THE ANATOMICAL RECORD 228:267-276 (1990) Estimating Anatom ical-F unctional Position Coordinates in Liver Tissue E. BARBERA-GUILLEM, A. ALONSO-VARONA, M.D. BOYANO, AND F. VIDAL-VANACLOCHA Department of Cell Biology and Morphological Sciences, School of Medicine and Dentistry, University of the Basque Country, Leioa, 48940 Vizcaya, Spain ABSTRACT Hepatocyte enzyme activity was demonstrated by examining adult C57BL/6 mouse liver cryostat sections under a succinate dehydrogenase (SDH) histochemical reaction, and quantified by microspectrophotometry and microdensitometry. The hepatocyte SDH activity gradient along the path between the portal veins (PV) and efferent terminal hepatic venules (THV) was analyzed by measuring the concefitration of the chromophore precipitated in 10 consecutive hepatic parenchymal domains located along imaginary lines drawn across the entire PV-to-THV distance. The profiles of intensity or of normalized relative optical density obtained on a high number of lines were correlated with distance values along the PV-to-THV pathway, enabling us to establish a general mathematical function relating SDH activity (chromophore concentration) to position values on a scale of 0 to 10 corresponding to the theoretical PV-to-THV distance. The equation can be used to interpolate the SDH activity surrounding any intrahepatic object located between the PV and the THV, thus making it possible to calculate the object’s anatomical-functional position coordinates in the liver acinus. To demonstrate how this method is used, we have calibrated the intrahepatic position of hemopoietic foci induced in the liver tissue of adult mice treated with phenylhydrazine (PHZ), and show that these foci are located on coordinate 3.31 (maximum range 1.25-4.86) of the sinusoidal domain-that is, on the borderline between Rappaport’s acinar zones 1 and 2. The biological variability of the hepatocytes and sinusoidal cells found along the hepatic sinusoidal pathway results in a functional zonation of adult liver tissue (Jungermann and Katz, 1982; Barbera-Guillem and Vidal-Vanaclocha, 1988; Gumucio and Chianale, 1988). Consequently, a regionalized distribution of normal functional processes and of pathological behaviour (Rappaport, 1976) is recognized in each zone. Given this functional heterogeneity, numerous studies have tried to correlate certain functional phenomena with their location within the hepatic lobule. Examples are the studies made of the intralobular distribution of Kupffer cells (Sleyster and Knook, 1982; Bouwens e t al., 19861, Pit cells (Kaneda and Wake, 1983) and fat storing cells (Wake, 1989), or studies on the possible existence of specific places within the hepatic lobule where certain functional activities take place (Thurman and Kauffman, 1985; Lamers et al., 1988; Teutsch, 1988; Barbera-Guillem et al., 1989a). However, despite the need to pinpoint the intralobular location of the element or process under study in order to interpret it at a more general functional level, the intralobular topographical coordinates used are poorly defined, due to the biological irregularity of the structural and functional organization of the liver tissue itself (Rappaport et al., 1954; Lamers et al., 1989; Teutsch, 1988). Certain studies, therefore, indicate the place where the phenomenon in question occurs by measuring in microns its distance from the portal or 0 1990 WILEY-LISS, INC. centrilobular veins (Hildebrand and Schleicher, 1986; Ebert et al., 1987; Arber et al., 1988). In other cases, the object is related to the different zones of microcirculatory influence (Rappaport, 1973; Sleyster and Knook, 1982). What are never given, however, are precise topographical references that would make it possible to establish a correlation with the functional characteristics of the location concerned. In this study, we have used cytophotometry and densitometry to quantify the SDH activity of the hepatocytes along the sinusoidal pathway from the portal venules (PV) to the terminal hepatic venules (THV). The data obtained make it possible to establish standard correlation curves between hepatocyte SDH activity and a microvascular reference position. In addition, the mathematical expression of these functions enables us to calculate through interpolation the position of any object with regard to its microcirculatory reference position, given the SDH activity of its environment. These coordinates of relative position arrived at through the enzyme activity of the neighboring hepa- Received November 15, 1989; accepted March 20, 1990. Address reprint requests to F. Vidal-Vanaclocha, Department of Cell Biology and Morphological Sciences, School of Medicine and Dentistry, University of the Basque Country, Leioa, 48940 Vizcaya, Spain. 