A PRELIMINARY STUDY OF MODELING AND SIMULATION IN INDIVIDUALIZED DRUG DOSAGE AZATHIOPRINE ON INFLAMMATORY BOWEL DISEASE

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1 This is a correcte version of the corresponing paper publishe in SIMS 26: Proceeings of the 47th Conference on Simulation an Moelling. Errata: equations.3 an.4 have been change to timecontinuous form an Fig. 5 has been change accoringly; the color-print in Fig. 5 has been replace by soli, ashe an otte lines; the ose curve in Fig 5. has been remove. A PRELIMINARY STUDY OF MODELING AND SIMULATION IN INDIVIDUALIZED DRUG DOSAGE AZATHIOPRINE ON INFLAMMATORY BOWEL DISEASE Martin Fransson Peter Fritzson Malin Linqvist 2 Ulf Hinorf 3 Sven Almer 4 Curt Peterson 2 Programming Environments Laboratory, Department of Computer Science, Linköping University, SE Linköping, Sween {marfr, petfr}@ia.liu.se 2 Division of Clinical Pharmacology, Department of Meicine an Care, Linköping University, SE Linköping, Sween 3 Division of Gastroenterology, Department of Clinical Sciences, Lun University, SE Lun, Sween 4 Division of Gastroenterology an Hepatology, Department of Molecular an Clinical Meicine, Linköping University, SE Linköping, Sween Abstract: Iniviualize rug osage base on population pharmacokinetic/ynamic moels is an important future technology use to reuce or eliminate sie effects of certain rugs, e.g. cancer rugs. In this paper we report preliminary results from work-in-progress: a simplifie linear moel of the metabolism of a cancer treatment rug was estimate from experimental ata. The moel was then valiate against the same ata as a test of the aequacy of the moel structure. From this investigation it became apparent that the moel structure coul not be use ue to its inability to recreate the ynamic properties of the system. Keywors: azathioprine, inflammatory bowel isease, pharmacokinetic. WHY INDIVIDUALIZED DRUG DOSAGE? Drug osage is usually optimize for, an aapte to, average ault white male persons. People who o not belong to that group, e.g. females, chilren, certain minority groups of people, very often get problems from rugs ue to incorrect osage. Although there are usually ifferent osage recommenations for chilren, an sometimes for females, the osage is still incorrect in many cases. In fact, there exist a vast number of parameters influencing the ecomposition an ingestion of a meical substance in a patient's boy, as well as the reactions cause by the substances. At present though, the most common personalization factors that may influence the osage are whether you are a chil or not, an sometimes your sex. Aitionally, incorrect osage usually leas to over consumption of rugs. The prescription from the octor is often too much, to be on the safe sie. This leas to increase costs for society an increase environmental pollution from chemical substances, not to mention the often hazarous treatment the patient has to enure, with possible sie-effects an the like. In orer to avoi over consumption of rugs, as well as sie effects cause by incorrect osages, it woul be very avantageous if it were possible to aapt rug osage iniviually. However, ue to the enormous complexity of biological systems, an the ifficulty in preicting cellular an subcellular processes, it has not yet been possible to evelop concepts for personalize rug osage. 2 MODELING AND SIMULATION FOR INDIVIDUALIZED DRUG DOSAGE The main iea of this work is to be able to give each person a personal osage base on avance computer simulation an a precise measure biochemical profile of the patient who is about to receive the treatment, as well as known properties of the use rug. This is very important in orer to reuce or eliminate sie-effects of certain rugs, e.g. cancer rugs such as cytotoxins.

