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First principles modelsas a tool to accelerate innovation in the design and operation of biotechnological

processes

Pablo A Rolandi, PhD

The more unpredictable the world is the more we rely on predictions. –Steve Rivkin.

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Overview

Models and model-centric technologies

The modeling landscape

Applications of first principles modeling:• soft-sensing• process troubleshooting• process and model uncertainty• process development• design space• bioreactors and bioseparations

Modeling: formalisms

All models are wrong, some are useful. – George EP Box.

Simplicity is the ultimate sophistication. – Leonardo da Vinci.

Nonlinear differential equation models:• Ordinary differential (ODE)• Differential-algebraic (DAE)• Partial differential (PDE) Regression models:

• Principal component analysis (PCA)

• Partial least squares (PLS)

Statistical models:• Maximum likelihood (ML)• Bayesian

And many more…• Petri nets • Delay differential equations

(DDE)• Boolean and Bayesian networks • Stochastic differential

equations (SDE)• Agent-based models (ABM) • Master equations• Artificial neural networks (ANN) • Gaussian process regression

(kriging)Key question: what are the requirements of the application?

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𝐹 (𝑥 , �̇� , 𝑦 ,𝑢 ,𝜃 ,𝑡 )=0

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Modeling: applicationsProcess operations[1]

[1] Rolandi, PA and Romagnoli, JA; Integrated model-centric framework for support of manufacturing operations. Part I: The framework.; Comp & Chem Engng, 2010

Modeling can be used in R&D and process development as well, not only in process

operations!

Bioreactor (Process)

Model (DAE)

Application: soft-sensingOverview

𝐹 (𝑥 , �̇� , 𝑦 ,𝑢 ,𝜃 ,𝑡 )=0

Controls/Manipulations

Disturbances

Measured variables

Predictions

Soft-sensing: use a model to compute the current (transient) values of unmeasured process variables of

interest

Issues: unmeasured disturbances, model fitness & unmeasured state variables

Benefits: real-time process monitoring for troubleshooting and optimisation

Bulk pH, exhaust CO2

Cell viability, biomass yield, dissolved CO2

A subset of the above

Substrate feed rate,gas flow rate,agitation speed

Inoculum(i.e., initial conditions)

Unmeasured variables

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Application: soft-sensingIndustrial continuous pulping digester[1]

Modeled in gPROMS v2.1 (~2005)

[1] Rolandi, PA and Romagnoli, JA; Smart Enterprise for Pulp and Paper: Digester Modeling and Validation; CACE 14, 2003

~10,000 variables/equations~1,000 states~100 degrees-of-freedom1 reactor + ~15 auxiliary process units

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Application: soft-sensingIndustrial continuous pulping digester[1]

Selectivity remains constant constant lignin to cellulose ratio

Yield decreases both lignin and cellulose were removed from the wood

Reactor design principle: early “impregnation” stages used for intra-particular diffusion, not heterogeneous reaction process operation inconsistent with process designHow fit-for-purpose are first principles models of bioprocesses?

Inspection of simulation profiles enabled troubleshooting:• Too high

temperatures• Too low alkali

concentrationsModel-based optimisation led to more favourable operation:• Benefits:

500,000-2,000,000 US$/year

[1] Rolandi, PA and Romagnoli, JA; Optimisation and Transition Planning of a Continuous Industrial Digester; ESCAPE 14, 2004

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Modeling: first principles modelsScale- and operation-invariant parameters[1]

[1] Craven, S; Shirsat, N; Whelan, J & Glennon, B; Process Model Comparison and Transferability Across Bioreactor Scales and Modes (…) ; Biotechnol Prog, 2013

Model of CHO cells (using Monod kinetics):• i) 3L bench-top and ii) 15L pilot-scale bioreactors • a) batch, b) bolus fed-batch and c) continuous fed-batch

conditions

6 parameters determined experimentally and

11 parameters fitted to experimental data(all with direct physical interpretation)

Good transferability of model better

scale-up

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Modeling: first principles modelsScale- and operation-invariant parameters[1]

