Document zo2ve5mQn1z2RBEYvOay2gdQ0

November 16, i960 Memo to: Dr. Kehoe From: T. Sterling Subject: Deposition of I^ead The reanalysis of the lead data was motivated mainly by the question whether one could assess the amount of lead deposited in the tissues of individuals who are exposed to lead in quantities greater than usual. I can now submit a solution to you of which I am reasonably certain. This report will deal with the bare bones of the problem, as we have discussed it during the year. It does not cover other as pects of last year's work which are in varying states of completion. Figures, tables, and a list of the symbols used and their meanings can be found at the end. I have also summarized some prospective work which appears imminently necessary. Conclusions or appli cations were avoided until further discussion with you. I would like to add one note of caution. In computing actual values I have been willing to generalize from the observation done on six subjects, under somewhat varying conditions. It is encouraging that a fairly consistent picture emerges at the end despite individual differences. Yet, the calculations are limited by this fact. Finally let me acknowledge the patient help and cooperation that was given by Mr. Shaefer (in generous quantities) by Mr. Creech, and by John Phair, who was willing to toss the problem around g&lmoet endlessly. 2 Some Preliminary Discussion We start with a simple descriptive model {F ig. 1). In this model lead may be Ingested or inhaled. Excretion of lead is through feces and urine. Lead may be deposited or returned to the body fluid compartment. Lead may also be lost through sweat or may be taken in without being measured. However the statement may Weuristically be made that unmeasured intake and output counter balance each other. A long term comparison of lead, in and out, as measured by the experimental procedures shows that over a long duration lead in{Pbl)is approximately equal to lead out (Pbo). Table 1 gives the comparison for a number of subjects. Primary Equilibrium An equality of Pbl and PbQ during the pre-experimental period may be taken to indicate that the subject is in a state of equilibrium in which the amount of lead exc reted ^pproxlmat s3~y)eq ua.1 a the amount of lead ingested. Since some of Pbl comes into the body compartment one cannot assume that the equilibrium is due to direct elimination of Pbl. However, even if some of the Pbl enters the body and even if some fraction of that amount is deposited it is etill possible to obtain such an equilibrium between Pbl and Pbfl. The logical steps by which such an equilibrium is possible can be conveniently discussed by a physical analogy. Let us take a beaker of water B in which the volume of fluid V is kept constant. A sample of fluid, S, is removed each day and an equal amount of clear fluid added. Case 1 Let us now add a constant amount X of a aolmble salt, to the beaker each day. The first day some of the salt will be removed K 0 013 0 b 7 3 with S. The precise amount removed will be S ^^ ] or that proportion of X in V that falls into S. It is obvious that after adding X once, only a fraction will have been removed. The level of the salt in the beaker will increase until the amount removed is equal to the amount of salt added. An equilibrium will be reached when \s) = x Case 2 (i) Let us assume next that we disturb this equilibrium by removing a constant amount of X, dX;through some other channel without modify ing V. Again it is obvious that the process will go to equilibrium at a time when (S {l-d ) x (2) Case 3 Let us assume that only part of x is added to B and that the re mainder is placed directly in S. Where k x is added to S and k^x is added to B and where kj x + k^x = x so that k + k. 1 1 equilibrium when +V (3) or when the amount of salt removed in the sample S equals to the amount added. Of course in the latter case HE 001 3058 4 Case 4 Let us assume that x is not a constant quantity but a random variable taking on values between x . < x < x . When mm. j max. fi>the amount of x^ varies at random S will vary so that the amount of salt removed ia S, will fluctuate between x , < S' i fin.