Stereological analysis of size and density of hepatocytes in the porcine liver

Abstract

The porcine liver is frequently used as a large animal model for verification of surgical techniques, as well as experimental therapies. Often, a histological evaluation is required that include measurements of the size, nuclearity or density of hepatocytes. Our aims were to assess the mean number‐weighted volume of hepatocytes, the numerical density of hepatocytes, and the fraction of binuclear hepatocytes (BnHEP) in the porcine liver, and compare the distribution of these parameters among hepatic lobes and macroscopic regions of interest (ROIs) with different positions related to the liver vasculature. Using disector and nucleator as design‐based stereological methods, the morphometry of hepatocytes was quantified in seven healthy piglets. The samples were obtained from all six hepatic lobes and three ROIs (peripheral, paracaval and paraportal) within each lobe. Histological sections (thickness 16 μm) of formalin‐fixed paraffin‐embedded material were stained with the periodic acid‐Schiff reaction to indicate the cell outlines and were assessed in a series of 3‐μm‐thick optical sections. The mean number‐weighted volume of mononuclear hepatocytes (MnHEP) in all samples was 3670 ± 805 μm³ (mean ± SD). The mean number‐weighted volume of BnHEP was 7050 ± 2550 μm³. The fraction of BnHEP was 4 ± 2%. The numerical density of all hepatocytes was 146 997 ± 15 738 cells mm⁻³ of liver parenchyma. The porcine hepatic lobes contained hepatocytes of a comparable size, nuclearity and density. No significant differences were identified between the lobes. The peripheral ROIs of the hepatic lobes contained the largest MnHEP with the smallest numerical density. The distribution of a larger MnHEP was correlated with a larger volume of BnHEP and a smaller numerical density of all hepatocytes. Practical recommendations for designing studies that involve stereological evaluations of the size, nuclearity and density of hepatocytes in porcine liver are provided.

Introduction

Porcine liver in experimental surgery

Human hepatobiliary surgery has achieved substantial progress in previous decades (Kwon et al. 2015; Song, 2015; Park et al. 2016). Operations such as extended resections, stage procedures and transplantations would not be possible without previous pre‐clinical research. Procedures necessary for experimental verification of newly developed surgical techniques cannot be evaluated in small animals because they lack anatomical and physiological similarities to the human organism. The porcine liver is currently the best described and most suitable large animal model of the human liver in terms of organ size as well as gross and microscopic morphology and physiology (Court et al. 2003; Arkadopoulos et al. 2011). The major difference between the microscopic morphology of porcine and human liver is that porcine liver has much more defined interlobular connective tissue septa. The use of pigs as the last step of pre‐clinical research prior to designing clinical trials is done not only for newly suggested surgical procedures but also in pharmacological research on liver excretory, detoxification and synthetic functions important for liver regeneration following a partial hepatectomy (Liska et al. 2012; Bruha et al. 2015). Similarly, the porcine liver is used in surgical experiments regarding therapy of small‐for‐size injuries that occur after partial liver transplantation or extended hepatectomy (Kelly et al. 2009; Hessheimer et al. 2014). The porcine model has been demonstrated to be useful when examining histological alterations of the liver during carbon dioxide pneumoperitoneum (Alexakis et al. 2008). Moreover, the porcine liver is used as a model for drug‐induced liver failure (Newsome et al. 2010), a model for hepatectomy with portocaval shunt (Iida et al. 2007), or for hepatic electrolytic ablation (Gravante et al. 2012).

The porcine liver has been suggested as a source of hepatocytes for bioartificial liver devices (Nicolas et al. 2016) and xenografts for transplantation (Cooper et al. 2015); however, these applications are controversial (Wang & Yang, 2012). Nevertheless, there is promising research on decellularized porcine hepatic lobes used for liver bioengineering (Hussein et al. 2015) in which porcine tissue scaffolds are supposed to be recellularized by human hepatocytes (Wu et al. 2015). Recently, Bähr et al. (2016) evaluated samples of liver and other organs in transgenic pigs that produced a recombinant protein that may be capable of modifying the T‐cell‐mediated rejection process, thus controlling cellular rejection in xenotransplantation.

Histological quantification of hepatocytes

Studies on pathophysiological mechanisms of liver diseases, liver regeneration, efficacy and toxicity of drugs, and evaluation of surgical techniques often require quantification. Numerous morphological characteristics may be estimated, preferably using design‐based histological techniques (Mouton, 2002; Howard & Reed, 2005) that make no further assumptions regarding the orientation or shape of liver cells and other structures under investigation (Marcos et al. 2012). The quantitative parameters of the liver that have been assessed in the frame of different studies include the whole liver volume, the volume densities of organ constituents (particularly of connective tissue), the mean volume of hepatocytes and other liver cells, the total numbers of liver cells and their numerical density per volume unit (Jack et al. 1990; Karbalay‐Doust & Noorafshan, 2009; Marcos et al. 2016). Knowledge regarding the variability of these microscopic parameters within the porcine liver is required for correct histological sampling.

