Influence of cell specific parameters in a dielectric spectroscopy conversion model used to monitor viable cell density in bioreactors

In the biopharmaceutical industry, the use of mammalian cells to produce therapeutic proteins is becoming increasingly widespread. Monitoring of these cultures via different analysis techniques is essential to ensure a good quality product while respecting good manufacturing practice (GMP) regulations. Process Analytical Technologies (PAT) tools provide real‐time measurements of the physiological state of the culture and enable process automation. Dielectric spectroscopy is a PAT that can be used to monitor the viable cell concentration (VCC) of living cells after processing raw permittivity data. Several modeling approaches exist and estimate biomass with different accuracy. The accuracy of the Cole–Cole and Maxwell Wagner's equations are studied here in the determination of the VCC and cell radius in Chinese hamster ovary (CHO) culture. A sensitivity analysis performed on the parameters entering the equations highlighted the importance of the cell specific parameters such as internal conductivity (σi) and membrane capacitance (Cm) in the accuracy of the estimation of VCC and cell radius. The most accurate optimization method found to improve the accuracy involves in‐process adjustments of Cm and σi in the model equations with samplings from the bioreactor. This combination of offline and in situ data improved the estimation precision of the VCC by 69% compared to a purely mechanistic model without offline adjustments.


INTRODUCTION
Over the last 30 years, growth of the market for therapeutic proteins has continued to accelerate. [1,2]Monoclonal antibodies (mAbs) account for nearly 50% of the market, predominantly for oncology and inflammatory diseases. [3]The use of animal cells to produce these mAbs is necessary for near-human structural properties, which ensure better specificity, efficacy of action, and tolerability in patients.More than 70% of therapeutic mAbs are produced using a Chinese hamster ovary (CHO) cell line, [4,5] grown in a regulated and controlled culture environment to maximize the quantity and quality of protein glycosylation.For several years, manufacturers have been encouraged by drug regulatory agencies such as the United States Food and Drug Administration (FDA) and the European Medicines Agency (EMA) to implement a quality by design (QbD) approach based on process control in the manufacture of these bio-products.An intrinsic understanding of the production process and monitoring culture conditions enable an increase in the yield and glycolytic quality of these mAbs. [6] meet this challenge, the Process Analytical Technology (PAT) approach consists of developing and using inline monitoring instruments for operational units to enable real-time predictive analytics and control strategies.These tools play a key role in the evolution of the industry toward "Bioprocessing 4.0" which is based on automation, intensified, and continuous process.However, apart from process control probes such as pH, temperature and dissolved O 2 concentration, cell culture bioreactors still rely on offline analysis to monitor essential physiological variables such as biomass, [7] radius, nutrient quantity, or metabolic indicators, [8] as well as critical parameters.These analyzers require daily manual samplings from the bioreactor which increase the risk of contamination or the process cost.Moreover, most of these tools are not currently available as in situ probes and do not provide real-time information for process automation.
To overcome the lack of inline and real-time sensors, spectroscopicbased technologies with process probe interfaces are being evaluated to monitor cell growth.They have the advantage of being non-invasive, non-destructive, offer rapid, and frequent analysis, and are based on dielectric, [9][10][11] near infrared, [12] or Raman spectroscopies. [13,14] date, these technologies are typically used for online monitoring of viable cell concentration (VCC) or compounds in the culture media. [15,16]Compared to reference offline analytical techniques, dielectric spectroscopy has been shown to be the most reliable inline technique for cell density monitoring. [6,17]Moreover, it is faster to integrate as it does not require a long model building process to be used as a real-time monitoring tool [18] compared to inline analytical tools as near infrared or Raman spectroscopy. [19]e