A second-generation challenge model of TNFa turnover with LPS provocations and drug intervention
Julia Larsson (1,2), Edmund Hoppe (3), Michael Gautrois (4), Marija Cvijovic (2), Mats Jirstrand (1)
(1) Fraunhofer-Chalmers Centre, Sweden. (2) Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Sweden. (3) Grünenthal GmbH, Germany. Current address: Boehringer-Ingelheim GmbH & Co. KG, Germany. (4) Grünenthal GmbH, Germany.
Objectives: Tumour necrosis factor alpha (TNFα) is a pro-inflammatory cytokine acting as a promising target for treatment against immune-mediated diseases [1]. Since TNFα is often undetectable in plasma in healthy organisms, pro-inflammatory challengers such as lipopolysaccharides (LPS) are used to induce release of TNFα. These LPS challenge studies are commonly used in drug discovery, and several pharmacokinetic and pharmacodynamic models have been created to describe this stimulatory and inhibitory relationship between LPS and drug in TNFα response data (see for example [2]). However, many of the current models keep the description of LPS stimulation simple, although LPS challenge studies are confounded by high batch-to-batch and inter-occasion variability [2,3]. It is thus questionable how well the stimulatory effect of LPS in TNFα response data is characterized, which in turn questions the reliability of the pharmacodynamic effects estimated from these models.
The goal with this work is to produce a framework of how to model TNFα response in LPS challenge studies in vivo and demonstrate its general applicability regardless of occasion or type of drug. With this framework we want to:
1) Accurately distinguish the stimulatory effect of LPS from the inhibitory effect of the drug, to get robust and reliable estimates of the pharmacodynamic parameters,
2) Introduce a model structure that considers inter-occasion variability and allows for testing of multiple drugs,
3) Fill the existing knowledge gaps concerning LPS challenge models from a biological perspective.
Methods: To reach the objectives, we improved a previously published model by our group [4], demonstrated the improved model’s general applicability, and validated our results by comparing them with previously published data. TNFα response data and drug concentrations in plasma from four different studies were used: Two studies for characterisation of the LPS stimulation using different intravenous doses of LPS, and two studies serving as drug interventions for characterisation of the pharmacodynamic effect. The experiments were conducted in male Sprague-Dawley rats, and all available data was utilised to construct the model in accordance to the 3R principles [5].
The model derived in the course of his work, named second-generation model, focuses on the general fit to multiple data sets and represents the natural extension of our previously published, first-generation model which captures specific trends in a limited data set [4]. The improvements include changes to the original model structure, modified inter-individual variability through non-linear mixed effects (NLME) modelling, and addition of inter-occasion variability. Furthermore, to accurately distinguish the stimulatory effect of LPS from the inhibitory effect of the drugs, the parameter estimation was performed in sequence. This was done by estimating the pharmacokinetics of the drugs and the parameters governing TNFα response after LPS provocation first, and then fix these parameters to their previously estimated values while estimating the pharmacodynamic effect of the drugs.
All modelling and parameter estimation was done using Wolfram Mathematica 12 and NLMEModeling – an NLME modelling package developed by Fraunhofer-Chalmers Centre [6].
Results: The mathematical model for TNFα response after LPS provocation captures the response for all LPS doses independent of study. The model predictions show both good population and individual fits, as well as a successful implementation of inter-occasion variability. For the pharmacodynamic effects, robust estimates of the median efficacy and potency were retrieved that correspond well to data. In addition, the comparison with previously published work shows that our findings are supported from a biological meta-analysis perspective, and concrete improvements of the modelling framework have been presented. As an example, our estimate of the potency for one of the drugs was shown to be seven times larger than the previously published estimate [4].
Conclusions:
1) Our proposed modelling framework fulfils our three objectives,
2) Characterising the LPS provocation correctly is of large importance when predicting pharmacodynamic effects in LPS challenge studies,
3) Usage of NLME modelling and pooling of data from different studies is advantageous from a 3R perspective, as the experimental data is used to its fully potential.
References:
[1] Palladino MA, Bahjat FR, Theodorakis EA, Moldawer LL (2003) Anti-TNF-alpha therapies: the next generation. Nat Rev Drug Discov 2 (9):736-746. doi:10.1038/nrd1175
[2] Gozzi P, Påhlman I, Palmér L, Grönberg A, Persson S (1999) Pharmacokinetic-pharmacodynamic modeling of the immunomodulating agent susalimod and experimentally induced tumor necrosis factor-alpha levels in the mouse. J Pharmacol Exp Ther 291 (1):199-203
[3] Wang Q, Zhang Y, Hall JP, Lin LL, Raut U, Mollova N, Green N, Cuozzo J, Chesley S, Xu X, Levin JI, Patel VS (2007) A rat pharmacokinetic/pharmacodynamic model for assessment of lipopolysaccharide-induced tumor necrosis factor-alpha production. J Pharmacol Toxicol Methods 56 (1):67-71. doi:10.1016/j.vascn.2007.02.001
[4] Held F, Hoppe E, Cvijovic M, Jirstrand M, Gabrielsson J (2019) Challenge model of TNFalpha turnover at varying LPS and drug provocations. J Pharmacokinet Pharmacodyn 46 (3):223-240. doi:10.1007/s10928-019-09622-x
[5] Russell WMS, Burch RL (1959) The principles of humane experimental technique. Methuen.
[6] Leander J, Almquist J, Johnning A, Larsson J, Jirstrand M (2020) NLMEModeling: A Wolfram Mathematica Package for Nonlinear Mixed Effects Modeling of Dynamical Systems. arXiv preprint arXiv:201106879