Presentation February 16, 2014 Slide 1 FOCUS Kinetics Training: Parameter Estimation with MatLab Dr. Dieter Schäfer BCS / Environmental Modelling Monheim,

Presentation • April 10, 2023 • Slide 1

FOCUS Kinetics Training:

Parameter Estimation with MatLab

Dr. Dieter Schäfer

BCS / Environmental Modelling

Monheim, Germany

FOCUS Degradation Kinetics Training • Brussels • January 27, 2005

What is MatLab?

MatLab ...

... stands for MATrix LABoratory

... is an interactive high-performance language for technical computing

... is a very flexible tool for solving a wide range of mathematical problems

... has a modular design (software toolboxes, ASCII control files)

... can be adapted to kinetic parameter estimation problems

=> see www.mathworks.com for further information


What is MatLab?

MatLab (basic module) for data handling, solving of differential equations, etc.

Optimisation Toolbox for non-linear parameter optimisation

Statistics Toolbox for additional statistics

MatLab Compiler (optional) to produce stand-alone executables

current version: MatLab 7, Release 14

costs for single-user licence: 4500 € (+ Compiler 6000 €)

For the estimation of kinetic parameters, the following modules of MatLab are relevant:


What is MatLab?

Potential weaknesses of MatLab in the context of FOCUS Kinetics

commercial software (costs of ~5000 € per license)

not a ready-to-use tool for kinetic parameter estimation, requires some programming skills

not too user-friendly, if run without a Graphical User Interface


What is MatLab?

Potential strengths of MatLab in the context of FOCUS Kinetics

full software support, ongoing software development

large user community in science and engineering (good availability of newsgroups, literature, experts)

extensive statistical capabilities (e.g., self-defined statistical output, including chi²-test and t-test)

extensive graphical capabilities (e.g., self-defined graphical output, development of Graphical User Interfaces)

optional generation of executable files that run independent of MatLab


On-screen Presentation of MatLab / Run via ASCII file

% KINTEST -- Test program for KINCALC% Author: Dr. Michael Warncke, Bayer Technology Services GmbH% Version / Date: 2.0 / 2004-12-17

% set up kinetic modellink = [1 2; 1 4; 2 3; 2 4; 3 4]; % list of connections between compartmentskinetic = {'sfo', 'sfo’, 'sfo', 'sink'}; % list of used kinetic models

% compartmentsvarnames = {{'P'}, {'M1'}, {'M2'}, {'S'}}; % names of state variablesboxnames = {'Parent','Met1','Met2','Sink'}; % compartment names

% kinetic parametersparamnames = {{'kP','FFM1'}, {'kM1','ffM2'}, {'kM2'}, {}}; % names of kinetic parametersiskfix = {[0, 0], [0, 0], [0], []}; % 0 = optimize kinetic parametersk = {[0.05, 0.5], [0.1, 0.5], [0.01], []}; % initial values for kinetic parametersklb = {[0, 0], [0, 0], [0], []}; % lower bounds for kinetic parameterskub = {[Inf, Inf], [Inf, Inf], [Inf], []}; % upper bounds for kinetic parameters

% M0 valuesisyfix = {[0], [1], [1], [1]}; % 0 = optimize M0y0 = {[NaN], [0], [0], [0]}; % NaN = obtain initial M0 from dataylb = {[0], [0], [0], [0]}; % lower bounds for M0yub = {[Inf], [Inf], [Inf], [Inf]}; % upper bounds for M0

% assign datamodel.filename = 'FOCUS-Training_Example2.txt'; % name of data filemodel.datanames = {'c1','c2','c3',''}; % column names of the measurement datamodel.weightnames = {'','','',''}; % column names of the weighting data


On-screen Presentation of MatLab / Run via GUI


How does MatLab perform?

Example data sets from the FOCUS Kinetics Draft Report

Data Set A (see Table 13-4a in FOCUS, 2004):

package M0 alpha beta DegT50 DegT90

ACSL 109.3 2930 780000 18.43 61.32

Excel 109.2 2360000 63300000 18.62 61.87

Kinetica 107.3 426000 9640000 15.68 52.09

Madonna 109.2 2080000 55900000 18.6 61.79

Mathematica 109.2 1070000 28700000 18.62 61.87

MatLab 101.2* 3 82 19.12 82.38

MatLab 109.5 27 718 18.39 62.93

ModelMaker 109.2 25400 682000 18.62 61.87

Modelmaker# 109.2 299 8040 18.66 62.15

ModelManager 109.2 515 13800 18.61 61.93

PRISM 109.2 550000 14800000 18.62 61.86

Statistica 109.2 12500 337000 18.62 61.87

Tablecurve 2D 109.1 -0.0003 -922 18.62 61.90# differentiated form * fixed to initial (measured) value



Example data sets from the FOCUS Kinetics Draft Report

Data Set D (see Table 13-7 in FOCUS, 2004):

Parameter Definition Kinetica Madonna Mathematica ModelMaker MatLab

M0 total size of compartment 99.59 99.77 98.21 99.59 99.55

k12 rate coefficient parent->metabolite 0.0507 0.098* 0.0541 0.0506 0.0508

k13 rate coefficient parent->rest 0.048 0.0443 0.0478 0.0478

k23 rate coefficient metabolite->rest 0.0052 0.0053 0.0062 0.0053 0.0053

f12 formation fraction metabolite 0.51 0.51 0.55 0.51 0.51

DegT50_p half life parent 7.03 7.05 7.04 7.04 7.03

DegT50_m half life metabolite 132.84 130.39 111.21 130.78 131.61

* K12 obtained with Madonna should be compared to k12 + k13 of the other packages.



Example data sets from the FOCUS Degradation Kinetics Training

Example 1 (parent SFO, two metabolites SFO):

ModelMaker MatLab

parameter optimised stand. error optimised stand. error

Pini 103.3 1.9 103.3 1.8

kP 0.0507 0.0021 0.0508 0.0021

ffM1 0.5813 0.0359 0.5826 0.0360

kM1 0.0999 0.0091 0.0999 0.0090

kM2 0.0114 0.0014 0.0114 0.0014

Substance DT50 DT90 DT50 DT90

Parent 13.9 46.1 13.6 45.3

Metabolite1 6.8 22.6 6.9 23.1

Metabolite2 60.9 202.3 60.9 202.2



Example data sets from the FOCUS Degradation Kinetics Training

Example 2 (parent FOMC, one metabolite SFO):

ModelMaker MatLab

parameter optimised stand. error optimised stand. error

Pini 96.87 2.46 96.96 2.46

alphaP 0.9425 0.124 0.9422 0.116

betaP 4.436 1.042 4.397 0.984

ffM 0.8018 0.0546 0.8003 0.0545

kM 0.02 0.0019 0.02 0.0019

Substance DT50 DT90 DT50 DT90

Parent 4.82 46.6 4.78 46.2

Metabolite 34.7 115.2 34.7 115.2

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Presentation February 16, 2014 Slide 1 FOCUS Kinetics Training: Parameter Estimation with MatLab Dr. Dieter Schäfer BCS / Environmental Modelling Monheim,