coupling only for substrate concentration. As for the particle number, ergodic
theorem is explained later on in the chapter. All these assumptions should be
based on prior knowledge and by having the end in mind as too little detail will
result in inaccuracy and too much detail will result in unfeasible resource utilization.
2.2 How to Get Biologically Sound Readouts?
After tracking individual particles and their properties, the analysis may be
performed in a different environment, such as MATLAB. For clustering particle
properties, proper regimes must be defined first. For instance, critical substrate
concentration may be set as thresholds distinguishing different metabolic states. Or
critical ε values and critical ε frequencies may be defined to qualify shear stress for
susceptible cultures. Another point of view is to integrate a more complicated kinetic
model based on multiple substrates and by-product lifelines taking exposure statistics into account which is an interesting view when investigating overflow metabolism [26] and many more, etc. In combination with regime constraints, residence
time distributions of cells resting within the defined regime borders should be
studied, too [12, 14, 15].
Often, turbulent movements reveal very rapid regime changes for those particles
possessing properties contiguous to the rigid regime borders. The resulting artificial
regime changes bias residence time distributions and should be curated, accordingly.
Haringa et al. [12, 14] distinguished between three types of rapid variations: rapid
successive regime crossings, integral scale variations, and subgrid variations by
small eddies. Based on the work of Linkès et al. [48], eddy micro-mixing is not
limited in nonviscous fluids, which translates to assimilation timescale being orders
of magnitude larger than the timescale of the smallest turbulent structures which is
referred to as Kolmogorov timescale
ν
ε
À Á 0:5 and therefore concluding that micromixing is not a limiting step considering substrate assimilation (no effect on gradient
formation). The other two effects occur at the Lagrangian timescale when applying
the DRW model and might have an effect on substrate assimilation and gradient
formation. For a tractable analysis, the turbulent variations need to be smoothed
using appropriate filters, with a filter time step corresponding to the Lagrangian
timescale.
Alternately, to soften the hard boundary conditions (which do not exist in reality)
a second “boundary” (fuzzy) filter can be applied (e.g., filter amplitude of Æ0.01 in
concentration changes). Besides, investigating the influence of highly fluctuating
substrate availability on the cellular performance may be an interesting research
topic for future studies.
In general, sound knowhow about cellular metabolism and regulation is mandatory to qualify the readout of lifelines. From a fluid mechanics point of view in
reality, a fluctuation in a concentration can be as small as the Kolmogorov scales, yet
it is only limited to the time resolution of the digital twin of the bioreactor. The same
236
C. S. S. Hajian et al.
theorem is explained later on in the chapter. All these assumptions should be
based on prior knowledge and by having the end in mind as too little detail will
result in inaccuracy and too much detail will result in unfeasible resource utilization.
2.2 How to Get Biologically Sound Readouts?
After tracking individual particles and their properties, the analysis may be
performed in a different environment, such as MATLAB. For clustering particle
properties, proper regimes must be defined first. For instance, critical substrate
concentration may be set as thresholds distinguishing different metabolic states. Or
critical ε values and critical ε frequencies may be defined to qualify shear stress for
susceptible cultures. Another point of view is to integrate a more complicated kinetic
model based on multiple substrates and by-product lifelines taking exposure statistics into account which is an interesting view when investigating overflow metabolism [26] and many more, etc. In combination with regime constraints, residence
time distributions of cells resting within the defined regime borders should be
studied, too [12, 14, 15].
Often, turbulent movements reveal very rapid regime changes for those particles
possessing properties contiguous to the rigid regime borders. The resulting artificial
regime changes bias residence time distributions and should be curated, accordingly.
Haringa et al. [12, 14] distinguished between three types of rapid variations: rapid
successive regime crossings, integral scale variations, and subgrid variations by
small eddies. Based on the work of Linkès et al. [48], eddy micro-mixing is not
limited in nonviscous fluids, which translates to assimilation timescale being orders
of magnitude larger than the timescale of the smallest turbulent structures which is
referred to as Kolmogorov timescale
ν
ε
À Á 0:5 and therefore concluding that micromixing is not a limiting step considering substrate assimilation (no effect on gradient
formation). The other two effects occur at the Lagrangian timescale when applying
the DRW model and might have an effect on substrate assimilation and gradient
formation. For a tractable analysis, the turbulent variations need to be smoothed
using appropriate filters, with a filter time step corresponding to the Lagrangian
timescale.
Alternately, to soften the hard boundary conditions (which do not exist in reality)
a second “boundary” (fuzzy) filter can be applied (e.g., filter amplitude of Æ0.01 in
concentration changes). Besides, investigating the influence of highly fluctuating
substrate availability on the cellular performance may be an interesting research
topic for future studies.
In general, sound knowhow about cellular metabolism and regulation is mandatory to qualify the readout of lifelines. From a fluid mechanics point of view in
reality, a fluctuation in a concentration can be as small as the Kolmogorov scales, yet
it is only limited to the time resolution of the digital twin of the bioreactor. The same
236
C. S. S. Hajian et al.