Mathematical modeling and simulation in animal health. Part III: Using nonlinear mixed-effects to characterize and quantify variability in drug pharmacokinetics.

A common feature of human and veterinary pharmacokinetics is the importance of identifying and quantifying the key determinants of between-patient variability in drug disposition and effects. Some of these attributes are already well known to the field of human pharmacology such as bodyweight, age, or sex, while others are more specific to veterinary medicine, such as species, breed, and social behavior. Identification of these attributes has the potential to allow a better and more tailored use of therapeutic drugs both in companion and food-producing animals. Nonlinear mixed effects (NLME) have been purposely designed to characterize the sources of variability in drug disposition and response. The NLME approach can be used to explore the impact of population-associated variables on the relationship between drug administration, systemic exposure, and the levels of drug residues in tissues. The latter, while different from the method used by the US Food and Drug Administration for setting official withdrawal times (WT) can also be beneficial for estimating WT of approved animal drug products when used in an extralabel manner. Finally, NLME can also prove useful to optimize dosing schedules, or to analyze sparse data collected in situations where intensive blood collection is technically challenging, as in small animal species presenting limited blood volume such as poultry and fish.

Toxicological effects of pet food ingredients on canine bone marrow-derived mesenchymal stem cells and enterocyte-like cells.

We developed an in vitro method to assess pet food ingredients safety. Canine bone marrow-derived mesenchymal stem cells (BMSC) were differentiated into enterocyte-like cells (ELC) to assess toxicity in cells representing similar patterns of exposure in vivo. The toxicological profile of clove leave oil, eugenol, guanosine monophosphate (GMP), GMP + inosine monophosphate, sorbose, ginger root extract, cinnamon bark oil, cinnamaldehyde, thyme oil, thymol and citric acid was assessed in BMSC and ELC. The LC50 for GMP + inosine monophosphate was 59.42 ± 0.90 and 56.7 ± 3.5 mg ml(-1) for BMSC and ELC; 56.84 ± 0.95 and 53.66 ± 1.36 mg ml(-1) for GMP; 0.02 ± 0.001 and 1.25 ± 0.47 mg ml(-1) for citric acid; 0.077 ± 0.002 and 0.037 ± 0.01 mg ml(-1) for cinnamaldehyde; 0.002 ± 0.0001 and 0.002 ± 0.0008 mg ml(-1) for thymol; 0.080 ± 0.003 and 0.059 ± 0.001 mg ml(-1) for thyme oil; 0.111 ± 0.002 and 0.054 ± 0.01 mg ml(-1) for cinnamon bark oil; 0.119 ± 0.0004 and 0.099 ± 0.011 mg ml(-1) for clove leave oil; 0.04 ± 0.001 and 0.028 ± 0.002 mg ml(-1) for eugenol; 2.80 ± 0.11 and 1.75 ± 0.51 mg ml(-1) for ginger root extract; > 200 and 116.78 ± 7.35 mg ml(-1) for sorbose. Lemon grass oil was evaluated at 0.003-0.9 in BMSC and .03-0.9 mg ml(-1) in ELC and its mechanistic effect was investigated. The gene toxicology studies showed regulation of 61% genes in CYP450 pathway, 37% in cholestasis and 33% in immunotoxicity pathways for BMSC. For ELC, 80% for heat shock response, 69% for beta-oxidation and 65% for mitochondrial energy metabolism. In conclusion, these studies provide a baseline against which differential toxicity of dietary feed ingredients can be assessed in vitro for direct effects on canine cells and demonstrate differential toxicity in differentiated cells that represent gastrointestinal epithelial cells.

Mathematical modeling and simulation in animal health. Part I: Moving beyond pharmacokinetics.