268 E. BARBERA-GUILLEM E T AL. tocytes guarantee a n empirical standardization of results that was lacking in other procedures. To demonstrate how this procedure is used to calculate position according to hepatocyte SDH activity, this study calibrates the exact location of the hemopoietic foci induced in the livers of adult mice subjected to acute hemolytic treatment using phenylhydrazine. Our results show that these hemopoietic foci occupy a specific, well-defined band within the sinusoidal structure. MATERIALS AND METHODS Animals Adult (age: 7 weeks, weight: 18-20 g) C57BL/6 mice were purchased from Iffa Credo Laboratories (France) and kept on a 12 h day-night rhythm with free access to food and water (standard diet). All animals were fasted 6 h before the experiments, and were anesthetized by intraperitoneal injection of pentobarbital (50 mgtkg body wt.) prior to sacrifice. Histochemistry An in situ histochemical reaction to reveal succinate dehydrogenase (SDH) activity was carried out on 10 pm cryostat sections as follows: tissue slides were incubated 3 min a t 37°C with 2-3 ml of a substrate solution made of sodium succinate (Merk, WG), nitrobluetetrazolium I11 (NBT) (Sigma Chem. Co., St. Louis, MO), and phosphate-buffered salts prepared as described previously (Barbera-Guillem et al., 1989b). After incubation, the slides were rinsed in cold phosphate buffer, fixed in 10% formaldehyde for 3 min, rinsed in distilled water, and mounted on glycerol gel. For SDH activity to show up more clearly in micrographs, the reaction was prolonged to 20 min in the photographed liver tissue sections. Section thickness homogeneity was evaluated by analytical interferential microscopy (POL optics, Zeiss). In Situ Cytophotometric Measurement of Cromophore Content Cytophotometric measurement of chromophore concentration was taken by a n integrating method with a 0.25 pm step size (0.06 pm2) to reduce distribution error, given the normally heterogeneous histochemical reaction with NBT. Four hundred points (24 pm2)were measured on a field of cytoplasm conforming to the shape of each hepatocyte. The wave length selected was 585 nm with a 5 nm band width (Butcher, 1978). The measurements were made with a Zeiss microspectrophotometer (Zeiss, Oberkochen, WG) connected on line with a p.c. microcomputer which was programmed to record the movements of the object and the 0.25 pm step scanning of irregularly shaped areas previously defined by the operator according to the form of the cytoplasm of each hepatocyte. Hepatocyte samples were obtained by selecting 10 lines connecting the portal venules (PV) and nearby terminal hepatic venules (THV) from each of 10 tissue slides selected from five different animals. There was at least 1 mm between each tissue slide. Next, the cytoplasmic chromophore content ( E ) of each of the hepatocytes around each line (Fig. 15 was measured. E , corresponded to integrated extinction of the 400 points included in the cytoplasmic field defined for each hepatocyte. The data were recorded in a file (“A”), with x being the relative chromophore concentration for each 0.06 pm2 point in the hepatocyte (E,/400), and y the position of the hepatocyte on the line a s measured on a scale of 0 to 10, beginning at the PV and going on up to 10 a t the THV. Densitometric Measurements of Histochemically Demonstrated Hepatic SDH Activity Quantification of liver SDH activity and further processing of the image was run with a n equipment setup of a n integrated automatic image analysis system (Southern Microcomp. Instruments, Inc., Atlanta), and a VANOX AHBT optical microscope (Olympus Optical Co., Ltd., Japan) equipped with a SIT66 TV camera (Dage-MTI, Inc., Michigan) used under the following conditions: 585 nm wavelength monochromatic lighting; recording of light intensity at each pixel on a scale of 0 to 255; projection of the object using a 20 x objective lens so that each pixel represents a n object area measuring 0.12 pm2 (imaginary circle of 0.39 pm in diameter). Once this was done, 100 lines were again drawn between the PV and the THV on the same 10 slides used previously and the intensity values of each of the pixels (Z,) on the lines were recorded in a file, together with a number indicating order of placement on the line (taking the PV as the starting point). The same operation as before was again carried out, but this time using a negative image so that the greater intensity now corresponded directly to the cells with highest chromophore content. Later, the data for each hepatocytic pixel were transformed, giving us two different