Mathematical Analysisfor Teratogenic SensitivityRICHARD H. LUECKE,1 WALTER D. WOSILAIT,2 AND JOHN F. YOUNG3*1Department of Chemical Engineering, University of Missouri-Columbia, Columbia, Missouri 652112Department of Pharmacology, School of Medicine, University of Missouri-Columbia, Columbia, Missouri 652123Division of Biometry & Risk Assessment, National Center for Toxicological Research, Jefferson, Arkansas 72079

ABSTRACT A mathematical structure is de-scribed for determining teratogenic sensitivity or sus-ceptibility from analysis of malformation incidence,dose-response, and pharmacokinetic data obtainedduring pregnancy as a result of exposure to a terato-genic agent. From the dosage or exposure of labora-tory animals, embryonic and maternal concentrationsof the xenobiotic are calculated using a physiologicallybased pharmacokinetic (PBPK) model. Malformationsobserved in the progeny are linked to the PBPK-derivedtarget tissue concentrations with a model for thesensitivity calculated as a function of the embryonicage. The PBPK model for internal disposition of chemi-cals during pregnancy was developed previously. Thisreport focuses on the development of the mathematicalrelations for the sensitivity of the embryo and effectfunctions on different organs. The concentrations of axenobiotic calculated for the site of action or targettissue(s) in the embryo are weighted using both anonlinear dose-response curve and a sensitivity distribu-tion function that depends on the age or stage ofdevelopment of the embryo. This weighted ‘‘exposure’’of the target tissue is regressed with the number ofobserved malformations to quantify the parameters ofthe model. This approach lends itself to integration ofdiverse sources of experimental data, with hydroxyureadata taken from several sources in the literature as anexample. This sensitivity function obtained from labora-tory animal data serves as a vehicle for prediction andextrapolation to human pregnancy for the teratogenicpotential of a substance. Teratology 55:373–380, 1997.r 1997 Wiley-Liss, Inc.

INTRODUCTION

The occurrence of malformations in human newbornsis a family tragedy as well as an important societalissue. Such events can be inherited or result fromexposure of the mother and embryo to drugs, occupa-tional and environmental toxicants, or other ingestedsubstances during critical and sensitive periods ofdevelopment. Numerous studies with laboratory ani-mals have indicated that the sensitivity or susceptibil-ity to a teratogen of the various organs and tissues ofthe embryo/fetus changes with gestational age. Wilson(’73) brought together these concepts and stated gen-

eral principles, but quantitative mathematical relation-ships have not been developed. White et al. (’80) andYoung et al. (’97) further delineated these principlesinto a ‘‘critical window’’ concept of teratogenesis, whichrequired the chemical exposure to be above a criticalconcentration, for a critical duration, and during acritical gestational time for a malformation to be pro-duced.

The incidence rate for teratogenic events after expo-sure to a xenobiotic depends on the stock/strain/species,the gestational time at which the dose is given, the rateand sensitivity of embryonic development at that time,the size of the dose, the ability to repair damage fromthe dose at that time, as well as the pharmacokineticprofile of the teratogenic agent. A dose that results in adevelopmental problem at one point during gestationmay cause no problem if given either earlier or later indevelopment (Wilson, ’73). If the chemical is present inthe embryo only before or only after some specific andcritical stage of development of a particular tissue, itwill not cause developmental problems in that tissue.For example, once the palate has closed, no amount ofchemical exposure can cause the palate to ‘‘unfuse’’ andresult in the formation of a cleft palate. Additionally, ifthe dose is too low to provide sufficient chemical to thesite of action, then no malformation will be observed.

Biological systems generally are too complex to ana-lyze at a fundamental level with mathematical rigor.However, for certain types of systems, semiempiricalmathematical models have proven extremely useful foranalysis and extension of data. A very successful ex-ample of this type of modeling is the physiologicallybased pharmacokinetic (PBPK) flow model for analysisof the disposition and elimination of drugs (Bischoff etal., ’71). PBPK models are formulated by proposingmechanisms for the chemical behavior that, althoughsimplified, is intended to be a summary of the operationof complex micro-level mechanisms in a physiologicallycorrect system. The model is developed at the macro

Contract grant sponsor: National Center for Toxicological Research.