The application of mathematical modeling to problems in animal health has a rich history in the form of pharmacokinetic modeling applied to problems in veterinary medicine. Advances in modeling and simulation beyond pharmacokinetics have the potential to streamline and speed-up drug research and development programs. To foster these goals, a series of manuscripts will be published with the following goals: (i) expand the application of modeling and simulation to issues in veterinary pharmacology; (ii) bridge the gap between the level of modeling and simulation practiced in human and veterinary pharmacology; (iii) explore how modeling and simulation concepts can be used to improve our understanding of common issues not readily addressed in human pharmacology (e.g. breed differences, tissue residue depletion, vast weight ranges among adults within a single species, interspecies differences, small animal species research where data collection is limited to sparse sampling, availability of different sampling matrices); and (iv) describe how quantitative pharmacology approaches could help understanding key pharmacokinetic and pharmacodynamic characteristics of a drug candidate, with the goal of providing explicit, reproducible, and predictive evidence for optimizing drug development plans, enabling critical decision making, and eventually bringing safe and effective medicines to patients. This study introduces these concepts and introduces new approaches to modeling and simulation as well as clearly articulate basic assumptions and good practices. The driving force behind these activities is to create predictive models that are based on solid physiological and pharmacological principles as well as adhering to the limitations that are fundamental to applying mathematical and statistical models to biological systems.

Mathematical modeling and simulation in animal health - Part II: principles, methods, applications, and value of physiologically based pharmacokinetic modeling in veterinary medicine and food safety assessment.

This review provides a tutorial for individuals interested in quantitative veterinary pharmacology and toxicology and offers a basis for establishing guidelines for physiologically based pharmacokinetic (PBPK) model development and application in veterinary medicine. This is important as the application of PBPK modeling in veterinary medicine has evolved over the past two decades. PBPK models can be used to predict drug tissue residues and withdrawal times in food-producing animals, to estimate chemical concentrations at the site of action and target organ toxicity to aid risk assessment of environmental contaminants and/or drugs in both domestic animals and wildlife, as well as to help design therapeutic regimens for veterinary drugs. This review provides a comprehensive summary of PBPK modeling principles, model development methodology, and the current applications in veterinary medicine, with a focus on predictions of drug tissue residues and withdrawal times in food-producing animals. The advantages and disadvantages of PBPK modeling compared to other pharmacokinetic modeling approaches (i.e., classical compartmental/noncompartmental modeling, nonlinear mixed-effects modeling, and interspecies allometric scaling) are further presented. The review finally discusses contemporary challenges and our perspectives on model documentation, evaluation criteria, quality improvement, and offers solutions to increase model acceptance and applications in veterinary pharmacology and toxicology.

Pharmacokinetics and pharmacodynamics of gamithromycin in pulmonary epithelial lining fluid in naturally occurring bovine respiratory disease in multisource commingled feedlot cattle.

The objectives of this study were to determine (i) whether an association exists between individual pharmacokinetic parameters and treatment outcome when feeder cattle were diagnosed with bovine respiratory disease (BRD) and treated with gamithromycin (Zactran(®) ) at the label dose and (ii) whether there was a stronger association between treatment outcome and gamithromycin concentration in plasma or in the pulmonary epithelial lining fluid (PELF) effect compartment. The study design was a prospective, blinded, randomized clinical trial utilizing three groups of 60 (362-592 lb) steers/bulls randomly allocated within origin to sham injection or gamithromycin mass medication. Cattle were evaluated daily for signs of BRD by a veterinarian blinded to treatment. Animals meeting the BRD case definition were enrolled and allocated to a sample collection scheme consisting of samples for bacterial isolation (bronchoalveolar lavage fluid and nasopharyngeal swabs) and gamithromycin concentration determination (PELF and plasma). Gamithromycin susceptibility of M. haemolytica (n = 287) and P. multocida (n = 257) were determined using broth microdilution with frozen panels containing gamithromycin at concentrations from 0.03 to 16 µg/mL. A two-compartment plasma pharmacokinetic model with an additional compartment for gamithromycin in PELF was developed using rich data sets from published and unpublished studies. The sparse data from our study were then fit to this model using nonlinear mixed effects modeling to estimate individual parameter values. The resulting parameter estimates were used to simulate full time-concentration profiles for each animal in this study. These profiles were analyzed using noncompartmental methods so that PK/PD indices (AUC24 /MIC, AUC∞ /MIC, CMAX /MIC) could be calculated for plasma and PELF (also T>MIC) for each individual. The calculated PK/PD indices were indicative that for both M. haemolytica and P. multocida a higher drug exposure in terms of concentration, and duration of exposure relative to the MIC of the target pathogen, was favorable to a successful case outcome. A significant association was found between treatment success and PELF AUC0-24 /MIC for P. multocida. The calves in this study demonstrated an increased clearance and volume of distribution in plasma as compared to the healthy calves in two previously published reports. Ultimately, the findings from this study indicate that higher PK/PD indices were predictive of positive treatment outcomes.