The volume fractions of hepatocytes within the liver and the numerical density of mononuclear hepatocytes (MnHEP) or binuclear hepatocytes (BnHEP) assessed by stereological methods have been published for mice, rats and humans (Altunkaynak & Ozbek, 2009; Karbalay‐Doust & Noorafshan, 2009; Odaci et al. 2009). Marcos et al. (2016) quantified hepatocytes, Kupffer cells and hepatic stellate cells in the rat liver, thereby combining the advantages of stereology with cytometric analysis of cell ploidy. However, other methods and techniques have also been used for the quantification of hepatocytes, namely, automated image analysis, cell proliferation assays, protein concentration measurements, DNA content methods and cytochrome P450 content methods (Carlile et al. 1997; Stegemann et al. 2000; Haga et al. 2005; Sohlenius‐Sternbeck, 2006; Deng et al. 2009; Miyaoka et al. 2012; Garrido et al. 2013; Best et al. 2015; Asaoka et al. 2016). Many of these techniques are based on the use of single cell suspensions or liver homogenates. An unbiased measurement of the fraction of MnHEP and BnHEP is important for correcting methods that estimate the hepatocellularity using DNA or protein contents (Marcos et al. 2007).

Aims of the study

To the best of our knowledge, no published data exist regarding quantitative histological parameters that demonstrate the normal interindividual variability in the size and density of hepatocytes in various macroscopic regions of porcine liver lobes, e.g. peripheral regions vs. the parenchyma located near the porta hepatis or adjacent to the caudal vena cava.

Therefore, our aim was to assess the number‐weighted volume of hepatocytes, the numerical density of hepatocytes, and the fraction of binuclear hepatocytes (subsequently abbreviated as ‘nuclearity’) in the porcine liver. These data were compared between the anatomical hepatic lobes as well as between three macroscopic regions with different positions related to the liver vasculature (region of interest, ROI): the peripheral regions of the liver lobes, the regions near the porta hepatis and the regions adjacent to the caudal vena cava.

Materials and methods

Animals

Liver samples were obtained from seven healthy Prestice Black‐Pied pigs (Vrtkova, 2015) aged 9–12 weeks and weighing 25–35 kg (35.7 ± 6.1 kg, mean ± SD). Five piglets were male and two female. The number of animals corresponds to the typical number of individuals in other studies using pig as an animal model in surgery (Darnis et al. 2015; Hazelton et al. 2015). The animals received humane care in compliance with the European Convention on Animal Care, and the project No. 27374/2011‐30 was approved by the Faculty Committee for the Prevention of Cruelty to Animals. The piglets were pre‐medicated intramuscularly with atropine 1.0 mg, ketamine 200 mg (5–10 mg kg⁻¹) and azaperon 160 mg (2–8 mg kg⁻¹). For general anesthesia, propofol and fentanyl were continuously administered through a peripheral or central venous catheter in the following total average doses: propofol (1% mixture 5–10 mg kg^–1 h⁻¹) and fentanyl (1–2 μg kg⁻¹ h⁻¹). The piglets received infusion and volume substitution when necessary (Plasmalyte; Baxter, Vienna, Austria, and Gelofusine; B‐Braun, Maria Enzersdorf, Austria, respectively). All surgical procedures were performed under aseptic and antiseptic conditions. The animals were sacrificed during deep general anesthesia via an intravenous administration of a cardioplegic solution (potassium chloride).

Immediately after sacrifice, the whole liver was removed. The volume of each freshly collected liver was measured using the water displacement method. A large graduated cylinder with a total volume of 3 L was filled with water precisely to the 1‐L marking, and the liver was fully submerged in the water. The liver volume was calculated by subtracting the water level before and after submersion. The liver volumes ranged from 640 to 910 mL and the mean ± SD values were 813 ± 85 mL (see Supporting Information Table S1 for details). The liver volume did not correlate with the bodyweight.

Tissue sample collection

Each liver was sectioned into 1‐cm‐thick slabs. The slabs were fixed with 10% buffered formalin. From each liver, 36 tissue probes (each approximately 25 × 25 × 25 mm) were sampled. Each of the six hepatic lobes (left lateral, right lateral, right lateral, right medial, caudate and quadrate lobes) was represented by six probes. Within each lobe, three ROIs with different positions relative to the liver vasculature were sampled: two probes represented the peripheral regions, two probes represented the paracaval region, and two probes represented the paraportal region according to Fig. 1. The peripheral regions were defined as located no more than 1 cm from the surface and periphery of each hepatic lobe. The paracaval localization was the region of each lobe immediately adjacent to the openings of the hepatic veins into the caudal vena cava. The paraportal (hilar) localization was immediately adjacent to the main branches of the portal vein followed from the hilum within each anatomical lobe. In total, 251 tissue probes were collected (one sample was lost during processing).

Figure 1.