principle of capacitance measurement is based on the approach that cells are considered to be dielectric entities, as cell membranes are non-conductive and isolative.In the presence of an electrical field in an ionic culture medium, the movement of ions contained in the cytoplasm is limited within a restricted sphere and the cells are polarized at their poles.Living cells therefore behave like capacitors.Thus, the measured permittivity is directly related to the volume of living cells in solution and described by its conductivity (σ, S m −1 ) and its permittivity (ε, F m −1 ).This technology is now adopted by many industrial processes and adapted to a variety of cells such as mammalian, [20] bacterial, [21] or even plants. [22]e capacitance signal is proportional to the total volume of living cells and can be correlated with a VCC value measured by an offline counting technique, using a simple linear regression. [23]Neverthe-less, to determine the linear correlation coefficient of the relationship between VCC and capacitance, it is necessary to perform at least one cell culture during which offline samples will be taken regularly.Capacitance measurements are captured at the same time as offline sampling, and values can be plotted against the corresponding offline VCC measurements.The more samples analyzed offline, the more refined the linearity and the better the determination of the correlation coefficient between the capacitance and the VCC.Thanks to this linear relationship, it is thus possible to multiply the capacitance value to the correlation factor in order to obtain a monitoring of the VCC. [24]major problem of this linear conversion for VCC monitoring is that the correlation factor varies according to the growth phase especially when cell viability is low during the stationary and decay phases and must be redefined during the cell culture with offline samplings.In fact, the linearity between the two sets of values is only correct in the exponential growth phase. [25,26]It is also not transferable to other cell culture processes because the correlation factor can vary significantly between cell lines with different sizes or growth kinetics. [24]This method is thus limited with regard to its use for process continuation and automation that favor "ready to use" approaches.
An alternative model used for converting capacitance measurements into inline biomass parameters is based on the Cole-Cole equation, which reproduces the dielectric behavior of suspended cells.
Indeed, the equation is used to fit the permittivity spectrum and allows extraction of dielectric parameters (fc, Δε) from the curve (see Section 2).The fitting is usually done using the Levenberg-Marquart algorithm. [27]These parameters are then used in the nonlinear Maxwell-Wagner's equation, as well as cell-specific parameters like membrane capacitance C m and internal conductivity σ i , allowing estimation of the intrinsic physiological properties of cells (VCC, radius). [26]vertheless, use of this purely mechanistic approach does not provide a satisfactory estimation accuracy compared to offline analyzers.
The imprecision of this method is mostly since the physiological parameters C m and σ i are often considered to be constant [28] when in fact, they evolve during mammalian cell culture. [29]For example, the value of the membrane capacitance is highly dependent on the lipid and protein composition, as well as its thickness, all of which evolve during growth. [30]Not considering the evolutions would reduce the accuracy of estimation of VCC and would make impossible to use it as a parameter to bioreactor control and automation.To overcome this issue, the authors proposed use of partial least square (PLS) regression to post-process data from dielectric spectroscopy and the offline analyzer. [31,32]Even if PLS model can provide accurate predictions, it requires several cell cultures to get enough data to cover an adapted design space for each monitored parameter.Also, a change of cell culture process makes the process conditions out of the design space predefined, so the PLS model sees its accuracy decreasing.A reduced transferability between processes may reduce the industrial adoption for real-time application.Thus, a real-time retuning of models may then support the possibility to use the capacitance sensor as a VCC sensor from the first cell culture run without any calibration and use the model output as input parameter for process control.

