Occupational and Environmental Medicine 1994;51:173-180

Prediction of the comparative intensity ofpneumoconiotic changes caused by chronicinhalation exposure to dusts of differentcytotoxicity by means of a mathematical model

B A Katsnelson, L K Konyscheva, N Ye Sharapova, L I Privalova

Centre ofProphylaxisand Protection ofHealth in IndustrialWorkers,Ekaterinburg, RussiaB A KatsnelsonL K KonyschevaN Ye SharapovaL I PrivalovaRequests for reprints to:Dr B A Katsnelson,Department of GeneralIndustrial Hygiene, MedicalResearch Centre forProphylaxis and HealthProtection in IndustrialWorkers, Popov St 30,Ekaterinburg 620014,Russia.

Accepted 28 June 1993

AbstractA multicompartmental mathematicalmodel has been used to simulate varia-tions in the cytotoxicity of dusts in thekinetics of the retention, in the pul-monary region and tracheobronchiallymph nodes, of practically insolublequartzite and titanium dioxide dust par-ticles deposited on the free surfaces ofthe acini from alveolar air. Experimentswith these dusts were conducted on ratsexposed to virtually the same dust con-centrations in the air for an experimentalperiod of 20 weeks and a period of10 weeks after exposure. Satisfactoryapproximation to the experimental dataon the retention of these dusts isobtained by using the model parametersthat depend either on damage to lungmacrophages by phagocytosed particlesor on the response of the host organismto this damage by enhanced recruitmentof neutrophilic leucocytes; all the othervariables of the model being unchanged.The values of the "action integral" com-

puted from this model and multiplied bythe index of comparative cytotoxicity ofparticles in vitro satisfactorily approxi-mate to quantitative differences in theintensity of pneumoconioses caused bythe dusts under study by the end of theexperimental period. On the whole, theresults of the mathematical model agreewith the hypothesis that the cytotoxicityof particles plays a key part in both theprocess of retention of dust in the lungparenchyma and lung associated lymphnodes, and the pathological processcaused by the retained dust. Thus giventhe factors and conditions on which thedeposition of practically insoluble dustsin the pulmonary region depends, it isnecessary to take into account the multi-plicative nature of these two effects ofcytotoxicity when predicting the compar-ative risk ofpneumoconiosis.

(Occup Environ Med 1994;51:173-180)

The breakdown of lung macrophages as a

result of ingesting poorly soluble dust parti-cles is a key link in the pathogenesis of pneu-moconioses. This link determines both theeffectiveness of lung clearance (and thus thekinetics of retention of dust in the lungparenchyma and lung associated lymphnodes) and the intensity of pathological

changes in these organs caused by long termdust retention. Most of the researchers in thisfield share this view, with subtle differences.It still remains, however, a hypothesis thathas not been treated quantitatively. The dualeffect of cytotoxicity of dust is not disputed,but the statement that it has a key role stillremains a speculative one.

One of the aspects of this problem may beformulated as the question: will the differ-ences in the cytotoxicity of two practicallyinsoluble mineral dusts be sufficient toexplain experimental quantitative differencesin both the kinetics of their retention and theintensity of the pneumoconiotic processescaused by them, provided that the conditionscontrolling the deposition of their particles inthe pulmonary region of the lung are similar?This question is important both theoreticallyand practically. A positive answer to it wouldbe a strong argument in favour of the hypoth-esis under study) and would ensure morereliable prediction of the comparative risk ofpneumoconiosis due to dusts, the cytotoxicityof which was compared in short term tests.The question requires mathematical model-ling.

Choosing and testing the model ofpulmonary dust retentionAlthough the physiological part played by thephagocytosis of dust particles deposited fromthe alveolar air is generally acknowledged, ithas not been given a sufficiently good mathe-matical description. Most models for thekinetics of the elimination and retention ofsuch particles and their translocation throughlymphatics either do not describe their phago-cytosis at all'-3 or do not attach sufficientimportance to it.4 It is not surprising, then,that in the only paper devoted to differencesin the retention of quartz and titanium diox-ide, in which a method for modelling suchdifferences was proposed,3 the authors used aformal (external) model of the process thatdoes not describe the role of any of its mecha-nisms. Specifically it does not describe thephagocytosis of dust particles, nor the break-down of lung macrophages and its conse-

quences. Thus the authors did not use themost striking difference in biological effectbetween the compared materials, namelytheir essentially different cytotoxicity tomacrophages, to explain the observed kineticdifferences-for instance, the most character-istic: a considerably lower aptitude of tita-nium dioxide to translocation into

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tracheobronchial lymph nodes. The authorsensured good approximation to experimentaldata only by assuming, without any mecha-nistic arguments, that the transport of parti-cles from the lung into lymph nodes beginsonly after the amount of dust retained in thelung parenchyma reaches a certain threshold.Moreover, in fitting the model to their data,they estimated this threshold to be consider-ably higher for titanium dioxide than forquartz.