Collection of tissue samples (rectangles) of the porcine liver for quantitative histology. Schematic drawing of the facies visceralis of the porcine liver showing the outlines of the left lateral lobe (LLL), left medial lobe (LML), right medial lobe (RML), right lateral lobe (RLL), quadrate lobe (QL) and caudate lobe (mostly hidden behind the vessels, the scheme shows its caudate process, CP, only). The gall bladder (GB) and the caudal vena cava (CVC) are also shown. Branching of hepatic arteries is shown as red, branching of portal vein as blue and branching of bile ducts as green. The LLL is used as an example of collection of histological probes from three regions of interest: paracaval region (dark blue rectangles drawn with a continuous line), paraportal region (red rectangles with a dashed line), and peripheral region (green rectangles with a dotted line). Samples of the other lobes were collected accordingly.

The orientation of each tissue block was randomized using the orientator scheme (Mattfeldt et al. 1990). The procedure was done according to Nyengaard & Gundersen (2006) and Mühlfeld et al. (2010). In the first step, each tissue block was placed on a circle divided into 100 equal distances with one edge parallel to the 1–1 direction. A random number between 1 and 100 was generated using the Microsoft excel rand function and the tissue block was cut at this angle. In the second step, the freshly cut surface of the block was laid on a second circle with cosine‐weighted angular divisions. Another random number was generated, and the block was cut parallel to this number. Thus, isotropic uniform random (IUR) histological sections were produced. The newly generated cutting plane was carefully maintained during histological processing and was used as the histological section plane. Although hepatocytes can be viewed as isotropic particles and simple cutting would be sufficient for producing isotropic sections (Mandarim‐de‐Lacerda, 2003), we decided to randomize the orientation of each tissue block with respect to further use of the same embedded blocks for analysis of hepatic microvessels in a future study.

Histological processing

The tissue blocks were embedded in paraffin. From each block, two consecutive histological sections randomly positioned within the block were prepared at a thickness of 16 μm and mounted on silanized SuperFrost®Plus slides (Menzel‐Gläser, Braunschweig, Germany). Periodic acid‐Schiff staining (PAS) was performed according to Romeis (1989) using a commercial PAS staining kit (Morphisto, Frankfurt/Main, Germany) to highlight the contours of the individual hepatocytes.

Microscopic sampling and quantification

Following the production of two sections for each of the 251 tissue blocks, the analysis was based on 502 randomly orientated histological sections. In each section, four fields of view (FOV) were selected by systematic uniform random sampling (SURS) as follows: The use of a Leica DM2000 microscope (Leica, Wetzlar, Germany) equipped with a Leica DFC425C camera and an oil immersion objective with 100× magnification (numerical aperture 1.25) resulted in a field of view (FOV) of a photographed size of 94.86 × 63.2 μm. The sampling started on the top left of the first section using two random numbers generated with the Microsoft excel rand function as x‐ and y‐coordinates, which represented the distances of the first FOV from the left and upper borders in μm. The distance interval between the FOVs increased or decreased proportionally, i.e. the sampling step ranged between 1 and 3 mm. The histological sampling strategy is illustrated in Fig. 2A,B.

Figure 2.

Sampling of fields of view (FOV) in micrographs of liver tissue, the disector and the nucleator method. (A,B) Systematic uniform random sampling of FOVs based on a randomly positioned first FOV and equidistant placement of further FOVs, four of which were photographed for the first section (red squares) of each tissue block and four further photographed for the adjacent section (green squares). Each quadrant of the section profile was represented by one FOV. Micrographs (A) and (B) represent different shapes of tissue profiles and the necessary adaptation of distances between the FOVs. (C,D) To estimate the numerical density of hepatocytes and the fraction of binuclear hepatocytes, two optical sections from the same FOV illustrate the disector principle as follows: Whole cell profiles that were inside the counting frame or that touched the green allowance borders but not the red forbidden borders were counted, provided that their nuclear profiles were in focus with clearly visible chromatin in the bottom reference plane (C) or two subsequent planes of the disector volume probe and absent or clearly out of focus on the fourth plane (D, the look‐up plane of the disector). The nuclei of the counted mononuclear hepatocytes are marked with yellow arrows, whereas the nuclei of counted binuclear hepatocytes are marked with black arrows. (E,F) To estimate the number‐weighted mean volume, the cell borders of the hepatocytes previously selected with the disector method were marked with six intersecting isotropically oriented rays of the nucleator probes. This analysis was performed separately for mononuclear (E) and binuclear hepatocytes (F). Periodic acid‐Schiff staining: note that cell borders are easy to identify notwithstanding the natural staining variability as shown in (C–D) vs. (E–F). The counting frame size in (C–D) was tested in a pilot study; however, the definitive size shown in (E–F) (95 × 63 μm) was used consistently throughout the main study. Scale bars: 1 mm (A,B) and 10 μm (C–F).

