, Volume 26, Issue 3, pp 295–307 | Cite as

Toxicodynamic modeling of zebrafish larvae to metals using stochastic death and individual tolerance models: comparisons of model assumptions, parameter sensitivity and predictive performance

  • Yongfei Gao
  • Jianfeng Feng
  • Lin Zhu


Process-based toxicodynamic (TD) models are playing an increasing role in predicting chemical toxicity to aquatic organism. Stochastic death (SD) and individual tolerance distribution (IT) are two often used assumptions in TD models which could lead to different consequences for risk assessment of chemicals. Here, using the toxicity data of single (Cu, Zn, Cd, and Pb) and their binary metal mixtures on survival of zebrafish larvae, we assessed the parameter sensitivity and evaluated the predictive performance of SD and IT models. The sensitivity analysis indicated the parameters related to toxicodynamics such as k k and threshold, had a great influence on the SD model’s output and α had a great influence on the IT model’s output. The predicted survival probability was highly sensitive to the assumptions of SD or IT models, and the SD model explained toxicity of single metal and binary metal mixtures better than IT model. Our results suggested that SD model is more suitable in assessing the metal toxicity to zebrafish larvae. Moreover, different combinations of laboratory metal-specific and species-specific experiments with SD and IT models need further study for better understanding and predicting toxic effects for different metals and organisms.


Toxicodynamic (TD) model Stochastic death (SD) Individual tolerance distribution (IT) Metal toxicity Predictive power 



This study was supported by the National Natural Science Foundation of China (21277076),Tianjin Natural Science Foundation (15JCYBJC22800), the National Water Pollution Control and Treatment Science and Technology Major Project (2012ZX07501003) and the Fundamental Research Funds for the Central Universities. We thank the editor and the two anonymous referees whose comments and suggestions greatly improved the quality of the article.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no competing interest.

Ethical approval

This study involving animals was conducted in accordance with the national and institutional guidelines for the protection of animal welfare.

Informed consent

This is an altruistic study on animals, and we all authors expect that results obtained from this study will enable us to improve the knowledge on heavy metal toxicity and finally may result in useful benefits for society as a whole.

