Though there have been many attempts to address growth kinetics in algal photobioreactors, surprisingly little have attempted an agent-based modelling (ABM) approach. ABM has been heralded as a method of practical scientific inquiry into systems of a complex nature and has been applied liberally in a range of disciplines including ecology, physics, social science, and microbiology with special emphasis on pathogenic bacterial growth. We bring together agent-based simulation with the Photosynthetic Factory (PSF) model, as well as certain key bioreactor characteristics in a visual 3D, parallel computing fashion. Despite being at small scale, the simulation gives excellent visual cues on the dynamics of such a reactor, and we further investigate the model in a variety of ways. Our parallel implementation on graphical processing units of the simulation provides key advantages, which we also briefly discuss. We also provide some performance data, along with particular effort in visualisation, using volumetric and isosurface rendering. 1. Introduction The motivation for optimising growth kinetics in phytoplankton, specifically algae, is rooted in their use for a variety of purposes including dietary supplements such as spirulina [1], and Astaxanthin [2]. Astaxanthin in particular, is a valuable carotenoid often used for pigmentation in salmon and trout, as well as for human consumption, due to its antioxidant qualities [3]. The mass cultivation of algae is not only done for extracting dietary supplements. It is also performed for other tasks such as effluent treatment [4] and biodiesel production (though this is still in infancy) [5]. Previous agent-based algal growth models typically assume a 1-dimensional lattice [6, 7]. Our work focuses on a 2-dimensional lattice in an attempt to better model the local interactions of hydrodynamics in order to more accurately determine illumination history. Illumination history is important to the cell division rates in a culture [8–10], and factors such as fluid dynamics determine the effects of mutual shading between cells, as well as their exposure (or overexposure) to the illumination source (in our work, we assume a parallel light source from either side of the lattice). In our simulation, this combination of photolimitation, photoinhibition, and mutual shading determines the illumination history of a cell. We attempt to capture these factors with some accuracy in counting the state transitions between specific states in the PSF model. In our previous work [11, 12], we have considered preliminary modelling of
References
[1]
A. Richmond and J. U. Grobbelaar, “Factors affecting the output rate of Spirulina platensis with reference to mass cultivation,” Biomass, vol. 10, no. 4, pp. 253–264, 1986.
[2]
R. Ranjbar, R. Inoue, H. Shiraishi, T. Katsuda, and S. Katoh, “High efficiency production of astaxanthin by autotrophic cultivation of Haematococcus pluvialis in a bubble column photobioreactor,” Biochemical Engineering Journal, vol. 39, no. 3, pp. 575–580, 2008.
[3]
M. Guerin, M. E. Huntley, and M. Olaizola, “Haematococcus astaxanthin: applications for human health and nutrition,” Trends in Biotechnology, vol. 21, no. 5, pp. 210–216, 2003.
[4]
W. Mulbry, S. Kondrad, and J. Buyer, “Treatment of dairy and swine manure effluents using freshwater algae: fatty acid content and composition of algal biomass at different manure loading rates,” Journal of Applied Phycology, vol. 20, no. 6, pp. 1079–1085, 2008.
[5]
L. Lardon, A. Hélias, B. Sialve, J.-P. Steyer, and O. Bernard, “Life-cycle assessment of biodiesel production from microalgae,” Environmental Science and Technology, vol. 43, no. 17, pp. 6475–6481, 2009.
[6]
E. Greenwald, A stochastic model of algal photobioreactors [M.S. thesis], Ben-Gurion University of the Negev, 2010.
[7]
？. Papá？ek, C. Matonoha, V. ？tumbauer, and D. ？tys, “Modelling and simulation of photosynthetic microorganism growth: random walk vs. finite difference method,” Mathematics and Computers in Simulation, vol. 82, no. 10, pp. 2022–2032, 2012.
[8]
M. C. García-Malea, C. Brindley, E. Del Río, F. G. Acién, J. M. Fernández, and E. Molina, “Modelling of growth and accumulation of carotenoids in Haematococcus pluvialis as a function of irradiance and nutrients supply,” Biochemical Engineering Journal, vol. 26, no. 2-3, pp. 107–114, 2005.
[9]
J. C. Merchuk and X. Wu, “Modeling of photobioreactors: application to bubble column simulation,” Journal of Applied Phycology, vol. 15, no. 2-3, pp. 163–169, 2003.
[10]
X. Wu and J. C. Merchuk, “A model integrating fluid dynamics in photosynthesis and photoinhibition processes,” Chemical Engineering Science, vol. 56, no. 11, pp. 3527–3538, 2001.
[11]
A. V. Husselmann and K. A. Hawick, “Intelligent individual agent-based simulation of photobioreactors and growth control,” Tech. Rep. CSTN-223, Computer Science, Massey University, Albany Auckland, New Zealand, 2013, Submitted to IASTED ISC’13, Marina del Rey.
