Dosimetric implications of pulmonary macrophage clusters observed within lungs of rats that have inhaled enriched UO2 particles.

Twenty-four Fischer 344 rats were exposed to enriched uranium dioxide (UO2) aerosols to give a mean initial lung burden of 291 +/- 89 (SD) micrograms. Groups of rats were killed at 1, 7, 180, 360, 540, and 720 days post-inhalation (PI). Their lungs were fixed and inflated. Sections cut from all five lung lobes were used to prepare CR-39 neutron-induced 235U fission fragment autoradiographs. A single traverse across a CR-39 autoradiograph of a tissue section, from the left lung of all the rats, was made using a motorized microscopic stage. The traverse was divided into 10 fields. The track counts per field were used to test for homogeneity of track distribution and to assess if there was any tendency for tracks to be related to the peripheral region of the lung. Full raster scans across the entire tissue image were made on left lung autoradiographs from two animals killed at each time point to assess the homogeneity of fission fragment track distribution throughout the entire section. There was no evidence of any temporal change in the proportion of tracks associated with the lung periphery. At all time points PI, the track distribution was significantly nonhomogeneous, suggesting a nonuniform pattern of tissue irradiation from the 234U alpha particles. At time points from 180 to 720 days PI, large clusters of macrophages were observed in some of the sections taken from all five lung lobes. The total number of macrophage clusters increased with time PI. These macrophage clusters produced many 235U fission fragment tracks within the CR-39 autoradiographs.(ABSTRACT TRUNCATED AT 250 WORDS) ImagesFIGURE 1.FIGURE 2.FIGURE 3.FIGURE 4.


Introduction
To satisfactorily assess the radiation dose to lung cells at risk of cancer induction, it is necessary to know the microscopic spatial distribution of the inhaled radioactive particles within the lung tissues. This is particularly important for highly insoluble particles (International Commission on Radiological Protection [ICRP] Class Y), such as plutonium oxide (PuG2) and uranium dioxide (UO2) that have long residence times in the lung. Data from animal studies suggest that such particles become increasingly less randomly distributed with time after inhalation (1). In particular, the particles appear to become more associated with the lung periphery and peribronchial tissue (2,3). Diel et al. (4) speculate that this association may be due to preferential clearance ofparticles from the more central alveolar regions. In 3Present address: Plasma Fractionation Laboratory, Churchill Hospital, cases ofhigh particle burdens or lung dose, it seems that particles also become associated with fibrotic areas of extensive tissue damage (5).
The principal agent for the clearance and redistribution ofparticles within the lung is the phagocytic alveolar macrophage. Sanders (6) showed that insoluble 239PuO2 particles retained in the lung from 1 to 2 days after inhalation were normally in macrophages. Large aggregates of macrophages containing insoluble anthracitic particles have been observed by Cottier et al. (7) in lungs from humans of "advanced age." The particle-laden macrophages were principally associated with pleural and septal lymphatics. Only 2% ofall the particles observed in the lung were associated with alveolar tissue. Cottier et al. (7) discuss the relevance of this finding to possible "hot spots" in lung doses after radionuclide inhalation. This paper presents data from a long-term study ofthe spatial distribution of inhaled, enriched U02 particles within the lung ofthe Fischer 344 rat. The work is concerned with the dosimetric importance of clusters ofalveolar macrophages observed to be laden with U02 particles. An assessment is made ofwhether the dose to tissues within the rat lung was likely to have been reasonably uniform over the lung during the 720-day post- MOR1RS ETAL. inhalation (PI) period. Earlier work with the sam sections suggested that the central alveoli, subpleura airway tissue regions would receive about the sE particle dose over the 720 days PI (8). In this pa domness ofthe U02 particle distribution in the lung vestigated to discover if the dose within these thre regions is likely to be uniform or highly uneven. Di other aspects ofthis U02 particle distribution study Morris et al. (8,9).