This kind of approach would not providean answer to the question formulated in theintroduction to this paper. Therefore we usethe model that was proposed previously fordescribing just kinetic processes directly orindirectly associated with the phagocytosis ofparticles and the resulting breakdown of lungmacrophages.5

This model makes it possible to explicitlysimulate differences due to unequal cytotoxi-city of the dusts under comparison. It is alsopossible to check whether such simulationwould be sufficient for predicting the accu-mulation of these dusts in the lungparenchyma and in tracheobronchial lymphnodes during chronic inhalation and after along period of recovery after exposure. Thusthe values should be close to correspondingexperimental data.

Figure 1 shows the structure of the model.As the identification of its compartments andof the flows between them is clear from thefigure and the arguments for this structurehave been examined in detail previously inthis journal,5 we do not dwell on them here.Briefly, the flows between the compartmentsare characterised by transfer rate constants-that is, the proportion of the substance leav-ing the compartment per unit time indirections defined in the model-rather thanby the mass of substance transported per unittime. In the notation adopted, ki is the con-stant of the rate of transfer from compart-ment X3 to compartment X, or beyond the

Figure 1 Structure ofmulticompartmental modelfor the kinetics of theretention and eliminationofdust deposited in thealveolar region of the lungfrom Katsnelson et al.5

Lung associatedlymph nodes

Pulmonaryinterstice I

system modelled (k.7). For long term experi-ments on animals, the week is the most con-venient unit of time, so the dimension of theconstants is weeks- 1.As this model considers only the fate of

particles deposited in the pulmonary region,the rate of this deposition should be given.Taking into account the absence of bothmathematical models for regional depositionof particles in the respiratory tract of rats andtechnically feasible methods of its direct mea-surement in small animals, we suggested5 anapproach to its calculation from the data of achronic experiment. Initially all the dustretained in the lung parenchyma is assumedto be contained in one compartment and thekinetics of its accumulation is described bythe equation y = a-be- the constants ofwhich are selected so as to ensure satisfactoryapproximation to the experimentally deter-mined mass of dust in the lung at varioustimes of exposure. Assuming that this esti-mate of k is the constant rate of dust outputfrom the one compartmental model, the con-stant rate of input may be easily calculated. Ingoing over to a multicompartmental modelthis constant is assumed to be the rate of thedeposition of particles in the alveolar regionC. We have already explained why the massof dust found in the lung after a sufficientlylong exposure, a period of 24 hours afterexposure or longer, and after bronchoalveolarlavage, may be assumed to be an experimen-tal correlate of the sum of compartments (X,+ X6) in such a multicompartment model.5Thus the model describes the kinetics ofinterstitial pulmonary dust burden ratherthan that of total pulmonary burden, as it isbased on experimental data which permit usonly to estimate the first.The same should be kept in mind when

considering the results of the experimentsdescribed next.

Taking into account the limitations consid-ered in the same paper,5 the set of constants

Free surface of the pulmonary regionAlveolar air

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found with the help of a special computerprogram provided a satisfactory approxima-tion to the amounts of quartzite dust foundexperimentally in the lung and in tracheo-bronchial lymph nodes during long terminhalation.5 This set required some adjust-ment after the first 20 weeks of exposure todescribe the breakdown of the mechanismresponsible for weakened recruitment of alve-olar macrophages with its compensatoryincrease in neutrophilic leucocytes. Theresults of another such experiment requiredonly minor adjustment of the constants fromthe same model. Before applying these con-

stants to the problem of variations in cytotox-icity of dusts we checked once again if thismodel was adequate to describe the retentionof quartzite dust from the same Pervouralskmineral deposit.The experiment was performed on ran-

domly bred white female rats with an initialaverage body weight of 185 g. The rats were

exposed to the dusts in a whole body cham-ber for five hours a day, five times a week.Some of the animals were killed after the first10 weeks, another group of rats was killedafter 20 weeks of exposure, and anothergroup at 10 weeks after the 20 week period ofexposure. The average concentration of totalairborne dust in the chamber as collected on

special AFA aerosol plastic fibre filters(Isotop Co, Russia) without size separationover the total inhalation period was 81-2(7-9)mg/m3 (i (SEM)). The free silicon dioxidecontent of the lung and tracheobronchiallymph node tissue was measured after burn-ing the samples. The ash was fused with a

mixture of sodium bicarbonate and sodiumchloride and then was leached in a 5% solu-tion of sodium bicarbonate; after filtering andneutralising the solution with 0 5 M sulphuricacid we measured the silicic acid by complexformation with ammonium molybdate in thepresence of tartaric and acetylsalicylic acidand measurement of the complex spectropho-tometrically at 600 nm. Analyses at eachexperimental time point were performed on

tissues from seven or eight rats from both theexposed and the control groups.The constant of alveolar deposition co cal-

culated by this method was 0 3 mg.week-1,which is about a fifth of the value found inearlier experiments. This difference may bedue partially to the use of another method fordetermining quartz in the tissue and partiallyto different particle sizes in the inhaled dusts.In any case, however, for a model describingthe kinetics of subsequent dust retention and

