Demonstration of fitting with Berkeley Madonna

FOCUS Degradation Kinetics, Ton van der Linden, January 27, 2005

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General information

Package

Version

contact

Berkeley Madonna

8.0.1

www.berkeleymadonna.com

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Additional information

• Java 1.1.8 (Sun Microsystems Inc) necessary for using Flowchart editor

• Windows 95 or later• Version for Macintosh available• Free demo version available (full functionality,

except for printing and saving)• User guide and examples available

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Opening screen

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Example

Soil metabolism study, parent + two metabolites

Parent

Metabolite 1

Metabolite 2

Sink

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Steps in the fitting procedure

1. Define model (equations / flow chart)

2. Initial values (substances / parameters)

3. Select parameters for fitting procedure

4. Set restrictions

5. Import datasets

6. Run

7. Export results

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Define model

d/dt (P) = -kp * Pd/dt (M1) = fpm1*kp * P - km1 * M1d/dt (M2) = fm1m2*km1 * M1 - km2 * M2

P = parentM1 = metabolite 1M2 = metabolite 2kx = degradation ratefx = formation fraction

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Flowchart

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Flowchart (simplified)

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Initial values

• Init P = 100• Init M1 = 0• Init M2 = 0• kp = .1• km1 = .1• km2 = .1• fpm1=1• fm1m2=1

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Total user defined code

METHOD RK4

STARTTIME = 0

STOPTIME=119

DT = 0.02

Init P = 100

Init M1 = 0

Init M2 = 0

d/dt (P) = -kp * P

d/dt (M1) = fpm1*kp * P - km1 * M1

d/dt (M2) = fm1m2*km1 * M1 - km2 * M2

kp = .1

km1 = .1

km2 = .1

fpm1=1

fm1m2=1

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Code automatically defined from flowchart

{

{Reservoirs}

d/dt (P) = - JPM1 - JPS

INIT P = 100

d/dt (M1) = + JPM1 - JM1M2 - JM1S

INIT M1 = 0

d/dt (M2) = + JM1M2 - JM2S

INIT M2 = 0

{Flows}

JPM1 = fPM1*kP*P

JM1M2 = fM1M2*kM1*M1

JPS = (1-fPM1)*kP*P

JM1S = (1-fM1M2)*kM1*M1

JM2S = kM2*M2

{Functions}

fPM1 = 1

fM1M2 = 1

kP = 0.1

kM1 = 0.1

kM2 = 0.1

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Parameter selection

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Parameter selection Select parametersrestrict

Import datasetsStart fitting

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Results

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Resultsgraph exported as .bmp

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Results

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Export resultsSave model / graph / table

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Results

• DT50 (parent) 13.8 d

• DT50 (metabolite 1) 6.9 d

• DT50 (metabolite 2) 60.8 d

• f.fraction (metabolite 1) 0.59

Results are very close to results ModelMaker

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Results

Uncertainty of parameters:

Not included in package

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Conclusions

Berkeley Madonna:• Easy to work with• Flexible• Robust• Compatible with many office packages

• Gives similar answers (results) as other packages• Has no built-in statistical routines