Materials and Methods
Inhalation Procedure Twenty-four male Fischer 344 rats were exposed r 100 min to an aerosol ofenriched U02 at a concentra 150 mg/r3. A complete description ofthe exposure F these rats is given by Morris et al. (9). The acti aerodynamic diameter ofthe aerosol ranged from 2 with a geometric standard deviation of 1.7. This sug median stokes equivalent diameter ofthe U02 parli 0.8 Am, assuming a U02 density of 11 g/cm3.
mass. This gives an a-particle activity ofabout 1.91 a mean a-particle energy of4.7 MeV, due mainly to of 234U. The total -y emission rate is about 40% ofti For comparison, 239PuO2 and U02 ofnatural isotoj tion (99.275 % 238U, 0.72 % 235U, and 0.005 % 23 particle activities of 2.027 x 103 Bq/itg and I respectively. At 5 days PI, the mass ofenriched U02 retained in estimated by using a small animal whole-body -y counter (9). The mean initial burden ofall the rats v ,ug (SD), with the lowest burden at 136 jg and the h Mg.

Lung Tissue Fixation
Two rats were killed at 1 and 7 days PI. Further g rats were killed at 180, 360, 540, and 720 days PI. 1 anesthetized by exposure to 4% halothane and then tratracheal instillation of 1% (weight/volume) OS04 bon FC80,* at an excess pressure of 15 cm above the method was selected because the nonpolar solvent 4 with aqueous lung fluids and has been shown to flr airway surfaces (10). The inflated lungs were disse4 body and all five lobes separated. Each lobe was c1 transverse slices and further fixed under vacuum f M glutaraldehyde. After fixation, the lungs were st sodium cocodylate buffer at 4°C. The uranium co] lung was estimated using a y scintillation counter.
The uranium contents ofthe trachea and extrapuln chi, thoracic lymph nodes, internal jugular and postc lymph nodes, kidneys, liver, spleen, and carcass ren determined by delayed neutron analysis. These da reported by Morris et al. (9). After scintillation counting, some ofthe 3-mm lung slices were tper the ran-systematically taken from all of the rats and embedded by the is further in-method of Spurr (11). Thirteen lung lobe slices were selected e lung tissue from each rat, 2 from right anterior, median, and cardiac lobes iscussions of (3rd and 6th slices from the apex), 3 from the right posterior lobe are given in (2nd, Sth, and 5th slices from the apex), and 4 from the left lung (2nd, 5th, 8th, and 11th slices from the apex). The resin blocks were cut serially by microtome to produce tissue sections ofnominally 5-ytm thickness. Bq/iAg, with lung section was produced in the CR-39 using the method of , the presence Gore et al. (12). This method creates a reasonably good resoluhe a activity. * tion tissue image ofthe lung section while retaining the neutrongic composiinduced 235U fission fragment tracks. The pr6cedure enabled us U) have ato locate 23sU fission fragment track foci within the tissue sec-0102 Bq/Mg, tion (see Figures 1-4). It is assumed that the 235U remains associated with the insoluble UO2 particles and that the number the lung was oftracks seen is related to the mass ofU02 in the tissue section. To investigate whetherthe lung sections showed any significant does not mix temporal changes in the percentage oftracks associated with the x cells on the lung periphery, a series of single traverses were made across a xcld from the selected CR-39 a-image autoradiograph made from a tissue secut into 3-mm tion taken from the slice from the apex ofthe left lung. This was or 1 hr in 0.1 the 3-mm tissue slice with the largest cut surface area. These bred in 0.1 M traverses were made using a light microscope, at 160x magnifintent of each cation, equipped with a motorized stage and attached to a Seescan Solitaire plus grey-level image analyzer (Seescan Ltd., nonary bron-Cambridge, UK). The image was captured from the microscope nriorcervical using a high-resolution monochrome Newvicon camera and fed nainder were into the Seescan image analyzer via a monochrome monitor. The ta have been traverse was taken across the widest part ofthe left lung section image, approximately from the ventral to the dorsal side of the rat. The single traverse was divided into 10 equal lengths such 05910, supplied fthat the opposite edges ofthe lung made the beginning and end )erbyshire, UK, of the traverse. The height of each of the 10 fields was 500 Am.
The width of each field varied between 1000 and 1500 Am, 202 depending on the width ofthe lung section image. The number of fission fragment tracks were then counted within each ofthe 10 fields. Small foci oftracks were counted by eye. The few large foci of tracks observed were measured by the Seescan image analyzer, where the area of the total track focus was divided by the mean area ofa single track to estimate the track number. This was repeated using left-lung eighth slices from each rat at every time point PI. The mean percentage oftracks per field was then calculated for each time PI. A chi-square homogeneity test (13) was applied to the data to see if the distribution oftracks across the traverse differed from that expected with uniform track distribution (i.e., 10% per field).