^. jJ max. If the best unbiased estimate of x, * I (x) It follows that over a duration of JL_ix, is considered a iafil.il = E (X) and that 2 s- 8 j `j or that the average output equals to average intake and that the 22 Variance of outjr&l, r , equals to the Variance of input, <r . If the variable input of x is considered for Case 3 it is still jEl xj .L but sum > 8tf because of the additivity of Variances. A similar statement applies to Case 2. KET 00130ba 5 Recovering Unknowns Let us assume that one can measure only the amount of salt removed in the sample S, while V, and x are unknown. From our discussion of Case 1 it is clear that if one permits the process to go to equilibrium one can then know X, the amount of salt added. If the amount of salt itself is added in variable quantities the average amount of salt removed during equilibrium emerges as the best estimate of S (x), the average amount added. Cases 2 and 3 present difficulties in that two unknowns have to be evaluated from a single measurement. However, a solution here is possible if we change the level of equilibrium. For instance, in Case 2 if a known amount A x is added to the beaker a new equilibrium will be reached when in measuring the proportionate increase of salt in the sample the c onstant d and the original value of x can be c omputed. In case 3 a simple comparison of two equilibria) is not sufficient used here. Chao could, for instance compare the rate with which the new equilibrium io reached for a number of different increments of x, ax,, gx., etc. It is obvious that the rate with which the salt in S reaches each now equilibrium is a function of ax and of k^ and k^. The discussion of the physical analogue points to the following conclusions: 1. A model constructed along its Unas should show the same properties presently exhibited by the data. HE 0013000 o 2. The analogue can be co-ordinated almost point for point with a reasonable picture o how the escchangs of inorganic l-oad takes place. a. The soluble salt ia variable quantities is equivalent to the daily inorganic lead intake. h. The constant volume in the beakers is equivalent to the body fluid. c. The sample, S, is equivalent to the day by day excretion. d. Casa 2 describes a deposition process that may possibly remove soma of the load from the body fluid and store it in tissue End bone. e. Casa 3 describes a process that may be similar to the direct focal ostcretion of a fraction f Isad ingested daily. f. Gaa 4 allows for tresdesaeat of the data even under variable conditions of intake and outpat. 3. The bvioa* advantage of tk model ia that some important con clusions can be reached from ksowlsdg of; a. lead removed by excretion b. lead intake c. additional lead added in fcasgvra lacrmanta. 4. The major concern will ba with tk consequence of adding an increment of lead through' the lungs. Both the increment s e 4 the possible aausnt of that incramat that is deposited css evaluated from tha dahi by ussa of a model similar to the ana logue. tf/r 0013061 7 We return now to the flow of lead intake and excretion of Figure 1. The pre-exposure period will be evaluated to begin with. During this period the subject's lead ingestion and excretion is measured but he is not yet exposed to an increment of lead in air. JLet PbOQ = f(PbI, FbY) where the function is linear so that PbU + PbF.a k|PbI + k PbV + a = PbO. J J j"* 2 J J (5) where Pb$j = total excretion of lead on the j th day. PbFj = fecal excretion of lead on the j th day Pb= urinary excretion of lead on the j th day Pblj ingestion of lead on the i th day tbssfSsr the j th day of measurement PbV^ * amount of lead in body fluid on the j th day * constant, a, may consist of three parts. 1. <|(PbY) * a fraction, d , of lead in body fluid that is deposited. 2. D = difference between unmeasured input and loss of lead. 3. e = error of measurement. n 2e assuming that in the long run 1 = 0, or that the error is not nr correlated to any of the other variables, then a = d PbV + D. |It is assumed that PbU, excretion of lead through urine, is simply a linear function of PbV and of urine volume YU. PbU. * c PbV + j1 j where again, n c YU + 2j e (6) 1 ---- * o n The last assumption appears to be reasonable. During the experimental period both urinary lead (PbU) and blood level of lead ft 001306 9 into the body, so that L * S+ L. (7) The amount of lead excreted after the first day is given by Pb0]L - k^Pbl^ + JLfl) +kJPbVQ + (1-1c 1)Lb + L^] + a The amount of lead excreted after the second day is given by Pb02= k1(PbI_i + Lg) + k2 CpbVo + (l-k1)(l-k2)L8 + (1-k )J. .f if we let a+*+ (l-k,)L +L bx = u-kj) b, = (i-k.) PbQ = k,(PbI + L, ) +k [pbV +{b,L + L. )(1 b,)~I + a 2 1 -i s 2 ** o Is b 2'-* <i ItfKcl Note that PbV^ stands for the amount^in total body fluid at the onset of the new additional increment. After the nth day, the amount of lead excreted will be given by the general expression {8a) (8a) Pbo = k,{PbI , +L ) + SC fPbV +(b,L +L)(l + b,+bS_____+b" Pbo n = k1l -is 2~ o lab 22 2 but n 2 f1 +b 2 2 `2 1 n- 1 >2 n 1 - b. 1 - b. and line 1 n--> oo 1 1 - b. so that (8bJ b +L PbOo = kl(Pb!