THEORETICAL ASPECTS
In this study, it was sought to estimate the VCC and average cell radius by using a permittivity probe.Below, the main equations summarize the process to obtain the estimated parameters.More details can be found in refs. [21,26]rmittivity characterizes the tendency of a certain material to polarize in the presence of an electric field.Permittivity probes emit an alternating electric field and living cells in the surrounding media act like capacitors because of insulating properties of the cell membrane, storing charged ions between cell culture medium and cell cytoplasm.
Cell polarization at the membrane is highly dependent on the frequency at which the electric field is emitted because it influences the duration of movement of the cytoplasmic ions.
For low frequencies (<0.1 MHz), the intracellular ions have enough time to migrate and fully polarize the cell, resulting in high values of permittivity.At higher frequencies (>1 MHz), there is insufficient time for cells to be polarized leading to an absence of permittivity signal. [33]is phenomenon is known as the β-dispersion; [34] between 0.1 and 10 MHz, the permittivity probe measures the parameters of the βdispersion.Based on the Debye equation, [35] the Cole-Cole equation reproduces the shape of the β-dispersion by expressing the permittivity as a function of frequency (f) and relates it to the cell's physiological parameters.
The Cole-Cole equation models the β-dispersion with several parameters [26] : • The permittivity increment Δε • The characteristic frequency f c • The Cole-Cole parameter α (slope of the curve at f c ) • The permittivity of free space ε 0 • The permittivity at high frequency ε ∞ • The permittivity at low frequency ε s The permittivity increment (Δε) corresponds to the magnitude of the recorded permittivity, that, the charge-storing capabilities of cells and thus the total living-cell volume in the bioreactor.As the biomass increases, so does the amount of cytoplasmic ions, the permittivity increment Δε will increase.The equation that summarizes this relationship is the following: where P p is the predicted biovolume fraction of living cells, r is the cell radius, and C m is the membrane capacitance (F m −2 ).
The characteristic frequency f c is the frequency value at which Δε is divided by half and is also calculated as follows: where σ i is the static internal conductivity and σ a is the static medium conductivity.The latter is calculated from the conductivity of the medium σ which is measured directly by the permittivity sensor, as shown in Equation ( 4): [36]  a = Values of Δε and f c are directly extracted from the firmware of the permittivity probe at least every 6 s.It calculates their values from a fit reproducing the β-dispersion curve applied on the permittivity values obtained for the 17 emitted frequencies.
Equation ( 5) enables direct computation of the cell radius r: Finally, Equation (6) shows how the VCC, assuming spherical cells, is calculated from the biovolume fraction and the volume occupied by cells: By transforming Equations ( 3) and ( 6) and knowing the actual state of the system, that is: sampling and measuring with an offline analyzer the viable cell density (VCD m ) and mean radius (r m ), it is possible to calculate the parameters C m and σ i as shown in Equation ( 7): With this method, it is possible to adjust C m and σ i at each offline sampling.
Abbreviations used in the model equations: • The cell membrane capacitance per area C m (F m −2 ) • The static medium conductivity σ a (S m −1 ) • The static internal conductivity of cells σ i (S m −1 ) • The medium conductivity σ (S m −1 ) • The predicted biovolume fraction Pp • The averaged radius of cells r (μm) • The offline estimated averaged radius of cells r m (μm) • The VCC (cells m −3 ) • The offline estimated VCD m (cells mL −1 ) • The volume occupied by cells V (m 3 )

Cell line
A suspension CHO cell clone (CHOZN Cell Line, MilliporeSigma) producing a recombinant mAb was used.Cells were thawed in EX-CELL Advanced HD Perfusion Medium (MilliporeSigma) and maintained in a 125 mL shake flask containing 28 mL pre-warmed complete medium, incubated at 37 • C in a humidified atmosphere of 5% CO 2 in air on an orbital shaker platform rotating at 120 rpm.Cells were seeded at 3-5 × 10 5 cells mL −1 and subcultured when densities reached 1-2 × 10 6 cells mL −1 and 80% viability.

Fed-batch process
A fed-batch culture was conducted in a 3-L bioreactor (BioFlo 320, Eppendorf).The bioreactor was inoculated with a starting density of 5 × 10 5 viable cells mL −1 at a starting volume of 2 L. Culture medium used was EX-CELL Advanced HD Perfusion Medium (MilliporeSigma).
Culture temperature was controlled at 37 • C, dissolved oxygen was set at 40% using a mix of air and O 2 through a ring sparger, pH was controlled at 7 (± 0.1) by using base NaOH and CO 2 .A mix of Cellvento 4Feed (MilliporeSigma) and EX-CELL Advanced CHO Feed 1 (MilliporeSigma) was added on days 3, 5, and 7 with a ratio of respectively 5%, 5%, and 7.5% v/v.Glucose solution was supplemented when needed throughout the 14-day culture.