Uniformity of Track Distribution throughout Entire Section
We randomly selected two of the CR-39 autoradiographs of sections taken from the eighth 3-mm slice from the apex of the left lung from rats killed at each time point. The CR-39 tissue images were systematically raster scanned with the Seescan image analyzer so that all of the section was viewed with no field overlapping. The field size was 500 x 500 jAm. The track number for each field was counted by eye for small track foci and by the image analyzer for the occasional large track foci, using the total track foci area method described above. There were 4-25 large foci (including track aggregates from macrophage clusters) in each section autoradiograph. The total number ofaccepted fields scanned per section varied from 450 to 650 fields. All fields within the section where no tissue was seen (mainly inside conducting airways) were discounted. Otherwise all fields were accepted, provided they had some tissue visible. We assumed that the percentage of fields with small fractions oftissue present would have been similar for all section images. A chi-square homogeneity test (13) was applied to the track count data from each section to assess whether the number of tracks present within each field was consistent with a uniform track distribution over the entire section.

Estimation of Number of Macrophage Clusters within CR-39 Autoradiographs
While scanning some ofthe CR-39 autoradiographs to obtain data for earlier work (8), it was noticed that occasionally some large foci of 235U fission fragment tracks were seen. These track aggregates were markedly larger than the normal circular foci of tracks and were made up of many overlying large foci (see . Studying the adjacent H&E tissue sections led to the conclusion that these track aggregates were caused by clusters of macrophages containing many clearly visible black particles that were assumed to be U02. As these track aggregates were visually quite striking, an attempt was made to assess their significance on total lung doses. A single CR-39 autoradiograph from each ofthe 13 lung slices was fully scanned, and the number of these track aggregates counted. This was repeated for all rats, at all time points, giving a total of 52 lung autoradiographs scanned from the 4 rats killed at 1 and 7 days PI and 260 lung autoradiographs scanned from the 20 rats killed at 180, 360, 540, and 720 days PI. The track aggregates were subclassified into large and small macrophage clusters. Small track aggregates typically consisted of 150-500 tracks, whereas large aggregates contained about 300-2000 tracks. The location of each track aggregate was noted and assigned to either subpleural alveolar, central alveolar, or ciliated airway tissue regions, in the manner of Morris et al. (8). The subpleural alveolar region was taken as all alveolar tissue within 100 um of the lung periphery.
For some ofthe left lung autoradiographs the total number of fission fragment tracks within the section was already known (8). This was true for all the autoradiographs from the eighth 3-mm slice from the left lung apex (one section per rat) and for all time points from 1 to 720 days PI (a total of24 autoradiographs). Using this information, the percentage contribution from the track aggregates to the total tracks counted in these left lung tissue sections, was calculated for each time PI.

Results and Discussion
Single Traverse across a Section from the Left Lung The meanpercentageoftracks foundwithineachofthe 10 fields per traverse across the left lung autoradiograph is given in Table  1. The results of the chi-square homogeneity test of these data, averaged forall rats per time PI and assuming an expected 10% of all tracks ineach field, were 1 + 7days PI, X = 20 ± 9(SD); 180 daysPI,X2-37±23;360daysPI,x2= 93 ± 98; 540days PI, X2 = 136 ± 102; and 720days PI, X2 = 114 ± 39. Inall cases the results ofthe chi-square test showed thatthe distributionoftracks across the traverse was significandty nonrandom (p < 0.001). The results ofa t-test comparing these mean chi-squarevalues showed thatthe 720 days PI point was significantly higherthan the two chi-square mean values measured at4 (1 + 7) and 180 days PI (p < 0.01). There was no significant difference between the mean chi-square values found at 4, 180, 360, and 540 days PI.
The results do not suggest an obvious movement of the particles, in terms oftrack counts, to the periphery ofthe lung. The most noticeable feature ofthe data is that the standard deviations ofthe means given in Table 1 tend to become larger with increasing time PI. Both this and the chi-square test data suggest that the track distribution throughout the traverse section is becoming increasingly less homogeneous with time PI.