2 Metabolism of thiopurines Incorporation in DNA an RNA Inhibition of the purine e novo synthesis Thioguanine nucleoties (TGN) Thioinosine monophosphate (TIMP) Methylthioinosine monophosphate (metimp) HGPRT HGPRT 6-Thioguanine 6-Mercaptopurine 6-Methylmercaptopurine XO Thiouric aci 6-Methylthioguanine Azathioprine The specific properties of the rug that are use for computing an optimal personalize osage are e.g. the effect of the rug on metabolic pathways. Such information may be obtaine from existing public ata bases, from rug manufacturers, or by experimental measurements from the patient. Fig.. The metabolism of thiopurines preict a suitable iniviualize osage level for a specific patient. 4 DETERMINING INDIVIDUALIZED DRUG DOSAGE 3 AZATHIOPRINE AND INFLAMMATORY BOWEL DISEASE In orer to test these ieas, we nee a isease an a corresponing rug for which accurate osage is very important. We selecte the isease inflammatory bowel isease (IBD) an the rug 6-mercaptopurine (6-MP) an its erivative azathioprine (AZA). Inflammatory bowel isease is a serious illness with a number of symptoms in the bowel. Approximately 7 to new cases occur annually in Europe (Linqvist, 25). The rug 6-MP/AZA belongs to a special group of rugs, thiopurines, i.e., cytotoxins, see Fig.. Drugs within this group are also use for cancer treatment, e.g. treating leukemia for chilren, an to prevent rejection of transplante organs (Duley et al., 25). During the 6th an the 7th, before treatment by cytotoxins ha starte, the only way to treat inflammatory bowel isease was to surgically remove part of the small intestine. After a number of such operations, not much remaine. Instea, more recently treatment by thiopurines has been introuce with very goo effects. Unfortunately, certain patients are very sensitive to the osage level; very strong sie-effects (even eaths) have occurre. Thus, it is very important to be able to reliably Fig. 2 shows the steps neee to obtain/compute an iniviualize rug osage:. Knowlege from earlier experiments makes it possible to etermine the biochemical pathways that escribes the most important moel equations that etermines how 6-MP/AZA is metabolize by the boy. If this knowlege is not complete enough, system ientification methos may be use for etermining the missing moel information. In the simplifie biochemical path after () the substrate A can be viewe as input signal an the metabolite C or the enzyme E4 as an output signal 2. The metabolic pathway is equivalent to a system of ifferential equations. This can be formulate in various ways, incluing an explicit state-space formulation where u represents the input signals an y the output signal(s). The state variables are represente by the vector x, whereas the functions f an h are functions relating the variables. 3. The moel can be graphically escribe as a biochemical pathway or as en explicit system of equations. 4. A biological sample from the patient gives the personal biochemical profile that is the basis for computing the iniviualize osage. This is typically a bloo sample, from which the genotypes for ifferent enzymes can be etermine. It can also be use measure the concentration of, IMPDH, HGPRT, an the metabolites that are create (e.g. TGN an

3 Fig. 2. Flow chart for iniviualize rug osage metimp). Also input parameters such as sex, age, an health status influence the biochemical profile. 5. When the biochemical pathway moel has been ajuste accoring to the iniviual biological sample, i.e., aapte to that iniviual, it can be use to simulate the effect of ifferent osage levels an etermine a suitable osage for that patient. Alternatively, a suitable osage of azathioprine can be irectly etermine if an exact criterion for the esire treatment effect can be formulate. x = [6-MP] x = [XO/6-MP] 2 x = [TUA] 3 x = [/6-MP] 4 x = [memp] 5 x = [HGPRT/6-MP] 6 x = [TIMP] 7 x = [TGN] 8 x = [/TIMP] x 9 = [metimp] (.) 5 EXPERIMENTAL DATA A group of 6 IBD-patients were observe uring 2 weeks. Of these, 27 patients complete the stuy. Measurements were mae once a week. 6 PATHWAY MODEL AND A SIMPLIFIED COMMON-SENSE MODEL Here we present two moels of the thiopurine metabolism: a straight-forwar mechanistic pathway moel, with many unknown parameters, an a simplifie "common sense" moel base on reasoning about the basic system properties. 6. Pathway Moel of the System The following is a pathway moel approximately the same as the one in Fig. 3. An arrow in the above pathway means an enzymatic reaction, approximately as follows: The moel, translate to explicit form, woul look approximately as (.2). x = k,tua ( C x 2) x + k,tua x 2 k ( C x x ) x + k x,memp 2 4 9,meMP 4 k ( C x ) x + k x,timp 3 6,TIMP 6 x = k ( C x ) x k x k x x 3 = k x cat,tua 2 x 4 = k,memp ( 2 4 9),meMP 4 k x 2,TUA 2,TUA 2 cat,tua 2 cat,memp 4 x5 = kcat,mempx4 x = k ( C x ) x k x k cat x x 7 = k cat,timp x 6 k,metimp ( C 2 x 4 x 9) x 7 + k x f ( x ) 6,TIMP 3 6,TIMP 6,TIMP 6,meTIMP 9 8 [S] + [E] k k- [ES] k cat [E] + [P] The pathway moel contains a number of state variables, corresponing to concentrations of the various metabolites accoring to (.). x 8 =... x 9 =... x =... (.2) However, there are far too many unknown coefficients in this moel, compare to the few ata points available. We will nee to create a moel with fewer parameters in orer to make progress.

