2019
DOI: 10.1007/s00449-019-02214-6
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The shortcomings of accurate rate estimations in cultivation processes and a solution for precise and robust process modeling

Abstract: The accurate estimation of cell growth or the substrate consumption rate is crucial for the understanding of the current state of a bioprocess. Rates unveil the actual cell status, making them valuable for quality-by-design concepts. However, in bioprocesses, the real rates are commonly not accessible due to analytical errors. We simulated Escherichia coli fed-batch fermentations, sampled at four different intervals and added five levels of noise to mimic analytical inaccuracy. We computed stepwise integral es… Show more

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Cited by 20 publications
(15 citation statements)
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“…[ 18 ] Accurate rate estimations are of great importance for robust bioprocess modeling, and achieving these as precisely as possible is of high interest. [ 19 ] Due to these advantages, hybrid modeling is gaining in popularity for bioprocess modeling. Even though a hybrid model provides improved performance compared to other approaches, [ 20 ] the possibility of misprediction still exists.…”
Section: Introductionmentioning
confidence: 99%
“…[ 18 ] Accurate rate estimations are of great importance for robust bioprocess modeling, and achieving these as precisely as possible is of high interest. [ 19 ] Due to these advantages, hybrid modeling is gaining in popularity for bioprocess modeling. Even though a hybrid model provides improved performance compared to other approaches, [ 20 ] the possibility of misprediction still exists.…”
Section: Introductionmentioning
confidence: 99%
“…Bayer et al. [ 33 ] point out that the choice of the rate calculation method largely impacts the accuracy of the calculated rates. They concluded that fitting a cubic smoothing spline function is better than a step‐wise integration.…”
Section: Discussionmentioning
confidence: 99%
“…The estimation of the rates can be accomplished in two different ways, a differential or integral way. [ 41–44 ] Since the interest was in analyzing changes in the specific rates over time, the differential way was adopted here, following the best practice, [ 45,46,28 ] that is, Starting from the integrate version of the material balance (Equation (5)), the rate related terms were isolated on the right‐hand side since they cannot be measured: cnormalexti·Vticnormalext0·Vt0t0tiu·dt=t0tiq·x·V·dt Fit arbitrary time dependent functions (e.g., cubic smoothing splines, gaussian process models, polynomials or others), f ( t , w ), to approximate the measured quantities, ymfalse(tifalse)=cex,mfalse(tifalse)·Vnormalmfalse(tifalse)cex,mfalse(t0false)·Vnormalmfalse(t0false)t0tiunormalm·dt, such that the residual ɛ was small, though the function also does not overfit the data. ynormalm=ft,w+ε Build the derivative of f ( t , w ) analytically with respect to time, that is, dffalse(t,wfalse)dt Evaluate the derivative at the time instance t i at which the concentrations have been measured (assuming that the concentrations have the lowest measurement frequency) and divide by the approximated biomass ( x m ( t ) · V m ( t ) = g ( t , ω...…”
Section: Methodsmentioning
confidence: 99%