Sampling and off-line analysis
Twice a day (morning and evening), a 5 mL sample was collected aseptically from the bioreactor and analyzed offline.Nova FLEX2 analyzer (Nova Biomedical, USA) was used to collect total cell density, VCC, and cell diameter.Results of the analysis is a triplicate of measurements and were averaged in what was called "offline measurements".These offline measurements were used as control references to determine the accuracy of estimations.

Online measurement of permittivity with sensors
The multi-use INCYTE Arc Sensor (Hamilton, Bonaduz, Switzerland) was used to measure raw permittivity throughout the culture dura-tion.After autoclaving, the probe was immersed in the medium the night prior to inoculation to ensure polarization of the electrodes.The probe was powered on and connected to a computer to collect measurements.To calibrate the probe, the cell-free permittivity reference point was set on the ArcAir software interface ("Mark Zero," ArcAir Basic Version 3.6.0,Hamilton).The probe generated a frequency scan to measure 17 frequency values from 0.3 to 10 MHz every 6 s.It also measured the medium conductivity (σ) and calculated, in the internal firmware, the parameters extracted from the fitted the β-dispersion curve (f c , Δε).

Data processing
Two different approaches were followed to calculate each minute cell radius and VCC values, by applying Equations ( 5) and ( 6) as described in Section 2.
In the first method called as the "fixed model," C m and σ i were set constant in the Equations ( 5) and ( 6) with values either from the literature [26] or estimated from the studied dataset.For this second case, a post-processing study was performed to determine the averaged specific values of C m and σ i by using data from a 14-day cell culture.The culture was monitored with a permittivity probe and daily offline samples were taken from the bioreactor.The offline VCD m and radius r m mean values were averaged over 14 days as well as the dielectric values (f c , Δε, σ) corresponding to the sampling times.
From the averaged values, C m and σ i were calculated thanks to the Equation (7).
The second method is known as the "adjusted model," where values of C m and σ i were adjusted during the process at each offline sampling.
An offline analysis of the sample performed in triplicate yielded a mean value of VCD m and r m .The parameters extracted directly from the probe firmware (fc, Δε, and the medium conductivity σ) were averaged within a 15-min window around the time of sampling from the bioreactor.C m and σ i could then be estimated with Equation ( 7) by using the averaged inline values of f c , Δε, σ and offline cell density (VCD m ) and radius (r m ).This second approach therefore considers that C m and σ i are likely to evolve throughout the cell culture.
To test the accuracy of the models, offline measures were interpolated with a smoothing spline and compared to the estimated valued by computing the mean absolute error (MAE) as follows: 1 ŷ is the estimated value, y is the offline measure, and n is the number of estimations made.
The computations were carried out with the MATLAB software (version 7.10.0,The MathWorks Inc, 2010) using the Curve Fitting Toolbox.

Sensitivity analysis
Sensitivity analysis enabled testing of the robustness of a model in the presence of uncertainties and provided a better understanding of the relationships between the input and output of variables.Its principle can be described in five steps (Figure 1A): 1. Define the model by declaring the function, the inputs, and the outputs.
2. Define the inputs range and their distribution.The normal distribution was chosen and a coefficient of variation of 5% was considered for the standard deviation of the normal law, according to the probe supplier recommendations.
3. Randomly sample N input values from the space defined in step 2.
4. Run the model with the N vectors sampled in step 3 to get outputs.
5. Analyze the variance of inputs (step 3) and outputs (step 4) with the Saltelli algorithm [37] which will calculate Sobol' indices.These indices quantify the influence of an input or a group of inputs on the output.
Sobol' indices have various orders.First-order indices represent the contribution of a single input to the output variance.The second and higher order indices represent the joint contribution of two or more inputs to the output of the model.Finally, total order indices account for the total contribution of a given parameter to the output variance, that is, its first order effect plus all higher order effects due to interaction with other inputs.The described sensitivity analysis was carried out with the open-source Python library SALib, which implements various sensitivity analysis techniques, including the Saltelli's algorithm.

