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Estimation of Process Model Parameters

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Animal Cell Biotechnology

Part of the book series: Methods in Molecular Biology ((MIMB,volume 2095))

Abstract

Cell culture technology has become a substantial domain of modern biotechnology, particularly in the pharmaceutical market. Today, products manufactured from cells itself dominate the biopharmaceutical industry. In addition, a limited number of products made of in vitro cultivated cells for regenerative medicine were launched to the market. Modeling of such processes is an important task since these systems are usually nonlinear and complex. In this chapter, a framework for the estimation of process model parameters and its implementation is shown. It is aimed to support the parameter estimation task, which increases the potential of implementation and improvement of mathematical process models into the novel and existing bioprocesses. Apart from the parameter estimation, evaluation of the estimated parameters plays an essential role in order to verify these parameters and subsequently the selected model. The workflow is outlined and shown specifically on the basis of a mathematical process model describing a mammalian cell culture batch process.

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Abbreviations

AIC:

Akaike information criterion

BIC:

Bayesian information criterion

GSA:

Global sensitivity analysis

LSA:

Local sensitivity analysis

NRMSD:

Normalized root mean square deviation

ODE:

Ordinary differential equations

c Glc :

Glucose concentration (mmol L−1)

c Gln :

Glutamine concentration (mmol L−1)

k Glc :

Monod kinetic constant for glucose uptake (mmol L−1)

k Gln :

Monod kinetic constant for glutamine uptake (mmol L−1)

K S,Glc :

Monod kinetic constant for glucose (mmol L−1)

K S,Gln :

Monod kinetic constant for glutamine (mmol L−1)

q Glc :

Cell-specific glucose uptake rate (mmol cell−1 h−1)

q Glc,max :

Maximum cell-specific glucose uptake rate (mmol cell−1 h−1)

q Gln :

Cell-specific glutamine uptake rate (mmol cell−1 h−1)

q Gln,max :

Maximum cell-specific glutamine uptake rate (mmol cell−1 h−1)

X v :

Viable cell concentration (cells L−1)

μ d :

Cell-specific death rate (h−1)

μ d,min :

Minimum cell-specific death rate (h−1)

μ :

Cell-specific growth rate (h−1)

μ max :

Maximum cell-specific growth rate (h−1)

A :

Constant matrix with 1 and 0 on diagonal

f(∙) :

Vector function

F(θ):

Objective function depending on parameter vector θ

g(∙):

m-Dimensional mapping of the state variables to the measurements

L :

Number of state variables

M :

Number of measurands

N :

Number of measurements

p :

Vector of all model parameters

p unknown :

Vector of unknown model parameters

R 2 :

Coefficient of determination, R-Squared

t :

Time

t 0 :

Starting time

t e :

End time

u :

External input signal or signals

w :

A weighting vector

x :

A vector of the state variables

x 0 :

Initial state vector

y i :

Measured data

yk(ti):

Measurement of the k-th measurand in time ti

\( \hat{y_k}\left(\hat{\boldsymbol{\theta}},{t}_i\right) \) :

Estimation of the k-th measurand at the time ti, depending on parameter estimate \( \hat{\boldsymbol{\theta}} \)

\( \overline{y_{\mathrm{m}}} \) :

Average of measured data

\( \overline{y_{\mathrm{s}}} \) :

Average of simulated observable

\( {\sigma}_{ki}^2 \) :

Variance of the k-th measurement at point in time ti

θ :

Parameter vector of unknown model parameter values and initial state vector

\( \hat{\boldsymbol{\theta}} \) :

Estimated parameter vector

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Acknowledgments

Example data and code provided by JM, tested and improved by THR. Parameter estimation itself has been established and used for many years within the groups of VCH, RP, and BF.

Author information

Authors and Affiliations

  1. Biotechnology & Bioprocess Engineering, Ostwestfalen-Lippe University of Applied Sciences and Arts, Lemgo, Germany

    Sahar Deppe, Björn Frahm & Tanja Hernández Rodríguez

  2. University of Applied Sciences, Hochschule Furtwangen University, Villingen-Schwenningen, Germany

    Volker C. Hass

  3. Institute of Bioprocess and Biosystems Engineering, Hamburg University of Technology, Hamburg, Germany

    Kim B. Kuchemüller, Johannes Möller & Ralf Pörtner

Authors
  1. Sahar Deppe
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  2. Björn Frahm
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  3. Volker C. Hass
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  4. Tanja Hernández Rodríguez
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  5. Kim B. Kuchemüller
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  6. Johannes Möller
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  7. Ralf Pörtner
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Corresponding author

Correspondence to Björn Frahm .

Editor information

Editors and Affiliations

  1. Institute of Bioprocess and Biosystems Engineering, Hamburg University of Technology (TUHH), Hamburg, Germany

    Ralf Pörtner

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Deppe, S. et al. (2020). Estimation of Process Model Parameters. In: Pörtner, R. (eds) Animal Cell Biotechnology. Methods in Molecular Biology, vol 2095. Humana, New York, NY. https://doi.org/10.1007/978-1-0716-0191-4_12

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  • DOI: https://doi.org/10.1007/978-1-0716-0191-4_12

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  • Publisher Name: Humana, New York, NY

  • Print ISBN: 978-1-0716-0190-7

  • Online ISBN: 978-1-0716-0191-4

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