Table 1 Kinetics of quartz retention in lung parenchyma and tracheobronchial lymphnodes (TBLN) during and after chronic inhalation exposure to dust and its simulation bymeans of a mathematical model

Mass of dust in lungs (mg) Mass of dustin TBLN

Duration of experiment x(SEM) (95 % CI) X4 + X6 (mg) * X5

10 weeks of exposure 1-74(0-27) (1-09 to 2-39) 1-44 0-102 0-04720 weeks of exposure 3 30(0 28) (2-57 to 4 03) 2-78 0-176 0-16110 weeks after exposure 2-17(0-14) (1-81 to 2 53) 2-39 0-220 0-265

*For the pooled tissue of the lymph nodes of all the rats in a given group in terms of one rat.

elimination the variables of deposition shouldbe given a priori. Therefore it is the repro-ducibility of the set of transfer rate constantsrather than the absolute values that are ofimportance for checking the adequacy of sucha model. To test this reproducibility we fixedall the values of the constants kj, that werefound earlier in an experiment of the sameduration,5 except the constant k,6, which wasautomatically determined by the computersuch that the model would provide a satisfac-tory approximation to the data from our cur-rent experiment. The criterion of the bestapproximation (as built into the program)was minimisation of the sum of the squares ofthe deviations of experimental data frommodel predictions. If the best approximationfound had been unsatisfactory, the next stepwould have been adjustment of some otherconstant, etc.

Table 1 shows that no such steps werenecessary, because the model predictions fellwithin the 95% confidence intervals (95%CIs) of all the experimental data on the lungand were close to the averaged data on tra-cheobronchial lymph nodes (with the excep-tion of the first term of exposure). Thisdegree of approximation may be regarded assufficient for modelling chronic toxicokineticprocesses. Also the model predicted: (1) adecrease in the rate of accumulation of quartzdust in the interstitium of the lungs duringthe second 10 weeks of exposure comparedwith the first 10 weeks (by 1-34 mg comparedwith 1-44 mg). This agrees well with theexperiment (1-56 mg compared with 1-74mg); (2) partial clearance of the lungparenchyma after exposure alongside a simul-taneous increase in quartz transferred to tra-cheobronchial lymph nodes. Such lymphaticclearance, however, accounts for only a smallproportion of the quartz dust eliminated fromlungs over the 10 weeks after exposure. Thisfact confirms the essential role of the continu-ing elimination of particles from the intersti-tial lung tissue to the free surface in thepulmonary region and further through thetracheobronchial region towards the gastroin-testinal tract. In the model, the part of thisbasic elimination route is played by the per-sisting flow from X6 into X2.The most surprising thing, in our opinion,

Table 2 Constants of the seven compartment modeldescribing the kinetics of quartz and titanium dustretention (week -')

Quartz

Experimentfrom Current TitaniumKatsnelson et al' experiment dioxide

k12 0-05 0-05 0-016k2l 0-25 0-25 2-655k26 0-06 0-05 0-215k,3 0-02 0-02 0-005k4, 0-50 0-50 0-50k46 0-03 0-03 0k54 0-01 0-01 0-01k64 0-15 0-15 1-316k7l 0-10 0-10 0-10k72 0-05 0-05 0-05k73 0-10 0-10 0-10ki7 5-00 5-00 5-00

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is that all these results were obtained for a

value of k,6 = 0 053, found by the computer,which is virtually equal to the previouslyreported value of 0 06.5 Table 2 shows thecomplete set of constants. Thus the modelproposed earlier has been proved adequateonce again.