files: File “B,” containing for each pixel a n x value equivalent to the Z, of the negative image and a y value equivalent to the position of the pixel on the line mapped onto a 0 to 10 scale. File “C” contained for each pixel a n x value equivalent to the normalized relative optical density (NROD) obtained by transformation according to the Z, values of the positive image: (a)E, = log(255/1,) (b) NROD = E p - Emin Emax - Emin where Em,, is the value of maximum E , found on a tissue slide and Eminis the value of minimum E found on the tissue slide. They value is the same as i n h l e B. Using the data in Files A, B, and C, adjustments were made for each, calculating the correlation between the values found and functions of n degrees expressed as y = ko + k l x + kzxz + . . . + k,x” from which we can extrapolate any position value, given the relative chromophore concentration, the negative image intensity, or the normalized relative optical density. Image Analysis of Hepatic Parenchymal Cells Using the integrated image analysis system, the hepatocytes stained with NBT due to the SDH reaction were digitalized and represented in only four gray levels using the integrated image analysis system. On these images, the relative surface area occupied by each gray level was calculated morphometrically. ESTIMATING POSITION COORDINATES IN LIVER TISSUE 269 Fig. 1. Liver cryostat section following an SDH histochemical reaction showing the procedure used for cytophotometric measurement of chromophore concentration in the cytoplasm of hepatocytes prior to correlation with position on the sinusoidal pathway from the portal vein (PV) to the terminal hepatic venule (THV). The imaginary line that runs from the PV to the THV is divided into 10 segments of equal length, with each of these measurements made in well-defined areas within the cytoplasm of the hepatocytes. Phenylhydrazine-InducedHepatic Hemopoiesis in Adult Mice value was calculated for each focus by solving the corresponding function: Animal treatment with phenylhydrazine has been described in a previous work (Barbera-Guillem et al., 1989b). Briefly, adult mice were administered with one daily intraperitoneal injection of 0.1 ml phosphatebuffered saline (PBS) containing 1mg of phenylhydrazine (PHZ) hydrochloride (Sigma Chem. Co., St. Louis, MO) for 7 days. Calibrating the Position of Hemopoietic Foci Within the Liver Tissue The cytoplasmic SDH activity of hepatocytes surrounding both portal and central vessels and hemopoietic foci was recorded by means of a computer-assisted Zeiss microspectrophotometer as described above. Five SDH activity measurements were taken around each type of liver structure on the basis of the maximum number of vessels and of hemopoietic foci found in 15 tissue sections from five different mice. Spectrophotometric values were expressed in arbitrary units normalized with respect to average periportal hepatocyte SDH activity. These values were then used to calculate the average for each focus, which was recorded in a file a s the x descriptor of each focus. Later, the y position y = ko + klx, + kzx; + . . . + k,& Statistics The Wilcoxon rank sum test was used to determine the significance of SDH activity differences in the hepatocyte populations measured (periportal,perivenous, and perihemopoietic focus). RESULTS Identification of Hepatic Parenchymal Cell Phenotypes According to Their Succinate Dehydrogenase Activity The SDH histochemical reaction enables us to obtain a clearly defined view of the hepatic tissue and its functional zones on cryostat sections. The hepatic areas of greatest enzyme activity are found around the portal veins as revealed by their dark color, while the areas of lesser SDH activity, found around the terminal hepatic venules, stand out in contrast due to their much lighter color (Fig. 1). Cytophotometric measurement of the hepatocyte chromophore content in hepatic cryostat sections subjected to the SDH histochemical reaction reveals a clear difference between the cells in the area closest to 270 E. BARBERA-GUILLEM ET AL. TABLE 1. Chromophore concentration in hepatic parenchymal cells of liver cryostat sections under a succinate dehydrogenase histochemical reaction' Parameters Total chromophore content Ranee AveFage chromophore Concentration Intraacinar heDatic areas Peri-THV Peri-PV 244.5 2 103.27 121-327 0.71 k 0.31 435.17 t 230.64 205-665 1.35 k 0.71 'THV, terminal hepatic venule; PV, portal venule Data are expressed as mean values f SD from measurements of integrated extintion of the 400 points included in the cytoplasmic field defined for each hepatocyte. The number of measurements per hepatic area was higher than 2000, being