*Correspondence to: John F. Young, National Center for ToxicologicalResearch, Division of Biometry and Risk Assessment, 3900 NCTRDrive, Jefferson, AR 72079–9502. E-mail: JYOUNG@NCTR.FDA.GOV

Received 17 September 1996; accepted 18 June 1997

TERATOLOGY 55:373–380 (1997)

r 1997 WILEY-LISS, INC.

level using mass and energy balances and transportequations. These equations can be solved analyticallyor numerically to give a representation of the dynamicbehavior. The extent to which these macro-level equa-tions succeed in summarizing the many micro-levelsystems is the measure of the success of the model. ThePBPK model has allowed many useful insights. Com-plex data can be modeled, and often it is possible toassign intuitive and physical interpretations to themodel parameters. Models that represent a physicalsystem can be fitted with only a few adjustable param-eters and validated with a minimal amount of measure-ment data. More complex nonlinear terms can be addedto the model as additional experimental informationbecomes available to more accurately represent thebehavior of the system over a broader range of condi-tions.

Welsch et al. (’95) has refined the concept of utilizingphysiologically based pharmacokinetic models to betterdescribe the disposition of a xenobiotic in both rodentsand humans. By better descriptions of the humanexposure to the relevant toxicant, better risk estima-tions should be made. Leroux et al. (’96) has incorpo-rated cell kinetics into dose-response modeling in orderto provide a more plausible biological basis for predict-ing malformation rates. This biological approach pro-vides for better rationale for high to low dose extrapola-tion as well as across species. The benchmark doseapproach has been expressed by numerous authors(e.g., Faustman et al., ’94; Kavlock and Setzer, ’96) as abetter way to utilize all of the available dose-responsedata. None of these approaches attempt to combinePBPK, dose-response, and sensitivity data into a singleintegrated model.

In this report we develop and describe a semiempiri-cal mathematical formulation for analysis of teratologi-cal data similar to the manner in which PBPK modelsdescribe drug disposition and elimination data. Insteadof a model of mechanistic routes, we formulate amathematical and statistical description of the basicprocesses outlined by White et al. (’80) and expanded byYoung et al. (’97) as governing the frequency andspecificity of the occurrence of a malformation incorpo-rating: (1) the xenobiotic concentration at the sensitivetarget tissue area, (2) the dose-response behavior of thexenobiotic, and (3) the sensitivity of the tissue in theembryo that changes with developmental time.

METHODS: DEVELOPMENT OF THEEQUATIONS

The mathematical analysis of teratogenic effects in-volves combining models for (1) the target tissue expo-sure, (2) the dose-response relations, and (3) the sensi-tivity of the animal and target tissue to the teratogen asa function of gestational times. Each of these is dis-cussed separately.

Target tissue concentration

The physiologically relevant concentration of theteratogenic agent is at the site of action or target tissue.Although this concentration is essentially unavailableby direct measurement, it can be estimated using adynamic PBPK model of the maternal and embryo/fetalsystem. Such a PBPK model is available for pregnancyfor a range of animal systems and includes the changein the growth of the embryo/fetus as well as many of thechanges in the mother and placenta (Luecke et al., ’94).This particular mathematical model and computerprogram calculates concentrations of a xenobiotic in 26tissue regions in the mother and 15 regions in theembryo/fetus for any time during pregnancy. Using thismodel, the target tissue concentrations can be esti-mated at the site of development of the malformationand/or in the tissue or organ regions having a causalrole in producing the malformation. With specificationof the dose and dose schedule, concentrations in eachtissue/organ system are computed as a function of time[C(t)]. The model includes the major routes for introduc-tion of the teratogen (i.e., ingestion, inhalation, dermalabsorption, and injection) and elimination (i.e., hepatic,renal, and respiratory). However, due to the normalpaucity of embryonic/fetal organ data, the embryo/fetusas a whole often must be used as a surrogate for theactual target tissue. This is not a particularly badsurrogate, since at least embryonically the system isnearly a single fluid pool.

Dose-response relations

Dose-response curves are known to differ in shapeand steepness of the curve; therefore, it was deemednecessary to include a means of incorporating suchdifferences in the analysis of teratogenic sensitivity. Afamily of dose-response curves that relate the magni-tude of the response to the xenobiotic concentration isshown in Figure 1. These curves were generated from a

Fig. 1. Dose-response curves generated from Equation 1 with bvalues of 12, 6, 4.9, 3, and approaching zero. Note that dose isrepresented as a fraction of the maximum concentration at the targettissue.

