Non-linear qualitative signal processing for biological systems: application to the algal growth in bioreactors

Dynamic coupling of photoacclimation and photoinhibition in a model of microalgae growth

The development of mathematical models that can predict photosynthetic productivity of microalgae under transient conditions is crucial for enhancing large-scale industrial culturing systems. Particularly important in outdoor culture systems, where the light irradiance varies greatly, are the processes of photoinhibition and photoacclimation, which can affect photoproduction significantly. The former is caused by an excess of light and occurs on a fast time scale of minutes, whereas the latter results from the adjustment of the light harvesting capacity to the incoming irradiance and takes place on a slow time scale of days. In this paper, we develop a dynamic model of microalgae growth that simultaneously accounts for the processes of photoinhibition and photoacclimation, thereby spanning multiple time scales. The properties of the model are analyzed in connection to PI-response curves, under a quasi steady-state assumption for the slow processes and by neglecting the fast dynamics. For validation purposes, the model is calibrated and compared against multiple experimental data sets from the literature for several species. The results show that the model can describe the difference in photosynthetic unit acclimation strategies between Dunaliella tertiolecta (n-strategy) and Skeletonema costatum (s-strategy).

Modelling of Microalgae Culture Systems with Applications to Control and Optimization

Mathematical modeling is becoming ever more important to assess the potential, guide the design, and enable the efficient operation and control of industrial-scale microalgae culture systems (MCS). The development of overall, inherently multiphysics, models involves coupling separate submodels of (i) the intrinsic biological properties, including growth, decay, and biosynthesis as well as the effect of light and temperature on these processes, and (ii) the physical properties, such as the hydrodynamics, light attenuation, and temperature in the culture medium. When considering high-density microalgae culture, in particular, the coupling between biology and physics becomes critical. This chapter reviews existing models, with a particular focus on the Droop model, which is a precursor model, and it highlights the structure common to many microalgae growth models. It summarizes the main developments and difficulties towards multiphysics models of MCS as well as applications of these models for monitoring, control, and optimization purposes.

The effect of photosynthesis time scales on microalgae productivity

Microalgae are often seen as a potential biofuel producer. In order to predict achievable productivities in the so called raceway culturing system, the dynamics of photosynthesis has to be taken into account. In particular, the dynamical effect of inhibition by an excess of light (photoinhibition) must be represented. We propose a model considering both photosynthesis and growth dynamics. This model involves three different time scales. We study the response of this model to fluctuating light with different frequencies by slow/fast approximations. Therefore, we identify three different regimes for which a simplified expression for the model can be derived. These expressions give a hint on productivity improvement which can be expected by stimulating photosynthesis with a faster hydrodynamics.

Modelling neutral lipid production by the microalga Isochrysis aff. galbana under nitrogen limitation

This article proposes a dynamical model of microalgal lipid production under nitrogen limitation. In this model, intracellular carbon is divided between a functional pool and two storage pools (sugars and neutral lipids). The various intracellular carbon flows between these pools lead to a complex dynamic with a strong discrepancy between synthesis and mobilization of neutral lipids. The model has been validated with experiments of Isochrysis aff. galbana (clone T-iso) culture under various nitrogen limitation conditions and under nitrogen starvation. The hysteresis behavior of the neutral lipid quota observed experimentally is accurately predicted.

Modeling continuous cultures of microalgae colimited by nitrogen and phosphorus

It is well documented that the combination of low nitrogen and phosphorus resources can lead to situations where colimitation of phytoplankton growth arises, yet the underlying mechanisms are not fully understood. Here, we propose a Droop-based model built on the idea that colimitation by nitrogen and phosphorus arises from the uptake of nitrogen. Indeed, since N-porters are active systems, they require energy that could be related to the phosphorus status of the cell. Therefore, we assumed that N uptake is enhanced by the P quota. Our model also accounts for the biological observations that uptake of a nutrient can be down-regulated by its own internal quota, and succeeds in describing the strong contrast for the non-limiting quotas under N-limited and P-limited conditions that was observed on continuous cultures with Selenastrum minutum and with Isochrysis affinis galbana. Our analysis suggests that, regarding the colimitation concept, N and P would be better considered as biochemically dependent rather than biochemically independent nutrients.

A new method for measuring dynamic change of tracer distribution using dynamic single photon emission tomography with a slip-ring rotational gamma camera

The clinical applicability of dynamic single photon emission tomograpy (SPET) using a dual-head gamma camera equipped with a slip-ring rotational mechanism, referred to as serial SPET, was examined in the present investigation. Serial SPET enables the production of tomographic images for any arbitrary time frame from an arbitrary range of data to 360 degrees. In a pre-clinical evaluation, a correlation between radioactivity concentration and serial SPET counts was evaluated in a phantom with continuous changes in 99mTc concentration. A differential value was obtained from each pair of SPET images; moreover, moving average approximation processing was investigated with respect to the elimination of noise in the data. In 11 and one patient presenting with cerebrovascular disease and meningioma, respectively, changes in SPET counts were evaluated when 99mTc ethyl cysteinate dimer (99mTc-ECD) was continuously administered at a constant rate in the resting state. Furthermore, in six of 11 subjects with cerebrovascular disease, changes occurring in SPET counts were examined by using acetazolamide loading while continuously administering 99mTc-ECD at a constant rate. Consequently, serial SPET enabled the evaluation of changes in radioactivity concentration over time in both the phantom and preliminary clinical studies. Data analysis by differential processing utilizing moving average approximation processing enabled the detection of minor changes in radioactivity concentration. An increase of 15.1+/-5.4% was observed in SPET counts of the unaffected cerebral hemisphere with acetazolamide loading. The response of the affected hemisphere was less prominent. These findings suggest that serial SPET would be an effective technique for the pharmacokinetic analysis of radiopharmaceuticals.