Toxicokinetic-toxicodynamic (TK-TD) models simulate the processes that lead to toxicity at the level of organisms over time. These dynamic simulation models quantify toxicity, but more importantly they also provide a conceptual framework to better understand the causes for variability in different species' sensitivity to the same compound as well as causes for different toxicity of different compounds to the same species. Thus TK-TD models bring advantages for very diverse ecotoxicological questions as they can address two major challenges: the large number of species that are potentially affected and the large number of chemicals of concern. The first important benefit of TK-TD models is the role that they can play to formalize established knowledge about toxicity of compounds, sensitivity of organisms, organism recovery times and carry-over toxicity. The second important aspect of TK-TD models is their ability to simulate temporal aspects of toxicity which makes them excellent extrapolation tools for risk assessment of fluctuating or pulsed exposures to pollutants.
(link at journal) or (download here)

Why do some individuals survive after exposure to chemicals while others die? Either, the tolerance threshold is distributed among the individuals in a population, and its exceedance leads to certain death, or all individuals share the same threshold above which death occurs stochastically. The previously published General Unified Threshold model of Survival (GUTS) established a mathematical relationship between the two assumptions. According to this model stochastic death would result in systematically faster compensation and damage repair mechanisms than individual tolerance. Thus, we face a circular conclusion dilemma because inference about the death mechanism is inherently linked to the speed of damage recovery. We provide empirical evidence that the stochastic death model consistently infers much faster toxicodynamic recovery than the individual tolerance model. Survival data can be explained by either, slower damage recovery and a wider individual tolerance distribution, or faster damage recovery paired with a narrow tolerance distribution. The toxicodynamic model parameters exhibited meaningful patterns in chemical space, which is why we suggest toxicodynamic model parameters as novel phenotypic anchors for in vitro to in vivo toxicity extrapolation. GUTS appears to be a promising refinement of traditional survival curve analysis and dose response models. (Published in Environmental Science & Technology, open access)

We found that toxicodynamic parameters cluster according to chemical class. Clustering of toxicodynamic parameters according to chemical MOA is more pronounced for GUTS-IT (panels C, D) than for GUTS-SD (panels A, B). (A) Parameters z and k_r in GUTS-SD, (B) Parameters k_r and z in GUTS-SD, (C) Parameters α and β in GUTS-IT, (D) Parameters k_r and α in GUTS-IT. Green squares: baseline toxicity, blue hexagons: uncoupling of oxidative phosphorylation, orange triangles: AChE inhibition (carbamate), red circles: AChE inhibition (organophosphates), purple diamonds: reactive toxicity.

This could have several applications: First, analyzing survival data in combination with toxicokinetics could indicate the mode of action. Second, it might be possible to predict the toxicity of untested chemicals of a known mode of action  by reading GUTS parameters from this figure and combining them with toxicokinetics to calculate a toxicity estimate.
Third, we suggest toxicodynamic parameters as novel phenotypic anchors for in vitro to in vivo toxicity extrapolation. Toxicity extrapolation from in vitro to in vivo systems should aim at predicting TK-TD model parameters on the organism level as they have a biological interpretation and appear to reflect the biochemical mechanisms of toxicity. For the same reasons TK-TD parameters may be potentially powerful end points for novel Quantitative Structure Activity Relationships. (read more: Environmental Science & Technology, open access)

This scheme illustrates the relation of different conceptual models and terms. Toxicokinetic-toxicodynamic models are quantitative models for those entities and processes that make up the Adverse Outcome Pathways.

Adverse Outcome Pathways were proposed  as a conceptual framework for risk assessment of chemicals (Ankley G, et al. (2010): Adverse outcome pathways: A conceptual framework to support ecotoxicology research and risk assessment. Environmental Toxicology and Chemistry 29(3), 730-741). (link to journal)

"A method to predict and understand fish survival under dynamic chemical stress using standard ecotoxicity data." Environmental Toxicology & Chemistry (link at ET&C, open access)

We present a method to predict fish survival under exposure to fluctuating concentrations and repeated pulses of a chemical stressor. The method is based on toxicokinetic-toxicodynamic modeling using the general unified threshold model of survival (GUTS) and calibrated using raw data from standard fish acute toxicity tests. The model was validated by predicting fry survival in a fish early life stage test. Application of the model was demonstrated by using Forum for Co-ordination of Pesticide Fate Models and Their Use surface water (FOCUS-SW) exposure patterns as model input and predicting the survival of fish over 485 d. Exposure patterns were also multiplied by factors of five and 10 to achieve higher exposure concentrations for fish survival predictions. Furthermore, the authors quantified how far the exposure profiles were below the onset of mortality by finding the corresponding exposure multiplication factor for each scenario. The authors calculated organism recovery times as additional characteristic of toxicity as well as number of peaks, interval length between peaks, and mean duration as additional characteristics of the exposure pattern. The authors also calculated which of the exposure patterns had the smallest and largest inherent potential toxicity. Sensitivity of the model to parameter changes depends on the exposure pattern and differs between GUTS individual tolerance and GUTS stochastic death. Possible uses of the additional information gained from modeling to inform risk assessment are discussed.

Jager T, Albert C, Preuss TG, Ashauer R (2011): General unified threshold model of survival - a toxicokinetic-toxicodynamic framework for ecotoxicology. Environmental Science and Technology, 45(7), 2529-2540. (link at journal) or (download here)

Toxicokinetic-toxicodynamic models (TKTD models) simulate the time-course of processes leading to toxic effects on organisms. Even for an apparently simple endpoint as survival, a large number of very different TKTD approaches exist. These differ in their underlying hypotheses and assumptions, although often the assumptions are not explicitly stated. Thus, our first objective was to illuminate the underlying assumptions (individual tolerance or stochastic death, speed of toxicodynamic damage recovery, threshold distribution) of various existing modeling approaches for survival and show how they relate to each other (e.g., critical body residue, critical target occupation, damage assessment, DEBtox survival, threshold damage). Our second objective was to develop a general unified threshold model for survival (GUTS), from which a large range of existing models can be derived as special cases. Specific assumptions to arrive at these special cases are made and explained. Finally, we illustrate how special cases of GUTS can be fitted to survival data. We envision that GUTS will help increase the application of TKTD models in ecotoxicological research as well as environmental risk assessment of chemicals. It unifies a wide range of previously unrelated approaches, clarifies their underlying assumptions, and facilitates further improvement in the modeling of survival under chemical stress.