1. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E Yongwimon Lenbury Deparment of Mathematics Wannapong Triumpo Department of Physics Mahidol University, Thailand Sompop Moonchai Deparment of Mathematics, Chiangmai University

2. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E Simulation can be used to evaluate complex health services and biomedical systems in situations where traditional methodologies are difficult or too costly to employ. A simulation model is developed to represent important aspects of the system under evaluation. Once validated, the model can be used to study the effects of variations in system inputs, differences in initial conditions and changes in the system structure (Anderson, 2003).

3. Monte Carlo cellular automaton model for cancer Simulation of HIV infection Conclusion Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E Introduction The modeling process

4. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E By the 1980s, investigators began applying simulation to biomedical processes and pharmacokinetics. These efforts have intensified during the 1990s. Simulation has been applied to epidemiological, physiological and genetic processes (Anderson, 2003). Many recent advances in technology, such as the Next Generation Internet, high bandwidth communication, object oriented software, distributed and parallel processing, and visualizing techniques, have greatly enhanced the power and expressiveness of simulation.

5. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E Identification of the elements of the system and the functional relationships among the elements. A system diagram is constructed to depict subsystems and components and relationships among them. Quantitative data are necessary to estimate system parameters such as arrival and service distributions, conversion and processing rates, and resource levels.

6. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E Model formulation: there are 2 types of simulation models. Discrete-event models, made up of components or elements each of which performs a specific function. systems are conceptualized as a network of connected components. Items flow thru the network from one component to the next. Each component performs a function before the item can move on to the next component. Arrival rates, processing times etc. are random and follow a probability distribution.

7. Continuous simulation models, used when the system consists of a continuous flow of info, material, resources, or individuals. The system is characterized in terms of state variables and control variables. Ex: A state variable is the accumulative number of medication orders written on a hospital unit at any time during the simulation. A control variable is the number of new medication orders written per time period. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E

8. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E Components interact with each other and may involve positive and negative feedback processes. Many relationships are nonlinear and may exhibit complex dynamic behavior over time (Anderson, 2003). Models may be a set of DEs or finite difference equations. Numerical solutions allows investigators to construct and test models that cannot be solved analytically.

9. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E Model validation: to ensure that it adequately represents the system and underlying processes under study. The model is run to see if it accurately generates the reference behavior. Sensitivity analysis should be performed. A few parameters are sensitive: a change in their values may result in major changes in the behavior pattern exhibited by the system. They may represent important means to change the system’s performance.

10. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E ( Boondirek, Lenbury, Wong-ekkabut et al.,2006) A Monte Carlo Cellular Automaton Cancer Model

11. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E

12. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E TICLs Tumor infiltrating cytotoxic lymphocytes

14. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E

16. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E

17. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E

19. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E

20. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E be

22. a a

28. รายละเอียดของแบบจำลองที่กำลังดำเนิการ 1. ใช้เซลลูลาร์ออโตมาตา 2 มิติ มีขนาด 700 700 1.2. ย่านใกล้เคียง (neighborhood) ย่านใกล้เคียงของเซลล์ (i,j ) พิจารณาในแบบของ Moore neighborhood ประกอบด้วย 8 เซลล์ซึ่งอยู่ประชิดกับเซลล์ (i,j) และ เซลล์ที่อยู่ใกล้เคียงกับเซลล์ (i,j) แบบเฉียง นั่นคือ เซลล์ A Monte Carlo Simulation of HIV Infection Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E

29. นอกจากนี้เซลล์ในย่านใกล้เคียงนี้สามารถแบ่งได้ เป็น 2 ชนิด คือ เซลล์ในย่านใกล้เคียงแบบตรง ได้แก่ เซลล์ในย่านใกล้เคียงแบบเฉียง ได้แก่

30. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E.. (D)(D)

31. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E (2001) at probability r 1 *= r 1 (1 – A 1 /K). (b) It gets infected by coming contact with virus at probability r v *= r v f(V(t)). (c) cell at probability r* 2 = r 2 (1 – A 1 /K). a healthy cell at probability 1 – r 1 * – r 2 * – r v *. (d)

32. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E

33. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E

34. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E (2001) I = virus producing cells (A 1 + A 2 )

35. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E (2001)

36. Cellular Automata Flowchart

37. Thus, simulation can be used to evaluate complex biomedical systems in situations where traditional methodologies are difficult to employ. Once validated, the model can be used to study the effects of variations in system inputs, differences in initial conditions and changes in the system structure or environment. Department of Mathematics, Mahidol University www.sc.mahidol.ac.th\scma Department of Mathematics Mahidol University C M E Thank You TRF, NRCT, BIOTECH