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A New Kinetic Structured Model for Cell Cultivation in a Chemostat
#1
We propose a new mathematical model for cell cultivation in a chemostat. Our model is based on the structuring of the biomass into two main groups: dividing and nondividing cells. The model is applicable both to existing static characteristics such as the Monod model and to the deviations from it.

We determined the range of chemostat stability at the specified flow rate D and concentration of the input limiting substrate S0. We also proposed the methods for determining parameters of the chemostat structured model.

The value of the derivative of dividing cells to nondividing cells of zero age is constant for a given flow rate. That value is no less important than the equality of specific growth rate and nutrient flow rate, which determines the equilibrium of the chemostat.

We showed that the corresponding specific rate constants of limiting substrate use by dividing and nondividing cells determine the system equilibrium. We also demonstrated that the new proposed structured model of the chemostat is more general than any other existing model. In each specific case, the model provides comparable equations to the well-known models of Monod, Pirt, Moser, Andrews and Ierusalimsky.

http://www.bioprocessintl.com/journal/20...tat-335634
#2
Dear colleagues,
This model is the a special case of the common model
http://iopscience.iop.org/1758-5090/3/4/045006
and
http://interesjournals.org/IRJBB/pdf/201...t%20al.pdf

I invite you to take part in the discussions in Linkedin at:
http://www.linkedin.com/groups/Mathemati..._125406484
#3
Hello Sergey,

Do you mind explaining in more details what is mathematical model for cell cultivation? I opened the link you posted but I get lost in equations. I'm biologist (not that familiar with the math), but your method seams interesting and I would like to find out something more.

Thanks,
Bojana
#4
(10-31-2012, 06:04 PM)BojanaL Wrote: Hello Sergey,

Do you mind explaining in more details what is mathematical model for cell cultivation? I opened the link you posted but I get lost in equations. I'm biologist (not that familiar with the math), but your method seams interesting and I would like to find out something more.

Thanks,
Bojana
============================================================
Hi Bojana,
Pls, see http://fermenter.ru/forum/viewtopic.php?id=24
Also,I advise you to re-read the beginning, which is given above:
Monod equation and other equations is known. However, these "other" equations arose due to the Monod equation " nonuniversality ". Our model has opened the cause of this Monod equation"nonuniversality " for continuous processes.
In general, the model provides for periodic processes in the journal "Biofabrication":
http://iopscience.iop.org/1758-5090/3/4/045006
Also, a universal law was given here that observed in any system:
equations (17-18) and (45).

Warm regards,

Sergey
  

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