The next step required focusing of optical sections. The Z‐direction feed rate of the fine focus of the Leica DM2000 microscope was verified using a Zeiss Imager.Z2 microscope equipped with an AxioCam MRc5 camera (Zeiss, Vienna, Austria) and the ZEN PRO2012 program, allowing precise computed Z‐stack measurement. With the 100× immersion objective of the Leica microscope, the distance between two scale lines indicating 1 μm in the fine focus of Leica DM2000 corresponded to the verified slice thickness of 0.97 μm.

Within each FOV, a series of four optical sections was captured at a resolution of 2592 × 1944 pixels. The Z‐step between the adjacent optical sections was set to 3 μm, which was sufficiently small to not lose the readability of the sequence of the optical sections. This made it possible to follow the continuity between the corresponding cell and nuclear profiles on adjacent optical sections. Starting from the bottom, the first sharp plane of the physical section was focused using the nuclear chromatin and outline of the nucleus and cell borders as reference points. In total, 8032 optical sections that documented 2008 FOVs were recorded. Using ellipse software (ViDiTo, Kosice, Slovak Republic), the four stereological parameters described in Table 1 were quantified in the optical sections.

Table 1.

Stereological parameters assessed for porcine hepatocytes in the frame of the study

Name and unit	Abbreviation and unit	Definition	Stereological technique used for quantification
Number‐weighted mean volume of mononuclear hepatocytes	${\overline{V}}_N\text{(MnHEP)}$ (μm3)	Average volume of hepatocytes that contained one nucleus	Optical disector (Gundersen et al. 1988; Marcos et al. 2012)
Number‐weighted mean volume of binuclear hepatocytes	${\overline{V}}_N\text{(BnHEP)}$ (μm3)	Average volume of hepatocytes that contained two nuclei	Optical disector
Fraction of binuclear hepatocytes	f(BnHEP) (−, parts of 1)	Relative amount of hepatocytes that contained more than one nucleus among all hepatocytes within the same reference volume	Optical disector
Numerical density of hepatocytes	N V(HEP) (mm−3)	Average number of hepatocytes per volume unit of liver tissue	Optical disector and nucleator (Gundersen, 1988; Gundersen et al. 1988; Marcos et al. 2012)

Numerical density of hepatocytes

Within each stack of micrographs that documented one FOV, the hepatocytes were counted using the optical disector method as shown in Fig. 2C,D. The nucleus with one or more nucleoli clearly in focus was selected as the decisive counting event (Gardella et al. 2003; Marcos et al. 2016). For the proper identification of the borders of individual hepatocytes and the chromatin of the hepatocyte nuclei, as well as for reliable measurements in the z‐direction, an oil immersion objective with 100× magnification and a high numerical aperture (1.25) was used. The optical disector counting rules (Gundersen, 1988) were used, with counting in whole cell profiles located inside the counting frame or touching the allowance borders, but not touching the forbidden borders. The cell and nuclear profiles were tracked starting from the first (reference) optical plane towards the last (look‐up) optical plane 4. Cells with nuclei visible at any of the planes 1–3 and lost before reaching the level of the look‐up plane were counted. The numerical density of the hepatocytes N _V(HEP) was calculated as follows:

$$N_V\text{(HEP)}=\frac{\sum _{i=1}^n{Q}_i^{-}(HEP)}{\sum _{i=1}^n{P}_i(ref)}·\frac{p}{a·h},$$

where Q _i ⁻(HEP) represents the number of hepatocytes with a clearly visible nucleus counted within the i‐th disector, P _i(ref) represents the number of points of the auxiliary grid that hit the i‐th reference space, p represents the total number of points of the auxiliary grid, a represents the area of the counting frame, h denotes the height of the disector and n denotes the total number of additions within the mathematical summation of all disectors and reference space points. At least 100 cells were counted in eight disectors applied to the two tissue sections of each sample. The reference space comprised all components of the liver tissue; however, the periportal areas composed of connective tissue were avoided.

Fraction of binuclear hepatocytes

In each sample, the relative amount of hepatocytes that contained two visible nuclei (BnHEP) was expressed as a ratio of these cells to the total number of all hepatocytes counted within the same reference volume. This assessment involved predominately binuclear hepatocytes. Trinuclear hepatocytes were observed very rarely and none of these was counted according to the disector rules.

Number‐weighted mean volume of hepatocytes

The nucleator method was used as a local stereological probe to estimate the volume of hepatocytes. This method is based on the use of a unique arbitrary point in every object under study, i.e. in every liver cell, provided the sections are isotropic uniform or vertical uniform (Gundersen 1988; Gundersen et al. 1988; Marcos et al. 2012). Briefly, in every stack of optical sections investigated, hepatocyte profiles were selected using the previously described disector method. The volume of every selected hepatocyte was measured in the central region, where the nucleus with nucleoli was visible. Using the Nucleator module of ellipse software, nucleated cell profiles sampled by the disector in the previous step were measured by marking the intersections of six isotropically oriented rays with the cell borders (Fig. 2E,F). The number of rays was based on a pilot study showing that using five, six or seven nucleator rays do not reduce the variability of measurements when compared with four nucleator rays. An average value independently calculated for the MnHEP and BnHEP resulted in number‐weighted mean volumes ${\overline{V}}_N$ of these cells (Table 1). In total, 29 054 hepatocytes were counted and evaluated in this study.