obtained from five mice (two tissue sections per mouse). the portal venules (PV) and those around the terminal hepatic venules (THV) (Table 1).In each of these areas, there is a high degree of variation, however, and a considerable percentage of hepatocytes could be erroneously classified if chromophore content were the only criterion taken into account. In fact, when we examined the distribution of the hepatocytes in the periportal and perivenous regions (Fig. 21, we found a small proportion of hepatocytes from the two regions with a clear overlap in their chromophore concentration (between 0.6 and 0.9%). Moreover, analysis of hepatocyte images pertaining to the three acinar zones shows a heterogeneous chromophore distribution inside the cells themselves. In general, the dye produces heavy precipitations in certain cytoplasmic zones, which contrast with zones where the coloring is relatively weak (Fig. 3). After grouping the entire range of optical densities into four levels (represented by four gray levels) with the image analyzer, it became clear that the majority of the pixels corresponding to hepatocyte images belong either to the densest class (level 4),or else to the low-intermediate category (level 2). By contrast, those corresponding to levels 1 and 3 are very scarce. Examination of these hepatocyte images also shows that in periportal cells, level-4 pixels occupy up to 80% of the total surface area of the hepatocyte, while in the THV region the hepatocytes offer the inverse image, since over 80% of these pixels are of the level-2 type. Between these two extremes there is a large number of hepatocytes whose cytoplasmic surface is partially occupied by pixels of all shades in varying proportions. The intermediate zone is where this type of hepatocyte is the most frequent. lntraacinar Cytophotometric Mapping of Hepatocyte SDH Activity Phenotypes To study the profile of the decline in hepatocyte SDH activity, cytophotometry was used to determine the average chromophore concentration in the cytoplasm of hepatocytes located along the sinusoidal PV or septumto-THV pathway. The results show the existence of hepatocytes with highly variable average concentration values, although in general they tend to decrease from the periportal to the perivenous area. Therefore, if we use these concentrations to determine a possible association between relative optical density value and lo- 0 0.5 1 1.5 2 CHROMOPHORE CONCENTRATION (ARBITRARY UNITS, Fig. 2. Histograms of frequency distribution of hepatocyte SDH activity around portal venules (dotted area) and terminal hepatic venules (open area). The average chromophore concentration, expressed in normalized arbitrary units, was 1.00 0.14 for periportal hepatocytes and 0.43 i 0.13 for peri-THV hepatocytes. * cation on the 0 to 10 scale corresponding to the points of measurement on the line between the portal and terminal hepatic veins, we find that the higher correlation coefficient responds to the adjustment of a third degree polynomic equation (correlation coefficient = 0.989) (Fig. 4). This standard curve makes i t possible, therefore, to correlate the different hepatocyte SDH activity values with precise locations on the microcirculatory network. Moreover, the mathematical expression of this curve enables us to calculate through interpolation the position of any object on the sinusoidal pathway if we know the SDH activity of the surrounding hepatocytes. lntraacinar Densitometric Mapping of Hepatocyte SDH Activity Phenotypes Densitometric measurement of chromophore concentration in the cytoplasm of hepatic parenchymal cells subjected to a reaction in order to reveal SDH activity coincides with the data obtained in the cytophotometric measurement. Quantifying the intensity of light in the pixels located on lines drawn from the PV to the THV on negative images of microscopic hepatic fields (Fig. 5) reveals a drop in the SDH activity gradient that becomes especially evident when we eliminate the pixels corresponding to the noncytoplasmic structures such as the sinusoidal lumen or cell nuclei (Fig. 6). Also, when we correlate the values of normalized relative optical intensity or density with those of the distance from the PV on the lines between the PV and the THV (Fig. 7), we once again obtain a standard curve that graphically represents a mathematical function. This equation relates the SDH activity (measured indirectly a s chromophore concentration) or independent variable, with the distance from the PV, or dependent variable. Calibrating the Position of PHZ-Induced Hemopoietic Foci in Adult Liver Tissue As previously described (Ploemacher and van Soest, 19771, daily