Fed-batch cultivations – hybrid modeling and intensified DoE

​Current strategies for bioprocess developments are strongly relying on design of experiments (DoE). Critical process parameters (CPP) are varied systematically and their influence on the critical quality attributes (CQA) are evaluated. This approach reduces the required number of experiments and gives insight in which process parameters are critical to process outcomes compared to OFAT (one-factor-a-time). A drawback of DoE, however, is that the comparison is done at the endpoint of the cultivation. The important information, however, often lies before the endpoint.

In our first use case, microbial fed-batch cultivations were performed. We varied the cultivation temperature, feed rate and induction strength in a DoE usual space (3x3x3 + 4 replicates = 31 cultivations). We investigated the performance of state-of-the-art DoE and hybrid models to predict the biomass concentration and product yield. The pure endpoint estimation from the DoE and hybrid modeling yielded similar model errors. The hybrid model, however, also gives information on the biomass and product concentration before the process is over. It, therefore, enables time-resolved modeling and additionally helps to answer the following questions:

  • How long do I have to run the upstream process before I run into product yield stagnation?
  • In which phase is my process? Is the biomass increasing exponentially, stagnating or even decreasing?


Figure 1. Comparison between DoE endpoint and hybrid model prediction

We conclude that hybrid models are more flexible at describing processes compared to common DoE approaches with similar errors and additional advantages.

In the second part of this use case, we investigated the benefits of intensified design of experiments (iDoE) over the regular DoE approach. In iDoE, process parameters are changed systematically within the same cultivation. This enables faster development times since fewer experiments have to be performed. We performed cultivations with two parameter shifts, resulting in three different process conditions during the same cultivation. Afterward, this generated iDoE bioprocess data, including off-line analytics, was used to train a hybrid model. This iDoE hybrid model was used to predict the biomass concentration and product titer of the regular cultivations without process parameter shifts. The results were comparable to the earlier derived hybrid model, developed using regular cultivations, but only required one-third of the data for model-training, leading to an accelerated process characterization of more than 66%.

Tangential flow ultrafiltration – hybrid modeling for flux prediction

​In our second use case, we investigated the benefits of hybrid modeling for crossflow ultrafiltration (TFF). TFFs are often optimized for their initial conditions by systematically changing mechanical parameters like the transmembrane pressure (TMP) or crossflow that yield a fast process without damaging the CQAs. This approach, however, neglects the influence of these parameters after the starting conditions, e.g., when at higher product concentrations during ultrafiltration or with an increasingly fouled filtration membrane. By incorporating multiple TMPs, crossflows and concentrations, hybrid modeling delivers time-resolved process models. These models predict the permeate flux, which describes how fast the process will be over, the concentration and the process duration at every time point.

The separation of the black and white box even allows predictions for different scales. A hybrid model that was trained on a regular batch TFF, can predict continuous fed-batch TFF with a slightly different white box structure. We showed the flexibility of these models for different protein and membrane types.


Figure 2. Driving factors of tangential flow filtration

In both scenarios, the hybrid modeling approach yields excellent descriptive models with a reduced number of experiments, high accuracy and time-resolved. Additionally, they allow in-silico process development. Here, lab experiments with different process parameters are simulated on computers – a so-called digital twin – and optimized based on trained hybrid models.

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