Corrections for shrinkage and z‐axis compression

Formalin fixation, dehydration and paraffin sectioning are steps that lead to volume shrinkage (Dorph‐Petersen et al. 2001; Gardella et al. 2003). Marcos et al. (2004) reported 38% shrinkage from fresh rat liver to mounted sections. As a result of shrinkage, cell volumes appear smaller and numerical cell densities appear larger compared with fresh organs prior to processing. According to Marcos et al. (2012), two main sources of shrinkage are expected to contribute bias to our study: (i) the volume shrinkage caused by the formalin fixation and paraffin embedding; and (ii) a decrease in the section thickness (compression) in the z‐axis in the thick sections as a result of the stretching of sections in the warm tissue flotation water bath. To compensate for the shrinkage, two corrections were applied to the results.

1. The volume shrinkage caused by the formalin fixation and paraffin processing was estimated as follows: 11 blocks were sectioned from the fresh liver, avoiding the hepatic capsule. Each block had a shape of a precisely shaped cuboid bounded with six quadrilateral faces. The x,y,z dimensions of each tissue block were precisely measured using a caliper with a reading error of 0.5 mm and the volume of each block was calculated. In all samples, the x,y,z directions were preserved consistently to allow for evaluation of the isotropy of the shrinkage as follows: the x‐direction was tangential to the liver surface from the periphery of liver lobe towards the hilum of the lobe; the y‐direction was tangential to the surface and perpendicular to the x‐direction; the z direction was perpendicular to the liver surface, thus running from the liver surface into the deeper parts of the lobe. Following routine fixation, dehydration and embedding, the tissue blocks were exhaustively cut into series of consecutive 5‐μm‐thick histological sections, and every 10th section was stained with hematoxylin and eosin. The x′,y′,z′ dimensions of each processed block were measured using the histological sections and the distance between the first and the last section and the volume of the block was calculated. The mean volume ratio after/before processing (± SD) was 0.675 ± 0.058. The cell volumes and disector volumes were corrected by multiplying the values measured in the paraffin sections by a correction factor of 1/0.675. Moreover, the mean ratio ± SD of dimensions after/before processing was calculated as follows: x′/x = 0.897 ± 0.071, y′/y = 0.938 ± 0.043, and z′/z = 0.803 ± 0.033. When comparing the linear shrinkages in the x‐, y‐, and the z‐directions, the Friedman anova revealed differences (P = 0.002), suggesting an anisotropic shrinkage. The post‐hoc Wilcoxon matched pairs tests showed that the shrinkage in the z‐direction (perpendicular to the liver surface) was more prominent than the shrinkage in the x‐direction (P = 0.003) or the y‐direction (P = 0.008). No difference was found when comparing the shrinkage in the x‐ and the y‐directions parallel to the liver surface.

2. The actual thickness of our final sections after stretching in the water bath and staining was measured using the z‐stack tool of the axio imager Z2 light microscope (Zeiss, Vienna, Austria) by manually focusing the first and last sharp optical planes of the sections. The mean distance between these planes was 13 μm. The microtome produced 16‐μm‐thick sections; thus, it demonstrated a compression factor 13/16 = 0.8125. The cell volumes and disector volumes were increased by multiplying the values measured in the thick paraffin sections by a correction factor of 1/0.8125.

Statistics

The software statistica base 11 package (StatSoft, Inc., Tulsa, OK, USA) was used for the statistical analysis. Part of the data did not pass the Shapiro–Wilk's W‐test for normality; thus, nonparametric methods were used for further analysis. The Kruskal–Wallis anova and the Mann–Whitney U‐test were used to assess the differences between the six lobes, the differences between the ROIs defined within the lobes, and the differences among the individual animals investigated. The correlations between the four stereological parameters were evaluated using the Spearman rank order coefficient. The coefficients of error (CE) estimating the sampling error were calculated according to Gundersen et al. (1999) separately on the level of tissue blocks and on the level of individual animals.

Results

The mean number‐weighted volume of mononuclear hepatocytes after shrinkage correction in all samples investigated was 3670 ± 805 μm³ (mean ± SD). The mean number‐weighted volume of BnHEP was 7050 ± 2550 μm³. The fraction of BnHEP was 4 ± 2%. The numerical density of all hepatocytes was 146 997 ± 15 738 cells mm⁻³. No pathological findings, such as inflammation, necrosis, fibrosis or extensive steatosis, were identified in the animals investigated. The CE ranged between 0.084 and 0.125 on the level of tissue blocks and between 0.014 and 0.018 on the level of individual animals. The complete stereological results for all samples are provided in Table S1.

Size, nuclearity and density of hepatocytes in the hepatic lobes of the pig

No differences between the hepatic lobes were identified when comparing the values of all four quantitative parameters investigated (Fig. 3A–D).