administration of phenylhydrazine to adult C57BLi6 mice produced a n acute hemolytic anemia, which was immediately accompanied by -a strong ESTIMATING POSITION COORDINATES IN LIVER TISSUE Fig. 3.Digitalized image of hepatic tissue subjected to a histochemical reaction for SDH. On the left is zone 1, and on the right, the zone closest to the THV (zone 3). The image is formed by pixels in four gray levels. The majority of zone 1hepatocyte pixels are of the highest gray 271 level (41. By contrast, most zone 3 hepatocytes have gray-level 2 pixels. There are also hepatocytes with intermediate characteristics in which there is a balanced combination of both gray-level 2 and 4 pixels. hemopoietic reaction involving several organs includ- paport, 1973), numerous studies were done in search of ing liver tissue. On the seventh day of PHZ treatment, topographical correlations between different metabolic hepatic sinusoids had expanded and showed a n in- activities (Jungermann and Katz, 1982) or between creased infiltration of hemopoietic cells. These cells formed small focal aggregates not associated with portal and central veins, which occluded sinusoidal lumen (Fig. 8). The average SDH activity of hepatocytes surrounding hemopoietic foci was similar to that of periportal hepatocytes and significantly different from that of peri-THV hepatocytes (P<O.Ol) (Table 2). Hemopoietic foci seemed to be located, therefore, in the high SDH activity domain of liver acini. Thus, to verify their exact location, the SDH activity values of the hepatocytes surrounding each focus were interpolated on the curve of the intraacinar SDH activity gradient in order to calculate the position of these values on the scale of 0 to 10 t ha t goes from the PV to the THV of any hepatic acinus. The result of these interpolations can be seen in Figure 9, which shows that the hemopoietic foci implant in the adult liver tissue of PHZ-treated mice in the sinusoidal segment extending from point 1.25 to 4.86 on the relative scale superimposed on the PV-to0 0.5 1 THV pathway, with 3.31 being the most probable point of location. - HEPATOCYTE S D H A C T I V I T Y [ A S CHROMOPHORE CONCENTRATION ARBITRARY UNITS 1 DISCUSSION Once the existence of well-differentiated functional zones had been demonstrated in the liver tissue (Rap- Fig. 4. Acinar gradient curve of hepatocyte SDH activity calculated from step-by-step recording for this enzyme activity at 10 consecutive equidistant points on an imaginary line drawn on the portalto-central vein distance. 272 E. BARBERA-GUILLEM ET AL. Fig. 5. Digitalized image of a liver tissue field taken from positive (a)and negative (b) images in 255 gray levels (a)and 255 intensity levels (b).The line is made up of all the lined-up pixels used to calculate the relation between the optic density (a)or the intensity of (b) and the correlation of either with the portal-to-central vein distance. certain cell types and the functional zone where they are found (Loud, 1968; Sleyster and Knook, 1982; Vidal-Vanaclocha and Barbera-Guillem, 1985; Wake, 1989). However, the delineation of the classical lobules and of the hepatic acini is often imprecise, and their form and function do not correspond to the geometric models normally used to describe them (Matsumoto and Kawakami, 1982; Teutsch, 1988; Lamers et al., TABLE 2. Hepatocyte succinate dehydrogenase 1989). Consequently, most of these studies have run up activity around portal venules, terminal hepatic against difficulties in calculating exact locations venules, and phenylhydrazine-induced hemopoietic within the lobular or acinar structure of the hepatic foci and relative position of foci within the liver acini of C57BL/6 mice tissue. The only clearly identifiable points of reference are the portal vessels (PV) and the terminal hepatic Average SDH Distance from the venules (THV), but these two points are separated by Hepatocyte activity portal venule variable distances and delimit theoretical areas of dif(RODU)' (DFPV)~ populations ferent sizes and shapes. The sinusoidal pathway itself, 1.00 2 0.20* 0 Periportal venules although theoretically radial in form and leading toPeriterminal hepatic 0.44 i 0.11 10 ward the THV, is also erratic when seen in histological venule section, due to a tridimensional superstructure that 0.83 2 0.24* 3.31 Perihemopoietic foci (range 1.25-4.86) is difficult to express on a plane (Matsumoto and Kawakami, 1982). 