Modelling peculiarities ofthe kinetics ofthe retention and elimination ofa poorlycytotoxic dustMost researchers regard titanium dioxide as a

reference dust that is characterised by lowfibrogenicity and low cytotoxicity. Althoughthe often cited statement that this material is"biologically inert" does not stand seriouscriticism, its considerably lower cytotoxicitycompared with quartz found support in a

number of studies including ours.6 Therefore,we consider titanium dioxide to be suitablefor modelling the peculiarities of the retentionand elimination of a poorly cytotoxic dust.When modelling, we should be altering onlythose variables of the model that directly or

indirectly depend on the intensity of the cyto-toxic effect. They should be altered only inaccordance with differences in cytotoxicitybetween titanium dioxide and the quartzitedust, the kinetics of which are described inthe pulmonary region by the basic model.The theoretical aim of such modelling as

considered in the introduction to this paperdoes not require high accuracy of prediction.The modelling should, however, provide gen-eral agreement between predictions andexperimental data if there is truth in the ini-tial hypothesis about the key role of damageto lung macrophages and associated conse-

quences in the kinetics of the retention ofpractically insoluble dust particles in the lungparenchyma and lymph nodes.The experiment with titanium dioxide dust

(rutile) was conducted in parallel to theexperiment with quartzite dust for a similaraverage concentration of total dust in thechamber (78.8(11-2) mg/M2). The particlesize distribution (as estimated by lightmicroscopy of the dust samples with the sameAFA filters made transparent by treatmentwith acetone vapours) was similar in bothexperiments. Thus the proportion of quartziteparticles under 2 gm was 59 0%, and under5 ,m was 92- 1%; the proportion of particlesof titanium dioxide under 2 pm was 54-5%and under 5 gm was 93 5%. No particlesover 20 pm were discovered in the total countof about 500 particles in both cases.

Samples of dry lung and tracheobronchiallymph node tissues taken from rats killed atthe same time points were burnt, fused withpotassium pyrosulphate, and leached in hot0 5% sulphuric acid. To the filtered solutionwas added a 10% solution of ammonia in thepresence of ferric (III) sulphate and then a

5% solution of sulphuric acid until the redsediment disappeared. After the reduction ofthe iron (III) with a 3% solution of acetylsali-cylic acid we added a 2% solution ofbisodium salt of chromotropic acid to the

sample and determined the concentration oftitanium spectrophotometrically at 470 nm.Each group had the same number of rats as inthe experiment with quartzite dust.

For modelling we assumed the same valueof co as it does not depend on cytotoxicity.For simulating the role of differences in cyto-toxicity we changed the constants kj, as fol-lows: as the constant k1, reflects theprobability of breakdown of pulmonary alveo-lar macrophages whereas the constant k,6reflects that of pulmonary interstitialmacrophages, there is every reason todecrease both constants in the case of tita-nium dioxide compared with their values forquartzite. In our earlier studies we provedthat the most informative criterion for theextent of breakdown of alveolar macrophagesis the resulting recruitment of neutrophilicleucocytes.6 In chronic experiments, however,increased recruitment of neutrophils and anincrease in their number in bronchoalveolarlavage (BAL) fluid may be due to other fac-tors.7 Therefore, comparison of the cellularcomposition of this fluid in rats that haveinhaled titanium dioxide or quartzite for along time reflects the comparative intensity ofa chronic pathological process rather than thecomparative cytotoxicity of different particles.

For estimating comparative cytotoxicity ofdifferent dusts we performed a special experi-ment with samples of these dusts taken in theexposure chambers. We injected 10 mg ofeach dust intratracheally (as a sterile suspen-sion in 1 ml of normal saline) into rats inwhich BAL was performed once in six hours.The absolute number of neutrophilic leuco-cytes in rats that had received quartzite dustwas 3-35(0-81) x 106 (0.42(0.09) x 106 incontrols) whereas in those that had receivedtitanium dioxide it was 0-85(0 16) x 106 -thatis, lower by a factor of 3-9. As in such teststhis index is practically linearly dependent onthe dose of macrophage breakdown products(administered into the lung or formed in itunder the action of cytotoxic dust) it was pos-sible to assume about a fourfold decrease inthe constant k,2. Judging by the other crite-rion that we used for comparative estimationof the dust's ability to destroy alveolarmacrophages, namely the neutrophilic leuco-cyte/alveolar macrophage ratio in BAL fluid(6I10(0v66) for quartzite and 1-99(0.65) fortitanium dioxide) the reduction in this con-stant might be threefold. Thus in a model forthe kinetics of titanium dioxide the values ofthe constant kl2 may be assumed to be withinthe range of 0'0125 to 0-0164 weeks-'.Low probability of breakdown of alveolar

macrophages in our model means a reducednumber of particles penetrating into the lunginterstitium (even with k4, being unchanged).This suggests that the probability that tita-nium dioxide particles will act on interstitialmacrophages is considerably lower than forquartz particles. In other words, the propor-tion of phagocytosing interstitial macrophagesbroken down as a result of this action is lowernot only because of its specific intensity butalso because of a lower dose of dust per pool

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Figure 2 Titaniumdioxide content of rat lungsduring and after chronicinhalation exposure;points = experimentaldata; curve = modelprediction.

Figure 3 Titaniumdioxide content oftracheobronchial lymphnodes of rats during andafter chronic inhalationexposure; points =experimental data; curve =model prediction.

