The Integral (area under the curve) of Viable Cell Density (IVCD) or Concentration (IVCC) is an essential calculated metric in cell culture operations. IVCC quantifies the effective working time for a dynamic viable cell concentration within a given frame of time, analogous to the calculation of man-hours. IVCC calculated for a specific culture timeframe can be combined with product titers to assess culture productivity trends within specified timeframes of the process or can be used to estimate nutrient consumption profiles based upon cell-specific nutrient requirements for a process.
In fed-batch processes the IVCC term becomes highly important for not only characterizing culture progression, but determining process action with regards to bolus feed additions.1 Specifically, calculated change in IVCC can be used to directly assess change of nutrient profiles in-culture and subsequently determine the concentration and volume of bolus addition needed to return to a specific concentration set-point.
Figure 1. Off-line trapezoid calculation compared to permittivity calculation.
How IVCC is Calculated
Traditionally, a numerical approximation of IVCC is determined using the trapezoid approximation between two off-line VCD data points (Figure 1). The accuracy and realistic representation of the trapezoid calculation on the culture is highly dependent upon the linearity of the culture growth between samples and the frequency of measurements. Large gaps between off-line samples, the inherent non-linearity of cell growth, and measurement error present in off-line sampling techniques all contribute to the limited predictive capacity that IVCC calculations based on off-line VCD can provide.2 The accuracy and usefulness of the IVCC calculation can be dramatically improved by replacing periodic off-line sampling with a continuous measurement of viable cell concentration using in-line permittivity measurement. Notably, a continuous permittivity-derived VCD measurement can be harnessed to improve the resolution and quantity of data input into the trapezoid calculation, providing a robust IVCC calculation. Additionally, the transition from off-line discrete sampling to continuous in-line measurement enables the development of automated calculation and process control strategies not possible with off-line sampling only. The benefits of improved control capabilities become apparent when assessing modified strategies for process improvement or improving consistency between replicate batches.
Uses of On-line Calculated IVCC Metrics
To date, permittivity-derived IVCC calculations have been used in both predictive and feedback control schemes in fed-batch processes. In one feedback control study for example, permittivity-calculated IVCC calculations were used to determine the amount of nutrients to add in each bolus addition on a 24-hour fixed-feed schedule, with process performance profiles compared against the historical off-line-calculated IVCC process (Figure 2). Between the runs, similar total feed volumes and process titers were attained, demonstrating equivalence of permittivity-calculated bolus addition against an established historical methodology without the need for manual labor and sampling efforts.2 Permittivity-derived IVCC calculations were also shown to be more consistent and less error prone than off-line VCD calculations, providing a more reliable signal in addition to reducing manual labor and increasing automation capabilities. Furthermore, in-line permittivity calculations enable automated process control.3
A follow-up study utilizing the same automated permittivity-calculated IVCC value found that automation enabled a modification of feeding frequency from 24-hour to 4-hour within the same process. Modification to a more frequent feed schedule enabled smaller volumes of nutrients to be implemented for a given bolus addition. IVCC calculations based on off-line VCD can provide limited predictive capacity due to large time gaps between off-line samples, the inherent non-linearity of cell growth, and error in the measurement itself. As a result, a notable increase in titer production (up to 20%) was obtained with the modified strategy compared to historical process benchmarks.3
In a separate study, predictive feed control was used with in-line permittivity signal to calculate culture growth rate using IVCC and anticipate future nutrient feed requirements for the next feed addition. Implementation of an automated dynamic feed system utilizing the permittivity-derived calculations and a 4-hour feed frequency initially showed insignificant improvement in yield compared to a fixed 72-hour bolus strategy. However, when the modified feed frequency was combined with IVCC-expedited media optimization titer increased ~50% compared to the baseline platform process and ~20% compared to the optimal feed without modified feed frequency.4 Establishing a dynamic feeding strategy was key to effective media optimization as well, with the growth rate feeding strategy removing the need to develop specific dose and frequency strategies for each iteration of media reformulation.
As PAT and automation take a larger role in biopharma operations, continuous in-line methodologies for process control will become more important. In-line permittivity provides a robust, low complexity tool for measuring biomass growth throughout a run and can replace off-line sampling and measurements in the calculation of parameters used to determine critical culture variables.
Figure 2. Benefits of permittivity control. Figure includes increased consistency (more accurate calculations), improved automation control (24 to 4 hr), and improved titer yield (dynamic control).
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