'Succinate dehydrogenase activity was expresssed as relative optical All these features of biological irregularity make i t density units (RODU) ? SD. The number of measurements was at least of 10,000, being obtained from five mice (15 liver tissue sections difficult to use distance to the hepatic vessels measured in microns a s a precise measurement of position correg% e:;'tT ':: DFPV of hemopoietic foci was obtained by interpolating latable to the data derived from the functional zonation perihemopoietic hepatocyte SDH activity values in the corresponding of the hepatic tissue. For these reasons, we feel that it curve of the intraacinar SDH activity gradient. *Significant differences from the peri-terminal hepatic venule SDH is important to transform these intrahepatic distance coordinates into others directly related to some wellactivity by Wilcoxon rank sum test, P<O.Ol. 273 ESTIMATING POSITION COORDINATES IN LIVER TISSUE 250 200 > k 150 v) 2 W zI- 100 50 O 1J , , , 50 75 , , , , I , I 250 200 > C 150 v) z W z_ + 100 50 0 0 25 100 125 150 175 200 225 250 DISTANCE FROM THE PORTAL VEIN (pm) Fig. 6. Representation of all the intensity values of the pixels on a line joining the portal vein with the central vein (top) in relation with their position in microns (at the 10 intervals used to calculate their relative position). Bottom, the pixels that actually are found on hepatocyte cytoplasm have been shaded. The fall in the intensity gradient is evident when the background pixels are eliminated (curve). known functional activity in order for the position coordinates to have a real and uniform value. Highly technical, detailed studies have demonstrated that hepatocytes have an activity gradient for some specific enzymes down the length of the sinusoidal pathway connecting the PV with the THV (Wimmer and Pette, 1979; Hildebrand and Schleicher, 1986; Ebert et al., 1987; Teutsch, 1988). Thus, relative position on these gradients (between maximums and minimums) could constitute a distance value closely linked to the functional activity of each hepatic topographical zone and, therefore, would represent a high information-content measurement. Studies that examine the form of the gradients mention the difficulty involved in measuring them with precision due to the difficulty of drawing lines of development of this gradient between zones (Hildebrand and Schleicher, 1986). Normally, straight lines are drawn between the portal and central vessels, and microbiochemical (Ebert et al., 1987) or microdensitometric (Hildebrand and Schleicher, 1986) measurements are taken down the length of the lines. However, there will inevitably be disparity in these measurements due to the very nature of the tissue, the histochemical reaction, and the methods of measurement. What we have done is take SDH activity as the reference enzyme activity-although any other hepatic enzyme recognized as zonal and with an intraacinar distribution along an activity gradient (Lamers et al., 1988)could be used as well. The histochemical reaction of SDH has a close correlation between the enzyme activity and quantity of chromophore precipitated (Nolte and Pette, 1972; Lippold, 1982). Measurements of the hepatocyte cytoplasmic chromophore content serve to establish a correlation between functional activity and positions in lobules or acini, as we confirmed. a b U 0 50 100 150 200 250 I N T E N S I T Y (ARBITRARY UNITS) 0 0.5 NORMALIZED R.O.D. U N I T S Fig. 7. Intensity (a)or normalized relative optical density (b) and distance values of the pixels located on 100 lines drawn between the PV and the THVs. The curves are the graphic representations of the functions adapted to the intensityidistance correlation (a)or to the NRODidistance correlation (b). 1 274 E. BARBERA-GUILLEM ET AL. Fig. 8. Light micrograph of a liver cryostat section under an SDH histochemical reaction from phenylhydrazine-treated mice. Hemopoietic colonies were identified as small unstained foci (arrows) selectively located within the high SDH activity parenchymal regions (dark areas surrounding portal veins defined a s Rappaport’s zone 1. Low SDH activity parenchymal cells were defined as Rappaport’s zone 3, where hemopoietic foci were never found. PV, portal vessels; THV, terminal hepatic venules. x 200 An ordering of the hepatocytes along the gradient was demonstrated, with a maximum found near the PV and septum and the minimum around the THV. Also, the standardization of geometric distance values between the PV and THV makes i t possible to establish a general function t h a t provides us with a position scale in the hepatic acinus correlatable with this functional zonation. The difficulty in measuring by microspectrophotometry is that what must be measured is the integration of the chromophore content in each cell. In order to avoid the problems posed by the irregular shape of each hepatocyte, we propose measuring a constant polygon within each