# Example of Production Culture KPI: Volumetric Productivity

Say you are running a 2g/L product from a ten-day process at your 1 x 6000L plant, with strict orders from management to minimize downtime. This product is selling like gangbusters, which means every gram you make gets sold, which means you've got to make the most of the 80-day campaign allotted for this product.

The volumetric productivity for the process is 2g/L/10days = 0.2 g/L/day.Running a 6000L capacity plant gives you
• 12 kilos every 10 days.
• 8 run slots given the 80-day campaign
• Maximum product is going to be: 96 kg for the campaign.

But suppose your Manufacturing Sciences team ordered in-process titer measurements and found that Day 8 titers were 1.8 grams per liter. Harvesting at day 8 means:
• 10.8 kilos every eight days.
• 10 run slots given the 80-day campaign
• Maximum product is going to be 108 kg.
By harvesting earlier, you gain two additional run slots... during which time you can make 21.6 kg; but since you lost 1.2 kg/run for 8 runs totalling 9.6 kg, the net gain is 12 kgs.

There are a lot of assumptions here:
• Your raw material costs are low relative to the price at which you can sell your product
• Your organization is agnostic to doing more work (ten runs instead of eight).
It is difficult for plant managers to end a culture early to get 10.8 kgs when simply waiting two more days will get you 12 kgs. It quickly becomes easy when you see how two-run slots open up and you have the opportunity to make 21.6 kgs to make up for the lost product from ending the fermentation early, or rather, the point of maximum volumetric productivity.

# How to Compute Production Culture KPI

Production culture/fermentation is the process step where the active pharmaceutical ingredient (API) is produced. The KPI for production cultures relates to how much product gets produced.

The product concentration (called "titer") is what is typically measured. Operators submit a sterile sample to QC who have validated tests that produce a result in dimensions of mass/length3, for biologics processes, this is typically grams/liter.

Suppose you measured the titer periodically from the point of inoculation; it would look something like this:

The curve for the majority of cell cultures is an "S"-shaped, also called "sigmoidal," curve. The reason for this "S"-shaped curve was described by Malthus in 1798 where he described population growth as geometric (i.e. exponential growth) while increases in agricultural production was arithmetic (i.e. linear); at some point, the food supply is incapable of carrying the population and thus the population crashes.

In the early stages of the production culture, there is a surplus of nutrients and cells - unlimited by nutrient supply - grow exponentially. Unlike humans and agriculture, however, a production fermentation does necessarily have an increasing supply of nutrient, so the nutrient levels are fixed. Some production culture processes are fed-batch, meaning at some point during the culture, you send in more nutrients. Regardless, at some point, the nutrients run low and the cell population is unable to continue growing. Hence the growth curve flattens and basically heads east.

In many cases, the titer curve looks similar to the biomass curve. In fact, the integral (area under that biomass curve) is what the titer curve typically mimicks.

The reason this titer curve is so important is because the slope of the line drawn from the origin (0,0) to the last point on the curve is the volumetric productivity.

Volumetric Productivity
Titer/culture duration (g/L culture/day)

The steeper this slope, the greater the volumetric productivity. Assuming your bioreactors are filled to capacity and that supplying the market with as much product as fast as possible, then maximizing volumetric productivity ought to be your goal.

Counter-intuitively, maximizing your rate of production means shortening your culture duration. Due to the Malthusian principles described above, your titer curve flattens out as your cell population stagnates from lack of nutrients. Maximizing your volumetric productivity means stopping your culture when the cells are just beginning to stagnate. End the culture early and you lose the opportunity cost of producing more product; end the culture late and you've wasted valuable bioreactor time on dying cells.

The good news is that maximizing your plant's productivity is a scheduling function:

1. Get non-routine samples going to measure the in-process titer to get the curve.
2. Study this curve and and draw a line from the origin tangent to this curve.
3. Draw a straight line down to find the culture duration that maximizes volumetric productivity.
4. Call the Scheduling Department and tell them the new culture duration.
5. Tell your Manufacturing Sciences department to control chart this KPI to reduce variability

There's actually more to this story for Production Culture KPI, which we'll cover next.

# How to Compute Seed Fermentation KPI

So,  if you agree that the purpose of seed fermentation (a.k.a inoculum culture) is to scale-up biomass, then the correct key performance indicator is final specific growth rate.

To visualize final specific growth rate, plot biomass against time:

The cell density increases exponentially, which means on a log-scale, the curve becomes linear. The specific growth rate (μ) is the slope of the line. The final specific growth rate (μF) is the slope of all the points recorded in the last 24-hours prior to the end of the culture.

To compute the final specific growth rate, simply put datetime or culture duration in the first column, biomass in the second column, and the natural log of biomass in the third column:

In Excel, use the SLOPE function to compute the slope of the natural log of biomass:

` =SLOPE(C5:C7,A5:A7)`
Alternatively, if you don't want to bother with the third column:

` =SLOPE(LN(B5:B6),A5:A7)`
This number has engineering units of inverse time (day-1). While this measure is somewhat hard to physically understand, we look towards the ln(2) = 0.693 as a guide: If a culture has a specific growth rate ~ 0.70 day-1, then its cell population is doubling once per day.