The high chi-square value at the 720-day PI point was due to one of the sections, which had two larw,e track aggregates, having a chi-square test value of260.0 x 10 . Ifall ofthe 3.873 x 103 tracks counted in this autoradiograph had been in one ofthe 552 fields scanned, the chi-square value would be 2.1 x 106. The section from the other rat killed at 720 days PI had a track homogeneity chi-square value of 31.0 x i03. A t-test ofthe mean chi-square values given above showed no significant difference between any ofthe PI points. However the single section from the rat killed at 720 days PI with the chisquare value of 260.0 x 103 was found to have a track distribution significantly less homogeneous than that found with the autoradiographs from the 1-and 7-day PI time points (p < 0.02).
So there is an apparent trend of an increasingly less homogeneous track distribution with time PI. Unfortunately, there was insufficient time to scan more sections, which would have improved the sensitivity of the statistical tests by increasing the degrees of freedom. Table 2 shows the number of macrophage clusters within each lung tissue region, from all the 13 lung lobe sections taken from each rat killed at I to 720 days PI. The number ofsmall and large clusters was found to increase consistently with time PI in the subpleural alveolar and airway tissue regions. The number of clusters in the central alveolar tissue region tended to reach a maximum after 360 days PI, falling slightly by 720 days PI. Morris et al. (8) reported that the U02 particles appeared to clear faster from the central alveolar region than from the subpleural alveolar and ciliated airway region. Thus, fewer, particles will aIn all cases the track aggregates appeared to be due to the clustering of alveolar or interstitial macrophages. The section was divided into the pulmonary regions of central alveolar tissue, alveolar tissue within 100 ym of the lung periphery (subpleural alveoli), and ciliated airway tissue. The numberof sections scanned (n) from all five lung lobes were: at 1 + 7 days PI, n = 52; at 180 days-720 days PI, n = 65 for each time point PI.

Estimation of Number of Macrophage Clusters within all CR-39 Autoradiographs
be available in the central alveolar region for the promotion of macrophage clusters. In general, except for clusters associated with airway tissue, the macrophage clusters appeared to be on the alveolar surface. However, the thickness ofthe H&E-stained section did not give good resolution at high magnification, which precluded detailed histological analysis. Occasionally, macrophage clusters were clearly seen within lymphatic tissue associated with the alveolar subpleural region, although this was only after 180 days PI. Serious lung disease was not observed in the animals until 720 days PI (9), so this should not be an important factor in the U02 particle distribution at earlier time points. A typical large macrophage cluster found within the central alveolar tissue region, at 360 days PI, is shown in Figures 1 and   2. A similar large macrophage cluster observed in the subpleural alveolar region at 360 days PI is shown in Figure 3.
At the 1-and 7-days PI time points, all the macrophage clusters within the sections were designated as small, and all were found on the inner airway surface (Fig. 4). These were probably in the process of being cleared by the mucociliary escalator. At later times points, all the macrophage clusters were under the airway epithelium and normally associated with airway lymphatic tissue, suggesting that particles within these interstitial macrophages would be retained in this location for long periods. Morris et al. (8) suggest that the observed U02 distribution pattern will lead to a significant dose to the airway tissue, similar to the accumulated dose received by the central and subpleural alveolar tissue from 4 to 720 days PI. No macrophage clusters were observed to be related to alveoli or airway perivascular tissue. Table 3 gives the percentage oftissue sections found to contain small and large track aggregates. It can be seen that, even at 720 days PI, the majority ofsections, 63 %, had no large macrophage clusters and that 45 % of sections had no macrophage clusters at all. It should be pointed out that even if sections had no macrophage clusters, at the later times PI the track distribution still appeared to be nonrandom within many ofthe sections, suggesting that the dosimetric pattern of tissue irradiation will be nonuniform. However, as the distribution pattern changes continuously with time due to alveolar and interstitial macrophage movement, and given the 40 jAm range of et particles in tissue (14), the actual tissue irradiation pattern may be more uniform than suggested by these observations. The total number of 235U fission fragment tracks were known for 24 ofthe 8th left lung slice autoradiographs. Using this information the proportion oftracks originating from the macrophage clusters could be found (Table 4). This gives a guide to the dosimetric significance of the small and large macrophage clusters. It can be seen that at the later PI time points, the number of tracks