_i+ Lj)+ k2 QpbVo+ - i\-h- ] a ( 8b) The increment in excreted lead is now given by the difference between the amount of lead excreted without the increment L., or PbO , and the amount of lead excreted on the nth day, or Pbo , (f) o' ' n KJE" 0053064 lo APbo = PbQ - PbO no fV-. + h, k L +k Is 2\ b2 <9) but `-b2 = k2 so that APbQ= k,L +(1 -k,)L +L=L+L=L la 1' a d sb , <\ckMut So that after n days, the increment of lead earrctecj>\is equal exactly to the additional increment of lead taken inr t <\cf< If now conditions of Case 2 hold and some of the lead present in the body is stored, it follows that the increment of excreted lead is given by (JL 0 ) A Pbo = (l~d)L where d = constant of deposition. (10) To find the constant of deposition one simply takes APbo I-- =d or 1- PbO - Pbf .n =d (11a) (lib) where PbO * the daily total lead excretion after equilibrium has been reached Pbo = the daily total lead excretion of the previous equili brium, before the increment, L, was given daily. L, = the daily increment of lead d = rate of deposition of L. ^ 0013065 Use of the Deposition Theorem in a Practical Solution Because of the variability of actually measuring intake and output of lead for human subjects, the theorem has to be modified to conform to conditions of Case 4 .(12) and (13) &PbQ = E (PbQn) - E (PbOQ) (12) E( APbQ) d E( L) (13) and where E(PbO) m E PbO.i m m E JL. E(L) = ----------------------m or the arithmetic average of daily intake or daily output, measured during periods of equilibrium. One could now obtain the necessary estimates to solve for the conditions of the lead chamber experiments by measuring excretion of lead previous to the experimental exposure and after the exposure period has gone on for a sufficient time span to permit a new equilibrium. In practice such an attempt will not work, unfortunately. All subjects show a change in food intake during the experiment which, while possibly due to changes in daily regimen, makes it impossible to use the mean excretion during the pre-experimental period as an estimate of E(PbO ). This difference is shown in Table 2. We could o' use another approach to get an estimate of PbOQ. It is reasonable to assume that input and output balance. In fact, the theorem states explicitly that the amount of lead ingested and absorbed from other 001 3 u t> o 12 sources and not measured in the experiment is counterbalanced bylead lost through other sources and not measured by the experiment, (such as sweaty One could^take the average intake measures during equilibrium periods for the best estimate of PbO . The validity of this procedure is testified by figures in Table 1. In short, one can take the average amount of lead ingested^during the experimental Cist periodic estimate the average amount that would have been excreted due to ingested lead. Table 3 gives the best estimated of PbOQ, Pbo , as well as the best estimate of L, as measured directly from the amount of air respired by each subject and from the chamber con centration.'- The constant of deposition, d, can now be recovered by the following expression E (d) = 1 E(PbO ) - E(PbO ) n_o E(L) The calculations and resulting proportion of storage are given in Table 4. (The values of L were obtained from measurements done by Mr. Shaeffer^ Lawful relation between d and L It is unlikely that d is a constant for any amount of lead absorbtion. A number of factors appear to'peak against such an assumption. For instance, the lead and tissue may interact as a jll CvWn* function of combined surfac areaV' Deposition of lead may increase the likelihood of additional deposition. Deposition of lead in some tissues may inhibit the elimination of lead k*Abody fluid. Variations in d values for different subjects became orderly when, at the suggestion of John Phair, the impact of L on d was considered. Table 5 shows that there appears to be an orderly and lawful relation between d and L. Increases In L.a*o associated quite obviously with exponential increases in d. With one single j^|: 0013u6 13 exception, the d values for all subjects fall on the equation (12). -5. 