### 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

cx(t)t = m(t)  cx(t) - D(t) cx(t)
cs(t)t = (-m(t)
/yxs - ms) cx(t) + D(t) (csf - cs(t))

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