environmental 
 regulations require comprehensive testing and risk assessment before 
 a chemical can be approved for use . in ecological risk assessment 
 of chemicals in water , fish play a very important role , being the 
 only vertebrate representative of freshwater systems .
quantification of chemical toxicity is generally based 
 on measurements of external exposure ; however , in order to understand , 
 interpret , and extrapolate toxicological effects , internal concentrations 
 of chemicals are more suitable .
for this reason , we 
 need to understand the relationship between the external and internal 
 concentration of chemicals in fish .
further , in silico ( model ) predictions of concentrations in fish ( i.e. , bioconcentration ) 
 could reduce or replace the need for in vivo ( animal ) 
 experiments which are costly and involve large numbers of fish .
toxicokinetics captures information about uptake , distribution , biotransformation , 
 and elimination of a toxicant in an organism , and is important in 
 risk assessment because a chemical needs to enter the organism and 
 reach the site of action in order to elicit an effect .
toxicokinetic models , when combined with toxicodynamic models , can 
 predict toxic effects on organisms .
in addition , they can be applied 
 to time - variable concentrations , a wide - range of chemicals , and to 
 extrapolation between different species and from in vitro to organism 
 scale .
provided that the necessary physiological parameters are known , 
 generally , two groups of tk models can be distinguished : models based 
 on a one - compartment assumption , according to which the chemical concentration 
 is the same throughout the organism , and multicompartment models , 
 which assume that chemical concentrations may differ among various 
 organs and tissues .
thus , the multicompartment approach , apart from 
 chemical uptake , biotransformation , and elimination , also describes 
 the movement of chemicals among various compartments that usually 
 represent different organs .
a comparison of toxicokinetic models 
 is required so that the most 
 suitable model can be chosen for a given question or condition .
a 
 comparison of different model structures was presented by landrum 
 and co - workers who described advantages 
 and disadvantages of equilibrium and kinetic models .
also , mackay 
 and fraser presented a review of bioaccumulation 
 models in which they compared the structure of empirical and mechanistic 
 approaches .
both these reviews compared different models based on 
 their underlying assumptions and model structures ; they did not compare 
 model predictions with measured data .
to our knowledge there is no 
 study using a wide scope of chemicals to test model performance on 
 independent data .
one - compartment models can be perceived 
 as simple , because they require only a few physiological parameters 
 and simulate one compartment only .
consequently they can only be used 
 to estimate a chemical concentration in the whole body of an organism . 
 on the other hand , a multicompartment model , e.g. , the physiologically 
 based toxicokinetic ( pbtk ) model developed for fish by nichols and 
 co - workers , may be viewed as more complex 
 than one - compartment models because it requires more physiological 
 data and simulates multiple compartments .
this model is generally 
 used when a chemical s concentration in a specific organ or 
 tissue plays an important role , e.g. , when the tissue or organ is 
 the dominant site of action .
this raises the question of whether the 
 pbtk model is a suitable model for predicting chemical concentration 
 in both organism tissues and whole body .
if so , another important 
 issue is whether it is worth using the more complex pbtk model with 
 many parameters to predict whole body chemical concentrations , or 
 whether the simpler one - compartment approach with only a few parameters 
 suffices .
thus , we aim to quantify model performance in predicting 
 fish internal concentrations in order to explain model differences 
 and to guide model selection . in the present study , we compared predictions 
 of one pbtk and two one - compartment models with measured concentrations 
 of organic chemicals in rainbow trout ( oncorhynchus mykiss ) and fathead minnow ( pimephales promelas ) , available 
 from the literature and databases . differences between models were 
 explained based on a sensitivity analysis of each approach .
two one - compartment models ( a and b ) and the pbtk model were used to simulate internal concentrations 
 of chemicals in fish . only respiratory uptake routes were considered 
 for both model types and they were described by mass - balance differential 
 equations .
chemical concentrations in water were used as model inputs 
 in order to calculate chemical concentrations in the whole fish body . 