0-5

E 04

a)-a

o 03 -._

E 0-2._

co

0-1

E 0-008a)-0

x 0-0060

_0

E 0-004

co 0-0021

10 20

Time (weeks)

0~~~~

- /

I

0 10 20 30Time (weeks)

of interstitial macrophages avaConsequently, the constant k46 mereduced for titanium dioxide compare(quartzite even more drastically than thistant k2. The orders of magnitudeobtained (<0.001 week-') have a negeffect on the mass of dust in the coiments as predicted by the model. Theof a particular value of this order camjustified by the degree of approximatexperimental data and becomes unciTherefore, k46 may be assumed to be eczero.The probability that dust will be

ported from the lung interstitium by recinterstitial macrophages that turn intolar macrophages (from compartmentcompartment X2 in our model) deperboth the intensity of this recruitment a]number of particles in a single intemacrophage. Earlier we discussed the ]bility of interaction between intemacrophages and particles, but here N

interested in the probability that afteiinteraction interstitial macrophages

Table 3 Kinetics of titanium dioxide retention in lung parenchyma and tracheobrlymph nodes during and after chronic inhalation exposure to dust and its simulationmeans of a mathematical model

Mass of dust in lungs (mg) Mass of dustin TBLN

Duration of experiment i(SEM) (95 % CI) X + X6 (mg) *

10 weeks of exposure 0-23(0-06) (0 09-0 37) 0-23 0-00420 weeks of exposure 0-48(0-15) (0-12-0-84) 0-28 0 00710 weeks after exposure 0-09(0-07) (0-0 26) 0-09 0-009

*Footnote as for table 1.

retain viability and functional (phagocytic andmigratory) activity. Judging by the data fromstudies on macrophage cultures and on cellsin the BAL fluid both after intratracheal andchronic inhalation, macrophages never con-tain quartz particles in quantities that areuncountable. In the case of titanium dioxide,however, the percentage of such overloadedmacrophages is high. The doses of dust beingequal, this striking difference may beexplained solely by the fact that themacrophage, even if it does not show obvious

40 morphological and tinctorial signs of damage,sharply reduces or even completely loses itsphagocytic ability after engulfing a few highlytoxic particles, but retains phagocytic abilityfor a long time in the case of particles of lowcytotoxicity. As in our model the constant k,6means a proportion of particles inside theinterstitial macrophages being transferred toX2 it should depend on the probability that adust loaded macrophage migrating to the freesurface of the acinus carries a high number ofparticles in it.

All these considerations suggest that theconstant k,6 should be increased rather thandecreased when modelling the kinetics of tita-nium dioxide (which is in agreement with a

40 sharp reduction in the constant k46). It was,however, impossible to even roughly estimatethe factor of this increase. For the same rea-sons we had to increase the constants k,, andkM4, which reflect the probability of a particle

Lilable. being phagocytosed by active alveolar anday be interstitial macrophages and thus how soond with its activity is inhibited in the course of phago-e con- cytosis. It is also impossible to estimate the

thus factor of the increase in these constants as it,ligible is impossible to count titanium dioxide parti-mpart- cles inside individual macrophages. Finally,choice the lower the cytotoxicity of dust, the lowernot be the total contribution of neutrophils to theion to alveolar phagocytosis of particles.6 Thiscertain. makes it possible to reduce the constant k,, iniual to proportion to the reduced recruitment of

neutrophilic leucocytes at a single exposure totrans- dust (that is: by a factor of 4, and to assume it-ruited equals 0-005). Thus a particular value is cho-alveo- sen not by means of model approximationX6 to but is based on a priori considerations andids on independent experimental data. Thereforend the there is no need to assume it to be zero as inrstitial the case considered above.proba- Careful consideration of the model and itsrstitial structure convinces us that with our assump-we are tions we have exhausted all the changes in ther such values of the variables that may be justified bywould differences in the cytotoxicity of particles.

Figures 2 and 3 and table 3 show the degreeof approximation to experimental data thatwe consider sufficient. It is clear that predic-

,onchial tions for compartment X5 agree or nearlyn by agree with experimental data on the amount

of titanium dioxide in tracheobronchiallymph nodes at all the four time points, but

X5 predictions for the sum of compartments0-003 (X4 + X6) agree with experimental data on0-007 the titanium oxide content of the lungs only0-008 at three of the four time points, namely at

time zero, after the first 10 weeks of exposure,

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and 10 weeks after the 20 week exposure. Fortime zero, the experimental points in the plots(figs 2 and 3) represent the titanium dioxidecontents of the lungs and tracheobronchiallymph nodes of control rats.The overshoot of the experimental point

corresponding to the amount of titaniumdioxide in the lungs by the end of the 20week exposure period may be due to a sam-pling error. This is indicated not only by thebroadest confidence interval of the averageresult obtained at this time point (includingthe value predicted by the model) but also bythe fact that the curve for accumulation andelimination drawn by the computer reflectsthe typical kinetics of the process in a morenatural way, with gradual attainment of theretention plateau and sufficiently rapid butstill gradual decay of the mass of dust in thelungs after exposure. If we assume that theexperimental point under consideration astrue, we have to conclude that the retentionof titanium dioxide increased linearly over theentire 20 weeks without any tendencytowards equilibrium (which is impossible)and dropped very steeply after the end ofexposure-which has never been found forpractically insoluble dusts.

