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A PRELIMINARY STUDY OF MODELING AND SIMULATION IN INDVIDUALIZED
DRUG DOSAGE – AZATHIOPRINE ON INFLAMMATORY BOWEL DISEASE
Martin Fransson* Peter Fritzson*
Malin Lindqvist** Curt Peterson**
* Programming Environments Laboratory, Department of Computer Science, Linköping University, SE-581 83 Linköping, Sweden ** Division of Clinical Pharmacology, Department of Medicine and Care, Linköping University, SE-581 85 Linköping, Sweden Abstract: Individualized drug dosage based on population pharmacokinetic/dynamic models is an important future technology used to reduce or eliminate side effects of certain drugs, e.g. cancer drugs. In this paper we report preliminary results from work-in-progress: a simplified linear model of the metabolism of a cancer treatment drug was estimated from experimental data. The model was then validated against the same data as a test of the adequacy of the model structure. From this investigation it became apparent that the model structure could not be used due to its inability to recreate the dynamic properties of the system. Keywords: azathioprine, inflammatory bowel disease, pharmacokinetic. treatment the patient has to endure, with possible Drug dosage is usually optimized for, and adapted to, average adult white male persons. People who do not In order to avoid over consumption of drugs, as well belong to that group, e.g. females, children, certain as side effects caused by incorrect dosages, it would minority groups of people, very often get problems be very advantageous if it were possible to adapt drug dosage individually. However, due to the enormous complexity of biological systems, and the Although there are usually different dosage difficulty in predicting cellular and subcellular recommendations for children, and sometimes for processes, it has not yet been possible to develop females, the dosage is still incorrect in many cases. In fact, there exist a vast number of parameters influencing the decomposition and ingestion of a medical substance in a patient's body, as well as the reactions caused by the substances. At present though, the most common personalization factors that may influence the dosage are whether you are a child The main idea of this work is to be able to give each person a personal dosage based on advanced computer simulation and a precise measured Additionally, incorrect dosage usually leads to over biochemical profile of the patient who is about to consumption of drugs. The prescription from the receive the treatment, as well as known properties of doctor is often too much, to be on the “safe” side. the used drug. This is very important in order to This leads to increased costs for society and reduce or eliminate side-effects of certain drugs, e.g. increased environmental pollution from chemical substances, not to mention the often hazardous Incorporation in DNA and RNA
Inhibition of the purine
de novo synthesis
Thioguanine nucleotides
Thioinosine monophosphate
Methylthioinosine
monophosphate
(meTIMP)
6-Methylmercaptopurine
6-Thioguanine
6-Mercaptopurine
Thiouric acid
6-Methylthioguanine
Azathioprine
The specific properties of the drug that are used for predict a suitable individualized dosage level for a computing an optimal personalized dosage are e.g. the effect of the drug on metabolic pathways. Such information may be obtained from existing public data bases, from drug manufacturers, or by experimental measurements from the patient. ows the steps needed to obtain/compute an 1. Knowledge from earlier experiments makes it possible to determine the biochemical pathways In order to test these ideas, we need a disease and a corresponding drug for which accurate dosage is very equations that determines how 6-MP/AZA is important. We selected the disease inflammatory metabolized by the body. If this knowledge is bowel disease (IBD) and the drug 6-mercaptopurine not complete enough, system identification (6-MP) and its derivative azathioprine (AZA). missing model information. In the simplified Inflammatory bowel disease is a serious illness with biochemical path after (1) the substrate A can be a number of symptoms in the bowel. Approximately viewed as input signal and the metabolite C or 70000 to 110000 new cases occur annually in Europe 2. The metabolic pathway is equivalent to a system of differential equations. This can be formulated The drug 6-MP/AZA belongs to a special group of in various ways, including an explicit state-space formulation where u represents the input signals within this group are also used for cancer treatment, and y the output signal(s). The state variables are e.g. treating leukemia for children, and to prevent represented by the vector x, whereas the rejection of transplanted organs (Duley et al., 2005). functions f and h are functions relating the During the 60th and the 70th, before treatment by 3. The model can be graphically described as a cytotoxins had started, the only way to treat biochemical pathway or as en explicit system of inflammatory bowel disease was to surgically remove part of the small intestine. After a number of 4. A biological sample from the patient gives the such operations, not much remained. Instead, more personal biochemical profile that is the basis for recently treatment by thiopurines has been introduced computing the individualized dosage. This is with very good effects. Unfortunately, certain typically a blood sample, from which the patients are very sensitive to the dosage level; very strong side-effects (even deaths) have occurred. determined. It can also be used measure the Thus, it is very important to be able to reliably concentration of TPMT, IMPDH, HGPRT, and the metabolites that are created (e.g. TGN and Fig. 2. Flow chart for individualized drug dosage.