374 R.H. LUECKE ET AL.

normalized logistic equation of the form:

D[C(t)] 5

1 21 1 exp (b)

1 1 exp 12b 32C(t)

Cmax2 14 2

1 21 1 exp (b)

1 1 exp (2b)

(Eq 1)

where C(t) 5 concentration at the target tissue as afunction of time, Cmax 5 maximum concentration at thetarget tissue, and b 5 parameter controlling the shapeof the response curve. As b approaches zero, the resultis a linear relationship for the dose-response. As b getslarger, the response function gets steeper as illustratedin Figure 1.

Equation 1 can be replaced by any dose-responserelationship where the response is scaled to calculateunity at the maximal effective concentration. The effectmay be nonzero at zero concentration to emulate abackground or threshold effect. If data are available atvarious doses for at least a single gestational time, thedose-response curve can be generated from the malfor-mation data. This normalized logistic equation has theproperty of requiring only one parameter (b) to charac-terize its deviation from the straight-line (proportional)relationship.

Sensitivity curve

Since only relative sensitivities are needed, the sensi-tivity is computed as a fraction of the maximum sensi-tivity and hence is a number between zero and one. Thesensitivity curve S(t) is assumed to be a normal distribu-tion curve of the form:

S(t) 5 e2(t2µ/s)2 (Eq 2)

where µ is the mean, s is the dispersion or standarddeviation, and t is time. The normal probability func-tion has the useful mathematical property of beingcompletely characterized by two parameters: the meanand the standard deviation. With respect to the physi-ological mechanisms of malformations, this function isattractive because normal distribution results whendiverse stochastic processes contribute to a single re-sult. Other probability distribution functions such aslog-normal are possible and may be used for the sensi-tivity calculation as described in this report.

Calculating the fraction malformed

The accumulated exposure to the chemical that causesa malformation is evaluated as the area under thesensitivity-concentration curve, or as the integral of theproduct of the sensitivity times the dose-response of theconcentration:

M 5 G et1

t2S(t) D[C(t)] dt (Eq 3)

where M is the fraction malformed for a specific type ofmalformation or any combination term, S(t) is the

sensitivity of the embryo or specific organ/tissue systemto the chemical (Eq. 2), D[C(t)] is the dose-responsefunction (Eq. 1), C(t) is the target tissue concentration,and G is a constant of proportionality for differentstocks/strains/species. For a given malformation, thecalculated M from Equation 3 is regressed against themeasured malformation data; the residual sum ofsquares is minimized by optimizing four parameters: µand s of the sensitivity function, and the gain (G) foreach of two stocks of animals, which may differ in theirresponses. The G parameter is necessary to quantita-tively relate the malformations with the integral evalu-ation. The assumptions made in the development ofthis model are listed in Table 1.

RESULTS

Hydroxyurea was chosen as an example due to theavailability of pharmacokinetic data (Wilson et al., ’75),single dose teratology data (Barr and Beaudoin, ’81),and dose-response data (Beliles et al., ’91) all in theWistar rat, which could be utilized in this mathematicalanalysis of teratogenic effect.

The pharmacokinetic data of Wilson et al. (’75) wereobtained on gestation day (GD) 12 after four consecu-tive daily ip doses of hydroxyurea starting on GD 9. Thematernal plasma and fetal levels were simulated usingthe PBPK model of pregnancy of Luecke et al. (’94). Thefit of the computed curves from the PBPK model to theexperimental maternal and fetal data are shown inFigure 2; note that all four sets of data are simulatedsimultaneously. The fetal concentrations peak laterthan the maternal values, which indicates that trans-port of the hydroxyurea to the fetus has a diffusionlimiting component. The last pair of maternal concentra-tion values (t , 480 minutes) appear to be ill fit by thesimulated lines, but the distance is exaggerated due tothe logarithmic scale of the hydroxyurea data; theabsolute difference is only ,0.2 mg/L compared to apeak value of ,80 mg/L.