tissue - specific concentrations were not taken into account , even for 
 the pbtk approach , because a comparison with one - compartment models 
 or whole body residue data is not meaningful .
measured 
 internal concentrations of organic chemicals in rainbow trout and 
 fathead minnow were found using the toxres database and by searching the peer - reviewed literature in the scopus 
 online database ( see details about search method in supporting information ) .
we used only references with exposure 
 via water and containing all required data , i.e. , fish weight , chemical 
 concentration in water , measured internal concentration , exposure 
 time , water temperature , and dissolved oxygen concentration in water 
 ( si tables s1s3 ) . in total , 
 measured internal concentrations for 23 different organic chemicals 
 ( 39 different chemical concentrations in water ) for rainbow trout 
 and for 24 different chemicals ( 68 different chemical concentrations 
 in water ) for the fathead minnow were taken from the toxres database 
 and studies identified in the scopus reference database ( tables s2s3 ) . for eight chemicals , internal 
 concentrations were available for both fish species .
internal 
 concentrations of phenol and 2,4,5-trichlorophenol in 
 the fathead minnow had already been used 
 in the original development of model b for calibration . for this reason , we show these two chemicals 
 in graphs ; however , we did not take them into consideration in the 
 statistical model evaluation . to our knowledge
, none of the other 
 internal concentrations presented have been used to calibrate any 
 of the models studied here .
we chose two one - compartment 
 approaches to predict internal concentrations of organic chemicals 
 in fish .
water 
 partition coefficients to quantify partitioning , and that they assume 
 that the chemical is homogeneously circulated within the organism . according to the one - compartment concept ,
this concept can be described with the following equation:1where cint(t ) is the internal chemical concentration ( amount  
 mass ) , cw(t ) is the chemical concentration in the water ( amount  
 volume ) , kin is the 
 uptake rate constant ( volume  mass  
 time ) , and kout is 
 the elimination rate constant ( time ) .
the 
 first model , herein referred to as the one - compartment model 
 a , was developed to predict the bioaccumulation processes 
 of organic chemicals in aquatic ecosystems with the aim of providing 
 data on site - specific toxicant concentrations and associated bioconcentration , 
 bioaccumulation , and biota  sediment accumulation factors in 
 organisms of aquatic food webs .
thus , 
 this model uses a small number of chemical , site - specific , and organism 
 parameters . according to arnot and gobas , it is possible to describe the exchange of nonionic organic chemicals 
 between the organism and its environment using a single equation for 
 various aquatic animals .
the second toxicokinetic approach , 
 referred to as one - compartment 
 model b , describes the accumulation kinetics of organic chemicals 
 as a function of the octanol  water partition coefficient ( kow ) , as well as the lipid content , weight , and 
 trophic level of the species .
this model 
 is driven by both species and chemical properties and its goal was 
 to explain differences in accumulation between various substances 
 and between species . according to hendriks et al .
, this model may be used in risk assessment , both for predicting 
 the equilibrium accumulation potential and for estimating nonequilibrium 
 kinetics . the 
 physiologically based multicompartment model for fish
was used and further developed 
 by incorporating a relationship between lipid fractions in the whole 
 body and the volume of fat compartment ( si eqs 
 s20s22 ) .
that relationship was suggested by nichols 
 and colleagues who assumed that the lipid 
 content of lean tissue ( consisting of all tissues except adipose fat ) 
 is independent of whole body lipid content .
support for this assumption 
 is provided by examining blood lipid content values reported by bertelsen 
 et al . for several fish species . in their 
 study , the extreme case was represented by channel catfish , which 
 tend to have a low whole - body lipid content . however , despite the 
  lean  nature of these animals , the blood lipid content 
 in catfish was essentially identical to that of trout .
thus we set 
 the lipid content of the lean tissues to the values derived by bertelsen 
 et al . while the volume of the adipose 
 fat compartment was adjusted to achieve the required whole body lipid 
 content .