Interspecies allometric meta-analysis of the comparative pharmacokinetics of 85 drugs across veterinary and laboratory animal species.

Allometric scaling is widely used for the determination of first dosage regimen and the interpolation or extrapolation of pharmacokinetic parameters across many animal species during drug development. In this article, 85 drugs used in veterinary medicine obtained from the Food Animal Residue Avoidance Databank database were selected for allometric scaling analysis. Outlier species were identified by statistical methods. The results showed that 77% and 88% of drugs displayed significant correlations between total systemic clearance (CL) and volume of distribution at steady status (Vss) vs. body weight (P < 0.05) on a log-log scale, respectively. The distribution of the allometric exponent b for CL and Vss displays approximate normal distribution, with means (0.87 and 0.99) and standard deviations (0.143 and 0.157) for CL and Vss, respectively. Twelve drugs were identified to have at least one outlier species for CL and ten drugs for Vss. The human CL and Vss were predicted for selected drugs by the obtained allometric equations. The predicted CL and Vss were within a threefold error compared to observed values, except the predicted CL values for antipyrine, warfarin and diazepam. The results can be used to estimate cross-species pharmacokinetic profiles for predicting drug dosages in veterinary species, and to identify those species for which interpolation or extrapolation of pharmacokinetics properties may be problematic.

Prediction of formulation effects on dermal absorption of topically applied ectoparasiticides dosed in vitro on canine and porcine skin using a mixture-adjusted quantitative structure permeability relationship.

Topical application of ectoparasiticides for flea and tick control is a major focus for product development in animal health. The objective of this work was to develop a quantitative structure permeability relationship (QSPeR) model sensitive to formulation effects for predicting absorption and skin deposition of five topically applied drugs administered in six vehicle combinations to porcine and canine skin in vitro. Saturated solutions (20 µL) of (14) C-labeled demiditraz, fipronil, permethrin, imidacloprid, or sisapronil were administered in single or binary (50:50 v/v) combinations of water, ethanol, and transcutol (6 formulations, n = 4-5 replicates per treatment) nonoccluded to 0.64 cm(2) disks of dermatomed pig or dog skin mounted in flow-through diffusion cells. Perfusate flux over 24 h and skin deposition at termination were determined. Permeability (logKp), absorption, and penetration endpoints were modeled using a four-term Abrahams and Martin (hydrogen-bond donor acidity and basicity, dipolarity/polarizability, and excess molar refractivity) linear free energy QSPeR equation with a mixture factor added to compensate for formulation ingredient interactions. Goodness of fit was judged by r(2) , cross-validation coefficient, coefficients (q(2) s), and Williams Plot to visualize the applicability domain. Formulation composition was the primary determinant of permeation. Compounds generally penetrated dog skin better than porcine skin. The vast majority of permeated penetrant was deposited within the dosed skin relative to transdermal flux, an attribute for ectoparasiticides. The best QSPeR logKp model for pig skin permeation (r(2) = 0.86, q(2) s = 0.85) included log octanol/water partition coefficient as the mixture factor, while for dogs (r(2) = 0.91, q(2) s = 0.90), it was log water solubility. These studies clearly showed that the permeation of topical ectoparasiticides could be well predicted using QSPeR models that account for both the physical-chemical properties of the penetrant and formulation components.

Use of population pharmacokinetic modeling and Monte Carlo simulation to capture individual animal variability in the prediction of flunixin withdrawal times in cattle.

The objective of this study was to develop a population pharmacokinetic (PK) model and predict tissue residues and the withdrawal interval (WDI) of flunixin in cattle. Data were pooled from published PK studies in which flunixin was administered through various dosage regimens to diverse populations of cattle. A set of liver data used to establish the regulatory label withdrawal time (WDT) also were used in this study. Compartmental models with first-order absorption and elimination were fitted to plasma and liver concentrations by a population PK modeling approach. Monte Carlo simulations were performed with the population mean and variabilities of PK parameters to predict liver concentrations of flunixin. The PK of flunixin was described best by a 3-compartment model with an extra liver compartment. The WDI estimated in this study with liver data only was the same as the label WDT. However, a longer WDI was estimated when both plasma and liver data were included in the population PK model. This study questions the use of small groups of healthy animals to determine WDTs for drugs intended for administration to large diverse populations. This may warrant a reevaluation of the current procedure for establishing WDT to prevent violative residues of flunixin.

