Thanks, Shu-Pei deriv(T = Kng * T (1-T/Tss)- K4T) deriv(K1 = ((kmax* C/(KC50+C))-K1)/tau) #deriv(K1 = ((AUCkmax* AUCt1/(AUCKC50+AUCt1))-K1)/tau) #deriv(AUCt1 = (t>0)*(t<24)*C) deriv(K2 = (K1 - K2)/tau) deriv(K3 = (K2 - K3)/tau) deriv(K4 = (K3 - K4)/tau)
Hi Shu-Pei, Not sure why you want to link an AUC which factor out the time component to a PD endpoint. It is very common to have a delay between PK and PD but using AUC don’t help it is better to go for a more mechanistic model for tumor growht that incoporate some indirect response or effect compartments delays. You can always any compartment amounts by using an extra differential equation like the following: deriv(AUCPK= PKcomparmtentname) this will integrate PK concentration from starting time till last recorded time for each individual. But Again I don’t recommend to use AUC instead of concentration in a PK/PD model.
Hi, smouksassi, By doing this, deriv(AUCPK= PKcomparmtentname) The AUCPK of certain compartment will be accumulating higher and higher, which is not realistic since if a drug PD is said to be driven by AUC, no matter what drug potency is, the efficacy and be acheive if taking this drug long enough. I totally agree with you that AUC is not a best PD driver, howerver, it is a tranditional way to link drug exposure to the efficacy (maybe wrong though). I actually want to model the tumor growh using daily AUC since the PD endpoint is by daily too. But I don’t know how to acheive this in ODE equation. Thanks, Shu-Pei
Indeed the solution deriv(AUCPK= PKcomparmtentname) provide you cumulative AUC if you want daily then you need to reset the compartment amounts at the end of each day. One way to do it is by taking advantage of the doafter statement: Observe (AUCPKObs, AUCPK+eps, doafter={AUCPK=0;}) Below is useful references: 1: Simeoni M, Magni P, Cammia C, De Nicolao G, Croci V, Pesenti E, Germani M, Poggesi I, Rocchetti M. Predictive pharmacokinetic-pharmacodynamic modeling of tumor growth kinetics in xenograft models after administration of anticancer agents. Cancer Res. 2004 Feb 1;64(3):1094-101. PubMed PMID: 14871843. 2: Terranova N, Germani M, Del Bene F, Magni P. A predictive pharmacokinetic-pharmacodynamic model of tumor growth kinetics in xenograft mice after administration of anticancer agents given in combination. Cancer Chemother Pharmacol. 2013 Aug;72(2):471-82. doi: 10.1007/s00280-013-2208-8. Epub 2013 Jun 29. PubMed PMID: 23812004; PubMed Central PMCID: PMC3718992. http://download.springer.com/static/pdf/231/art%253A10.1007%252Fs00280-013-2208-8.pdf?auth66=1401546841_63bc58b2f03a2490da55ec23cf2737f0&ext=.pdf