4 [TUA] [XO] [HGPRT] [] [6-MP] [TIMP] [metimp] [] [several reactions] [memp] [TGN] Fig. 3. A pathway moel of the thiopurine metabolism. 6.2 Simplifie "Common-Sense" Moel As alreay mentione, the pathway moel has far too many unknown parameters to estimate from the scarce ata. Instea we create the following simplifie common sense moel with only 7 unknown parameters to estimate: [ metimp]( t) = k [ metimp]( t) + k AccD( t) met [ TGN ]( t) met, AccD = k [ TGN]( t) + k AccD( t) TGN [ WBC]( t) TGN, AccD = k [ metimp]( t) k [ TGN ]( t) WBC, met WBC, TGN + k ( WBC [ WBC]( t)) WBC (.3) Here AccD = the accumulate weekly osage (i.e. total osage uring one week), RBC means Rea Bloo Cell, WBC means White Bloo Cell, an WBC = WBC uring week, which is assume to be the normal boy concentration in bloo of the quantity in question. 7 SYSTEM IDENTIFICATION OF MISSING PARAMETER VALUES In orer to use the above moel for simulation of rug concentration effects, we nee to estimate the seven unknown parameters from the patient ata. This is one using a grey-box moel, where the system ientification process an the limitations for the specific problem are shown in Fig. 4. Fig. 4. The grey-box ientification process We use the linear grey-box moel (.4) for ientification. xɺ ( t) = Ax( t) + Bu( t) kmet A = ktgn k k k B WBC, met WBC, TGN WBC k met, AccD = ktgn, AccD k WBC 8 RESULTS The parameters of the linear common sense moel were estimate with patient measurements as output ata an rug osage as input ata. The ability of the moel to recreate the properties of the system, i.e., the curve fitting to patient ata was evaluate for 8 patients. One such example is shown in Fig. 5. Parameter estimations were mae in Matlab using the System Ientification Toolbox. If the future nonlinear moel (see below) proves to be a better choice, OpenMoelica (Fritzson et al., 25), (Fritzson, 24) will be use for simulation purposes. (.4)

5 .9.8 y.5 metimp. (sim) MPata; measure MPmpem; fit: 3.39% y TGN. (sim) MPata; measure MPmpem; fit: 42.55% WBC. (sim).2. y 3 MPata; measure MPmpem; fit: -.54% Soli=[WBC], Dashe=[meTIMP], Dotte=[TGN] norm( ysim y) Fit = norm( y mean( y)) Fig. 5. The simplifie moel use to simulate the response for patient 9, compare to experimental ata. Ieally, the simple moel woul fit reasonably well to the measure output ata an certainly capture the ynamics of the system, such as number of peaks. The moel is able to capture some aspects, see Fig. 5, especially for the first two equations but there are still large eviations between the simulate an measure results. Thus, our moel is apparently too simple. There are probably important nonlinear effects in the rug metabolism that are not part of this simple moel. Another thing that shoul be taken into account is the frequency of the ose istribution that can have an effect on the bloo concentrations (Bell et al., 24). 9 CONCLUSION AND FUTURE WORK We have one a preliminary stuy of moeling an simulation in iniviualize rug osage, employing the rug 6-MP/AZA for treatment of IBD. An experimental stuy of a group of patients was mae. The ata was use to estimate unknown coefficients in a linear "common sense" moel. Due to the simplicity of the moel it was not able to recreate the measure output ata use to estimate the parameters. The next step will be to create a more complex moel that can capture more of the possible nonlinear effects in the metabolism. A new experimental stuy will be neee to calibrate that moel, i.e., to capture ata on more of the etaile ynamics of the metabolism. REFERENCES metabolites in chilren with acute lymphoblastic leukemia who receive oral mercaptopurine twice aily or once aily: a Peiatric Oncology Group stuy (now The Chilren's Oncology Group). Peiatr Bloo Cancer. Aug;43(2):5-9. Duley JA (25), Florin TH. Thiopurine therapies: problems, complexities, an progress with monitoring thioguanine nucleoties. Ther Drug Monit. Oct;27(5): Review. Fritzson P (25), Aronsson P, Lunvall H, Nyström K, Pop A, Salamli L, an Broman D. The OpenMoelica Moeling, Simulation, an Software Development Environment. In Simulation News Europe, 44/45. Fritzson P (24). Principles of Object-Oriente Moeling an Simulation with Moelica 2., 94 pp., ISBN , Wiley-IEEE Press. Linqvist M (25). Pharmacogenetic Stuies of Thiopurines Focus on Thiopurine Methyltransferase. Linköping University Meical Dissertations No ACKNOWLEDGEMENTS This work has been supporte by the Sweish Knowlege Founation through the Inustrial PhD program in Meical Bioinformatics at the Centre for Meical Innovations (CMI) at the Karolinska Institute, by MathCore Engineering AB an by the Faculty of Health Sciences, Linköping University. Bell BA (24), Brockway GN, Shuster JJ, Ermann G, Sterikoff S, Bostrom B, Camitta BM. A comparison of re bloo cell thiopurine