Tomografía helicoidal

A spreadsheet template shall contain columns of raw data entry followed by columns of cumulative data for all measurement data for nutrients which are consumed and products. Any time point of row that incurs feed addition will incur a total mass balance that takes volume change into consideration. A simple way to account for volume change is to perform calculations in total mass balance (concentration of nutrient: x volume) instead of on concentrations alone. In this case the amount consumed between two time points is simply S_tV_t- S_t+1V_t+1)=S_t cumulative consumption is then the sum of St over time. Forgetting to account for volume change in material balance is a

common mistake in fedbatch culture data analysis. The calculation of cumulative data can be automated once the measurement data are entered. The next set of columns are specific rates. Specific rates are best calculated for cumulative data by regression. The regression of cumulative data can be automated. Usually a third order polynomial fitting works well for most data. However, inspection is necessary to ensure a good fit. The measurement data, cumulative consumption/production and specific rate data shall be all automatically for visualization. Upon the calculation of cumulative data stoichiometric ratios are also automatically plotted. This allows for detection of metabolic changes in culture. If a stoichiometric ratio deviates significantly from historical data, it may also serve as a diagnosis alert for checking pasable process abnormality. An add-on to the spreadsheet template is an algorithm for metabolic flux analysis. If the measurements include all the major carbon compounds, glucose, lactate, glutamine and other amino acids (if not all, the majority), ammonium, then material balance can be performed on the nitrogen balance. Carbon balance will require the measurement of CO₂ produced in metabolism and is not easily done without isotope labeling. If oxygen consumption data is available, one can assume that R.Q. being 1.0 and set CO₂ production to be same as oxygen consumption. From the extent of carbon, nitrogen balance one can assess the reliability of some stoichiometric ratio data. If the carbon and nitrogen is reasonably closed the data can then be further subjected to metabolic flux analysis.MFA algorithm is typically in MatLab or other mathematical solvers. The Excel template can build in an exportable table for ready transfer of the specific rate data to those programs.

• Two-point specific growth rate calculations and specific nutrient calculation for fedbatch culture

q _{x V} dS_dt x V x V t t S S 1 2 1 2 2 1 1 2 1 2 1 s $ $ . $ $ $ = + - -

• Slope calculation from curve of regression data

Specific Rates Cumulative Data IVCt V dt IVC v v t t t t t t 0 1 1 1 $ $ . $ $ \ \ \ =

#

S

q

x V dt

V s

V s

V s

$ $

$

$

$

$

=

#

=

-

+/

S_i,t: Cumulative amount (mMole or g) of nutrient i consumed or produced at time t

V: Volume of culture

s_i: Concentration of component i in the culture broth

V_f: Volume of feed medium added

s_f: Concentration of component i in the feed medium

k: Total number of feed medium additions up until time t

IVC: Integral Viable Cell number

a_i,j: Stoichiometric ratio for nutrient i with respect to nutrient

j at time t S S S S S S , , , , j t j t i t i t j i t 2 1 2 1 T T - - =c m Stoichiometric Ratio

Multidimensional/Interactive Data Exploration

Data Visualization

deeper understanding of the effect of various parameters on process performance. Each cell culture run usually entails many measurements over multiple time points. Instead of browsing data through tables, we plotted each quantity as a concentration profile over time. We also plotted data of one variable against another variable, to specifically examine the ratio of specific rates or the stoichiometric ratios. As data accumulate over time, it is even more important to plot data of multiple runs together, so that different runs under the same or different experimental conditions can be compared easily. In such analyses, mathematical and statistical tools are important; however, the importance of data visualization in the analysis of multiple runs cannot be overemphasized. When working with a large set of data from multiple runs, visualization software is very useful. Quick access to data, the rearrangement of data into different combinations of dimensions, or the filtering of data by different process performance or other criteria can greatly facilitate deeper insight. In the plot shown, lactate concentration profiles from over 250 runs are colored by the final product titer. One can see that high-titer runs mostly consume lactate in the late stage of culture, while the low-titer runs produce lactate. The trend is easily seen when all data are plotted together. We then plot the specific rates of glucose consumption and lactate production at different time points, for all runs. It can be seen that lactate consumption (negative values) occurs only when glucose consumption is also low. One can further see that even when the cells are consuming lactate, the glucose consumption rate is still significant. With the aid of a visualization tool, data from all of these runs can be easily plotted in different ways. To take advantage of the data trove from large number of runs, a means for quick visualization is very important.

• Process data are intrinsically multidimensional and should be examined in multiple dimensions (e.g. time course and stoichiometric ratios) to provide different insights

• Data from multiple cultures can be consolidated and examined for trends

• Software for visualization interactive for multiple dimensional viewing analysis – E.g.: Spotfire DecisionSite .

Fig. 7.2: Plots of archived historical data for discerning process patterns