within clusters can represent a significant proportion ofthe total tracks counted throughout the section ( Table 4). The maximum percentage of tracks present within macrophage clusters ranged from 0 to 0.4% ofall tracks throughout the section at 4 (1 + 7) days PI. At 180 days PI this value ranged from 0 to 3.77%, at 360 days PI it ranged from 0 to 40.5 %, at 540 days PI it ranged from 0 to 6.9%, and at 720 days the tracks within clusters ranged from 11.0 to 83.9 % ofthe total tracks within the section. Thus, even as early as 360 days PI, macrophage clusters could contain enough U02 particles to represent up to 40% ofthe relative mass ofU02 present within the entire section. All these 204 205 ---FIGURE 1. A CR-39 autoradiograph of a section from the eighth 3-mm slice from the apex of the left lung of a rat killed at 360 days PI. A large aggregate of 235U fission fragment tracks can be seen within the central alveolar tissue region. The total number oftracks emanating from the macrophage cluster was estimated to be 750 tracks using the Seescan image analyzer, which represents 18% of the total track count across the section. AL, central alveolar tissue region; A, conducting airway designated as ciliated airway tissue region; B, airway blood vessel designated as ciliated airway tissue region. Bar = 300 jim.   . A CR-39 autoradiograph ofa section from the third 3-mm slice from the apex of the right cardiac lobe of a rat killed at 7 days PI. A small aggregate of ..5U fission fragment tracks can be seen on the surface ofa conducting airway, presumably in the process ofbeing cleared via the mucociliary escalator. The total number of tracks emanating from the small macrophage cluster was estimated to be 210 tracks using the Seescan image analyzer. The total section track count was not obtained. AL, central alveolar tissue region; A, conducting airway designated as ciliated airway tissue region; B, airway blood vessel designated as airway perivascular tissue region. Bar = 300 um. particles of U02 would be within a tissue volume (assuming a uniform section thickness) of less than 0.1% of the total tissue volume within the section (8).
However, a lot of sections did not have any macrophage clusters, although they still had comparable numbers of23U fission fragment tracks. This fact will reduce the mean percentage of tracks counted within macrophage clusters ifrelated to total sections scored. The second column in Table 4 gives these values. At time points less than 720 days PI, the percentage of tracks within clusters is noticeably lower than the value obtained when only sections with macrophage clusters were considered. At 720 days PI, all sections scored had macrophage clusters, so the values do not change. Given that less than 4% ofall tracks were typically associated with clusters at all the time points up to 540 days PI, this suggests that the clusters were not important in terms of the total dose received by the lung over this period. However, the dose rate will obviously be higher to cells within exposure range ofthe U02 particles inside the macrophage clusters compared to the more uniform U02 distribution throughout the rest ofthe section. The significance ofthis higher dose rate is difficult to determine and depends on how important any "hot spot" irradiation is assumed to be in terms of cancer induction. At the later 720-day PI time point, the macrophage clusters clearly have a marked effect on the dosimetric pattern of tissue irradiation, and it appears that the increasingly nonuniform track distribution pattern (as determined by the chi-square test in previous sections) is mainly due to the increase in the number of these macrophage clusters with time PI.
However, by 720 days PI the animals were near the end oftheir lives, and only about 16% ofthe initial lung burden was still retained in the lung (9 . The animals will have received most of their total lifetime 3U c-particle dose well before 540 days PI. By 45, 90, 180, 360, 540, and 720 days PI, the animals were estimated to have received a total a-particle dose, averaged over the whole lung, of0.9, 1.6,2.9, 4.4, 5.2, and 5.7 Gy, respectively (9). Thus the large macrophage clusters observed may have occurred too late in the animals' lives to be important in terms of dose to cells at risk ofcancer induction. If the total 235U fission fragment tracks counted in the eighth left lung slice sections and the total number oftracks counted emanating from macrophage clusters within these sections are plotted against time PI, the area under the curve, from 4 to 720 days PI, is 46 times greater in the case of the total section counts. This suggests that about 2 % of all 234U a-particle emissions occur within the macrophage clusters, and 98 % occur within the rest of the lung, over the 720-days PI period. Owing to the increasing number of macrophage clusters observed with time PI, about half of the 2 % of 34U a-particle emissions within clusters appear to be emitted between 540 and 720 days PI. Thus, over the 720ay PI period, by far the greater proportion of cell hits will be from a particles emitted from U02 located outside the macrophage clusters.