note , that this simplification will not work for the extreme 
 situation when the whole body lipid content is lower than the assumed 
 lipid content of lean tissues . according to si 
 eq s22
the pbtk model for rainbow trout takes into account 
 five different compartments ( liver , kidney , fat , richly perfused tissues , 
 and poorly perfused tissues ) . due to the lack of data characterizing 
 the kidney , a four - compartment ( liver , fat
, richly perfused tissues , 
 and poorly perfused tissues ) pbtk model was created for the fathead 
 minnow .
the model assumes that all parts of the whole body belong 
 to one of the compartments , so the sum of the weight or volume of 
 all compartments is equal to the weight or volume of the whole organism . 

the amount of the chemical in each compartment is calculated based 
 on eq 2 , and the 
 total amount of the chemical can be used for calculating the internal 
 concentration in the whole fish body ( eq 3).2where ai(t ) is the amount of chemical in compartment i ( amount ) , qi is the arterial blood flow to compartment i ( volume 
  time ) , cart(t ) is the chemical concentration in arterial blood 
 ( amount  volume ) , cvi(t ) is the chemical concentration 
 in venous blood after compartment i ( amount  
 volume ) , and t is time.3where cint(t ) is the internal chemical concentration ( amount  
 mass ) , ai(t ) is the amount of chemical in 
 all compartments ( amount ) , and bw is the body wet weight ( mass ) .
detailed model descriptions and parameters for running the models 
 are presented in si . in this study , models were used as 
 calibrated by their original authors .
the one - compartment model a 
 was calibrated with measured field bioaccumulation factors , while 
 the one - compartment model b was calibrated with measured values of 
 uptake and elimination rates from laboratory experiments . in general
, 
 the pbtk model does not have to be calibrated as it is based on physiological 
 parameters and processes that can be measured directly .
however , some 
 parts of this model , e.g. , partition coefficients between tissues 
 and blood were calibrated separately by their original authors ( all 
 model equations and parameters are available in the si ) . in the model sensitivity 
 analysis , we took into account the impact of changes of four parameters 
 ( log kow , fish weight , water temperature , 
 and lipid content in fish ) on model predictions .
the minimum and maximum 
 values of the possible parameter range for each fish species were 
 taken from the literature .
the sensitivity analysis was carried out 
 by varying each parameter separately ( one at a time sensitivity analysis , 
 99 runs each ) .
all simulations and sensitivity 
 analyses were carried out using modelmaker software , version 4.0 , 
 developed and published by cherwell scientific ltd .
in addition , all calculations were also checked in mathcad 14 ( parametric 
 technology corporation , needham , ma ) . to evaluate and 
 compare the tk models , we have used the following three methods:(i)coefficient of determination ( r ) , here ,
refers to the square of the correlation 
 coefficient between measured and modeled values , and quantifies the 
 fraction of the variability in the data that is explained by the model 
 ( eq 4 , based on the focus guidance document ) .
the closer r is 
 to 1 , the better the model predicts the measured internal concentrations.4where
n is the total number 
 of paired observations ( p , o ) , pi is the i value of the predicted internal concentration ( with i = 1,2, ...
,n ) , oi is the i value 
 of the measured internal concentration ( with i = 
 1,2, ...
,n ) , p is the mean 
 of all values for predicted internal concentrations , and o is the mean of all values for measured internal concentrations.(ii)factor_10 ( or factor_5 , 
 see eq 5 ) quantifies internal chemical concentrations 
 that 
 are predicted with differences between measured and predicted values 
 equal to or smaller than 1 order of magnitude ( or five times ) .
this 
 can be seen as a practitioners view of model performance . if factor_10 
 or factor_5 is closer to 100% , the model is in better agreement with 
 the measured internal concentrations.5where oi is the i value of the measured 
 internal concentration ( with i = 1,2, ...
,n ) , pi is the i value of the predicted internal concentration 
 ( with i = 1,2, ...