Mention should be made, however, that insome inhalation experiments with titaniumdioxide, the lung burden was also found todisplay a tendency towards a linear increase."Although such data cannot be disregarded,we still believe that, in the course of a longterm experimental exposure of this kind, thetendency towards equilibrium would sooneror later establish itself. Otherwise the entiretheory of pulmonary dust kinetics should bedrastically reviewed. Indeed, why shouldcomparatively harmless titanium dioxide par-ticles impair the clearance mechanisms to agreater extent than very harmful quartz parti-cles, for which the onset of equilibrium hasbeen shown many times? The formation of aretention plateau depends on the relationbetween the rate of alveolar deposition andthe efficiency of clearance. Experimentingwith another harmful dust, the sameresearchers proposed that an impairment ofthe clearance mechanisms was responsible forthe retention curve (lung burden) becominglinear.'We think that for a model of this class,

ideal approximation to seven experimentalresults out of eight may be considered satis-factory. Comparison of tables 1 and 3 showsthat, in full compliance with the experiment,the model predicts lower retention of tita-nium dioxide than quartz, and an evengreater difference in the retention of thesedusts in tracheobronchial lymph nodes, andfaster clearance of the lungs of titanium diox-ide than of quartz.

Comparison of the sets of constants (table2) shows that all these results were attainedwhile adhering to the already formulatedrequirements of adaptation of the model. Itwas sufficient to take into account theoreti-cally assumed kinetic consequences ofreduced cytotoxicity for the mathematical

description of essential differences in theaccumulation and elimination of differentlycytotoxic insoluble particles.

Predicting the intensity ofpathologicalchanges in lungsEarlier we proposed a toxicokinetic criterion,called the action integral,5910 for predictingthe intensity of pathological changes associ-ated with the chronic retention of harmfulsubstances in the organism (practically insol-uble dust in the lungs in particular). Theaction integral is a definite integral of thefunction describing the accumulation of sub-stances during chronic exposure and reduc-tion in the accumulated mass as a result ofstopping the exposure taken from the begin-ning of exposure to the moment at which theintensity of pathological changes due to thesesubstances is estimated.

It is easy to see that the basic assumptionsof this criterion are: (1) the harmful effect islinearly proportional to both the mass ofretained substance and the time for whicheach discrete part of this mass stays in theorganism (or a target organ); (2) equal dura-tion of this time are toxicologically equivalentirrespective of the chronological part of theperiod within which they fall; (3) the reversalof pathological changes during the periodafter exposure can be neglected. Of course,the degree of validity of these assumptions isdifferent for different pathological processes.Changes in the action integral associated withchanges in the conditions of chronic inhala-tion of quartz for equal cumulative exposure9or with changes in the kinetics of the reten-tion of quartz in the lungs and the tracheo-bronchial lymphnodes due to a cytoprotector5were shown to simulate quantitative changesin the intensity of silicosis in rats.More recently other workers have sug-

gested a basically similar (although mathe-matically different) criterion for predictingdifferences in the pathological response of theorganism to quartz and titanium dioxide asmeasured by one index only, that is: the num-ber of neutrophilic leucocytes in BAL fluid.'As well as the kinetics of dust accumulationin the lungs these authors take into account aspecial "harmfulness function" as an addi-tional factor when calculating their criterion,the incremental dose. This function describesthe harmfulness of particles accumulated inthe lung tissue. The concept of the actionintegral did not require such a factor as theaim was to predict the effect of exposure tothe same substance under different condi-tions. As for predicting the effects producedby dusts of different cytotoxicity we decidedto check whether the action integral needs the"harmfulness" of particles to be taken intoaccount as well.

Having computed the values of the actionintegral for compartments X, and X6 in ourmodel, we found that the total action integralwas 55-53 mg. week-' for quartz, whereas fortitanium dioxide it was only 5-57 mg. week-'-that is lower by a factor of 10. The action

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integrals were computed for the entire 30week experimental period. In this case we didnot use the neutrophilic leucocyte count ratiothat was used in short term tests on rats as

the criterion of comparative "harmfulness" ofthese dusts. As was noted in the previous sec-

tion of this paper, the neutrophilic leucocytecount corresponds to the number ofdestroyed alveolar macrophages. Also impor-tant are less noticeable cytotoxic effects pro-

duced by particles accumulated in the tissue.Therefore we directed our attention towardsthe comparative cytotoxicity of the dustsunder study for a culture of rat peritonealmacrophages.