Beliles et al. (’91) reported dose-response data forsingle doses given on GD 9 through GD 12 at dosesranging from 100–1,000 mg/kg (Fig. 3). Even thoughthe slope of these dose-response curves decreases withincreasing gestational time, analysis of this hydroxy-urea dose-response data collectively provided a b 5 4.9

TABLE 1. Modeling assumptions at the threesubmodel stages

Submodel Assumption

Target tissueconcentrations

PBPK model for estimation of embry-onic tissue concentration

Whole embryo level estimates specifictarget tissue

Dose-responserelationships Normalized logistic equation

Sensitivity curve ofembryonic tissue

Normally distributed (for thisexample)

TERATOGENIC SENSITIVITY 375

for Equation 1 (Fig. 1), which was in turn used for allsubsequent regression calculations with Equation 3.

Barr and Beaudoin (’81) reported fetal malformationfrequency data resulting from a single ip dose ofhydroxyurea to two stocks (A and B) of pregnant Wistarrats. They also reported the percent of fetuses mal-formed for each day, which combined all individualmalformation data into a single term. Barr and Beau-doin (’81) increased the dose by 25 mg/kg for eachquarter-day interval, starting at 200 mg/kg on GD 9and ending at 375 mg/kg at GD 10.75.

After the pharmacokinetic data of Wilson et al. (’75)were fit, the PBPK model was used to simulate singledose fetal levels [C(t)] at the various days and dosesreported by Barr and Beaudoin (’81). The family ofcalculated curves for concentrations in the embryos(Fig. 4) become broader with increasing gestationaltime and produce the highest peak value at GD 10.These curves account for both the increasing dose and

the growing maternal and embryonic systems. The timeperiod from GD 9–11 is a period of very rapid embryonicgrowth for the rat. The embryonic weight of a singlepup increases from a little over 1 mg at GD 9 to nearly10 times that value after 11 days. Since 10 embryos perlitter were assumed in these calculations, the increasedchemical storage capacity due to growth has a notice-able effect on the concentrations.

Using these calculated concentration curves and thedose-response b value of 4.9, Equation 3 was fit for eachset of malformation data. Figure 5 illustrates the typeof data that were available from Barr and Beaudoin(’81) for the malformation category of anophthalmia/microphthalmia in two different stocks of rats. Singledose malformation incident data were obtained start-

Fig. 2. Physiologically based pharmacokinetic model simulation onGD 12 of the maternal and embryonic hydroxyurea data of Wilson etal. (’75) after four daily ip doses. Both doses were fit simultaneouslywith the pregnancy model of Luecke et al. (’94).

Fig. 3. Hydroxyurea dose-response data adapted from Table 3 ofBeliles et al. (’91). A value of b 5 4.9 was obtained from this data forEquation 1.

Fig. 4. Physiologically based pharmacokinetic model simulation ofthe concentrations in the embryos following single dose administra-tion of hydroxyurea for each day and dose of the data of Barr andBeaudoin (’81). This is not a multidosing scheme, but a compilationscheme of single doses that increase with each quarter-day of gesta-tion at times indicated by the broken lines.

Fig. 5. Percent malformation data for the anophthalmia/microphthal-mia category taken from Table 2 of Barr and Beaudoin (’81). Theabscissa depicts both the increasing gestational days and the increas-ing dose. Note that the percent malformed in both stocks approachzero despite the increasing dose.

376 R.H. LUECKE ET AL.

ing at GD 9 with a dose of 200 mg/kg. On quarter-dayintervals, the dose was increased by 25 mg/kg to resultin eight malformation incidence values for each stock ofrat. The day and dosage information was combinedwith the PBPK generated data [C(t)] to obtain a calcu-lated fraction malformation (Eq. 3) for each stock of ratat each day of treatment. Regression analysis of Equa-tion 3 for an individual malformation and including thedata from both stocks of rats varied µ and s of thesensitivity curve (Eq. 2) and the gains from the twostocks (GA & GB) while minimizing the differencebetween the calculated (Eq. 3) and observed (Table 2)(Barr and Beaudoin, ’81) malformation rate. The regres-sion results for the anophthalmia/microphthalmia end-point are presented in Figure 6 for this malformationcategory. The R2 value is 0.87 for these 16 data points.The sensitivity curve resulting from this regression isshown in Figure 7 and has a mean value of 9.31 daysand a dispersion of 0.83 days.