,n ) , and n is the total number of paired observations ( p , o).(iii)general distance ( gd ) evaluates 
 the model accuracy ( i.e. , agreement with absolute values of measured 
 data ) .
this approach characterizes over- or under - prediction of measured 
 internal concentrations by the model by quantifying the distance between 
 measured and predicted values ( eqs 6 and 7 ) .
the closer gd is to 1 , the better is the model 
 in agreement with the measured internal concentrations.67where gdi is the i value of general distance ( with i = 1,2, ...
,n ) , oi is the i value of the measured 
 internal concentration ( with i = 1,2, ...
,n ) , pi is the i value of the predicted internal concentration 
 ( with i = 1,2, ...
,n ) , and n is the total number of paired observations ( p , o ) .
coefficient of determination ( r ) , here , refers to the square of the correlation 
 coefficient between measured and modeled values , and quantifies the 
 fraction of the variability in the data that is explained by the model 
 ( eq 4 , based on the focus guidance document ) .
the closer r is 
 to 1 , the better the model predicts the measured internal concentrations.4where
n is the total number 
 of paired observations ( p , o ) , pi is the i value of the predicted internal concentration ( with i = 1,2, ...
,n ) , oi is the i value 
 of the measured internal concentration ( with i = 
 1,2, ...
,n ) , p is the mean 
 of all values for predicted internal concentrations , and o is the mean of all values for measured internal concentrations .
factor_10 ( or factor_5 , 
 see eq 5 ) quantifies internal chemical concentrations 
 that 
 are predicted with differences between measured and predicted values 
 equal to or smaller than 1 order of magnitude ( or five times ) .
if factor_10 
 or factor_5 is closer to 100% , the model is in better agreement with 
 the measured internal concentrations.5where oi is the i value of the measured 
 internal concentration ( with i = 1,2, ...
,n ) , pi is the i value of the predicted internal concentration 
 ( with i = 1,2, ... ,n ) , and n is the total number of paired observations ( p , o ) .
general distance ( gd ) evaluates 
 the model accuracy ( i.e. , agreement with absolute values of measured 
 data ) .
this approach characterizes over- or under - prediction of measured 
 internal concentrations by the model by quantifying the distance between 
 measured and predicted values ( eqs 6 and 7 ) .
the closer gd is to 1 , the better is the model 
 in agreement with the measured internal concentrations.67where gdi is the i value of general distance ( with i = 1,2, ...
,n ) , oi is the i value of the measured 
 internal concentration ( with i = 1,2, ...
,n ) , pi is the i value of the predicted internal concentration 
 ( with i = 1,2, ...
,n ) , and n is the total number of paired observations ( p , o ) .
for rainbow trout , differences between 
 the tk models were small ( figure 1 and table 1 ) and r values for 
 the one - compartment models a and b and the pbtk model were 0.76 , 0.80 , 
 and 0.78 , respectively . however , overall , the distance between the 
 predicted and measured values of internal concentrations was the smallest 
 for the pbtk model ( gd was equal to 3.7 , 3.73 , and 3.54 for the one - compartment 
 a , the one - compartment b , and the pbtk model , respectively ) . comparison 
 of predicted internal concentrations of chemicals ( based 
 on one - compartment a [  ] , one - compartment b [ + ] , and pbtk [  ] 
 models ) and measured internal concentrations in ( 1.1 ) rainbow trout 
 and ( 1.2 ) fathead minnow ; circles :  outlier  chemicals 
 explained in text ; green : hexachlorobenzene ( see also black and white 
 graph in si figure s2 ) .
not all chemicals internal concentrations 
 in fathead minnow were predicted well using the tk models ( figure 1 ) .
for one internal concentration of hexachlorobenzene , 
 the pbtk model underestimated the measured value by a factor of over 
 20 ( predicted : 0.014 g / g , observed : 0.3014 g / g ) .
however , 
 in the same experiment , various chemical concentrations were taken 
 into account ( green points in figure 1 ) , 
 and only for the lowest concentration , the pbtk model underestimated 
 results by such a large margin .
