Gilbert Koch (1), Freya Bachmann (2), Marc Pfister (1), Gabor Szinnai (1), Johannes Schropp (2)
(1) Pediatric Pharmacology and Pharmacometrics, University of Basel, Children’s Hospital (UKBB), Basel, Switzerland, (2) Department of Mathematics and Statistics, University of Konstanz, Germany
Objectives: Every patient deserves the most effective individual treatment to assure the best possible disease progression. An effective treatment depends on individual factors such as disease state, drug clearance, age in case of infants and many others. Additionally, the optimal treatment may depend on state constraints, e.g. to account for side effects [1]. Recently, an optimal dosing algorithm (OptiDose) based on optimal control theory was developed that computes the optimal individual doses for any PKPD model [2]. Although, OptiDose was highly customized to exploit typical PKPD model properties, the necessary computational time strongly depends on the complexity of the PKPD model. Hence, the computational time can be too large (> 1 to 10 minutes) for clinical application. Therefore, we developed an artificial neural network (ANN) solution that mimics the OptiDose algorithm and predicts the optimal doses in real-time (< 1 second).
Methods: An ANN is able to mimic the behavior of complex mathematical algorithms [3]. From a mathematical perspective, an ANN is an approximation method that is capable to learn input-output relations seen in data. Five steps are necessary to train an ANN that predicts the optimal individual doses: First, a non-linear mixed effects (NLME) analysis based on a representative clinical dataset has to be performed. Second, a larger dataset has to be simulated based on the NLME results. Third, OptiDose has to compute for all individual patients in the simulated dataset the optimal doses. Fourth, the simulated dataset (step 2) together with the optimal doses (step 3) will be applied to train an ANN in a supervised fashion. Fifth, the trained ANN has to be validated based on new (simulated) data and also tested on patients with extreme behavior. Two typical PKPD examples of different complexity (an indirect response model and a tumor growth inhibition model) are applied as examples.
Results: The trained ANN is able to mimic the behavior of OptiDose and consequently can predict the optimal doses for every individual patient. Depending on the amount of neurons and number of hidden layers, the difference between the optimal doses computed with OptiDose and the prediction of the trained ANN is for almost all patients (>99%) less than 1%. Utilizing the Matlab Deep Learning Toolbox [4], training and testing of different numbers of neurons and layers can be performed within a few hours on a standard laptop.
Conclusions: The advantage of a well-trained ANN is its computational power to perform predictions in real-time. This is possible because the computational effort is outsourced to the generation of the dataset and the training of the ANN. The final trained ANN is entirely independent of the PKPD model and OptiDose, hence no differential equation solver or optimization method is required. In fact, a trained ANN is a straightforward network structure characterized by a few matrix multiplications, and can therefore be simply implemented on any kind of (portable) device.
References:
[1] Bachmann F, Koch G, Pfister M, Schropp J. OptiDose: Computing the optimal individual dosing regimen with constraints on model states to include side effects. ACoP10 Trainee Award.
[2] Bachmann F, Koch G, Pfister M, Szinnai G, Schropp J. OptiDose: Computing the individualized optimal drug dosing regimen for pharmacokinetic-pharmacodynamic models using optimal control. (submitted).
[3] Hornik K (1991) Approximation capabilities of multilayer feedforward networks. Neural Networks 4(2):251-257.
[4] Matlab and Deep Learning Toolbox 2019b, The Math Works Inc., Natick, MA, USA.
Reference: PAGE () Abstr 9470 [www.page-meeting.org/?abstract=9470]
Poster: Oral: Methodology - New Tools