[1] Craven, S; Shirsat, N; Whelan, J & Glennon, B; Process Model Comparison and Transferability Across Bioreactor Scales and Modes (…) ; Biotechnol Prog, 2013

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Modeling: first principles modelsA simple benchmark bioreactor model[1]

𝑉 ∙ �̇�=(𝜇 ∙𝑉 −𝑞 )𝐵𝑉 ∙ �̇�=𝑞 (𝑆0−𝑆 )−𝑟 1 ∙𝑉 ∙𝑚𝑤 ∙𝐵

𝑟1=𝑟1 ,𝑚𝑎𝑥 ∙𝑆/ (𝐾 𝑠+𝑆 )𝑟2=𝑘2 ∙𝐸 ∙𝑀1/ (𝐾𝑀1+𝑀 1 )𝑟3=𝑘3 ,𝑚𝑎𝑥 ∙𝐾 𝐼/ (𝐾 𝐼+𝑀2 )

�̇� 1=𝑟1−𝑟 2−𝜇 ∙𝑀 1

�̇� 2=𝑟 2−𝑟 3−𝜇 ∙𝑀2

�̇� 3≡ �̇�=𝑟3−𝜇 ∙𝐸

𝜇=𝑌 𝐵 /𝑆 ∙𝑟 120 vars, 9 eqns 3 dof (), 8 parameters ()

A more realistic model than [1] can be found on [2] (e.g., taking into account full set of amino acids in CHO cell)

Parameters in bold are estimated numerically

𝐹 (𝑥 , �̇� , 𝑦 ,𝑢 ,𝜃 ,𝑡 )=0

[ /𝜇𝑚𝑜𝑙.ℎ]𝑔𝐷𝑊

𝑢={𝑉 ,𝑞 ,𝑆0 }𝜃={𝑀𝑊 ,𝒀 𝑩 /𝑺 ,𝑟1 ,𝑚𝑎𝑥 ,𝐾 𝑆 ,𝒌𝟐 , ,𝐾𝑀 1 ,𝒌𝟑 ,𝒎𝒂𝒙 ,𝑲 𝑰 , }

[g/h]

[ /𝜇𝑚𝑜𝑙.ℎ]𝑔𝐷𝑊

[ /𝜇𝑚𝑜𝑙.ℎ]𝑔𝐷𝑊

[1/ℎ]

[ /𝜇𝑚𝑜𝑙.ℎ]𝑔𝐷𝑊

[1] Kremling, A et al.; Genome Research, 2004; [2] Kontoravdi, C et al.; Biotechnol Prog, 2007

Modeling: model calibrationDynamic parameter estimation

𝐿 (𝜃 ,𝜎|𝑧𝑚 )=(2𝜋𝜎 2)−𝑁 /2𝑒𝑥𝑝(− 12∑ ( 𝑧𝑚−𝑧𝑝 (𝜃)𝜎 )

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)

𝐹 (𝑥 , �̇� , 𝑦 ,𝑢 ,𝜃 ,𝑡 )=0𝑧𝑝(𝜃)=H (𝑥 , �̇� , 𝑦 ,𝑢 ,𝜃 ,𝑡 )

𝜃𝑀𝐿=𝑎𝑟𝑔 min𝜃 𝐿𝐵≤ 𝜃≤ 𝜃𝑈𝐵

∑ ( 𝑧𝑚−𝑧𝑝(𝜃)𝜎 )

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Likelihood function:

Maximum Likelihood (ML) formulation:

Numerics:• Global solutions (hybrid gradient-free,

gradient-based algorithms)

• Discretisation: i) simultaneous (OCFE+NLP-IP) or ii) sequential (IVP+NLP-SQP)

• Gradient calculations: i) exact/symbolic hessian (AD) or ii) augmented/adjoint[1] sensitivities

Bayesian formulation:

Prior and posterior parameter densities

(and likelihood)

𝑝 (𝜃 )=𝑐 ∙𝐿 (𝜃 ,𝜎|𝑧𝑚 ) ∙𝑝0(𝜃)

[1] e.g., SUNDIALS 2.6 or DASPK 3.111

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Modeling: model calibrationA simple benchmark bioreactor model*

What do we do with this residual parametric uncertainty?

