A multiscale modelling approach for Haematococcus pluvialis cultivation under different environmental conditions

Structured population balances to support microalgae-based processes: Review of the state-of-art and perspectives analysis

“…Motivated by this analysis, with only a few exceptions [59] , [64] , [65] , PBEs so far proposed in the microalgae literature were written using the cell mass as the internal coordinate [19] , [43] , [58] , [59] , [64] , [66] , [67] .…”

“…The latter one can be attributed to specific physiological phenomena such as respiration, maintenance and catabolites excretion, and it was typically assumed to be constant. A Monod-type expression was usually adopted to quantify the dependence of on the nutrient concentrations in the growth medium, except for Usai et al [65] . In the latter study, adoptes a double affinity law to describe the ability of microalgae to growth at high and low levels of intracellular nitrates concetrations.…”

“… : mass of the cell : mass of the mother cell parameters of the beta function for division into i daughter cells Euler beta function [19] Multiple fission in terms of mass. : volume of the cell : volume of the mother cell parameters of the beta function for division into i daughter cells Euler beta function [65] …”

“…Usai et al [65] presented a PBE based on the same fission modelling framework proposed by Concas et al [19] , [23] but using the cell volume as the principal internal coordinate. However, their model considered two distinct compartments, i.e., an intracellular and an extracellular compartment, which exchange nutrients along with light.…”

Parameter estimation combined with model reduction techniques for identifiability analysis of biological models

“…Cross-validation combined with a Least Absolute Shrinkage and Selection Operator (LASSO) regularisation method is used to reduce the complexity of linear empirical equations for predicting the performance of downdraft biomass gasification (Binns and Ayub, 2021). Sensitivity and identifiability methods utilizing the Fischer Information Matrix (FIM) are used to reduce the complexity of a nonlinear system of partial integral differential equations describing a population balance model for microalgae cultivation (Usai et al, 2022). Application of these methods allows the number of parameters to be reduced depending on the tolerance and/or accuracy required.…”