Barr and Beaudoin (’81) reported 16 other types ofmalformations. The same regression procedure wasrepeated for each malformation and also for the com-bined percent affected data. Figure 8 illustrates thecalculated versus the measured malformation for all ofthe individual data sets. All of the data of Barr andBeaudoin (’81) for each individual malformation havebeen given a single symbol (j) and the combined (alleffects) term from that work has been given a different

symbol (d). All of the data fall fairly well on the 45° line(R2 5 0.97; n 5 288).

The results of the regression of Equation 3 versus theactual malformation data of Barr and Beaudoin (’81) foreach malformation are given in Table 2. The meanvalue (µ, peak location) and the standard deviation (s)of the sensitivity curve as determined by nonlinearregression analyses were different for each type ofmalformation. The majority of the malformationspeaked during gestational day 9 with a standard devia-tion of ,1 day. Several of these data sets yielded a widedispersion with a mean value outside the gestationaldays of the reported data (PAL, UMB, HIN; see Table 2for these codes). This was partially due to the sparse-ness of the data, the peak malformation rate being nearthe edge or apparently outside of the data set, and/orthe uniformity of the response across time. The widedispersion is also reflected in a poor fit of the data(R2 , 0.7) in most of these cases. The sensitivity curvefor the combined effects (all effects) was also very broad

TABLE 2. Parameters for the nonlinear regression fitto the data of Barr and Beaudoin (’81) by Equation 3

Malformation Codeµ

(days)s

(days) GA GB R2

Anophthalmia/micro-phthalmia AM 9.31 0.83 0.154 0.24 0.87

Hydrocephaly HYD 9.30 0.67 0.047 0.080 0.79Encephalocele ENC 9.21 0.45 0.0146 0.034 0.98Exencephaly EXE 9.33 0.30 0.0129 0.083 0.96Ear dysplasia EAR 9.45 0.38 0.0064 0.060 0.92Micrognathia MIC 8.94 0.56 0.019 0.025 0.98Maxillary

hypoplasia MAX 9.32 0.30 0.028 0.100 0.92Facial

asymmetry FAC 9.27 0.40 0.0081 0.023 0.76Pointed

mandible MAN 9.44 0.31 0.0147 0.041 0.95Protruding

tongue TON 9.33 0.30 0.0108 0.069 0.99Cleft lip LIP 9.22 0.26 0.0116 0.029 0.88Cleft palate PAL 81 0.96 0.038 0.058 0.78Hydronephrosis NEP 9.79 2.2 0.074 0.028 0.70Left umbilical

art. UMB 81 2.5 0.035 0.051 0.37Hindlimb

dysplasia HIN 151 4.7 0.00076 0.012 0.35Tail dysplasia TAI 10.5 0.46 0.0024 0.048 0.93Anal atresia ANA 10.4 0.26 0.00103 0.033 0.83All effects ALL 8.11 2.3 0.25 0.30 0.761Pinpointing the mean outside the experimental interval isinherently inaccurate. Codes represent abbreviations used forthe curves in Figure 9.

Fig. 6. Measured malformations (i.e., data from Table 2 of Barr andBeaudoin, ’81) vs. calculated malformations (from Eq. 3) for theanophthalmia/microphthalmia category. The regression value (R2) of0.87 re-enforces the visual goodness of fit for the data.

Fig. 7. Sensitivity curve obtained from the regression data fit of theanophthalmia/microphthalmia data set.

TERATOGENIC SENSITIVITY 377

(8.1 6 2.3 days) as might be expected since the sensitiv-ity to at least one effect or another extended over theentire dosing interval. However, examination of thedata for percent affected for all malformations (Table 1in Barr and Beaudoin, ’81) appears to indicate that thehighest malformation frequency occurred at 9.25–9.50days. Our calculations of the sensitivity curve illustratethat the increased dosage as used in these experimentsat increasing time intervals overcompensates for thedecreased susceptibility of the rats to the teratogeniceffects of hydroxyurea as gestation progresses.