Plasma pharmacokinetics and milk residues of flunixin and 5-hydroxy flunixin following different routes of administration in dairy cattle.

The objective of this study was to determine if the plasma pharmacokinetics and milk elimination of flunixin (FLU) and 5-hydroxy flunixin (5OH) differ following intramuscular and subcutaneous injection of FLU compared with intravenous injection. Twelve lactating Holstein cows were used in a randomized crossover design study. Cows were organized into 2 groups based on milk production (<20 or >30 kg of milk/d). All cattle were administered 2 doses of 1.1mg of FLU/kg at 12-h intervals by intravenous, intramuscular, and subcutaneous injections. The washout period between routes of administration was 7d. Blood samples were collected from the jugular vein before FLU administration and at various time points up to 36 h after the first dose of FLU. Composite milk samples were collected before FLU administration and twice daily for 5d after the first dose of FLU. Samples were analyzed by ultra-HPLC with mass spectrometric detection. For FLU plasma samples, a difference in terminal half-life was observed among routes of administration. Harmonic mean terminal half-lives for FLU were 3.42, 4.48, and 5.39 h for intravenous, intramuscular, and subcutaneous injection, respectively. The mean bioavailability following intramuscular and subcutaneous dosing was 84.5 and 104.2%, respectively. The decrease in 5OH milk concentration versus time after last dose was analyzed with the nonlinear mixed effects modeling approach and indicated that both the route of administration and rate of milk production were significant covariates. The number of milk samples greater than the tolerance limit for each route of administration was also compared at each time point for statistical significance. Forty-eight hours after the first dose, 5OH milk concentrations were undetectable in all intravenously injected cows; however, one intramuscularly injected and one subcutaneously injected cow had measurable concentrations. These cows had 5OH concentrations above the tolerance limit at the 36-h withdrawal time. The high number of FLU residues identified in cull dairy cows by the United States Department of Agriculture Food Safety Inspection Service is likely related to administration of the drug by an unapproved route. Cattle that received FLU by the approved (intravenous) route consistently eliminated the drug before the approved withdrawal times; however, residues can persist beyond these approved times following intramuscular or subcutaneous administration. Cows producing less than 20 kg of milk/d had altered FLU milk clearance, which may also contribute to violative FLU residues.

Development of a physiologically based pharmacokinetic model to predict tulathromycin distribution in goats.

Physiologically based pharmacokinetic (PBPK) models, which incorporate species- and chemical-specific parameters, could be useful tools for extrapolating withdrawal times for drugs across species and doses. The objective of this research was to develop a PBPK model for goats to simulate the pharmacokinetics of tulathromycin, a macrolide antibiotic effective for treating respiratory infections. Model compartments included plasma, lung, liver, muscle, adipose tissue, kidney, and remaining poorly and richly perfused tissues. Tulathromycin was assumed to be 50% protein bound in plasma with first-order clearance. Literature values were compiled for physiological parameters, partition coefficients were estimated from tissue:plasma ratios of AUC, and the remaining model parameters were estimated by comparison against the experimental data. Three separate model structures were compared with plasma and tissue concentrations of tulathromycin in market age goats administered 2.5 mg/kg tulathromycin subcutaneously. The best simulation was achieved with a diffusion-limited PBPK model and absorption from a two-compartment injection site, which allowed for low persistent concentrations at the injection site and slower depletion in the tissues than the plasma as observed with the experimental data. The model with age-appropriate physiological parameters also predicted plasma concentrations in juvenile goats administered tulathromycin subcutaneously. The developed model and compilation of physiological parameters for goats provide initial tools that can be used as a basis for predicting withdrawal times of drugs in this minor species.

Tulathromycin assay validation and tissue residues after single and multiple subcutaneous injections in domestic goats (Capra aegagrus hircus).