If this were the case, it is possible that the similar clusters of macrophages, all laden with anthracitic particles, which were observed in postmortem human lungs from elderly individuals by Cottier eteal. (7), may not have important dosimetric implications. These interstitial macrophage clusters were within pleural and septal lymphatics, not normally the location ofmacrophages that have recently phagocytized particles from alveolar surfaces.
Cottier et al. (7) found few particle-laden macrophages within the human alveoli region of these old individuals. However, as most ofthe particles seen are likely to have originally come from the alveolar region, the unknown residence times in the human alveoli and latterly in the lymphatic tissue must also be taken into account. Also, the majority ofparticles inhaled would normally be cleared from the lung over the individuals lifetime (15), either completely from the individual via the mucociliary escalator or, probably to a much lesser extent, to the thoracic lymph nodes (9). It is likely that a substantial part ofthe total aparticle irradiation ofthe lung will come from those particles that clear in such a manner and leave the lung long before lung disease would be clinically detected.
An estimate can be made ofthe 234U a-particle dose within the small and large macrophage clusters observed within sections from the eighth left lung slices. As the neutron flux used to produce CR-39 autoradiographs ofthese sections is known, the mass of U02 within the sections can be calculated (16). It was estimated that one fission fragment track would be expected for every 0.17 pg ofU02 after exposure to a thermal neutron fluence of 5 x 1012 neutrons/cm2, assuming that all 235U fissions will result in one track being detected within the CR-39. The tissue area within each individual macrophage cluster was found from alternate H&E sections to that used to produce the autoradiographs. Assuming a uniform section thickness of 5 ,um, the approximate tissue volume of each macrophage cluster was calculated, excluding air spaces. The tissue density was taken as 1 g/cm3, and the mass ofU02 per gram oftissue was calculated.
From these values the dose rate within the macrophage clusters was calculated, ignoring all clusters found at 1 and 7 days PI, which were on the airway surface. The dose rate within the small macrophage clusters was estimated to be 0.033 ± 0.015 Gy/day (n = 11), and the dose rate within the large macrophage clusters 207 was estimated to be 0.130 ± 0.083 Gy/day (n = 6). In comparison, the dose rate averaged over the whole lung was estimated to be 0.021 Gy/day at 4 days PI, 0.0057 Gy/day at 360 days PI, and 0.0026 Gy/day at 630 days PI (9). If it is assumed that the macrophage clusters remain at the same location within the lung once formed, this suggests the total accumulated dose within small clusters will be 18 Gy over the 180to 720-day PI period. Similarly, the total accumulated dose within large macrophage clusters would be 47 Gy over the 360to 720-day PI period. Thus, the local dose to cells intimately associated with the macrophage clusters could be much higher than the estimated accumulated dose of 5.7 Gy averaged over the whole lung from 4 to 720 days PI (9). However, the assumption that these macrophage clusters remain at a fixed location for such long periods may not be valid.

Conclusions
The distribution ofthe 235U fission fragment tracks within the left lung of the rat was found to be nonhomogeneous at all time points from 1 to 720 days PI. This suggests that the pattern of234U a-particle irradiation within the lung will be consistently nonuniform throughout the life of the individual after exposure. There was an apparent increase in the nonhomogeneity ofthe fission fragment track distribution throughout the lung with increasing time PI. Even at the later times PI, there was no evidence that tracks were becoming increasingly associated with the peripheral regions of the lung.
Macrophage clusters were found within many of the rat lung sections taken from all five lobes. The number and size ofthese clusters increased with time PI. From data taken from the left lung, it appeared that the percentage of tracks associated with these macrophage clusters was less than 4% up to 540 days PI. At 720 days PI, typically 40% ofall tracks were counted within these macrophage clusters. This suggests that these macrophage clusters may not be a significant factor in contributing to the total lung dose, as by 540 days PI the rats have received more than 90% oftheir total accumulated 234U a-parficle lung dose, averaged over the whole lung. However, from 180 to 720 days PI, the estimated dose rate within these macrophage clusters was much higher than the corresponding dose rate calculated by averaging over the whole of the rat lung.
This work was supported in part by the U.K. Department ofEnergy under contract HM-4-54-64 and by the Commission ofthe European Conununities under contract B16-D-076-UK. The authors thank Christine Stirling for her technical assistance and advice and Graham Patrick and Leon Cobb for many useful discussions, all of M.R.C. Chilton.