The sensitivity curves resulting from the regressionanalysis for the various malformations are given inFigure 9 with the magnitudes of the individual curvesbeing proportional to the maximum of gain A or gain B(Table 2). These curves illustrate the relative frequency

and timing of each category of malformation. Thosecurves with the mean outside the experimental data(i.e., ,GD 9 or .GD 10.75) appear as only line seg-ments in Figure 9 (MIC, PAL, UMB, HIN, All). Remem-ber, to obtain a quantitative estimate for the frequencyof malformation, these curves must be integrated withthe dosage and pharmacokinetics. Figure 9 is strikinglysimilar to Figures 2–4 from Wilson in 1973. Wilson (’73)presented a group of organ/tissue curves illustratingthe theoretical sensitivity to a hypothetical teratogenicagent based on his years of experience working with avariety of agents. Figure 9 is derived from our math-ematical model based on data from a single chemical.

DISCUSSION

The insights of Wilson (’73) have passed the test oftime and are as relevant today as they were 20 yearsago. His principles of teratology present the concept oftime-related sensitivity of organ systems, and the pres-ent work describes a mathematical framework for thissensitivity.

One of the basic advantages of a mathematical modelis that the structure can be exploited, not only inanalyzing the data but also in extending the analysis tosimilar systems. For a given animal species and aspecific organ/tissue malformation, we would expectthe values for the parameters for the sensitivity curveto be somewhat fixed. The gestational period of greatestsensitivity (µ) and the range of the sensitivity (s) wouldbe expected to be a function of the animal system andthe gestational progress of the affected organ/tissuegroup. For example, various chemicals might affect thedevelopment of the limb buds, but the sensitive gesta-tional period for limb buds would depend mainly on thespecies. However, one would expect the absolute andrelative values for the gain parameters to be morexenobiotic dependent.

Any comparison of sensitivity curves between differ-ent animal species must be based on the relative timingof embryonic/fetal development. A malformation involv-ing a particular tissue, such as a developing limb bud,in one species would involve similar tissue in anotherspecies, or at least tissues/organs that are at similarsensitivity stages. That is, the critical sensitive periodwould be expected to occur at the same relative stage ofdevelopment for the two species. If the sensitivity curveis located on a particular day in one species (e.g.,laboratory rodent), then developmental landmarks canbe used to locate the same equivalent time in anotherspecies (e.g., humans).

Several studies of developmental landmarks compar-ing the human and rat have been reported (Hoar andMonie, ’81; Shepard, ’86). A plot of these markers (Fig.10) shows an exponential relationship, and the scatterof the data reflects the inclusion of developmentallandmarks from numerous organs and tissues. Theshape of the locus of data points in Figure 10 suggests

Fig. 8. Measured malformations (i.e., data from Table 2 of Barr andBeaudoin, ’81) vs. calculated malformations (from Eq. 3) for all 18 datasets. There is no presentation differentiation among the variousindividual malformations; however, the combination term of affectedfetuses (‘‘all effects’’ category) have been represented by a separatesymbol.

Fig. 9. Estimated sensitivity curves for all data sets. Curves arelabeled with the code presented in Table 2. The magnitude of theindividual curves is proportional to the maximum of GA or GB fromTable 2.

378 R.H. LUECKE ET AL.

an exponential curve with the following features:

y 5 a(1 2 e2bx) (Eq 4)

However, both rat and human data need to be adjustedfor the implantation time (i.e., c and d; y–c and x–d);parameters ‘a’ through ‘d’ are fit by regression. Theexpanded form of Equation 4 is

y 2 c 5 a(1 2 e2b(x2d)) (Eq 5)

Nonlinear regression of Equation 5 for the data inFigure 10 yields the following relationship:

DAYSrat 5 4.6 1 16.4(1 2 e2(DAYShuman25.2)/41) (Eq 6)

From this equation time values for the sensitivity curvefor the rat (DAYSrat) can be converted to the correspond-ing time values for the human (DAYShuman). Since thetime conversion is nonlinear (Eq. 6), the normal sensi-tivity curve that was assumed in the rat mathemati-cally would become a somewhat skewed distribution forthe human. However, the amount of skewing is small,and the normal distribution was assumed also for thehuman.