hepatocyte cytoplasm, rather than the hepatocyte itself. This makes it possible to avoid measuring other neighboring types of cell, ensures identical adjustment, and reduces enormously the time taken in carrying out the measurement. We also tested the viability of the method with TV microdensitometry. The main difficulty in using this instrument is that the unit of measurement used is the intensity value of each pixel, the size of which depends on the optics used. After a detailed analysis of the densitometric image of the hepatocytes, we verified that the chromophore content or concentration is a very pre- cise amount that is difficult to calculate with the intensity values of the pixels, since the latter fall within very few gray levels. The concentration or quantity values, on the other hand, are arrived a t by adding the different proportions of pixels. According to our results, it is possible to find pixels of all values in any zone of the hepatic acinus, and what varies is the probability of finding a given value in each zone. These circumstances have already been described in image analysis studies of the liver and its functional zones (Hildebrand and Schleicher, 1986). Our examination of a large number of pixels showed that, although there is enormous disparity on a line drawn from a PV to a THV, i t is possible to discover the gradient by programming out all the pixels that do not belong to hepatocyte images. With this approach a gradient is established with characteristics similar to the gradient obtained through microspectrophotometric measurement. In this regard, it might be a s useful to use direct intensity measurements obtained from a n inverted image (a negative) of a section of liver subjected to the SDH reaction, a s to use values programmed into standard units of optical density. In this case, however, it would be necessary to first introduce a function transforming the intensity of the ESTIMATING POSITION COORDINATES IN LIVER TISSUE ____- L I V E R ACINUS -- / i-/ L- J / Z0,NE 1 53187 from the University of the Basque Country awarded to F.V.-V. Q .................................... \ ................... ................... .................... ................... ..................... 1 ................... .................. ...... \ 1 DOMAIN OF HEMOPOIETIC LITERATURE CITED \ ‘ PV \SINUSOIDAL 275 PATHWAY HEMOPOIETIC FOCI & - - -% L I V E R LOBULE Fig. 9. Diagrammatic representation of acinar and lobular models of liver tissue organization and the distributions of liver hemopoietic foci from phenylhydrazine-treated adult mice. Liver sinusoids run from the terminal portal venules (PV) to the terminal hepatic venules (CV) and define a functional pathway that we have scaled 0 (at the PV end) to 10 (at the CV end). The dotted area defines the specific domain of hemopoietic foci implantation. The average position of hemopoietic foci on the sinusoidal pathway was 3.31 (range 1.25-4.86). pixels into their corresponding normalized optic density value. To summarize the procedure, we calculate the anatomical-functional position of a n object in a liver section subjected to SDH histochemical reaction using the following procedure: (1) Verification that the experiment in question does not alter the pattern of functional activity of the hepatocytes used a s our reference for determining the gradients. (2) Calculation of maximum and minimum activity by the procedure preferred for the histological section as a whole. (3) Calculation of the function relating the enzyme activity gradient with its relative position. (4) Calculation of hepatocyte activity around the object. (5) Interpolation of the anatomical-functional position using the value t h a t represents the average activity of the hepatocytes surrounding the object in the mathematical function relating both variables. From earlier studies, we knew that the position of PHZ-induced hemopoietic foci in the liver is intrasinusoidal (Ploemacher and van Soest, 1977), but it was not known in what functional area they occurred. The present results show that hemopoietic foci are not disturbed a t random, but occupy positions in Rappaport zone 1. The exact estimate of anatomical-functional coordinates demonstrates foci within a narrow functional band. This border area (Barbera-Guillem et al., 1989b) is between Rappaport’s acinar zone 1 and zone 2. We feel that the value of this procedure is in pinpointing the precise spot where implantation occurs, and demonstrating the regularity with which this position is selected. Possible functional and cellular implications associated with this selective implantation process in hepatic tissue need to be addressed. ACKNOWLEDGMENTS Supported by C.I.C.Y.T. Grant PR-0910184 awarded to E.B.