Figure 3.

Estimates of size, nuclearity and density of hepatocytes in six porcine hepatic lobes. (A) Number‐weighted mean volume of mononuclear hepatocytes ${\overline{V}}_N\text{(MnHEP)}$. (B) Number‐weighted mean volume of binuclear hepatocytes ${\overline{V}}_N\text{(BnHEP)}$. (C) Fraction of binuclear hepatocytes among all hepatocytes f(BnHEP). (D) Numerical density of hepatocytes N_V(HEP). Kruskal–Wallis anova indicated that there were no differences among the lobes in the parameters. Data are displayed as median values with boxes that span the limits of the first and third quartiles and whiskers that span the minimum and maximum values for each group.

Size, nuclearity and density of hepatocytes in paraportal, peripheral and paracaval ROIs

The greatest number‐weighted mean volume of mononuclear hepatocytes ${\overline{V}}_N\text{(MnHEP)}$ was identified in the peripheral regions of the liver lobes (P < 0.05); however, there was no difference between the paraportal and paracaval regions (Fig. 4A). The number‐weighted mean volume of binuclear hepatocytes ${\overline{V}}_N\text{(BnHEP)}$ (Fig. 4B) and the fraction of binuclear hepatocytes among all hepatocytes f(BnHEP) (Fig. 4C) were not different among the ROIs. The numerical density of the hepatocytes N _V(HEP) was smaller in the peripheral region than in the paracaval region (P < 0.01) or the paraportal region (P < 0.001, Fig. 4D).

Figure 4.

Estimates of size, nuclearity and density of hepatocytes in three macroscopically defined regions with respect to their proximity to the liver vasculature in the pig. (A) The largest number‐weighted mean volume of mononuclear hepatocytes ${\overline{V}}_N\text{(MnHEP)}$ was identified in the peripheral region. (B) Number‐weighted mean volume of binuclear hepatocytes ${\overline{V}}_N\text{(BnHEP)}$ exhibited no differences between the regions. (C) Fraction of binuclear hepatocytes among all hepatocytes f(BnHEP) exhibited no differences between the regions. (D) The smallest numerical density of hepatocytes N_V(HEP) was identified in the peripheral regions of the liver. Significant differences (*P < 0.05, **P < 0.01, ***P < 0.001) identified using the Mann–Whitney U‐test are presented. Data are displayed as median values with boxes that span the limits of the first and third quartiles and whiskers that span the minimum and maximum values for each group.

Size, nuclearity and density of hepatocytes compared among the individual animals

In all four parameters investigated (Fig. 5A–D), significant interindividual differences were identified.

Figure 5.

Estimates of size, nuclearity and density of hepatocytes in seven piglets investigated. All parameters investigated exhibited differences among the animals, as illustrated in (A) for the number‐weighted mean volume of mononuclear hepatocytes ${\overline{V}}_N\text{(MnHEP)}$, (B) for the number‐weighted mean volume of binuclear hepatocytes ${\overline{V}}_N\text{(BnHEP)}$, (C) for the fraction of binuclear hepatocytes among all hepatocytes f(BnHEP), and (D) for the numerical density of hepatocytes N_V(HEP). Significant differences (***P < 0.001) identified using the Kruskal–Wallis anova are presented. Data are displayed as median values with boxes that span the limits of the first and third quartiles and whiskers that span the minimum and maximum values for each animal.

Correlation between the size, nuclearity and density of hepatocytes

The number‐weighted mean volume of mononuclear hepatocytes ${\overline{V}}_N\text{(MnHEP)}$ was moderately correlated (Spearman R = 0.55) with the number‐weighted mean volume of binuclear hepatocytes ${\overline{V}}_N\text{(BnHEP)}$ identified in the same samples. The numerical density of hepatocytes N _V(HEP) exhibited a moderate negative correlation with the number‐weighted mean volume of mononuclear hepatocytes ${\overline{V}}_N\text{(MnHEP)}$ (R = −0.52) as well as with the number‐weighted mean volume of binuclear hepatocytes ${\overline{V}}_N\text{(BnHEP)}$ (R = −0.33).

Discussion

The mean number‐weighted volume of MnHEP (Table 2) partially corresponds with the number‐weighted mean cell volume of MnHEP published in other mammalian species. Using model‐based stereology, Rohr et al. (1976) reported the volume of human hepatocytes as 11 305 μm³. For a direct comparison with studies that used similar design‐based stereological methods applied in histological sections, Jack et al. (1990) reported the number‐weighted mean cell volume as 4740 μm³ in MnHEP and 6930 μm³ in BnHEP in female rats. Karbalay‐Doust & Noorafshan (2009) determined the volume‐weighted mean cell volume of mice to be 5300 μm³. Marcos et al. (2016) determined the number‐weighted mean cell volume of MnHEP to be 6044 μm³ in male rats and 4789 μm³ in female rats, whereas the number‐weighted mean cell volume of BnHEP was 7530 μm³ in male vs. 6565 μm³ in female rats. Hammad et al. (2014) determined the mean volume of hepatocytes in mice to be 5128 μm³. Moreover, the porcine BnHEP in our study had volumes comparable with BnHEP in the rat liver (Jack et al. 1990; Marcos et al. 2016). We found that BnHEP had almost twice the volume of MnHEP. According to Watanabe & Tanaka (1982) and Peinado et al. (1990), the size of hepatocytes corresponds to the sum of ploidy of all the nuclei and is also linked to the volume of stored lipid droplets. To date, there is no information published regarding the volume of BnHEP within a tissue context (i.e. not in single cell suspension) in species other than rats and pigs.