Computing this KPI for seed fermentation and then control charting this KPI is the best start you can make towards monitoring and controlling your process variability.

# KPIs for Cell Culture/Fermentation

Control charting each process step of your biologics process is a core activity for manufacturing managers that are serious about reducing process variability.

Sure, there's long-term process understanding gained from the folks in manufacturing sciences, but that work will be applied several campaigns from now.

What are the key performance indicators (KPIs) for my cell culture process today?

1. Grow cells (increase cell population)
2. Make product (secrete the active pharmaceutical ingredient)

#### Seed Fermentation (Grow Cells)

There are plenty of words that describe cell cultures whose purpose is to scale-up biomass; to wit, seed fermentation, inoculum cultures, inoc train etc. Whatever your terminology, the one measurement of seed fermentation success is growth rate (μ), which is constant in the exponent of the Arrhenius equation:

X = X0eμΔt

Where:
• X = current cell density
• X0 = initial cell density
• Δt = elapsed time since inoculation

For seed fermentation, the correct KPI is the final specific growth rate; which is the growth rate in the final 24-hours prior to transfer. The reason the final specific growth rate is the KPI is because the way seed fermentation ends is more important than how it starts.

#### Production Fermentation (Make Product)

The output of the Production Fermentor is drug substance; the more and the faster, the better. This why the logical KPI for Production Fermentation is Capacity-Based Volumetric Productivity.

A lot of folks look at culture titer as their performance metric. Mainly because it's easy. You ship those samples off to QC and after they run their validated tests, you get a number back.

Culture Titer
Mass of product per volume of culture (g/L culture)

The problem with using culture titer is that it does not take into account the rate of production of product. After all, if it took culture A takes ten days to make 2g/L and culture B takes 12 days to make the 2g/L, according to titer, they are equivalent, even though A was better. This is why we use volumetric productivity:

Volumetric Productivity
Titer/culture duration (g/L culture/day)

Culture volumetric productivity takes into account the rate of production pretty well, and in our example culture A's performance is 0.20g/L/day while culture B's performance is 0.17 g/L/day. But what of the differences between the actual amount of product manufactured? I can run a 2L miniferm and get 0.40g/L/day, but that isn't enough to supply the market. This is why bioreactory capacity must be included in the true KPI for production cultures.

Capacity-based Volumetric Productivity
Volumetric Productivity * L culture / L capacity (g/L capacity/day)

Capacity-based Volumetric Productivity is the Culture Volumetric Productivity multiplied by the percent of fermentor capacity-used, such that a filled fermentor scores higher than a half-full fermentor.

KPIs are generally not product-specific; instead, they are process class specific. For instance, all seed fermentation for CHO processes ought to have the same KPI.

Generally, KPIs are simple calculations derived from easily measured parameters such that the cost of producing the calculation is insignificant relative to the value it provides.

KPIs deliver significant value when they can be used to identify anomalous performance and actionable decisions made by Production/Manufacturing in order to amend the special cause variability observed.

# PIModuleDB: "It's What Makes PI Batch Possible!"

In addition to correlating unit/alias to tags, the PI Module Database is the foundation for PI Batch, in fact, it is a requirement.

You see, there's a special type of module called, "PIUnit". And the main difference between a PIUnit and a regular module is that a PIUnit can keep track of start/end times (a.k.a. PIUnitBatches or UnitProcedures as defined by S88).

If you go to your Module Database, you can discern modules from piunits because they have different icons. The Module looks like a red/yellow/green cube with an "M" in the center of it. The PIUnit looks like a half-filled tank of water with pipes in and out.

When you right-click on the PIUnit and select Edit, the following form will present itself:

Pay particular attention to the Unique ID attribute of the PIUnit. The key here is that when you create a PIUnit, the PI server will create a PIPoint (a tag) for the purpose of storing PIUnitBatches.

You can prove it to yourself by doing a tag search on that gibberish text. In my case, I went straight to the PI SMT > Data > Archive Editor

What's more is that these events correspond with the unitbatches stored in PI Batch. The batch information about the batchid, product, procedure and endtime are stored at the starttime of the batch.

You see, PI Batch is rationally a simple table... one with 7 columns and as many rows as you have batches. But if you are OSIsoft and alls you have is PI (hammer), everything starts looking like a tag (nail).

This is why PI Batch Database... while seemingly tabular... is actually a data structure that is a hybrid of the hierarchical structure presented by the PI Module Database and PI tags. What makes PI Batch possible is that uniqueID of a PIUnit in PIModuleDB is the name of the tag that archives unitbatch information.

# SQLite Insert Rate ranges from 50 to 250 inserts/second.

SQLite is a file-based database. It's used in browsers, it's used on your iPhone. We use it as a placeholder for RDBMS. We're troubleshooting a data-write problem and it turns out that the problem is somewhere else.

Our hardware is WinXP 32-bit, Lenovo laptop running SQLite.NET and plotted here is the number of rows inserted per second.

If you have an application that needs no more than 30 inserts/second, SQLite works just fine.

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