5. meTIMP). Also input parameters such as sex, 6. When the biochemical pathway model has been adjusted according to the individual biological sample, i.e., adapted to that individual, it can be used to simulate the effect of different dosage levels and determine a suitable dosage for that patient. Alternatively, a suitable dosage of azathioprine can be directly determined if an exact criterion for the desired The model, translated to explicit form, would look A group of 60 IBD-patients were observed during 20 weeks. Of these, 27 patients completed the (C x )x + k study. Measurements were made once a week. (C x x )x + k (C x )x + k (C x )x k Here we present two models of the thiopurine metabolism: a straight-forward mechanistic pathway model, with many unknown parameters, (C x x )x k and a simplified "common sense" model based on reasoning about the basic system properties. (C x )x k The following is a pathway model approximately (C x x )x The pathway model contains a number of state variables, corresponding to concentrations of the However, there are far too many unknown coefficients in this model, compared to the few data points available. We will need to create a model with fewer parameters in order to make progress. Fig. 3. A pathway model of the thiopurine metabolism.
Simplified "Common-Sense" Model As already mentioned, the pathway model has far too many unknown parameters to estimate from the scarce data. Instead we create the following simplified common sense model with only 7 unknown parameters to estimate: Fig. 4. The grey-box identification process We use the linear grey-box midentification. x(t +1) = Ax(t) + Bu(t) Here AccD = the accumulated weekly dosage (i.e. total dosage during one week), RBC means Read Blood Cell, WBC means White Blood Cell, and WBC0 = WBC during week 0, which is assumed to be the normal body concentration in blood of the The parameters of the linear “common sense” model were estimated with patient measurements as In order to use the above model for simulation of output data and drug dosage as input data. The drug concentration effects, we need to estimate the ability of the model to recreate the properties of the seven unknown parameters from the patient data. system, i.e., the curve fitting to patient data was evaluated for 8 patients. One such example is This is done using a grey-box model, where the system identification process and the limitations for in Matlab using the System Identification Toolbox. If the future nonlinear model (see below) proves to be a better choice, OpenModelica (Fritzson et al., 2005), (Fritzson, 2004) will be used for simulation purposes. Fig. 5. The simplified model used to simulate the response for patient 19, compared to experimental data. Ideally, the simple model would fit reasonably well BM. A comparison of red blood cell thiopurine to the measured output data and certainly capture the dynamics of the system, such as number of lymphoblastic leukemia who received oral peaks. The model is able to capture some aspects, mercaptopurine twice daily or once daily: a pecially for the first two equations but there are still large deviations between the Children's Oncology Group). Pediatr Blood simulated and measured results. Thus, our model is apparently too simple. There are probably Duley JA (2005), Florin TH. Thiopurine therapies: important nonlinear effects in the drug metabolism problems, complexities, and progress with that are not part of this simple model. Another thing monitoring thioguanine nucleotides. Ther Drug that should be taken into account is the frequency of the dose distribution that can have an effect on Fritzson P (2005), Aronsson P, Lundvall H, the blood concentrations (Bell et al., 2004). Nyström K, Pop A, Saldamli L, and Broman D. The OpenModelica Modeling, Simulation, and Fritzson P (2004). Principles of Object-Oriented We have done a preliminary study of modeling and Modeling and Simulation with Modelica 2.1, simulation in individualized drug dosage, employing the drug 6-MP/AZA for treatment of IBD. An experimental study of a group of patients Lindqvist M (2005). Pharmacogenetic Studies of was made. The data was used to estimate unknown Thiopurines – Focus on Thiopurine coefficients in a linear "common sense" model. Due Methyltransferase. Linköping University to the simplicity of the model it was not able to recreate the measured output data used to estimate The next step will be to create a more complex model that can capture more of the possible This work has been supported by the Swedish nonlinear effects in the metabolism. A new experimental study will be needed to calibrate that Knowledge Foundation through the Industrial model, i.e., to capture data on more of the detailed PhD program in Medical Bioinformatics at the Centre for Medical Innovations (CMI) at the Karolinska Institute, by MathCore Engineering AB and by the Faculty of Health Sciences, Bell BA (2004), Brockway GN, Shuster JJ, Erdmann G, Sterikoff S, Bostrom B, Camitta

Source: https://www.modelica.org/publications/papers/2006-09-Fransson-Fritzson-Lindqvist-Peterson-SIMS06-drugdosage.pdf

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