Table 2.

Estimated number‐weighted mean volume of mononuclear hepatocytes ${\overline{V}}_N\text{(MnHEP)}$ and binuclear hepatocytes ${\overline{V}}_N\text{(BnHEP)}$, fraction of binuclear hepatocytes among all hepatocytes f(BnHEP), and numerical density of hepatocytes N _V(HEP) in three macroscopic regions of the porcine liver with respect to their proximity to the liver vasculature. Data are presented as medians and quartile ranges (the value of the 75th percentile minus the value of the 25th percentile, including 50% of the cases)

		Paraportal regions	Peripheral regions	Paracaval regions
${\overline{V}}_N\text{(MnHEP)}$ (μm3)	Median Quartile range	3536 841	3880 1277	3593 866
${\overline{V}}_N\text{(BnHEP)}$ (μm3)	Median Quartile range	7015 3258	7397 2991	6739 2786
f(BnHEP) (−)	Median Quartile range	4% 3%	4% 3%	4% 3%
N V(HEP) (mm−3)	Median Quartile range	150 776 20 328	141 413 20 963	148 845 19 693

Porcine hepatic lobes contain hepatocytes of comparable size, nuclearity and density

Our results (Fig. 3) demonstrated that the six hepatic lobes of the porcine liver have a similar distribution of hepatocytes of various sizes, numbers of nuclei and densities. This finding suggests that individual lobes may be chosen as technically appropriate for experiments on liver regeneration such as partial lobectomy or hepatectomy (Bruha et al. 2015), even if quantitative histology is applied. The morphometry of hepatocytes would remain unbiased by the finding that some tissue probes would originate from various hepatic lobes, provided the sampling of tissue probes is not substantially lower than in the present study.

Peripheral regions of hepatic lobes contain the largest MnHEP with the smallest numerical density

The finding of intralobar differences in the hepatocyte size and density (Fig. 4) clearly demonstrates the importance of systematic sampling when obtaining histological probes from hepatic lobes that exhibit a prominent anatomical hierarchy of blood vessels. However, the biological interpretation of these results is not straightforward. The mammalian cell size is regulated in correlation with the cell cycle progression (e.g. Shen et al. 2000); however, it has been demonstrated that cell growth and cell cycling are separable and thus distinct processes (Fingar et al. 2002). The coordination of cell growth with cell replication has also been suggested for liver regeneration (Fausto & Campbell, 2003). However, it is not known how the hepatocyte volume changes during the cell cycle and whether the proliferation rate and duration or dynamics of the cell cycle differ with distance from the large branches of the portal vein and hepatic proper artery.

Proteins such as membrane transporters, volume‐sensitive ion channels, and stretch‐activated channels, as well as molecules that function as cellular osmolytes play a crucial role in cell size regulation (Hoffmann & Dunham, 1995). It is not known whether the expression of these proteins differs within the liver lobe, which would provide an explanation for the cell size variability. A specific lobular zonality as described for some hepatic enzymes (Spear et al. 2006) may be expected with differences between periportal vs. pericentral regions.

Polyploidization of hepatocytes increases with age (as well as after stress) and leads to an increased cell volume (Pandit et al. 2013). It may be hypothesized that the peripheral parts of the liver lobes represent the developmentally oldest hepatic regions and thus contain more large polyploid cells. Tanami et al. (2016) mapped the zonation of liver polyploidy in rat, revealing that liver polyploidy proceeds in spatial waves, advancing more rapidly in the mid‐lobule zone than the periportal and perivenous zones. The findings of Gerlyng et al. (1993) suggest that polyploid hepatocytes in rat liver have a greater tendency to replicate; however, they predominately divide into mononuclear daughter cells. Diploid and polyploid hepatocytes originate predominantly through failed cytokinesis (Duncan, 2013; Gentric & Desdouets, 2014) and it was suggested that they promote liver homeostatic and regenerative turnover (Gentric et al. 2012; Pandit et al. 2013; Wang et al. 2015). Moreover, aneuploid hepatocytes seem to be differentially resistant to chronic liver injury, and regenerate the liver (Duncan, 2013).

Irrespective of the cause of intralobar differences in the hepatocyte size and density, it should be noted that the morphometry of hepatocytes may be easily biased when samples for quantitative histology are collected from regions with different positions between large vessels and the periphery of liver lobes.

