department of mathematics, mahidol university

Department of Mathematics, Mahidol University Department of Mathematics, Mahidol University

www.sc.mahidol.ac.th\www.sc.mahidol.ac.th\scmascma

Department of MathematicsDepartment of Mathematics

Mahidol University Mahidol University C

Yongwimon LenburyDeparment of Mathematics

Wannapong TriumpoDepartment of Physics

Mahidol University, Thailand

Sompop Moonchai Deparment of Mathematics,

Chiangmai University

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).

Monte Carlo cellular automaton model for cancerSimulation of HIV infectionConclusion

www.sc.mahidol.ac.th\scmawww.sc.mahidol.ac.th\scma

IntroductionThe modeling process

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.

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.

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.

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.

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 andtest models that cannot be solved analytically.

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.

( Boondirek, Lenbury, Wong-ekkabut et al.,2006)

A Monte Carlo Cellular Automaton Cancer Model

(Qi, 1993).

Few discrete models have used the

TICLsTumor infiltrating cytotoxic

lymphocytes

. (Modified from Jain, 2002, and Matzavinos and Chaplain, 2004)

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A Monte Carlo Simulation of HIV Infection

),,1(),1,(),1,(),,1( jijijiji

)1,1(),1,1(),1,1(),1,1( jijijiji

),1(),1,(),1,(),,1( jijijiji

)1,1(),1,1( jiji),1,1( ji )1,1( ji และ

นอกจากน�(เซลล�ในย่�านใกล�เคี�ย่งน�(สามาร์ถแบ�งได�เป,น 2 ช้น�ด คี'อ เซลล�ในย่�านใกล�เคี�ย่งแบบตร์ง ได�แก�

เซลล�ในย่�านใกล�เคี�ย่งแบบเฉี�ย่ง ได�แก�

(2001)

at probability r1*= r1(1 – A1/K).

(b) It gets infected by coming contact with virus at probability rv*= rvf(V(t)) .

cell at probability r*2 = r2(1 – A1/K).

a healthy cell at probability 1 – r1* – r2* – rv*.(d)

(2001)

I = virus producing cells (A1 + A2)

(2001)

Cellular Automata Flowchart

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.

Thank YouThank You TRF, NRCT, BIOTECH

department of mathematics, mahidol university

system parameters

system inputs

system diagram

system structure anderson

continuous simulation

types of simulation

expressiveness of simulation

model formulation

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