Tulathromycin is a macrolide antimicrobial labeled for treatment of bacterial pneumonia in cattle and swine. The purpose of the present research was to evaluate tissue concentrations of tulathromycin in the caprine species. A tandem mass spectrometry regulatory analytical method that detects the common fragment of tulathromycin in cattle and swine was validated with goat tissues. The method was used to study tulathromycin depletion in goat tissues (liver, kidney, muscle, fat, injection site, and lung) over time. In two different studies, six juvenile and 25 market-age goats received a single injection of 2.5 mg/kg of tulathromycin subcutaneously; in a third study, 18 juvenile goats were treated with 2.5, 7.5, or 12.5 mg/kg tulathromycin weekly with three subcutaneous injections. Mean tulathromycin tissue concentrations were highest at injection site samples in all studies and all doses. Lung tissue concentrations were greatest at day 5 in market-age goats while in the multi-dose animals concentrations demonstrated dose-dependent increases. Concentrations were below limit of quantification in injection site and lung by day 18 and in liver, kidney, muscle, and fat at all time points. This study demonstrated that tissue levels in goats are very similar to those seen in swine and cattle.

Pharmacokinetics of tulathromycin after single and multiple subcutaneous injections in domestic goats (Capra aegagrus hircus).

Tulathromycin, a novel triamilide in the macrolide class, is labeled for treatment of bacterial pneumonia in cattle and swine. This manuscript evaluates pharmacokinetics of tulathromycin in goats. In two different studies, six juvenile and ten market-age goats received a single injection of 2.5 mg/kg of tulathromycin subcutaneously; in a third study, 18 juvenile goats were treated with 2.5, 7.5, or 12.5 mg/kg tulathromycin weekly with three subcutaneous injections. Pharmacokinetic parameters estimated from the plasma concentrations from single injections were similar between the two groups of goats and to previously reported parameters in cattle and swine. Mean terminal half-lives were 59.1 ± 7.6 and 61.2 ± 8.7 h for juvenile and market-age goats, respectively. In the multi-dose study, pharmacokinetic parameters estimated from plasma concentrations demonstrated significant differences at P < 0.05 among repeated injections but not among doses. Overall, pharmacokinetic parameters in goats are similar to those reported in cattle and swine, and tulathromycin may prove a useful drug for treating respiratory disease in goats.

A physiologically based pharmacokinetic model linking plasma protein binding interactions with drug disposition.

Combination drug therapy increases the chance for an adverse drug reactions due to drug-drug interactions. Altered disposition for sulfamethazine (SMZ) when concurrently administered with flunixin meglumine (FLU) in swine could lead to increased tissue residues. There is a need for a pharmacokinetic modeling technique that can predict the consequences of possible drug interactions. A physiologically based pharmacokinetic model was developed that links plasma protein binding interactions to drug disposition for SMZ and FLU in swine. The model predicted a sustained decrease in total drug and a temporary increase in free drug concentration. An in vivo study confirmed the presence of a drug interaction. Neither the model nor the in vivo study revealed clinically significant changes that alter tissue disposition. This novel linkage approach has use in the prediction of the clinical impact of plasma protein binding interactions. Ultimately it could be used in the design of dosing regimens and in the protection of the food supply through prediction and minimization of tissue residues.

Prediction of dermal absorption from complex chemical mixtures: incorporation of vehicle effects and interactions into a QSPR framework.

Significant progress has been made on predicting dermal absorption/penetration of topically applied compounds by developing QSPR models based on linear free energy relations (LFER). However, all of these efforts have employed compounds applied to the skin in aqueous or single solvent systems, a dosing scenario that does not mimic occupational, environmental or pharmaceutical exposure. We have explored using hybrid QSPR equations describing individual compound penetration based on the molecular descriptors for the compound modified by a mixture factor (MF) which accounts for the physicochemical properties of the vehicle/mixture components. The MF is calculated based on percentage composition of the vehicle/mixture components and physical chemical properties selected using principal components analysis. This model has been applied to 12 different compounds in 24 mixtures for a total of 288 treatment combinations obtained from flow-through porcine skin diffusion cells and in an additional dataset of 10 of the same compounds in five mixtures for a total of 50 treatment combinations in the ex vivo isolated perfused porcine skin flap. The use of the MF in combination with a classic LFER based on penetrant properties significantly improved the ability to predict dermal absorption of compounds dosed in complex chemical mixtures.

A system coefficient approach for quantitative assessment of the solvent effects on membrane absorption from chemical mixtures.