other chemicals for which measured 
 internal concentrations were underestimated by the tk models by more 
 than a factor of 10 were phenol , 2,4,5-trichlorophenol ( for the pbtk 
 model ) , and 4-nitrophenol .
a possible explanation is that these are 
 polar organic compounds , whose partitioning behavior can not be well 
 characterized by means of octanol 
yet , an internal concentration of the polar 
 compound , 4-nitrophenol , was also predicted in rainbow trout ( si table s1 ) but without any underestimation 
 ( figure 1 ) .
it was noticed by call and co - workers that phenolic compounds are much more bioconcentrated 
 in fathead minnow than in rainbow trout . in general , the bioconcentration 
 of weak acids , such as 4-nitrophenol , can differ due to water ph .
however , in the experiments considered here , 
 the water ph values were not sufficiently different to account for 
 the difference in bioconcentration between species , but we can not 
 totally exclude its influence as ph might differ also at the actual 
 site of uptake ( e.g. , gill surface ) . in the present study , apart 
 from phenol , 2,4,5-trichlorophenol , 
 and 4-nitrophenol , only c12las ( sodium dodecylbenzene sulfonate )
can 
 be classified as a polar compound . however , unlike the above - mentioned 
 polar toxicants , measured internal concentrations of this chemical 
 were overestimated by all three tk approaches .
c12las is a surfactant , 
 which is amphiphilic in nature , with a polar head and a nonpolar chain , 
 and if the system is not constantly mixed , this chemical tends to 
 concentrate at interphases ( e.g. , water / air ; water / plastic ) . for this reason
, there are problems in estimating 
 how much c12las in water is available for an organism ( bioavailability ) , 
 which may result in very low measurements of internal concentrations 
 in comparison with apparent concentrations in water . for hexachlorocyclopentadiene , 
 internal concentrations
based on the octanol  water 
 partition coefficient of hexachlorocyclopentadiene ( log kow = 5.04 ; table s3 ) , this 
 chemical should bioconcentrate . according to epi suite ,
the calculated 
 bioconcentration factor ( bcf ) is equal to 3606 while with euses , a 
 bcf of 3800 was estimated ; however , experiments 
 carried out by podowski and colleagues have shown that this chemical is hardly bioconcentrated in fish , 
 likely due to biotransformation . according to spehar and co - workers
thus , predicting internal concentrations of hexachlorocyclopentadiene , 
 without taking its biotransformation into account , causes overestimation 
 by tk models . according to the gd ( table 1 ) for fathead 
 minnow , all three approaches overestimated internal concentrations 
 by more than 1 order of magnitude on average .
moreover , the correlations 
 of model predictions and data were lower than for rainbow trout ( r for the one - compartment a , the one - compartment 
 b , and the pbtk models were equal to 0.64 , 0.77 , and 0.73 , respectively ) . 

the difference in agreement between the modeled and measured data , 
 indicated by factor_10 ( equal to 6888% ) and gd ( 16.229 ) 
 methods , can be explained by the  outlier
 group of 
 chemicals ( described above ) which was included in the calculation 
 of both statistical methods .
not many chemicals belong to this  outlier  
 group ( which influences the factor_10 ) . for most of these ,
however , 
 tk models over- or underestimated measured internal concentrations 
 much more than by a factor of 10 ( which influences the gd ) . differences between results for rainbow trout and fathead minnow 
 can be caused by several factors .
first , different data sets were 
 used for each fish species . from the  outlier  group 
 of chemicals
( chemicals for which internal concentration was over- 
 or underestimated by more than a factor of 10discussed above ) 
 for the fathead minnow , only hexachlorobenzene and 4-nitrophenol were 
 also used in the tk models for rainbow trout . however , it was decided 
 not to compare predicted internal concentrations of 4-nitrophenol 
 in both fishes , due to the presumed impact of its polar nature and 
 water ph on bioavailability ( see fathead minnow section ) .