Determination of influential parameters in the Cole-Cole model
While considering a modeling method based on the Maxwell-Wagner equation, the cell specific parameters C m and σ i are considered as constant during the entire time series.Yet, if they vary over time or are wrongly estimated, it can affect the conversion accuracy from permittivity data to VCC and cell radius.The effects on the output were explored in two ways.First, a sensitivity analysis was applied to study the relative impact of the three dielectric parameters (Δε, f c , σ) as well as C m and σ i on the VCC and radius estimation in the Maxwell-Wagner model.
Second, averaged values of C m and σ i were computed (Equation 7) to minimize the error between offline measures and their estimated counterparts from permittivity data over the entire experiment.From the analysis, it appeared that f c was the dominant parameter for both VCC and cell radius estimations, accounting for 40% of the output variance, followed by C m and σ i accounting for 25%-35%.
Δε and σ were the least impactful factors.The negligible difference between the first order and the total order indices for each individual parameter showed that there were no higher order effects on the model.Thus, there were no joint contributions to the output variances.
As f c emerged as the most influential parameter in the equations for estimating VCC and radius, f c values obtained by the internal firmware of the probe were compared to values computed with a fit of β-dispersion applied in post-processing on the raw permittivity data of the studied dataset.No significant accuracy improvement of the model was observed (data not shown), therefore values from the probe were used throughout the study.The parameters C m and σ i , which were the second most impactful parameters to the output variance, could be computed from the current state of the culture to represent the physiological properties of cells.Both can be determined from offline measures by using Equation ( 7) and therefore our efforts focused on finding their optimal values to improve the model accuracy.

Influence of C m and σ i in the accuracy of prediction
Considering the importance of the parameters C m and σ i , their values have been adapted to the studied cell line for application of the Cole-Cole and Maxwell-Wagner's model.It was assumed that these parameters depend on the cell line and can vary over processes because of physiological changes.
From the literature, a typical CHO cell line has the following values: C m = 1.1 μF cm −2 and σ i = 4.0 mS cm −1 . [26]After calculation of the averaged values corresponding to the dataset of the studied CHO ZN-GS cell line, it was found that C m = 0.5 μF cm −2 and σ i = 2.3 mS cm −1 , representing a difference of about two times.As both parameters had a strong influence on the model, the VCC and cell radius estimations were recomputed by the model with the adapted values of C m and σ i .
Figure 2 shows the results for one cultivation run modeled with the literature or optimized values.When comparing statistical results of MAE, it was observed that the model accuracy was improved thanks to the optimized values of C m and σ i by 70% for the VCC estimation and approximately 50% for the radius estimation (Figure 2 and Table 1).
Up to 80 hours post-inoculation (HPI), the radius estimate is very high and far from the experimental data.This is because the radius calculation (Equation 5) includes the characteristic frequency f c in the denominator.Studied separately, it varied up to 40% in the first 20 h (Figure 2C) due to the low cell density at the beginning of the culture during the latency phase and thus to a weak and noisy dielectric signal.
Over the same time interval, both VCC estimates overlaid on offline values.This is a scale-related perception, optimizing C m and σ i values increases the calculated VCC values 17% closer.Overall, with the optimized values of C m and σ i , the model generated estimations closer to the offline measures (Figure 2).Similar improvements were observed for five other cultivation runs (data not shown).Thus, adapting the cell specific parameters to the study cell line had a significant effect on model accuracy.
Maxwell-Wagner's Equations (7) enabled definition of the average specific values of C m and σ i after monitoring one data set from a culture batch.This led to a higher accuracy in the estimation of VCC and cell radius compared to the approach based on values of C m and σ i from the literature.However, this could be challenged for three reasons.
First, the overall accuracy of VCC and cell radius estimation remains 30% off compared to the offline measurements, especially at the end of the culture after 150 HPI when the kinetics of cell death reduces the dielectric signal intensity.Second, the user must do at least one cultivation run to perform post-processing estimation of these parameters, so the calibration-free concept is lost as there is a preliminary work to the use of the sensor.Third, C m and σ i evolve during the cell growth according to cell metabolism [29] so calculating constant values over a culture does not reflect the biological reality.