[12]
K. A. Hawick and A. V. Husselmann, “Photo-penetration depth growth dependence in an agent-based photobioreactor model,” Tech. Rep. CSTN-204, Computer Science, Massey University, Auckland, New Zealand, 2013.
[13]
K. Kawasaki, “Diffusion constants near the critical point for time-dependent ising models. I,” Physical Review, vol. 145, no. 1, pp. 224–230, 1966.
[14]
P. H. C. Eilers and J. C. H. Peeters, “A model for the relationship between light intensity and the rate of photosynthesis in phytoplankton,” Ecological Modelling, vol. 42, no. 3-4, pp. 199–215, 1988.
[15]
B. Rehák, S. ？elikovsky, and ？. Papá？ek, “Model for photosynthesis and photoinhibition: parameter identification based on the harmonic irradiation O2 response measurement,” IEEE Transactions on Automatic Control, vol. 53, pp. 101–108, 2008.
[16]
P. H. C. Eilers and J. C. H. Peeters, “Dynamic behaviour of a model for photosynthesis and photoinhibition,” Ecological Modelling, vol. 69, no. 1-2, pp. 113–133, 1993.
[17]
C. Posten, “Design principles of photo-bioreactors for cultivation of microalgae,” Engineering in Life Sciences, vol. 9, no. 3, pp. 165–177, 2009.
[18]
C. U. Ugwu, H. Aoyagi, and H. Uchiyama, “Photobioreactors for mass cultivation of algae,” Bioresource Technology, vol. 99, no. 10, pp. 4021–4028, 2008.
[19]
T. E. Gorochowski, A. Matyjaszkiewicz, T. Todd et al., “Bsim: an agentbased tool for modeling bacterial populations in systems and synthetic biology,” PLoS ONE, vol. 7, no. 8, 2012.
[20]
J.-U. Kreft, G. Booth, and J. W. T. Wimpenny, “BacSim, a simulator for individual-based modelling of bacterial colony growth,” Microbiology, vol. 144, no. 12, pp. 3275–3287, 1998.
[21]
C. M. Macal and M. J. North, “Tutorial on agent-based modeling and simulation part 2: how to model with agents,” in Proceedings of the Winter Simulation Conference (WSC '06), pp. 73–83, Monterey, Calif, USA, December 2006.
[22]
Reynolds and C. Flocks, “herds and schools: a distributed behavioral model,” in Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques (SIGRAPH ’87), M. C. Stone, Ed., pp. 25–34, ACM, 1987.
[23]
C. Reynolds, “Boids background and update,” 2011.
[24]
M. Scheffer, J. M. Baveco, D. L. DeAngelis, K. A. Rose, and E. H. Van Nes, “Super-individuals a simple solution for modelling large populations on an individual basis,” Ecological Modelling, vol. 80, no. 2-3, pp. 161–170, 1995.
[25]
A. Leist, D. P. Playne, and K. A. Hawick, “Exploiting graphical processing units for data-parallel scientific applications,” Concurrency Computation Practice and Experience, vol. 21, no. 18, pp. 2400–2437, 2009.
[26]
NVIDIA, “CUDA C Programming Guide. 5. 0 edn,” 2012.
[27]
K. S. Perumalla and B. G. Aaby, “Data parallel execution challenges and runtime performance of agent simulations on GPUs,” in Proceedings of the Spring Simulation Multiconference (SpringSim '08), pp. 116–123, ACM, New York, NY, USA, April 2008.
[28]
K. Hawick, “Visualising multi-phase lattice gas fluid layering simulations,” in Proceedings of the International Conference onModeling, Simulation and Visualization Methods (MSV ’11), pp. 18–21, CSREA, Las Vegas, Nev, USA, July 2011.
[29]
Y. K. Lee and J. S. Pirt, “Energetics of photosynthetic algal growth: influence of intermittent illumination in short (40 s) cycles,” Journal of General Microbiology, vol. 124, no. 1, pp. 43–52, 1981.
[30]
J. H. Lambert and E. Anding, Lambert’s Photometrie: Photometria, Sive De Mensura et Gradibus Luminis, Colorum et Umbrae, W. Engelmann, 1892.
[31]
A. Beer, “Bestimmung der absorption des rothen lichts in farbigen flüssigkeiten,” Annalen der Physik Und Chemie, vol. 86, pp. 78–90, 1852.
[32]
J. T. O. Kirk, Light and Photosynthesis in Aquatic Ecosystems, Cambridge University Press, 2011.
[33]
A. V. Husselmann and K. A. Hawick, “Random flights for particle swarm optimisers,” in Proceedings of the 12th IASTED International Conference on Artificial Intelligence and Applications, IASTED, Innsbruck, Austria, February 2013.