Supplementary material

10646_2017_1763_MOESM1_ESM.doc (46 kb)
Supplementary Information


  1. Ashauer R, Boxall ABA, Brown CD (2006) Predicting effects on aquatic organisms from fluctuating or pulsed exposure to pesticides. Environ Toxicol Chem 25:1899–1912Google Scholar
  2. Ashauer R, Boxall ABA, Brown CD (2007a) New ecotoxicological model to simulate survival of aquatic invertebrates after exposure to fluctuating and sequential pulses of pesticides. Environ Sci Technol 41:1480–1486CrossRefGoogle Scholar
  3. Ashauer R, Boxall ABA, Brown CD (2007b) Simulating toxicity of carbaryl to Gammarus pulex after sequential pulsed exposure. Environ Sci Technol 41:5528–5534CrossRefGoogle Scholar
  4. Ashauer R, Brown CD (2008) Toxicodynamic assumptions in ecotoxicological hazard models. Environ Toxicol Chem 27:1817–1821CrossRefGoogle Scholar
  5. Ashauer R, Hintermeister A, Caravatti I, Kretschmann A, Escher BI (2010) Toxicokinetic-toxicodynamic modeling explains carry-over toxicity from exposure to diazinon by slow organism recovery. Environ Sci Technol 44(10):3963–3971CrossRefGoogle Scholar
  6. Ashauer R, Thorbek P, Warinton JS, Wheeler JR, Maund S (2013) A method to predict and understand fish survival under dynamic chemical stress using standard ecotoxicity data. Environ Toxicol Chem 32(4):954–965CrossRefGoogle Scholar
  7. Ashauer R, Wittmer I, Stamm C, Escher BI (2011) Environmental risk assessment of fluctuating diazinon concentrations in an urban and agricultural catchment using toxicokinetic-toxicodynamic modeling. Environ Sci Technol 45:9783–9792CrossRefGoogle Scholar
  8. Bliss CI (1935) The calculation of the dosage-mortality curve. Ann Appl Biol 22:134–167CrossRefGoogle Scholar
  9. Brock TCM, Alix A, Brown CD, Capri E, Gottesbüren B, Heimbach F, Lythgo CM, Schulz R, & Streloke M (Eds.) (2010) Linking aquatic exposure and effects. Society of Environmental Toxicology and Chemistry, Pensacola, FLGoogle Scholar
  10. Cheng T, Allen H (2001) Prediction of uptake of copper from solution by lettuce (Lactuca sativa romance). Environ Toxicol Chem 20:2544–2551CrossRefGoogle Scholar
  11. Cho E, Arhonditsis GB, Khim J, Chung S, Heo TY (2016) Modeling metal-sediment interaction processes: Parameter sensitivity assessment and uncertainty analysis. Environ Modell Softw 80:159–174CrossRefGoogle Scholar
  12. Dauterman WC (1994) Adaptation to toxicants. In: Hodson E, & Levi P (Eds.) Introduction to biochemical toxicology. Apleton and Lange, NorwalkGoogle Scholar
  13. Gao YF, Feng JF, Zhu L (2015) Prediction of acute toxicity of cadmium and lead to zebrafish larvae by using a refined toxicokinetic–toxicodynamic model. Aquat Toxicol 169:37–45CrossRefGoogle Scholar
  14. Gao Y, Feng J, Han F, Zhu L (2016) Application of biotic ligand and toxicokinetic–toxicodynamic modeling to predict the accumulation and toxicity of metal mixtures to zebrafish larvae. Environ Pollut 213:16–29CrossRefGoogle Scholar
  15. Gao Y, Feng J, Wang C, Zhu L (2017) Modeling interactions and toxicity of Cu−Zn mixtures to zebrafish larvae. Ecotox Environ Safe 138:146–153CrossRefGoogle Scholar
  16. Ge Y, MacDonald D, Sauvé S, Hendershot W (2005) Modeling of Cd and Pb speciation in soil solutions by WinHumicV and NICA-Donnan model. Environ Modell Softw 20(3):353–359CrossRefGoogle Scholar
  17. Goussen B, Beauduin R, Dutilleul M, Buisset-Goussen A, Bonzom JM, Pery AR (2015) Energy-based modelling to assess effects of chemicals on Caenorhabditis elegans: a case study on uranium. Chemosphere 120:507–514CrossRefGoogle Scholar
  18. He E, Gestel C (2013) Toxicokinetics and toxicodynamics of nickel in Enchytraeus crypticus. Environ Toxicol Chem 32(8):1835–1841CrossRefGoogle Scholar
  19. Jager T, Albert C, Preuss TG, Ashauer R (2011) General unified threshold model of survival: a toxicokinetic-toxicodynamic framework for ecotoxicology. Environ Sci Technol 45:2529–2540CrossRefGoogle Scholar
  20. Jager T, Heugens EHW, Kooijman SALM (2006) Making sense of ecotoxicological test results: Towards application of process-based models. Ecotoxicol 15:305–314CrossRefGoogle Scholar
  21. Newman MC, McCloskey JT (2000) The individual tolerance concept is not the sole explanation for the probit dose-effect model. Environ Toxicol Chem 19:520–526Google Scholar
  22. Nyman AM, Schirmer K, Ashauer R (2012) Toxicokinetic-toxicodynamic modelling of survival of Gammarus pulex in multiple pulse exposures to propiconazole: model assumptions, calibration data requirements and predictive power. Ecotoxicol 21:1828–1840CrossRefGoogle Scholar
  23. Otero-Muras I, Franco-Uría A, Alonso AA, Balsa-Canto E (2010) Dynamic multi-compartmental modelling of metal bioaccumulation in fish: identifiability implications. Environ Modell Softw 25(3):344–353CrossRefGoogle Scholar
  24. Pianosi F, Beven K, Freer J, Hall JW, Rougier J, Stephenson DB, Wagener T (2016) Sensitivity analysis of environmental models: a systematic review with practical workflow. Environ Modell Softw 79:214–232CrossRefGoogle Scholar
  25. Reinert KH, Giddings JM, Judd L (2002) Effects analysis of time-varying or repeated exposures in aquatic ecological risk assessment of agrochemicals. Environ Toxicol Chem 21:1977–1992CrossRefGoogle Scholar
  26. R Core Team. 2014. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. URL
  27. Simkiss K, Taylor MG (1995) Transport of metals across membranes. In: Tessier A, & Turner DR (Eds.) Metal speciation and bioavailability in aquatic systems. Wiley, Chichester, pp 1–44Google Scholar
  28. Stadnicka J, Schirmer K, Ashauer R (2012) Predicting concentrations of organic chemicals in fish by using toxicokinetic models. Environ Sci Technol 46:3273–3280CrossRefGoogle Scholar
  29. Sunda WG, Huntsman SA (1998) Processes regulating cellular metal accumulation and physiological effects: phytoplankton as model systems. Sci Total Environ 219:165–181CrossRefGoogle Scholar
  30. Walcher S, Altschuh J, Schramm KW, Mayer S (2003) Estimates in deterministic fate modelling of environmental chemicals. Environ Modell Softw 18(10):929–936CrossRefGoogle Scholar
  31. Zhao Y, Newman MC (2007) The theory underlying dose-response models influences predictions for intermittent exposures. Environ Toxicol Chem 26:543–547CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Key Laboratory of Pollution Process and Environmental Criteria of Ministry of Education and Tianjin Key Laboratory of Environmental Remediation and Pollution Control, College of Environmental Science and Engineering, Nankai UniversityTianjinChina

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