A system coefficient approach is proposed for quantitative assessment of the solvent effects on membrane absorption from chemical mixtures. The complicated molecular interactions are dissected into basic molecular interaction forces via Abraham's linear solvation energy relationship (LSER). The molecular interaction strengths of a chemical are represented by a set of solute descriptors, while those of a membrane/chemical mixture system are represented by a set of system coefficients. The system coefficients can be determined by using a set of probe compounds with known solute descriptors. Polydimethylsiloxane (PDMS) membrane-coated fibres and 32 probe compounds were used to demonstrate the proposed approach. When a solvent was added into the chemical mixture, the system coefficients were altered and detected by the system coefficient approach. The system coefficients of the PDMS/water system were (0.09, 0.49, -1.11, -2.36, -3.78, 3.50). When 25% ethanol was added into the PDMS/water system, the system coefficients were altered significantly (0.38, 0.41, -1.18, -2.07, -3.40, 2.81); and the solvent effect was quantitatively described by the changes in the system coefficients (0.29, -0.08, -0.07, 0.29, 0.38, -0.69). The LSER model adequately described the experimental data with a correlation coefficient (r(2)) of 0.995 and F-value of 1056 with p-value less than 0.0001.

Biocorona formation on gold nanoparticles modulates human proximal tubule kidney cell uptake, cytotoxicity and gene expression.

Gold nanoparticles (AuNP) adsorb macromolecules to form a protein corona (PC) after systemic delivery, to which the kidney as the primary excretory organ is constantly exposed. The role of the PC on AuNP cell uptake and toxicity was investigated in vitro in human proximal tubule cells (HPTC) using 40 and 80nm branched polyethylenimine (BPEI), lipoic acid (LA) and polyethylene glycol (PEG) coated AuNP with or without (bare) PCs composed of human plasma (HP) or human serum albumin (HSA) for 0.25 to 24h. Time-dependent intracellular uptake, assessed by ICP-MS showed PC modulated cell uptake and cytotoxicity; with bare 40nm BPEI-AuNP showing the greatest responses. All AuNP showed minimal to no cytokine release. At the nontoxic dose, 40nm bare BPEI-AuNP significantly modified gene expression related to immunotoxicity, steatosis, and mitochondrial metabolism; while at the high dose, pathways of DNA damage and repair, apoptosis, fatty acid metabolism and heat shock response were modulated. HP corona BPEI-AuNP response was comparable to control. These studies clearly showed reduced uptake and cytotoxicity, as well as differentiated gene expression of AuNP with PCs, questioning the utility of in vitro studies using bare NP to assess in vivo effects. Significantly, only cationic bare BPEI-AuNP had HPTC uptake or cytotoxicity suggesting the relative safety of PEG and LA-AuNP as nanomedicine constructs.

A physiologically based pharmacokinetic model of organophosphate dermal absorption.

The rate and extent of dermal absorption are important in the analysis of risk from dermal exposure to toxic chemicals and for the development of topically applied drugs, barriers, insect repellents, and cosmetics. In vitro flow-through cells offer a convenient method for the study of dermal absorption that is relevant to the initial processes of dermal absorption. This study describes a physiologically based pharmacokinetic (PBPK) model developed to simulate the absorption of organophosphate pesticides, such as parathion, fenthion, and methyl parathion through porcine skin with flow-through cells. Parameters related to the structure of the stratum corneum and solvent evaporation rates were independently estimated. Three parameters were optimized based on experimental dermal absorption data, including solvent evaporation rate, diffusivity, and a mass transfer factor. Diffusion cell studies were conducted to validate the model under a variety of conditions, including different dose ranges (6.3-106.9 microg/cm2 for parathion; 0.8-23.6 microg/cm2 for fenthion; 1.6-39.3 microg/cm2 for methyl parathion), different solvents (ethanol, 2-propanol and acetone), different solvent volumes (5-120 microl for ethanol; 20-80 microl for 2-propanol and acetone), occlusion versus open to atmosphere dosing, and corneocyte removal by tape-stripping. The study demonstrated the utility of PBPK models for studying dermal absorption, which can be useful as explanatory and predictive tools that may be used for in silico hypotheses generation and limited hypotheses testing. The similarity between the overall shapes of the experimental and model-predicted flux/time curves and the successful simulation of altered system conditions for this series of small, lipophilic compounds indicated that the absorption processes that were described in the model successfully simulated important aspects of dermal absorption in flow-through cells. These data have direct relevance to topical organophosphate pesticide risk assessments.