Example: Unstructured growth of trichosporon cutaneum (TRICHO) 

Background:
An unstructured growth model of trichosporon cutaneum is to be developed in form of a system of two ordinary differential equations.

The Mathematical Model:
The underlying ordinary differential equations are

c_x(t)_t = m(t)  c_x(t) - D(t) c_x(t)
c_s(t)_t = (-m(t) /y_xs - m_s) c_x(t) + D(t) (c_sf - c_s(t))

with m(t)  =  m_max c_s(t) / (K_s + c_s(t)) and  D(t) = u(t)/V₀. We have  u(t) = 0  if t < t_f  and  u(t) = a (t - t_f) otherwise. Initial values are  c_x(0)=0.5 and c_s(0)=6. We have to guarantee that there is a continuous transition at t=t_f, where the model changes. Parameters to be estimated, are K_s, m_max, a, and an intermediate time value t_f, which is unknown in advance and where the model changes. The lower index t denotes the time derivative of the time-dependent state variables  c_x(t) and c_s(t).

Literature:
Baltes M., Schneider R., Sturm C., Reuss M. (1994): Optimal experimental design for parameter estimation in unstructured growth models, Biotechnical Progress, Vol. 10, 480-488
 

Implementation:
The complete solution of a data fitting problem is described in six steps:

1. Define model type and document the experiment
   ... set some informative strings, define the mathematical structure and the variables
2. Specify details of the model structure
   ... set number of equations, tolerances, constraints, concentration values, ...
3. Use editor for declaring variables and for defining functions
   ... the essential part, you have to know the mathematical equations and how to relate them to the format required by EASY-FIT^ModelDesign
4. Insert measurement data
   ... the dirty job, can become boring (but you may import data from text files and EXCEL spreadsheets!) 
5. Select termination tolerances and start a data fitting run
   ... only a few mouse clicks
6. A separate process is started and all computed data are displayed
   ... MODFIT estimates parameters and performs a statistical analysis

Results:
Then you would like to take a look at reports and graphs:
    - parameter values
   - experimental data versus fitting criterion
 

Documentation and parameters:

Model structure:

Model equations (or use your own favorite editor):

Measurement data (or use import function for text file or Excel):

Parameters, tolerances and start of a data fitting run:

Numerical results (computed by the least squares code DFNLP):

Report on parameter values, residuals, performance, etc. (or export to Word):

Experimental data versus fitting criterion (also available for Gnuplot):

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