Judging by the trypane blue exclusion test,the percentage of non-viable macrophages inthe control culture was 11-78% (0-14%),whereas in a culture incubated with a sampleof quartzite dust from air from the exposurechamber it was 33-89% (0O78%) and in thatwith a similar sample of titanium dioxide dust27-80% (0 44%). The difference between theexposed and control cultures for quartzitewas a factor of 1-4 higher than that for tita-nium dioxide. For estimating the comparativecytotoxicity of a large number of dusts we

also successfully used the 5'-nucleotidaseactivity reduction test as measured in jig ofinorganic phosphorus. In this case it was

equal to 18-87%(0-65%) for the control cul-ture and 9.45%(1.18%) and 13-02%(0 86%)for the cultures incubated with quartzite andtitanium dioxide. The difference between theexposed and control cultures was 1 6 timeshigher for quartzite than titanium dioxide.Thus we assumed an average factor of 1-5 toexpress the higher aggressiveness of quartzite,and taking into account the 10-fold differencebetween the action integral values, quartzitemay be expected to cause a pathologicalprocess in the lungs with an index of intensity15 times greater than titanium dioxide.

If the difference in group average charac-teristics between the exposed and controlgroups is an index of the intensity of thepathological process, then the ratio of theseindices for the dusts under comparison (table4) shows that the prediction is true only fortwo criteria of intensity, the increase in thelipid content of lungs and the number ofneutrophilic leucocytes in the BAL fluid. (Wehave already mentioned that against the back-ground of a developed pneumoconiosis thisnumber can be regarded not so much an

index to the intensity of breakdown of alveo-lar macrophages at the moment of perform-ing the BAL as a criterion for the intensity of

the pathological process in the lungs.)At the same time, the mass of the lungs

and their hydroxyproline content are higherfor quartzite than for titanium dioxide butonly by a factor of three to five; however, 10weeks after the exposure the difference inhydroxyproline content was already 10-fold:3270(155) ug in the control; 5242(457) jgfor quartzite (higher by 1972 Mg);3464(153) jug for titanium dioxide (higher by194 Mg only). (Unfortunately we have no dataon the retention of dust in the lung for thistime point; therefore, we did not take it intoaccount when checking the model.) Note alsothat at both time points the difference in thehydroxyproline content between lungs thataccumulated low fibrogenic titanium dioxideand control lungs was not significant; there-fore the true difference between this shift andthe significant shift caused by quartzite couldbe higher.The response of tracheobronchial lymph

nodes, estimated in our experiments only byincrease in their mass, provided experimentaldata given in table 4 that indicate that theshift due to quartzite is greater than that dueto titanium dioxide by a factor of 9-8.Meanwhile, the value of the action integralfor compartment X5 is equal to 3-38mg.week-' in the case of quartzite and to 0 15mg.week-I in the case of titanium dioxide-that is, titanium dioxide is lower by a factor of22-5. Taking into account the index of com-parative "harmfulness" (that is: the factor of1-5) a 34-fold difference between the effectscan be predicted.

Predictions of this kind cannot be totallyaccurate quantitatively. We regard as chancethe "accurate hit" for two indices of the fiveand regard the "deviation from the target" forthe other three as normal. We think it moreimportant that predictions based on the prod-uct of the action integral and the factor ofcomparative cytotoxicity are generally more

reliable than predictions based on any ofthese individual criteria or on the estimate ofthe ultimate dust content of lungs only.

It is important that the experimental dataand our predictions show that dusts of greatercytotoxicity cause a greater increasing drymass of tracheobronchial lymph nodes thanof the lungs. Indeed, quartzite caused a 9-8times greater increase in the dry mass of tra-cheobronchial lymph nodes and only a 4-65times greater increase in the lung mass com-

pared with titanium dioxide, that is: com-

pared with lungs the difference between dustsfor tracheobronchial lymph nodes was higher

Table 4 Some indices of intensity ofpathological changes in lungs of rats due to inhalation exposure to dusts at the end ofa 10 week period after exposure (x SEM)

Groups of DTy mass of DTy mass Hydroxyproline Lipids Neutrophils x 106rats lungs (mg) of TBLN (mg) in lungs, (jg) in lungs (mg) in BAL fluid

A Controls 295 2(8-2) 5-5(0-05) 2818(160) 29-0(1-4) 0 38(0 09)B Exposed to quartz 486-8(30 05)* 23-1(2-9)* 3936(286)* 111-7(13-6)* 6-21(0-73)*C Exposed to titanum oxide 336-4(13-2)*t 7-3(0 5)t 3257(232) 34-9(2 2)t 0-77(0-14)*tBC-A 4-65 9-78 2-55 14-02 14-95

*p < 0-05 v controls irrespective of type of exposure.tp < 0 05 groups exposed to titanium oxide v corresponding group exposed to quartz.

