DEDiscover Differential Equation Modeling Solution

DEDiscoverDifferential Equation Modeling Solution

CANGLIN WUJune-18-2007

June-18-2007 2007 Pittsburgh Workshop Canglin Wu

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DEDiscover is a cross-platform software tool for building and understanding differential equation models, with special attention to the features necessary for modeling the immune system and viral infection.


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General Features• Cross-platform: Windows, Linux

and Mac OS • Import models and export

standard data and image formats (e.g. CellML, SBML, PNG, JPEG, PS, EPS etc.)

• Plug in architecture


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Model Support• Standard mathematical notations,

plus macros, indicator functions, time-varying parameters, history functions, and constraints

• ODE and DDE models• Pre-defined or user specified models


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Model input and solver selection


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DEDiscoverDifferential Equation Modeling olution

Parameters and initial conditions


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Simulation Support• Several ODE and DDE solvers• Real-time solutions allow

interactive exploration• Tabular and Graphical display

of results • Customizable displays


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Simulation result - Combined plot


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Simulation result - Individual plot


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Simulation result - Table


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Estimation Support • Several estimation & optimizer methods• Point estimates and confidence intervals • Estimation of both initial conditions and

parameters• Properly fits data with experiment,

treatment, and technical replicates• Interactive display and control of

estimation progress


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Formula Syntax• Dependent variable, dEP/dt• Delay variable, TE(t-tau_T)• Temporary variable like MACRO,

suggest use temp_ as prefix, for example temp_var= k*T1*V• Suggest capital for variable and low-

case for parameter


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Formula Syntax

• Indicator functionI(tau_T,100)(t) tau_T<I<100I[tau_T,100)(t) tau_T<=I<100I(tau_T,100](t) tau_T<I<=100I[tau_T,100](t) tau_T<=I<=100• Initial condition in formula, D(0) • Comment, // for comment one line, /* */ for

comment multiple lines


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Formula Syntax• Case insensitive, V and v are same

variable NOT two variables• DO NOT use * as a part of variable

name, reserved for multiple operation

• DO NOT use T or t as variable name, reserved for independent variable


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Reserved Words• T, t, //, /*, */, + , - , * , / , = , , , . ,

( , ) , < , > , ‘ , ^ , e , log , sin , cos , tan etc

• You CAN NOT use reserved word as variable and parameter name


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Operator• + Add• - Subtract• * Multiply• / Divide• % Modulus • ^ Power: y = x ^ 2( ) • () Parenthesis. For example: (2 + 3) * 5


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Math functions• sin(x) Calculate sine• sinh(x)Calculate hyperbolic sine• Cos(x) Calculate cosine • Cosh(x) Calculate hyperbolic cosine• tan(x) Calculate tangent• tanh(x) Calculate hyperbolic tangent• asin(x) Calculate arcsine • acos(x) Calculate arccosine• atan(x) Calculate arctangent• atan2(x, y) Calculate arctangent with two parameters to preserve

quadrant angle• bessj(n, v) Bessel function of the first kind. n isorder and v is input

value.• bessy(n, v).Bessell function of the second kind. nis order and v is

input value• hypot(a,b) Calculate hypotenuse of right triangle


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Math functions• abs(x) Return absolute value• max(x) Return larger of two values• min(x) Return smaller of two values• sqrt(x) Find square root• Ceil(x) Find integer ceiling • floor(x) Calculate hypotenuse of right triangle• exp(x) Calculate exponential function: ex• log(x) Calculate natural logarithm• log10(x) Calculate base-10 logarithm• rand(x) Get pseudorandom number between 0 and 1• srand(x) Initialize pseudorandom series


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Download • Log in CBIM website first • Download at

http://cbim.urmc.rochester.edu/software

• Install DEDiscover package in your computer


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DEDicover DEMO


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Acknowledgment• NIAID/NIH grant NO1 AI50020Center for Biodefense Immune Modeling • Design : Hulin Wu, Gregory Warnes,

Dongwen Wang• Program: Hongyu Miao, Alain Leblanc• Model: Alan Perelson, HY Lee, SY Lee• Other: Jeanne Holden-Wiltse, Temple

Herlong


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ThanksQ & A

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DEDiscover Differential Equation Modeling Solution