CHO intensification: from fed-batch to controlled perfusion

EXECUTABLE MODEL REPORT · 30-DAY SCENARIOS

From culture dynamics to a perfusion operating decision

This report implements the published inhibition and cell-population structure with an original constant-volume operating schedule. Every chart and table below is recalculated from the same executable model. The reference coefficients are separated from our controller, numerical settings and sensitivity assumptions.

State variables and balance boundaries

Reference coefficients

The five coefficients below use the combined parameter set in the publication’s Table 1. Time is expressed in days in this implementation. Inspect the original article for its nomenclature, fitted experiments and uncertainty estimates.

Dynamic equations

μ = μmax / [1 + (B / KI)³]
δ = kd + kt Xl
dXv/dt = (μ − δ − Db) Xv
dXd/dt = δ Xv − (kl + Db) Xd
dXl/dt = kl Xd − D Xl
dB/dt = Xv − D B
Viability = 100 Xv / (Xv + Xd)
D = inlet flow / V; Db = bleed flow / V
Harvest flow / V = D − Db; dV/dt = 0

Viable and dead cells are retained by an ideal harvest filter; lysed material and the inhibitor wash out at the full exchange rate. Bleed removes the retained populations. The empirical inhibitor production term follows the model’s normalized convention and should not be interpreted as a calibrated physical mass-production measurement.

Operating scenarios and initial conditions

All simulations start with Xv = 0.3 ×10⁶ cells/mL and Xd = Xl = B = 0. The medium-exchange switch at day 3 and constant-volume reference are demonstration choices; the original paper’s individual feed profiles and process-switch table are not replayed here.

Explore exchange rate and viable-cell target

Mode-by-mode result table

Integrated viable-cell density measures cell exposure over time, not antibody yield or product quality. A comparison of actual productivity would additionally require measured or validated specific productivity, harvest recovery and quality attributes.

Controller implementation

e = Xv − target
Db = clamp(0.08 e + 0.015 ∫e dt, 0, D)
Update integral only when not driving farther into saturation
Hold flow inputs during each RK4 step
V = 0.2 L; harvest = (D − Db) V

Gains are our illustrative tuning, not the authors’ controller settings. Non-negative flow bounds and conditional integration reduce windup. When growth cannot support the target, the controller cannot create cells; negative target error is a process-feasibility signal.

Parameter variation and prediction spread

64 deterministic simulations vary each coefficient independently and uniformly by ±10%. The seed is 20261013. The 5th, 50th and 95th percentiles summarize this assumed parameter ensemble; they are a sensitivity envelope, not a calibrated confidence interval.

One-at-a-time sensitivity

Each row changes one coefficient while holding the others fixed. Ranking is based on final viable-cell density for the selected controlled scenario. A controller can compensate for a parameter change, so small final-VCD sensitivity does not establish that viability or medium use is insensitive.

Numerical method and reproducibility

Fourth-order Runge–Kutta integrates 30 days with a 0.02-day step. States are bounded at zero, and reports sample every half day. The automated checks compare 0.02- and 0.01-day solutions, enforce finite non-negative states and non-negative harvest, and verify repeatable ensemble output.

import { simulate, ensemble, sensitivity } from './cho-intensification.mjs';
const options = { mode: 'perfusion', perfusion: 2.25, target: 50 };
console.table(simulate(options).points);
console.table(sensitivity(options));
console.table(ensemble(options));

Calculated values

What the analysis supports

Compare whether medium exchange reduces the modeled inhibitor burden, whether a selected target is maintainable, and how much medium is used. Inspect the viability trajectory alongside viable-cell density. These calculations support exploration of the stated mathematical model and assumptions; they are not measured process performance.

Scope, missing mechanisms and next experiments

• No explicit glucose, glutamine, oxygen, CO₂, product titer or product-quality state is included.
• Mixing, mass transfer, temperature shifts, nonideal retention, fouling, sampling loss and sensor delays are omitted.
• Lysed-cell and inhibitor states are not independently observed in this demonstration.
• Before deployment, calibrate on actual runs, evaluate parameter identifiability, test held-out operating modes, and confirm controller behavior with equipment and scientific experts.
• Measure viable/dead cells, lysis markers, feed/bleed/harvest flows and quality outcomes to challenge the predicted mechanisms.

Original open-access research, model equations and experiment details ↗