17(L) + 1.4 d = e"C (12) An independent check exists partially for the validity of this expression. When L equals zero, or before the individual starts his daily exposure in the chamber, the value of d, refering now simply -Hi toKingested lead, should equal to e * or . Q& -># This value is very close to the actual observed difference between daily intake and excretion of lead for those subjects for whom Pbl > Pbo . oo Additional Empirical Validation Neither the reasonableness of the model nor the satisfactory computation of the deposition constants are by themselves completely sufficient to validate the constructs here developed. A very simple experiment could decide this issue satisfactorily. This experiment will use 5 groups of animals, each group consisting of 4 to 5 subjects. A control group will be fed ad libitum, and the only measurements made will be of the lead consumed and excreted. The other 4 groups will be given, as a dietary supplement, specified increments of lead. Depositions constants, d, will be com puted as was done here and verified by completely ashing the animals and measuring their total lead content. In each case, the differences between control and experimental animals should be an amount of n lead equal to dXL. and the d's themselves should show an exponential association to the varying increments. If this experiment has the predicted outcome, it will be desir able next to establish d as a function of body size, blood level of lead, and of other and related variables. 0v I 3 'bo 14 Since the model should apply to other inorganic substances as well, another, and perhaps more easily measurable agent could be used. KB /v in) * i 3 3 6 'J 15 Takle ) . Observed average daily intake (Pbl) and output (PbO) of lead during the last 22 weeks of the control period preceeding exposure to lead in the chamber's air. (In mg of lead) Subject Creech exp. 1 Creech exp. 2 Barber exp. 1 Barber exp. 2 Blackstone Svetlik E (Pbl ) o for each day E (PbO ) o for each day Difference E(PbIQ)-E(PbO . 329 . 145 . 24o . 198 . 188 . 171 . 294 . 141 . 229 . 241 . 203 . 169 + - 03S + . 004 + .011 - .043 - .015 + . 002 Mean Difference = .001 00130 7 0 16 Table 2 Observed average daily intake E (Pbl), during the last 22 weeks of control and experimental periods. (In mgs. ) Subject Creech exp. 1 Creech exp. 2 Barber exp. 1 Barber exp. 2 Blac kstone Svetlik E(PbI ) o for each day E (Pbln) for each day Difference E(PbI }-E(PbI o . 329 . 145 . 24o . 198 . 188 . 171 . 2c6 . 138 . 182 . 125 . 186 . 220 + . 113 + . 007 + . 058 + . 073 + . 002 1 o * <3 Mean rence = + . 034 KE 0013071 17 Table 3 Observed values of daily food intake during the last 22 weeks of the experimental period. These value3 are taken as the best es timate of E (PbO ). Observed values of average daily total ex cretion cSOP^cinJ^itAd oE-inhal&tios of leadyi &{L) during the same period Subject E(PbI )=E(Pbo ) no E(PbOn) E(L) Creech exp. 1 Creech exp. 2 Barber exp. 1 Barber exp. 2 Blackstone Svetlik . 2058 . 1384 . 1819 .1253 . 1862 . 2201 . 3290 . 3205 . 2347 . 3006 . 3336 . 3932 . 1488 . 3392 . 0627 . 24q 2 . 3552 . 2706 Kr 0013 0 'i 18 Table 4 Computation for (PbO) and given in Table 3. based on the figures & (PbO) = E (p*>0n) - E (PbOQ) i . d = ft (-fbo) E(L) Subject (PbOn )- E(PbOo ) E ( L) ( 1 -d) (proportion of L excreted each day.) d ( proportion of L. deposited each day) Creech exp. 1 .3290 - .2058 . 1488 . 8280 . 1720 Creech exp. 2 . 3205 - . 1384 . 3392 . 5368 . 4632 Barber exp. 1 . 2347 - . 1819 . 0627 . 8421 . 1579 Barber exp. 2 . 3006 - . 1253 . 24o2 .7298 . 2702 Blac ketone . . 3336 - . 1862 . 3552 .4150 . 5850 Svetlik . 3932 - .2201 . 2706 . 6390 . 3410 HE 0013073 19 Table 5 Observed relation between the L. and d of each subject Subject Blacketone Creech exp. 2 Svetlik Barber exp. 2 Creech exp. 1 Barber exp. 1 Rank 1 2 3 4 5 6 L . 3552 . 3392 . 2706 . 24q 2 . 1488 . 0627 D . 5850 .4632 . 3410 . 2702 . 1720 . 1579 -5. 17 (L) + 1.4 e d= e HP 0013074 20 Abbreviations and Symbols: Pbl. x pbj Ingested lead on the i th day, in mgs. Total excreted lead on the j th day, in mgs. PbF. 3 PbU. J PbVj Lead excreted in feces in the j th day, in mgs. Lead excreted in urine on the j th day, in mgs. Amount of lead in body fluid on the j th day, in mgs. vu. 3 L Volume of urine on the j th day, in gm. Constant increment of lead taken in through the atmosphere L Part of L, reaching the body via the stomach 0 Part of L reaching the body directly through the lungs. APbo I^Lfference between excretion solely due to Pbl and excretion due to Pbl + L k Proportion of Pbl removed directly in feces 1 k 2 proportion of lead in body fluid that is removed through fecea and urine d Constant of deposition: Proportion of L that is deposited in tissues b - t 1 - k,| 1 b 2 = (l-k2) KP 0013 sJ 4 v 2o VJ w 1* \j l r <^o vfcO v/t ^ or HZ 00130 '4,?n