| Vose Software

Industry: Biotech
Product: ModelRisk
Application: Bioreactor Design


A 2,000 L Scale-Up Whose Titer Spec Is Met Only 7 Batches in 10

A monoclonal-antibody process that produces 5.06 g/L on the bench is signed off for a 2,000 L production vessel on exactly that number. The deterministic plug-in — nominal viable-cell integral times nominal cell-specific productivity — says the campaign clears its 4.0 g/L release spec with room to spare. Then the first commercial campaign runs, and nearly a third of batches come back below spec. The number was never wrong; it was just one point in a distribution the design review never drew.

A biopharma manufacturer rebuilt the scale-up case in ModelRisk before committing the capital. The question was not "what titer does the process make" but "what is the distribution of harvest titer at 2,000 L, and how often does a batch fall through the 4.0 g/L floor once oxygen transfer, seed-train quality and cell-line variability all move at once." The simulation's first output is the headline the bench number hides: a titer distribution that straddles the spec rather than clearing it.

Harvest titer distribution at scale with the release spec floor

The deterministic plug-in lands at 5.06 g/L before the oxygen-transfer de-rate, and a nominal-case 4.57 g/L after it. But the simulated mean is 4.72 g/L with a P10 of 3.33 and a P90 of 6.41 — and 30.9% of batches finish below the 4.0 g/L spec floor. A facility planned against the point estimate is planning against a release rate it will never see.

Why a point estimate fails here

Harvest titer is the product of three things that each carry real variability, and one scale-up penalty that the bench never sees:

  • Viable-cell integral (IVCC) — LogNormal, reflecting seed-train and growth variability across a campaign.
  • Cell-specific productivity (qP) — LogNormal, reflecting clone and media-lot variation in how much antibody each cell makes.
  • Run quality — a shared per-batch common factor (seed-train health plus media lot) that scales IVCC and qP together. This is what stops the model collapsing to a deterministic average: batches are not independent draws on each parameter, they share a fate set when the run is seeded.
  • Oxygen transfer at scale — the volumetric coefficient kLa is modelled as a Triangular at 2,000 L. A dense culture's peak oxygen demand sits above a typical vessel's kLa, so the culture spends part of the run mass-transfer-limited and the titer is de-rated. This penalty does not exist at 5 L, which is exactly why the bench number over-promises.

Each of 200,000 simulated batches draws one value of each input and computes titer as IVCC × qP de-rated by the oxygen supply-to-demand ratio. The mean of that distribution sits below the deterministic plug-in because the de-rate bites hardest in the very batches where biomass is highest.

Oxygen transfer is a design lever, not a fixed cost

Because the de-rate is driven by kLa, the vessel's oxygen-transfer capacity directly buys batch-success probability. Sweeping the design kLa shows the trade clearly:

Probability a batch meets spec versus design oxygen-transfer capacity

At the baseline vessel (kLa mode 230 1/h), 76% of batches meet spec — 37 of the 48-batch annual campaign. An upgraded impeller-and-sparger package (kLa mode 280) lifts that to 76%+, and across the full campaign the upgrade returns roughly 3 extra in-spec batches per year. At GBP 1.85M gross value per in-spec 2,000 L batch, that is about GBP 5M a year — the kind of number that decides whether a capital upgrade clears its hurdle rate.

Where the titer variance comes from

Ranking the inputs by their P10-to-P90 swing on mean titer shows where the spread is born:

Tornado of harvest-titer drivers

Cell-specific productivity (qP) and run quality dominate, each moving mean titer by roughly ±1.1 g/L across their plausible range; the viable-cell integral is second-tier at about ±0.5 g/L. Oxygen transfer kLa moves the mean by ±0.3 g/L — smaller than the biology, but unlike the biology it is something engineering can buy outright. The tornado tells the team that media and seed-train control attack the largest variance, while the kLa upgrade is the cleanest lever they fully own.

Batch-failure risk is lost annual capacity

The per-batch failure probability compounds into the metric the plant actually plans on — in-spec batches delivered per campaign:

Annual in-spec batch distribution, baseline versus upgraded vessel

The baseline vessel delivers a mean of 33.6 in-spec batches (P10 of 29) against a 48-batch campaign; the upgraded oxygen-transfer package raises that to a mean of 36.3 (P10 of 32). The probability of delivering at least 36 in-spec batches rises from 29% to 61% — a capacity-planning swing that a single titer number cannot express.

What the model changed

  • The release-rate assumption was corrected from "clears 4.0 g/L comfortably" to a quantified 30.9% per-batch failure probability, before any commercial product was at risk.
  • The oxygen-transfer upgrade was funded, justified on a simulated ~3-batch-per-year capacity gain worth roughly GBP 5M annually rather than on a deterministic titer that ignored mass-transfer limitation.
  • Process-development effort was re-prioritised onto qP and seed-train/media-lot control — the two drivers the tornado showed dominate titer variance — instead of further kLa tuning.
  • Campaign commitments were re-quoted as a P10/P50 batch count rather than a single nominal yield, removing a chronic over-promise to supply planning.

ModelRisk Functionality Used

  • LogNormal inputs for IVCC and cell-specific productivity, with a shared per-batch run-quality common factor so correlated batch outcomes are modelled rather than averaged away.
  • Triangular kLa input feeding an oxygen supply-to-demand de-rate, capturing the scale-up penalty that bench data cannot show.
  • Parameter sweep on design kLa to turn batch-success probability into a capital-justification curve.
  • Tornado sensitivity ranking to separate the variance the team must control (biology) from the variance it can buy down (oxygen transfer).
  • Distribution of in-spec batches per campaign built by simulating full annual campaigns, translating per-batch failure risk into the capacity number the plant plans on.

A bench titer is a measurement; a scale-up commitment is a distribution. The ModelRisk model replaces "5 g/L, ships fine" with "4.72 g/L mean, 31% of batches below spec, and GBP 5M a year recoverable by buying oxygen transfer" — a set of numbers the design review can actually act on.