Toxicokinetics of Metals in Terrestrial Invertebrates: Making Things Straight with the One-Compartment Principle
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{"title"=>"Toxicokinetics of metals in terrestrial invertebrates:making things straight with the one-compartment principle", "type"=>"journal", "authors"=>[{"first_name"=>"Boris", "last_name"=>"Skip", "scopus_author_id"=>"6506115816"}, {"first_name"=>"Agnieszka J.", "last_name"=>"Bednarska", "scopus_author_id"=>"23033109400"}, {"first_name"=>"Ryszard", "last_name"=>"Laskowski", "scopus_author_id"=>"7007150967"}], "year"=>2014, "source"=>"PLoS ONE", "identifiers"=>{"doi"=>"10.1371/journal.pone.0108740", "sgr"=>"84907495399", "scopus"=>"2-s2.0-84907495399", "issn"=>"19326203", "pui"=>"600080001"}, "id"=>"25f364fc-58a6-3ccf-9efc-f418b3c1ba8f", "abstract"=>"In this analysis, we first performed a critical review of one-compartment models used to describe metal toxicokinetics in invertebrates and found mathematical or conceptual errors in almost all published studies. In some publications, the models used do not represent the exact solution of the underlying one-compartment differential equations; others use unrealistic assumptions about constant background metal concentration and/or zero metal concentration in uncontaminated medium. Herein we present exact solutions of two differential-equation models, one describing simple two-stage toxicokinetics (metal toxicokinetic follows the experimental phases: the uptake phase and the decontamination phase) and another that can be applied for more complex three-stage patterns (toxicokinetic pattern does not follow two phases determined by an experimenter). Using two case studies for carabids exposed via food, based on previously published data, we discuss and compare our models to those originally used to analyze the data. Our conclusion is that when metal toxicokinetic follows a one-compartment model, the exact solution of a set of differential equations should be used. The proposed models allow assimilation and elimination rates to change between toxicokinetic stages, and the three-stage model is flexible enough to fit patterns that are more complex than the classic two-stage model can handle.", "link"=>"http://www.mendeley.com/research/toxicokinetics-metals-terrestrial-invertebratesmaking-things-straight-onecompartment-principle", "reader_count"=>11, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>3, "Researcher"=>3, "Student > Ph. D. Student"=>3, "Student > Master"=>1, "Professor"=>1}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>3, "Researcher"=>3, "Student > Ph. D. Student"=>3, "Student > Master"=>1, "Professor"=>1}, "reader_count_by_subject_area"=>{"Unspecified"=>1, "Environmental Science"=>6, "Agricultural and Biological Sciences"=>1, "Physics and Astronomy"=>1, "Chemistry"=>2}, "reader_count_by_subdiscipline"=>{"Chemistry"=>{"Chemistry"=>2}, "Physics and Astronomy"=>{"Physics and Astronomy"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>1}, "Unspecified"=>{"Unspecified"=>1}, "Environmental Science"=>{"Environmental Science"=>6}}, "reader_count_by_country"=>{"Poland"=>3}, "group_count"=>2}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1697055"], "description"=>"<p>Symbols used in the article and the units of model parameters.</p>", "links"=>[], "tags"=>["metal toxicokinetic", "pattern", "phase", "solution", "background metal concentration", "model"], "article_id"=>1187272, "categories"=>["Biological Sciences"], "users"=>["Boris Skip", "Agnieszka J. Bednarska", "Ryszard Laskowski"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0108740.t001", "stats"=>{"downloads"=>0, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Symbols_used_in_the_article_and_the_units_of_model_parameters_/1187272", "title"=>"Symbols used in the article and the units of model parameters.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-09-30 02:50:34"}
  • {"files"=>["https://ndownloader.figshare.com/files/1697053"], "description"=>"<p>Two-stage toxicokinetic models fitted to mean Cd concentrations in the ground beetle <i>Poecilus cupreus</i> (data from Kramarz <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0108740#pone.0108740-Kramarz1\" target=\"_blank\">[2]</a>): a) model by Janssen at al. <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0108740#pone.0108740-Janssen1\" target=\"_blank\">[4]</a> with constant <i>C<sub>I0</sub></i> = 0.15 mg kg<sup>−1</sup> and <i>C<sub>Eu</sub></i> = 154.6 mg kg<sup>−1</sup>; b) model originally used by Kramarz <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0108740#pone.0108740-Kramarz1\" target=\"_blank\">[2]</a> with <i>C<sub>I0</sub></i> = 0.15 mg kg<sup>−1</sup> and <i>C<sub>Eu</sub></i> = 154.6 mg kg<sup>−1</sup>; c) exact-solution model (<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0108740#pone.0108740.e008\" target=\"_blank\">Eqs. 8</a> and <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0108740#pone.0108740.e009\" target=\"_blank\">9</a>) with the same uptake and elimination rates in both phases of the experiment, <i>C<sub>Eu</sub></i> = 154.6 mg kg<sup>−1</sup> and <i>C<sub>Ed</sub></i> = 0.92 mg kg<sup>−1</sup>; d) exact-solution model with different uptake and elimination rates in the first and second phases of the experiment, <i>C<sub>Eu</sub></i> = 154.6 mg kg<sup>−1</sup> and <i>C<sub>Ed</sub></i> = 0.92 mg kg<sup>−1</sup>. Vertical broken line indicates the day of changing to uncontaminated food (<i>t<sub>c</sub></i>).</p>", "links"=>[], "tags"=>["metal toxicokinetic", "pattern", "phase", "solution", "background metal concentration", "model"], "article_id"=>1187270, "categories"=>["Biological Sciences"], "users"=>["Boris Skip", "Agnieszka J. Bednarska", "Ryszard Laskowski"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0108740.g001", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Two_stage_toxicokinetic_models_/1187270", "title"=>"Two-stage toxicokinetic models.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-09-30 02:50:34"}