Using synthetic process data (i.e., simulation with noise)

𝑆𝑆𝑅 (𝜃 )−𝑆𝑆𝑅 (𝜃𝑀𝐿)≤ 𝜒 𝑁𝑃 , 1−𝛼

Confidence regions (ML):

Issue: are linearised(i.e., ellipsoid-like) confidence regions

good approximations?[1]

* Rolandi, PA; ongoing research towards an MSc on Digital Biology at the University of Manchester.

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Modeling: uncertainty quantificationProcess and model uncertainty

Improve actuation, re-design control system

Reduce uncertainty, ignore, improve quantification

Parameter values

Factors : Critical Process Parameters

(CPPs)

Reduce uncertainty,ignore, measure directly

UQ and GSA are very powerful methods to develop process understanding, ensure quality and develop predictive models

with targeted experimentation

Responses: Critical Quality Attributes

(CQAs)

Bioreactor (Process)

Model (DAE)

𝐹 (𝑥 , �̇� , 𝑦 ,𝑢 ,𝜃 ,𝑡 )=0

Controls/Manipulations

Disturbances

Measured variables

Predictions

Exhaust CO2, bulk pH

Biomass, protein yield, bulk concentrations

A subset of the above

Unmeasured variables

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Application: soft-sensingUncertainty quantification*

Numerics: Monte Carlo (MC) techniques (not OAT)• Efficient sampling: low discrepancy sequences/quasi-random numbers,

correlated factors (e.g., Iman-Conover method)• Pleasingly parallel computations: each run is independent of the others• Number of runs: O(10^4 – 10^5)

Benefits: more realistic predictions taking into account process/model uncertainties (a family of trajectories!)

Monte Carlo

Assessing the impact of parametric uncertainty…

… this framework can be applied to any

CPP!* Rolandi, PA; ongoing research towards an MSc on Digital Biology at the University of Manchester.

Modeling: first principles modelsHybrid multi-scale modeling[1]

Is the “well-mixed” (homogeneous) bioreactor assumption valid?What can we learn from rigorous hydrodynamic calculations?

[1] Bezzo, F; Macchietto, S & Pantelides, CC; General Hybrid Multizonal/CFD Approach for Bioreactor Modeling; AIChE Journal, 2003

10, 15, 20, 25 zones

300, 450, 600 rpm

CSTR vs hybrid, 300 (lhs) & 600 (rhs) rpm

representative zones

Xantan rate (lhs) & effective viscosity (rhs)aggregation

disaggregation

CFD

Zones

Modeling strategy: multi-compartmental model (based on CFD simulations with decoupled or

coupled data flows)

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Modeling: first principles modelsIndustrial bioseparations[1]

[1] Close, EJ; Salm, JR; Bracewell, DG & Sorensen, E; Modelling of industrial biopharmaceutical multicomponent chromatography; Chem Eng Res Des, 2014

𝜕𝐶𝑚𝜕𝑡

+(1−𝜖𝑇 )𝜖𝑇

𝜕𝐶𝑎𝜕𝑡

+𝑢𝜕𝐶𝑚𝜕 𝑧

−𝐷 𝐴

𝜕2𝐶𝑚𝜕 𝑧 2

=0

𝐶𝑎=𝛼

1−𝜖𝑇∙𝑞𝑠 ∙𝑘𝑎 ∙𝐶𝑚1+∑ 𝑘𝑎 ∙𝐶𝑚

𝜕𝐶𝑚𝜕𝑡 |

𝑧

=0𝑧 ∈(0 ,𝐿)

𝜕𝐶𝑚𝜕 𝑧 |

𝑧=𝐿,𝑡=0 𝑡∈[0 , 𝑡 𝑓 ]

𝐶0(𝑡)=(𝐶𝑚− 𝐷𝐴

𝑢𝜕𝐶𝑚𝜕 𝑧 )|

𝑧=0 ,𝑡𝑡∈[0 , 𝑡 𝑓 ]

