Multiobjective Dynamic Optimization of Ampicillin Batch Crystallization: Sensitivity Analysis of Attainable Performance vs Product Quality Constraints

Abstract

Ampicillin is a broad spectrum antibiotic and World Health Organization Essential Medicine whose crystallization is an essential unit operation in its production. A published model for the solubility of ampicillin as a function of pH as well as growth and nucleation kinetics allows for dynamic simulation and optimization of its batch crystallization. While experimental approaches to investigating different dynamic pH profiles have been considered in the literature, dynamic mathematical optimization of pH modulations to meet specific production objectives for ampicillin batch crystallization has yet to be implemented; therein lies the novelty of this study. This work performs dynamic simulation and optimization of the batch crystallization of ampicillin to establish optimal pH trajectories for different production objectives. Simulation of already published batch seeded ampicillin crystallization experiments is performed prior to definition and solution of a dynamic optimization problem for maximization of mean crystal sizes and minimization of size distribution width. The effects of seed loading, time domain discretization and mean crystal size and size distribution width objective function weights are considered and discussed. Pareto fronts showing tradeoffs between different objectives and constraints are then investigated.

Dynamic Optimization of a Fed-Batch Nosiheptide Reactor

“…The differential profiles (Equation ( 13)) can be approximated by Equation (20), where ∆t i is the length of element i and dx/dt i,j is the derivative of the state variable in element i at the j th collocation point. Ω j is a j th order polynomial satisfying Equation (21). Continuity of the state trajectories is ensured by Equation (22).…”

“…Human antibiotic production, particularly β-lactams (whose broad applications and importance in global healthcare make them high priority), has received a lot of attention in process systems engineering in the past decade; a summary of pertinent literature examples on modeling and optimization of antibiotic production is provided in Table 1. Application of artificial neural networks (ANNs) to model complex reaction scheme for penicillin G acylase (PGA)-catalyzed synthesis [12] Inclusion of additional experimental data to improve ANN in reference [12] [13] Maximization of API formation vs. different operating conditions in either methanol/ethylene glycol as reaction solvents [14] Sensitivity analysis on previous ANN study [12] [15] Modeling and simulation of continuous reactive crystallization in presence of substrates and impurities [16,17] Dynamic optimization of non-isothermal batch reactor [18] Ampicillin UTIs Pneumonia Gonorrhea Meningitis Abdominal infections Regression of nucleation and growth kinetics for pH crystallization model [19] Modeling and simulation of reactive crystallization in presence of substrates and impurities [20] Modeling and simulation of continuous reactive crystallization in presence of substrates and impurities [16,17] Multi-objective dynamic optimization of pH crystallization [21] Cephalexin UTIs…”

“…A bi-objective problem is considered, defined by Equations ( 24)- (26). Multiple optimization objectives can also be formulated as a single objective function by considering a sum of weighted individual objectives as in other studies by our group [21,41]; however, such methods can be used in studies considering full-scale industrial operation with ample experimental and dynamic production data acquisition, whereas for comparison of modeling and optimization results vs. a relatively small experimental dataset (as is the case here), a bi-objective problem defined as a product of individual objectives is more appropriate. Constraints impose bounds on the control profiles (Equations ( 27)-( 29) as well as the broth volume being limited by the reactor size (Equation ( 30)).…”

Multi-objective Dynamic Optimisation of Ampicillin Batch Crystallisation

“…The solubility of ampicillin as a function of pH is described using the extended Pitzer model (de Pessôa Filho et al, 2008) in Eqs. 1-2, where constants ε, σ, pKA1 and pKA2 are taken from the literature (Encarnación-Gómez et al, 2016), kB = Boltzmann constant, NA = Avogadro number, ρ = ampicillin density and the isoelectric point (pI) and its corresponding solubility (S(pI)) are regressed in previous work (Dafnomilis et al, 2019) log…”

“…We consider WSTD = 1.0, WMCS = 1.5 and the number of equispaced time discretisation intervals in the time domain, N = 30. The number of state variable collocation points, Kx = 3, and the initialisation pH profile is constant pH(t) = 7, unless stated otherwise in Section 4; the effects of varying Wi on the objective function and values of N have been considered and analysed previously (Dafnomilis et al, 2019).…”