-G. and by Grants 075.327-52/87 and 075.327- Arber, N., G. Zajicek, and I. Ariel 1988 The streaming liver 11. Hepatocyte life history. Liver, 8:80-87. Barbera-Guillem, E., A. Alonso-Varona, and F. Vidal-Vanaclocha 1989a Selective implantation and growth of experimental liver metastasis in acinar zone one. Cancer Res., 49:4003-4010. Barbera-Guillem, E., R. Ayala, and F. Vidal-Vanaclocha 1989b Differential location of hemopoietic colonies within liver acini of postnatal and phenylhydrazine-treated adult mice. Hepatology, 9:29-36. Barbera-Guillem, E., and F. Vidal-Vanaclocha 1988 Sinusoidal structure of the liver. R.B.C., 16:l-68. Bouwens, L., M. Baekeland, R. De Zanger, and E. Wisse 1986 Quantitation, tissue distribution and proliferation kinetics of Kupffer cells in rat liver. Hepatology, 6:718-722. Butcher, R.G. 1978 The measurement in tissue sections of the two formazans derived from nitroblue tetrazolium in dehydrogenase reactions. Histochem. J., 10:738-744. Ebert, S., R. Hildebrand, and I. Haubitz 1987 Sinusoidal profiles of lactate dehydrogenase activity in rat liver. Histochemistry, 87: 371-375. Gumucio, J.J., and J. Chianale 1988 Liver cell heterogeneity and liver function. In: The Liver: Biology and Pathobiology. I.M. Arias, W.B. Jakoby, H. Popper, D. Schachter, and D.A. Shafritz, eds. Raven Press, New York, Chap. 53, pp. 931-947. Hildebrand R., and A. Schleicher 1986 Image analysis of the histochemical demonstration of glucose-6-phosphatase activity in rat liver. Histochemistry, 86:181-190. Jungermann, K., and N. Katz 1982 Functional hepatocellular heterogeneity. Hepatology, 2:385-395. Kaneda, K., and K. Wake 1983 Distribution and morphological characteristics of the pit cells in the liver of the rat. Cell Tissue Res., 233:485 -505. Lamers, W.H., J.W.G. Jansen, A.F.M. Moorman, R. Charles, E. Knecht, A. Martinez-Ramon, J . Hernandez-Yago, and S. Grisolia 1988 Immunohistochemical localization of glutamate dehydrogenase in rat liver: Plasticity of distribution during development and with hormone treatment. J . Histochem. Cytochem., 36:4147. Lamers WH, A.F.M. Moorman, and R. Charles 1989 The metabolic lobulus, a key to the architecture of the liver. R.B.C., 19:5-26. Lippold, H.J. 1982 Quantitative succinic dehydrogenase histochemistry. A comparison of different tetrazolium salts. Histochemistry, 76:381-405. Loud, A.V. 1968 A quantitative stereological description of the ultrastructure of normal rat liver parenchymal cells. J . Cell Biol., 37:27-46. Matsumoto, T., and M. Kawakami 1982 The unit-concept of hepatic parenchyma-A reexamination based on angioarchitectural studies. Acta Pathol., Jpn., 32(Suppl 2):285-314. Nolte, J., and D. Pette 1972 Microphotometric determination of enzyme activity in single cells in cryostat sections. I. Application of the gel film technique to microphotometry and studies on the intralobular distribution of succinate dehydrogenase and lactate dehydrogenase activities in rat liver. J. Histochem. Cytochem., 20:567-576. Ploemacher, R.E., and P.L. van Soest 1977 Morphological investigation on phenylhydrazine-induced erythropoieisis in the adult liver. Cell Tissue Res., 178:435-461. Rappaport, A.M. 1973 The microcirculatory hepatic unit. Microvasc., Res., 6t212-228. Rappaport, A.M. 1976 The microcirculatory acinar concept of normal and pathological hepatic structure. Beitr., Pathol., 157t215-243. Rappapid, A.M, Z.J. Borowy, W.M. Lougheed, and W.N. Lotto 1954 Subdivision of hexagonal liver lobules into a structural and functional unit; role in hepatic physiology and pathology. Anat. Rec., 119:ll-34. Sleyster, E. Ch., and D.L. Knook 1982 Relation between localization and function of rat liver Kupffer cells. Lab. Invest., 47,484-490. Teutsch, H.F. 1988 Regionality of glucose-6-phosphate hydrolysis in the liver lobule of the rat: Metabolic heterogeneity of “portal” and “septal” sinusoids. Hepatology, 8r311-317. Thurman, R.G., and F. Kauffman 1985 Sublobular compartmentation of pharmacological events (SCOPE): Metabolic fluxes in periportal and pericentral regions of the liver lobule. Hepatology, 5: 144-151. Vidal-Vanaclocha,F., and E. Barbera-Guillem 1985 Fenestration pat- 276 E. BARBERA-GUILLEM ET AL. terns in endothelial cells of rat liver sinusoids. J. Ultrastruct. Res., 90:115-123. Wake, K. 1989 Rapid Golgi method contributes notably to the study of liver sinusoidal cells. In: Cells of the Mepatic Sinusoid, Vol. 2. E. Wisse, D.L. Knook, and K. Decker, eds. Kupffer Cell Foundation, Rijswijk, pp. 449-450. Wimmer, M., and D. Pette 1979 Microphotometric studies on intraacinar enzyme distribution in rat liver. Histochemistry, 64r23-33.