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Katsnelson, Konyscheva, Sharapova, Privalova

by a factor of 2' 1. Our prognostic criterionobtained by multiplying the action integral bythe comparative harmfulness index differs forthese' dusts for compartments (X4 + X6) by afactor of 15, whereas for compartment X5 bya factor of 34-that is, that difference isgreater by a factor of 2-3. Agreement betweenthe prediction and the experimental result isnearly perfect.

Another important consideration is that,according to most of the effects, the differ-ences caused by the dusts in both lungs andtracheobronchial lymph nodes is more sub-stantial than expected based only on theindex of their comparative cytotoxicity with-out taking the action integral into account.Finally, the mass of the dusts under compari-son in the interstitial lung 10 weeks afterexposure differs greatly: by a factor of 24 inthe experimental data, and by a factor of 27in the model predictions (tables 1 and 3).Taking into account the 1-5 factor, this sug-gests about a 40-fold difference in the inten-sity of pathological reaction if we took intoaccount only the final retention of dust ratherthan the history of its accumulation and elim-ination as reflected by the action integral.

ConclusionThe cytotoxicity of dust particles has a dualrole as a characteristic that determines themathematical prediction of the comparativerisk of developing pneumconiosis due to theaction of different dusts. On the one hand,this characteristic determines the kinetics ofthe accumulation and retention of particles inlungs and lymph nodes, and thereby the valueof the action integral. On the other hand,comparative cytotoxicity permits the compar-ative "harmfulness" of particles retained inthe tissue of these organs to be judged.

Mathematical modelling shows that it isnecessary to consider the combination ofthese two effects for explaining importantquantitative differences between the patho-logical changes due to chronic inhalation ofpractically insoluble dusts of different cyto-toxicity, assuming similar conditions for theirdeposition from the alveolar air.

1 Bolton RE, Vincent JH, Jones AD, Addison JA, BeckettST. An overload hypothesis for pulmonary clearance ofUICC amosite fibers inhaled by rats. Br Jf Ind Med1983;40:264-72.

2 Vincent JH, Johnston AM, Jones AD, Bolton RE, AddisonJA. Kinetics of deposition and clearance of inhaled min-eral dusts during chronic exposure. Br _7 Ind Med1985;42:707-15.

3 Vincent JH, Donaldson K. A dosimetric approach forrelating the biological response of the lung to the accu-mulation of inhaled mineral dust. Br _7 Ind Med1990;47:302-7.

4 Smith TJ. Development and application of a model forestimating alveolar and interstitial dust levels. AnnOccup Hyg 1985;29:495-516.

5 Katsnelson BA, Konysheva LK, Privalova LI, MorozovaKI. Development of a multicompartmental model of thekinetics of quartz dust in the pulmonary region of thelung during chronic exposure of rats. Br I Ind Med1992;49:172-81.

6 Katsnelson BA, Privalova LI. Recruitment of phagocytiz-ing cells into the respiratory tract as a response to thecytotoxic action of deposited particles. Environ HealthPerspect 1984;55:313-25.

7 Privalova LI, Katsnelson BA, Yelnichnykh LN. Somepeculiarities of the pulmonary phagocytotic response:dust retention kinetics and silicosis development duringlong-term exposure of rats to high quartz dust levels. Br7Ind Med 1987;44:228-35.

8 Vincent JH, Jones AD, Johnston AM, McMillan C,Bolton RE, Cowie H. Accumulation of inhaled mineraldust in the lung and associated lymph nodes: implica-tions for exposure and dose in occupational lung dis-ease. Ann Occup Hyg 1987;31:375-93.

9 Baidosov VA, Katsnelson BA, Privalova LI. An approachto the mathematical analysis of the pattern organizationof shortening the cumulative working period underexposure to harmful substances with marked cumulativeability, taking pulmonary dust retention as example. In:Mazurov I D, Smirnov A I, eds. Mathematical models ofbiological and medical systems. Sverdlovsk, Russia:Publishing House Nauka, 1988:67-8 (in Russian).

10 Privalova LI, Katsnelson BA, Baidosov VA. The "actionintegral" as a criterion for comparative assessment andcontrol of exposure patterns to substances with markedmaterial cumulation. Gig Sanit 1986;12:12-5 (inRussian).

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