for the other chemicals from this group ( i.e. , phenol , 
 2,4,5-trichlorophenol , hexachlorocyclopentadiene , and c12las ) , no 
 data on internal concentrations in rainbow trout were available .
the 
 comparison of tk models was made for chemicals that were used in both 
 fishes ( tables s2 and s3 and figure 2 ) .
comparison of tk models : one - compartment a (  ) , 
 one - compartment 
 b ( + ) , and pbtk (  ) , for the same chemicals for rainbow trout 
 and fathead minnow ( 8 chemicals , 45 data points ) ; blue : results for 
 rainbow trout , green : results for fathead minnow ( see also black and 
 white graph in si figure s3 ) . according to figure 2 ,
results 
 demonstrate 
 a clear relationship between predicted and measured internal concentrations 
 for all models and for both fishes .
this indicates that the difference 
 between the statistical results for rainbow trout and fathead minnow 
 was caused mainly by the
however , 
 we noticed that both the values of the coefficients of determination 
 and the factor_5 are now much lower for rainbow trout than for fathead 
 minnow ( table 2 ) .
additionally , the gd between 
 predicted and measured internal concentrations increased for rainbow 
 trout in relation to gd for all chemicals in this species ( table 1 ) , while for fathead minnow , the gd is now much 
 lower than it was for all chemicals .
the difference between the results 
 for both fish species might be due to two main reasons .
the first 
 of them results from the fact that five ( out of 12 ) of the measured 
 internal concentrations used in rainbow trout came from the same study , and all measured internal concentrations taken 
 from this reference were underestimated by all tk models used .
the 
 second reason is that different exposure times were used in the experiments . 

generally , fathead minnow were not exposed to chemicals for short 
 durations ( the shortest exposure time : 28 days ; average : 32 days ) 
 compared to rainbow trout ( the shortest exposure time : < 3 h ; average : 
 70 days ) .
in addition , if steady - state conditions 
 occur , the difference between tk models might be smaller 
 than under non - steady - state conditions .
differences between tk model 
 predictions in relation to exposure times are shown in figure 3 .
model - based predictions differ during short - term 
 exposure ( shorter than 10 days , figure 3 ) more than during long - term exposure ( figure 3 and 3 ) .
this disparity between approaches 
 can be explained by a sensitivity analysis of the model . in figure 4 , the impact of log kow and lipid fractions on model performance is presented .
figure 4 shows that internal 
 concentration increases with an increase of the lipid fraction in 
 the organism , and that the difference between both one - compartment 
 models is very small .
in addition , according to these approaches , 
 chemical internal concentrations in rainbow trout after 4 days are 
 higher for low lipid fractions ( < 5% ) and lower for higher lipid 
 fractions than is the case in the pbtk model . however , after longer 
 exposure ( 400 days , figure 4 ) , the pbtk 
 model predicts lower internal concentrations than one - compartment 
 models for all lipid fractions simulated .
that observation might be 
 caused by reaching steady - state conditions with the pbtk model much 
 faster than with one - compartment models .
there is no or a smaller 
 difference between the pbtk model after 4 and 400 days than between 
 one - compartment models after 4 and 400 days .
for the parameter values 
 used in the sensitivity analysis , according to the pbtk model , the 
 steady - state conditions were almost reached within 4 days for rainbow 
 trout ( with lipid content below 5% ) . for fathead minnow ( figure 4 and 4 ) , the pbtk model 
 predicts lower internal concentrations than the one - compartment models 
 for all lipid fractions simulated ( at both time points , 4 and 400 
 days ) .
this observation results from achieving steady - state conditions 
 in fathead minnow earlier than in rainbow trout with all tk models , 
 which is due to different fish parameters and environmental conditions . 