4.2
Periodic adjustments of C m and σ i values with offline measurements

4.2.1
Effect of in-process adjustments of C m and σ i values on the accuracy of VCC and radius estimation compared to offline analysis Based on the previous results, the study was oriented on how to decrease errors of the model estimations by considering the biological variations of C m and σ i .To do so, their values were optimized during the culture by adjusting them after each offline measurement of VCD m and r m (Equation 7).The accuracy improvement was evaluated with one or two adjustments per day, and then compared with the model taking constant values of C m and σ i calculated for the studied cell line.
At first, one sampling per day was taken and model accuracy after the single adjustment was evaluated.With the unique daily adjustment method, MAE values decreased by 11% for the radius and increased by 27% for the VCC compared to the model with no on-process adjustment (Figure 3 and Table 1).In Figure 3A, a peak appears at 180 HPI until the next readjustment point (200 HPI).An addition of feed in the bioreactor was performed at this time, which induced a perturbation in the dielectric signals.In Figure 3C, Δε is decreasing upon addition at 180 HPI.This parameter alone is involved in the numerator of the equation to calculate the VCC (Equation 6) which explains the VCC increase.
At 200 HPI, C m and σ i are recalibrated by sampling and the model is fitted to the offline data, which will lead to a peak. in dielectric parameters and C m and σ i . [26]us, the number of samples was increased to at least two per day during the whole process to reduce these errors.
Adjusting the parameters twice per day increased accuracy by 44% for the VCC but decreased it by 16% for the cell radius (Table 1) when comparing MAE of predictions between the fixed model with

CONCLUSION
In the current study, conversion of raw permittivity data into quantita- The importance of these adjustments was highlighted by the decrease in estimate quality when the number of samples was reduced to one per day.
The transferability and scalability of the model to alternative cell lines or other experimental setups will further be evaluated and the application of dielectric spectroscopy for monitoring cell cultures could be validated and generalized in biotherapeutic production.[40] The full extent of applications of this technology is still being determined and it is promising that other modeling strategies will provide more information on cell physiology in culture.
The goal of this study was to improve the accuracy of the model conversion of the permittivity measurements by (i) characterizing the most influential parameters in the model by performing a sensitivity analysis, (ii) determining which of these parameters can be optimized in the context of the experimental setup and quantify the subsequent accuracy improvement, (iii) integrating the parameter optimization in the model with respect to bioprocessing operation constraints as well as real-time monitoring requirements and minimized effort for sensor calibration.It was determined that an optimized model based on periodic adjustments with offline analysis to be the most accurate conversion model.

F I G U R E 1
(A) Simplified diagram of the sensitivity analysis.Study of contribution to the output variance of parameters involved in viable cell concentration (VCC) (B) and radius calculation (C).First (red dots) and total (blue squares) order of the Sobol' indices relative to the input parameters.
using the Saltelli's algorithm was performed to evaluate how much the variability due to uncertainties on input parameters (f c , Δε, σ, C m , σ i ) of the Cole-Cole and Maxwell-Wagner's equations affected the accuracy of the output estimations (VCC, radius).Figure 1B,C show the first and total order of the Sobol' indices relative to the input parameters.