This approach has the potential to extrapolate quan-titatively, or at least quantitatively compare, terato-genic events in different species. Figure 11 depicts thisextrapolation of sensitivity for the anophthalmia/microphthalmia (AM) category from the rat (Fig. 11A,dashed line) to the human (Fig. 11B, dashed line).Figure 11A (dashed line) is the same as Figure 7, butwith the x-axis compressed to parallel the humangestational time in Figure 11B (i.e., 20 days). Thesensitivity distribution values for the rat (i.e., µ 5 9.31,s 5 0.83) maps to a mean of 18.9 days and a dispersionof 2.9 days for the human. Conversion or mapping of thesensitivity curve of the rat to the human is simply aspreadsheet operation of choosing a range of gesta-

tional times for the rat and calculating the correspond-ing days in the human utilizing the relationship inEquation 6. The relative shape of the sensitivity curveis the same for both species, but the time frame isdifferent to account for differences in gestation.

The solid lines in Figures 11A and 11B depict therelationship of the ‘‘all effects’’ category from Table 1 forthe rat and the projected values for the human. Thebroader curves reflect this more encompassing cat-egory. The rat values of 8.1 6 2.3 days map to values of14.9 6 7.3 days in the human. From a risk assessmentviewpoint, these broader curves predict a more conser-vative window of vulnerability in the human, i.e., thereis a wider gestational time window for which pregnanthumans should be protected. These projections to hu-man developmental time are not intended to imply thatidentical malformations may occur in the human thatwere seen in the rodent. However, it does imply that thegreatest potential for human embryonic insult may liewithin this time-curve.

The sensitivity probability of the human calculatedin this way is, of course, theoretical. Other examplesare needed further to test the model. Many otherfactors could intervene to modify this prediction, suchas altered pharmacokinetics, altered metabolism, in-creased or decreased susceptibility to the xenobiotic,strain or stock differences, and exposure differences.But if we perform the mapping properly, these curvesindicates that the ‘‘AM’’ tissue or ‘‘all effects’’ category inthe human embryo are probably very sensitive to insultby hydroxyurea during these specific periods. As impor-tant, these results indicate that a malformed embryo isunlikely to result if hydroxyurea is administered two orthree standard deviations away from these means.

The calculations presented here form a new way tointegrate teratogenic and pharmacokinetic data. Locat-ing in developmental time and measuring the sensitiv-ity curve are central factors for quantitative correlation

Fig. 10. Comparison of the timing of developmental landmarksbetween the rat and human; from data reported by Shepard (’86) andHoar and Monie (’81). The curve, presented by Equation 6, wasobtained by nonlinear regression.

Fig. 11. Sensitivity curves for the category of anophthalmia/microphthalmia (AM, dashed line) and for all the malformation datacombined (All, solid line) for the rat (A) and projected for the human(B).

TERATOGENIC SENSITIVITY 379

and estimation of teratological data. The maximumsensitivity and its span in time are determined by thestage of development of the particular target organ ortissue. This approach provides a theoretical frameworkfor quantitative evaluation of fundamental effects anda means logically to extrapolate laboratory studies topotential human vulnerability. Although these ideasneed to be thoroughly tested with additional observedexperimental data, they provide a mathematical frame-work to extrapolate between species for risk assess-ment calculations. These concepts also provide a frame-work for designing future experiments for furthertesting with other xenobiotics and organ/tissue systemswithin species and between species, thus providingvaluable information for human risk assessment.

Another powerful advantage of modeling phenomenasuch as teratological events is the ability to alter one ormore parameters to simulate conditions difficult toanalyze experimentally. Such simulations provide theo-retical insight to the complexities of the phenomenathat may be difficult to discern from the various equa-tions and parameters. Such simulations are readilycarried out by modern desk top computers and providevivid graphic results.

ACKNOWLEDGEMENTS

This research was supported in part by an appoint-ment to the Faculty Research Participation Program atthe National Center for Toxicological Research adminis-tered by the Oak Ridge Institute for Science andEducation through an interagency agreement betweenthe U.S. Department of Energy and the U.S. Food andDrug Administration.

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NOMENCLATURE

D[C(t)] Effect of teratogenic activity as a function ofconcentration; the dose-response relation

C(t) Concentration of the teratogenic agent at thesite of action

Cmax Maximum concentration of the teratogenicagent at the site of action

t Timeb Parameter defining the shape of the dose-

response curveS(t) Sensitivity functionµ Mean of sensitivity curve; corresponds to maxi-

mum value for the normal distributions Standard deviation or dispersion of sensitivity

curveM Fraction malformedG Gain parameter necessary to relate malforma-

tions with the integral function for differencesbetween stocks or strains of animals

380 R.H. LUECKE ET AL.