generally , fathead minnow are smaller than rainbow trout and they 
 live in warmer water , which also influences the velocity of chemical 
 uptake and elimination processes .
in addition , after 400 days , according 
 to both one - compartment models , internal concentrations are almost 
 the same in rainbow trout and in fathead minnow ( for the same range 
 of lipid fraction ) while they differ during shorter exposure periods 
 ( i.e. , non - steady - state conditions ) .
the pbtk model predicts slightly 
 different internal concentrations in both fishes at both time points , 
 which is caused by different physiological parameters of both species . 

thus , during steady - state conditions , parameters such as body weight 
 or water temperature do not have an impact on predictions while during 
 shorter exposure periods they strongly influence results .
comparison 
 of toxicokinetic models depending on exposure time ; 
 3.1 : rainbow trout , 3.2 : fathead minnow . tk model predictions for rainbow trout and fathead minnow : 
 4.1 , 
 4.2 : internal concentrations for various lipid fractions ( after 4 
 d ) ; 4.3 , 4.4 : internal concentrations for various lipid fractions 
 ( after 400 d ) ; 4.5 , 4.6 : internal concentrations in both fish species 
 for various log kow ( after 4 d ) .
simulation 
 parameters : chemical concentration in inspired water : 100 g / l ; 
 log kow = 4.4 ; water temperature : 12.8 
 c for rainbow trout and 24.8 c for fathead minnow ; body 
 weight : 0.13 kg for rainbow trout and 0.00018 kg for fathead minnow ; 
 lipid fraction of body weight : 0.12 for rainbow trout and 0.05 for 
 fathead minnow .
lower internal concentrations of chemicals predicted 
 by the pbtk 
 model than by one - compartment models can be explained by the impact 
 of log kow on model performance . for rainbow 
 trout , after 4 days ( figure 4 ) , the pbtk 
 model generally predicts higher internal concentrations than the one - compartment 
 approaches , which is in agreement with figure 4 ( see values for the same log kow and 
 lipid fractions in both graphs ) .
however , during steady - state conditions , 
 the relationship between tk models in rainbow trout looked more like 
 that of the fathead minnow after 4 days ( where steady - state conditions 
 have almost already been reached , figure 4 ) . here ,
chemical internal concentrations are higher according to 
 the one - compartment models for the middle range of log kow values , while for low and high log kow , the pbtk model predicts higher internal concentrations 
 than the one - compartment approaches .
this is also caused by steady - state 
 conditions which are reached with the pbtk model earlier than with 
 the one - compartment models ( lower pbtk values in this case ) but which 
 are not achieved with any of the tk models at the time points used 
 here for chemicals with a high log kow ( lower one - compartment values in this case ) .
thus , for log kow equals 4.4 ( figure 44 ) , the pbtk model predicts lower 
 internal concentrations during steady - state conditions and higher 
 internal concentrations during non - steady - state conditions than the 
 one - compartment approaches .
overall , the internal concentration 
 increases faster over time 
 in simulations with the pbtk model , but eventually such concentrations 
 reach lower values at steady - state than is the case in simulations 
 with the one - compartment models .
this difference originates from different 
 elimination rate constants in the one - compartment models and from 
 the exchange coefficient between water and fish gills in the pbtk 
 model . in the pbtk model ,
the exchange coefficient between water and 
 fish gills is much higher than uptake and elimination rate constants 
 in the one - compartment approaches .
hence , the chemical is absorbed 
 very fast in the beginning in the pbtk model ; however , its final concentration 
 during steady - state conditions is also impacted by other limiting 
 factors ( such as partition coefficient between water and blood or 
 oxygen consumption rate which influences predicted gill uptake clearance  see si eqs s18 and s19 ) . according to one - compartment models ,
the concentration of a chemical 
 is the same in all tissues and organs ; however the pbtk model assumes 
 that chemical concentrations differ among various organs and tissues
. 
 in our study , based on the pbtk model , the rank order of concentrations 
 in tissues was the following : fat > kidney ( liver ) > liver ( kidney ) 
 > muscle > blood ( chemical concentrations in liver were higher 
 than 
 in kidney only at very short exposure time ) .
