• Paweł Drąg Wrocław University of Science and Technology, Wrocław, Poland
  • Krystyn Styczeń Wrocław University of Science and Technology, Wrocław, Poland
  • Konrad Matyja Faculty of Chemistry, Wrocław University of Science and Technology, Poland
Keywords: differential-algebraic models, ecotoxicological models, measurement system, nonlinear optimization


We present a general framework for measurements and optimization of differential-algebraic models. Moreover, we propose an application of the considered methodology in ecotoxicology. The differential-algebraic models can be used to describe different ecotoxicological relations. One of them is the influence of the environmental pollution on the Daphnia's movement characteristics. Changes in these characteristics can be used as a tool for assessment of neurotoxicity. The camera-based measurement and optimization system enable us to obtain the differential-algebraic ecotoxicological relations in a fully automated way.


Ahlkrona, J., Lötstedt, P., Kirchner, N., and Zwinger T,. Dynamically coupling the non-linear Stokes equations with the Shallow Ice Approximation in glaciology: Description and first applications of the ISCAL method. Journal of Computational Physics, 2016, 308:1-19.

Balsa-Canto, E., Vassiliadis, V.S., and Banga, J.R. Dynamic Optimization of Single- and Multi-Stage Systems Using a Hybrid Stochastic-Deterministic Method. Ind. Eng. Chem. Res., 2005, 44:1514-1523.

Betts, J.T. Practical Methods for Optimal Control and Estimation Using Nonlinear Programming. Second Edition. SIAM, Philadelphia, 2010.

Biegler, L.T. Nonlinear Programming. Concepts, Algorithms and Applications to Chemical Processes. SIAM, Philadelphia, 2010.

Brenan, K.E., Campbell, S.L., and Petzold, L.R. Numerical Solution of Initial-Value Problems in Differential Algebraic Equations. SIAM, Philadelphia, 1996.

Diehl, M., Bock, H.G., Schlöder, J.P., Findeisen, R., Nagy, Z., and Allgöwer, F. Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations. Journal of Process Control, 2002, 12:577-585.

El-Doma, M.O. Daphnia: Biology and Mathematics Perspectives. Nova Science Pub Inc, 2013.

Fingerman, M., Devi, M., Reddy, P.S., Katyayani, R. Impact of Heavy Metal Exposure on the Nervous System and Endocrine-Mediated Processes in Crustaceans. Zoological Studies, 1996, 35:1-8.

Guilhermino, L., Lopes, M.C., Carvalho, A.P., and Soares, A.M.V.M. Inhibition Of Acetylcholinesterase Activity As Effect Criterion In Acute Tests With Juvenile Daphnia magna. Chemosphere, 1996, 32:721-738.

Hatano, A. and Shoji, R. A new model for predicting time course toxicity of heavy metals based on Biotic Ligand Model (BLM). Comparative Biochemistry and Physiology Part C: Toxicology and Pharmacology, 2010, 151:25-32.

Mach, R. and Schweitzer F. Modeling Vortex Swarming In Daphnia. Bulletin of Mathematical Biology, 2007, 69:539-562.

Matyja, K., Małachowska-Jutsz, A., Mazur, A.K. and Grabas, K. Assessment of toxicity using dehydrogenases activity and mathematical modeling. Ecotoxicology, 2016, 25:924-939.

Nocedal, J. and Wright, S.J. Numerical Optimization. Springer, New York, 2006.

Optronis GmbH: Make time visible. CamRecord CL600x2 High Speed Camera, http://www.optronis.com/fileadmin/Upload/Product/CL/CL600x2_engl.pdf.

Ordemann, A., Balazsi, G., and Moss, F. Pattern formation and stochastic motion of the zooplankton Daphnia in a light field. Physica A: Statistical Mechanics and its Applications, 2003, 325:260-266.