  • {"files"=>["https://ndownloader.figshare.com/files/1697056"], "description"=>"<p>Please refer to <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0108740#pone-0108740-t001\" target=\"_blank\">Table 1</a> for symbols description.</p><p>*- calculated value from estimated parameter a (metal accumulation rate) for the corresponding model.</p>#<p>- R<sup>2</sup> adjusted for degrees of freedom.</p>&<p>- bioaccumulation factor (BAF) calculated based on assimilation and elimination constants for the first stage of the one-compartment models (<i>k<sub>A1</sub>/k<sub>E1</sub></i>).</p>‡<p>- p value for the model.</p><p>Comparison of the four two-stage toxicokinetic models fitted to mean Cd concentrations in <i>Poecilus cupreus</i><a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0108740#pone.0108740-Kramarz1\" target=\"_blank\">[2]</a>; 95% confidence intervals in brackets.</p>", "links"=>[], "tags"=>["metal toxicokinetic", "pattern", "phase", "solution", "background metal concentration", "model"], "article_id"=>1187273, "categories"=>["Biological Sciences"], "users"=>["Boris Skip", "Agnieszka J. Bednarska", "Ryszard Laskowski"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0108740.t002", "stats"=>{"downloads"=>4, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_the_four_two_stage_toxicokinetic_models_fitted_to_mean_Cd_concentrations_in_Poecilus_cupreus_2_95_confidence_intervals_in_brackets_/1187273", "title"=>"Comparison of the four two-stage toxicokinetic models fitted to mean Cd concentrations in <i>Poecilus cupreus</i>[2]; 95% confidence intervals in brackets.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-09-30 02:50:34"}
  • {"files"=>["https://ndownloader.figshare.com/files/1697057"], "description"=>"<p>Parameters have been estimated based on geomean Ni concentrations; 95% confidence intervals in brackets. Please refer to <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0108740#pone-0108740-t001\" target=\"_blank\">Table 1</a> for symbol description.</p>†<p>- Asymptote – the semi-steady Ni concentration reached in the second stage of the toxicokinetics (cf. <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0108740#pone.0108740-Laskowski1\" target=\"_blank\">[17]</a>).</p>&<p>- Final concentration – the ultimate concentration reached during the decontamination phase (cf. <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0108740#pone.0108740-Laskowski1\" target=\"_blank\">[17]</a>).</p>#<p>- R<sup>2</sup> adjusted for degrees of freedom.</p>‡<p>- p value for the model.</p><p>Comparison of the three three-stage models of the complex nickel toxicokinetics in <i>Pterostichus oblongopunctatus</i><a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0108740#pone.0108740-Laskowski1\" target=\"_blank\">[17]</a>.</p>", "links"=>[], "tags"=>["metal toxicokinetic", "pattern", "phase", "solution", "background metal concentration", "model"], "article_id"=>1187274, "categories"=>["Biological Sciences"], "users"=>["Boris Skip", "Agnieszka J. Bednarska", "Ryszard Laskowski"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0108740.t003", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_the_three_three_stage_models_of_the_complex_nickel_toxicokinetics_in_Pterostichus_oblongopunctatus_17_/1187274", "title"=>"Comparison of the three three-stage models of the complex nickel toxicokinetics in <i>Pterostichus oblongopunctatus</i>[17].", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-09-30 02:50:34"}
  • {"files"=>["https://ndownloader.figshare.com/files/1697054"], "description"=>"<p>Three-stage toxicokinetic models fitted to geomean Ni concentrations in the ground beetle <i>Pterostichus oblongopunctatus</i>: a) model by Laskowski et al. <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0108740#pone.0108740-Laskowski1\" target=\"_blank\">[17]</a>; b) exact-solution model, case scenario with one uptake rate and two different elimination rates; c) exact-solution model with all assimilation and elimination rates stage-specific (<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0108740#pone.0108740.e015\" target=\"_blank\">Eqs. 15</a>–<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0108740#pone.0108740.e021\" target=\"_blank\">19</a>). Vertical broken line indicates the day of changing to uncontaminated food (<i>t<sub>c</sub></i>).</p>", "links"=>[], "tags"=>["metal toxicokinetic", "pattern", "phase", "solution", "background metal concentration", "model"], "article_id"=>1187271, "categories"=>["Biological Sciences"], "users"=>["Boris Skip", "Agnieszka J. Bednarska", "Ryszard Laskowski"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0108740.g002", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Three_stage_toxicokinetic_models_/1187271", "title"=>"Three-stage toxicokinetic models.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-09-30 02:50:34"}

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