F I G U R E 2 F I G U R E 3
Comparison of mechanistic modeling results with two sets of initial values for C m and σ i .(A) Viable cell concentration (VCC) estimate.(B) Radius estimate.Blue curve: estimations with values from literature (C m = 1.1 μF cm −2 and σ i = 4.0 mS cm −1 ).Red curve: estimations with values specific for the study cell line (C m = 0.5 μF cm −2 and σ i = 2.3 mS cm −1 .Yellow dots: reference values obtained by sampling and offline analysis.Error bars: offline 95.0%-confidence interval.Grey highlighting: online 95.0%-confidence interval.(C) Evolution of f c throughout the culture.TA B L E 1 Statistical values for the study of the estimation accuracy with two different modeling approaches, and their evolution of accuracy.Mean average error Modeling approach Radius [μm] VCC [cells mL −1 ] "Reference": equations based model with values of C m and σ i calculated for the studied cell line 0.6 1.8E+6 Adjusted values of C m and σ i in the model with one sampling per day 0.7 1.3E+6 Evolution of the accuracy compared to the "reference" model −16% +27% Adjusted values of C m and σ i in the model with two samplings per day 0.7 1.0E+6 Evolution of the accuracy compared to the "reference" model −16% +44% Comparison of the "adjusted" model with C m and σ i values calculated once per day during process (red curve) with the "fixed" model with constant C m and σ i values calculated for the studied cell line (blue curve).(A) Viable cell concentration (VCC) estimate.(B) Radius estimate.Yellow dots: reference values obtained by sampling and offline analysis Error bars: offline 95.0%-confidence interval.Gray highlighting: online 95.0%-confidence interval.(C) Evolution of Δε throughout the culture.As previously shown, in Figure 3A the cell radius is very noisy due to its dependency on the f c evolution and thus on the growth phases of the culture.During lag (0-50 HPI) and decay phases (150-250 HPI) some stress and nutrient limitation give rise to metabolic changes, variations

F I G U R E 4
calculated constant values of C m and σ i and the adjusted one.The addition of samplings did not improve the accuracy of the radius estimate.However, the VCC values obtained with the model adjusted twice a day (red curve, Figure 4A) were closer to the offline values (yellow dots, Figure 4A).The addition of samplings and therefore of adjustments during the lag and decline phases allowed a better monitoring of cell metabolism and growth.Thus at least twice a day, combining the offline measures with permittivity data for the adjustment of C m and σ i improved the accuracy of estimation and the good reflection of the true state of growth.Comparison of the "adjusted" model with C m and σ i values calculated twice per day during process (red curve) with the "fixed" model with constant C m and σ i values calculated for the studied cell line (blue curve).(A) Viable cell concentration (VCC) estimate.(B) Radius estimate.Yellow dots: reference values obtained by sampling and offline analysis.Error bars: offline 95.0%-confidence interval.Gray highlighting: online 95.0%-confidence interval.Nevertheless, the adjustments resulted in jumps of the estimated parameters which could affect user perception when considering realtime monitoring (arrow in Figure4A).It could be envisaged to apply smoothing strategies to filter these jumps related to the model adjustment to offline data.However, the offline measurements have an uncertainty related to the offline analyzer which amplifies the model error during the adjustment.In this study, errors varied up to 15% within a triplicate from the same sample and were therefore found in the values of C m and σ i .Predictive models could be used to anticipate the evolution of C m and σ i during all the process, reducing the needs of offline samplings and limit peaks between adjustments, thus increasing the model accuracy.Finally, autosampler devices could support the "adjusted" model by giving rise to adjustments of C m and σ i in a more regular and automated way.This could further increase the robustness of the VCC and radius estimation by coupling online and offline data.
tive information (VCC, radius) has been implemented to monitor CHO cell cultures, using the Cole-Cole and Maxwell-Wagner's equations.The performance of the model was optimized by considering the biological variations of the studied cell line specific parameters, C m and σ i .A readjustment of the model during the cell culture run was possible due to addition of offline values (VCC, radius) in the equations, thus allowing calculation of new values of C m and σ i at each sampling.This reduced the inaccuracy related to the model itself, while maintaining a minimized calibration process prior to the cell culture monitoring.