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Department of Mathematics Mahidol University. C. Department of Mathematics, Mahidol University. M. E. www.sc.mahidol.ac.th\scma. Monte Carlo Simulation Technique in Health Science. Yongwimon Lenbury Deparment of Mathematics Wannapong Triumpo Department of Physics - PowerPoint PPT PresentationTRANSCRIPT
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
ME
Yongwimon LenburyDeparment of Mathematics
Wannapong TriumpoDepartment of Physics
Mahidol University, Thailand
Sompop Moonchai Deparment of Mathematics,
Chiangmai 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
ME
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
Department of Mathematics, Mahidol University Department of Mathematics, Mahidol University
www.sc.mahidol.ac.th\scmawww.sc.mahidol.ac.th\scma
Department of MathematicsDepartment of Mathematics
Mahidol University Mahidol University C
ME
IntroductionThe modeling process
Department of Mathematics, Mahidol University Department of Mathematics, Mahidol University
www.sc.mahidol.ac.th\scmawww.sc.mahidol.ac.th\scma
Department of MathematicsDepartment of Mathematics
Mahidol University Mahidol University C
ME
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.
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
ME
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.
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
ME
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.
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
ME
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
ME
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.
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
ME
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.
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
ME
( Boondirek, Lenbury, Wong-ekkabut et al.,2006)
A Monte Carlo Cellular Automaton Cancer Model
(Qi, 1993).
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
ME
Few discrete models have used the
.
,
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
ME
TICLsTumor infiltrating cytotoxic
lymphocytes
. (Modified from Jain, 2002, and Matzavinos and Chaplain, 2004)
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
ME
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
ME
.
.
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
ME
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
ME
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
ME
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A Monte Carlo Simulation of HIV Infection
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
ME
),,1(),1,(),1,(),,1( jijijiji
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Department of Mathematics, Mahidol University Department of Mathematics, Mahidol University
www.sc.mahidol.ac.th\scmawww.sc.mahidol.ac.th\scma
Department of MathematicsDepartment of Mathematics
Mahidol University Mahidol University C
ME
.
.(D)
Department of Mathematics, Mahidol University Department of Mathematics, Mahidol University
www.sc.mahidol.ac.th\scmawww.sc.mahidol.ac.th\scma
Department of MathematicsDepartment of Mathematics
Mahidol University Mahidol University C
ME
(2001)
at probability r1*= r1(1 – A1/K).
(b) It gets infected by coming contact with virus at probability rv*= rvf(V(t)) .
(c)
cell at probability r*2 = r2(1 – A1/K).
a healthy cell at probability 1 – r1* – r2* – rv*.(d)
Department of Mathematics, Mahidol University Department of Mathematics, Mahidol University
www.sc.mahidol.ac.th\scmawww.sc.mahidol.ac.th\scma
Department of MathematicsDepartment of Mathematics
Mahidol University Mahidol University C
ME
Department of Mathematics, Mahidol University Department of Mathematics, Mahidol University
www.sc.mahidol.ac.th\scmawww.sc.mahidol.ac.th\scma
Department of MathematicsDepartment of Mathematics
Mahidol University Mahidol University C
ME
Department of Mathematics, Mahidol University Department of Mathematics, Mahidol University
www.sc.mahidol.ac.th\scmawww.sc.mahidol.ac.th\scma
Department of MathematicsDepartment of Mathematics
Mahidol University Mahidol University C
ME
(2001)
I = virus producing cells (A1 + A2)
Department of Mathematics, Mahidol University Department of Mathematics, Mahidol University
www.sc.mahidol.ac.th\scmawww.sc.mahidol.ac.th\scma
Department of MathematicsDepartment of Mathematics
Mahidol University Mahidol University C
ME
(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.
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
ME
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