differences in the pattern 
 of chemical accumulation in each tissue depended on exposure time 
 and log kow of the chemical ( see si for more details ) .
organ - specific accumulation 
 might be important to understand toxicity pathways specific to target 
 sites located in only some organs as well as for food - chain bioaccumulation 
 if predators preferentially consume certain organs .
we compared how well 
 three different tk models predict internal 
 concentrations in different fish species ( rainbow trout and fathead 
 minnow ) and for different chemicals and concentrations in water ( 39 
 different organic chemicals , concentrations varying from 0.000038 
 to 26185 g / l ) .
all models tested predict at least 68% of the 
 measured internal concentrations in fish within 1 order of magnitude . 

in addition , the pbtk model , which predicts chemical concentrations 
 in the whole fish as well as in various tissues , outperformed the 
 one - compartment models with respect to simulating chemical concentrations 
 in the whole body ( at least 88% of internal concentrations were predicted 
 within 1 order of magnitude using the pbtk model ) .
like the one - compartment 
 approaches , this model could also be used to extrapolate to another 
 fish species without additional experiments .
however , it is important 
 to take model limitations into account , e.g. , in order to use these 
 models for polar narcotics , they should take lipid  water partition 
 coefficient into account since such chemicals tend to partition into 
 polar lipids ( of the membrane ) more than nonpolar compounds .
modeling of lipid  water partition coefficients was presented 
 by toropov and roy and by pola et al .
in addition , simulating internal concentrations 
 of chemicals which are quickly biotransformed ( i.e. , rate constant 
 of biotransformation at least in the same order of magnitude as elimination 
 rates ) in the organism requires adding biotransformation to the models 
 ( which usually requires additional experiments ) .
nichols et al . described procedures for adding in vitro biotransformation 
 data into the pbtk model and tested this incorporation of biotransformation 
 into the pbtk and one - compartment a models . according to their results , at very high rates of biotransformation , 
 the pbtk approach predicts a greater impact of biotransformation on 
 bioaccumulation than the one - compartment model a , which results from 
 the structures of both models .
in conclusion , this study shows 
 that the difference between tk 
 models is small and all approaches can successfully predict the internal 
 concentrations of many organic chemicals .
however , as the pbtk model 
 slightly outperformed one - compartment approaches , and can also be 
 used to predict chemical concentrations in tissues , we encourage efforts 
 to parameterize pbtk models for additional species . in addition , further 
 development of tk models ( e.g. , by adding biotransformation data or lipid  water partition coefficient for polar compounds ) 
 would improve all these models .
 quantification of chemical toxicity continues to be generally 
 based 
 on measured external concentrations . yet 
 , internal chemical concentrations 
 have been suggested to be a more suitable parameter . to better understand 
 the relationship between the external and internal concentrations 
 of chemicals in fish , and to quantify internal concentrations , we 
 compared three toxicokinetic ( tk ) models with each other and with 
 literature data of measured concentrations of 39 chemicals . 
 two one - compartment 
 models , together with the physiologically based toxicokinetic ( pbtk ) 
 model , in which we improved the treatment of lipids , were used to 
 predict concentrations of organic chemicals in two fish species : rainbow 
 trout ( oncorhynchus mykiss ) and fathead minnow ( pimephales promelas ) . 
 all models predicted the measured 
 internal concentrations in fish within 1 order of magnitude for at 
 least 68% of the chemicals . 
 furthermore , the pbtk model outperformed 
 the one - compartment models with respect to simulating chemical concentrations 
 in the whole body ( at least 88% of internal concentrations were predicted 
 within 1 order of magnitude using the pbtk model ) . 
 all the models 
 can be used to predict concentrations in different fish species without 
 additional experiments . however 
 , further development of tk models 
 is required for polar , ionizable , and easily biotransformed compounds . 
Introduction
Materials and Methods
Results and Discussion
Relevance for Risk Assessment