Competitive Langmuir adsorption isotherm

Mass balance

Initial conditions

Boundary conditions

Optimal parameter values (6) resulting from model calibration

(ML)

Model validation

[mg/ml]

3 dimers; 2 resins

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Application: process troubleshootingIndustrial bioseparations[1]

Disturbances:• Dimer protein concentrations: AA ~N(0.108,

0.024); AB ~N(0.127, 0.023); BB ~N(0.104, 0.023)

Controls:• Mass challenge (mg/ml) and wash length

(CV)Control (decision) space:• Continuous (region) or discrete (grid)Product quality: the probability of meeting the product spec constraint: 0.25 < B (monomer) <0.45 for both resins

Narrow operating region with >75% chance of meeting

the CQA!

HIGH & LOW

[1] Close, EJ; Salm, JR; Bracewell, DG & Sorensen, E; A model based approach for identifying robust operating conditions (…); Chem Eng Sci, 2014

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Application: process developmentIndustrial bioseparations[1]

Better: no feed variability (computed with deterministic feed deterministic design space)

Baseline: variability in feed (SD~0.02) and p>75% (computed with deterministic parameter values)

Worse: variability in feed (SD~0.01) and p>95%(computed with deterministic parameter values)

Reactive process troubleshooting pro-active robust process development: probabilistic design space (i.e., QbD)

Model-based quantification of the

effect of different levels of uncertainty/

variability in feed composition!

(can be extended to account for model uncertainty as

well)

[1] Close, EJ; Salm, JR; Bracewell, DG & Sorensen, E; A model based approach for identifying robust operating conditions (…); Chem Eng Sci, 2014

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Engineering workflows:Iterative model and process development

Model development by model-based design of experimentsProcess development by model-targeted experimentationGlobal Sensitivity Analysis (GSA)[1]:• Algorithms: Sobol indices or DGSM• Numerics: based on Monte Carlo

integration

Goals (factor CPP; response CQA):• Which factors are most important?• Which factors are unimportant?• Which factors can reduce response

variance to an acceptable value?• Which factors effect the responses of

interest?• Meta-modeling

Modeling

Experimentation

Process

[1] Saltelli, A et al; Sensitivity analysis practices: Strategies for model-based inference; Reliab Eng Syst Safe, 2006

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Further applications:Industrial continuous pulping digester[1]

Offline dynamic optimisation:• Digester: yield maximisation, economic maximisation

• Benefits: ~1,400,000 US$/year (and simpler control structure)

• Bioreactors: yield maximisation, batch-time minimisation(controls: substrate feed and aeration rate)

Dynamic data reconciliation:• Digester: bias estimation (mass balance closure)

• Benefits: ~ 500,000 US$/year in utility savings (evaporators)

Real-time dynamic optimisation (advanced process control):• Digester: optimal set-point tracking (during grade transitions)

• Benefits: on-spec product (selectivity)• Bioreactors: model-based control for disturbance rejection (e.g.,

feed failure)

[1] Rolandi, PA; Model-Based Framework for Integrated Simulation, Optimisation and Control of Process Systems; PhD Thesis, 2005

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Today’s modeling landscape

Numerical techniques are widely available• Some key components of the puzzle are not implemented in

commercial tools

Parallel computing (e.g., cloud) is a key enabler• Amazon Web Services (AWS) sells ~15.6 hours of compute time

for $1

Structured/segregated models of fermentation processes are being developed and calibrated• Is this the decade they will become sufficiently predictive?

First principles modeling is becoming widely applied in industry• Corporate modeling functions are being establishedFirst principles modeling:• Generates unparalleled process understanding• Accelerates innovation in process development (e.g.,

scale-up/scale-down) and process operations (e.g., soft-sensing and troubleshooting)

• Provides competitive advantage and delivers value to organisations

Thank youp.a.rolandi@gmail.com[1]

[1] This presentation is not distributed under Creative Commons (CC). A (CC) version will follow shortly.