Size, density and fraction of BnHEP exhibit considerable interindividual differences

As shown in Fig. 5, healthy pigs of the same age and breed with a similar total liver volume of 813 ± 85 mL (mean ± SD, see Table S1), and identical diet and handling may have significant interindividual differences at the level of hepatocytes evaluated within their tissue context. However, Stegemann et al. (2000) demonstrated with sufficient precision and accuracy that the average size of isolated porcine hepatocytes remained consistent among individuals. The number of animals in our study does not enable a reliable comparison between males and females; however, we speculate that sexual dimorphism may explain, at least in part, this variability. Nevertheless, the piglets investigated were prepubescent, and the influence of sex hormones could be expected to remain small. Detailed studies on the rat liver (Marcos et al. 2015b, 2016) showed that the female liver contained an increased number of hepatocytes per gram and contained more binucleate cells, thus suggesting an increased regenerative potential in female compared with male rat liver. Moreover, it should be noted that the number of nuclei visible in the optical microscope using routine histological sections is completely different from the cell ploidy hepatocytes assessed using advanced methods, such as single molecule fluorescence in situ hybridization. Hepatocytes with one or two nuclei may contain two, four, eight or even more haploid chromosome sets (Tanami et al. 2016). In contrast to our findings (4% of BnHEP), Vinogradov et al. (2001) reported in pig of unknown age that 54% of binuclear hepatocytes had 2 × 2c ploidy. The most probable explanation of this discrepancy is the gradual increase in liver ploidy during aging, which has been reported by Guidotti et al. (2003) and Gentric & Desdouets (2014).

Distribution of larger MnHEP correlates with a larger volume of BnHEP and a smaller numerical density of all hepatocytes

When interpreting the biological meaning of the numerical results of hepatocyte morphometry, it should be noted that the morphological parameters are statistically correlated, rather than entirely independent. Our study demonstrated that in regions with large MnHEP, the size of BnHEP was also large. Simultaneously, the regions that contained hepatocytes with a large volume had a tendency to contain a smaller ration of BnHEP. It remains to be determined whether an increased degree of polyploidy, which has been indicated to lead to larger cell sizes and increased occurrence of bi‐ and multinuclear cells (Pandit et al. 2013), may provide an explanation for these correlations.

Regions with a greater volume of hepatocytes exhibited a smaller density of hepatocytes per unit of volume. One explanation for this correlation is that if cells grow larger, fewer cells fit in the reference space. However, the volume fractions of the hepatic vascular bed and the intralobular connective tissue would have to be taken into account for a correct interpretation of this finding. Mapping of the volume fractions of the main porcine liver components remains to be performed. As shown in recent studies (Debbaut et al. 2012, 2014b), this may be done economically by combining the histological approach with a three‐dimensional analysis and stereological quantification of hepatic microvessels using high‐resolution X‐ray microtomography of vascular corrosion casts (Eberlova et al. 2016; Jiřík et al. 2016). Moreover, quantitative data regarding the size and density of hepatocytes may also be combined with multi‐level modeling of hepatic perfusion (Debbaut et al. 2014a; Peeters et al. 2015).

Study implications

When evaluating the histomorphometry of hepatocytes in experiments with porcine livers, a high variability should be expected in interindividual differences. Another major source of variability as demonstrated in our study was the position of the tissue probes with respect to the distance from the major hepatic blood vessels. Moreover, the samples collected from various hepatic lobes exhibited no differences in healthy piglets; however, interlobar differences have been reported in various cases of liver alterations (e.g. Richardson et al. 1986; Faa et al. 1995; Regev et al. 2002; Irwin et al. 2005; Palladini et al. 2012). Our findings fully comply with the well‐known recommendations of Gundersen & Østerby (1981), who demonstrated that in a typical biological experiment, the interindividual biological variability is responsible for up to 70% of the overall observed variance.

As practical suggestions for further studies that involve stereological evaluation of the size, nuclearity and density of hepatocytes in porcine liver, we would recommend the following:the use of sufficient numbers of pigs per study group; a power analysis for estimating the minimum number of animals per study group may be easily calculated from our results. For example, when planning an experiment and expecting the mean numerical density to be decreased by 20% (i.e. from 97 500 to 78 000 cells μm⁻³), the minimum number of animals per group would be eight, using the typical test power 1 − β = 0.8 (where β is the type II error) and α=0.05 (where α is the type I error) (Chow et al. 2008). systematically obtaining histological probes from both the peripheral parts of the hepatic lobes and the vicinity of the major intrahepatic blood vessels; using the six hepatic lobes of porcine liver independently in experiments that address partial lobectomy or hepatectomy because tissue probes sampled from various lobes yield comparable results provided that the paraportal and peripheral regions are sampled accordingly; when analyzing 36 probes per animal, the CE was reasonably low (0.014–0.018); reducing the number of probes to 18 would result in an increased CE of approximately 0.15, which can be derived from the Table S1. Therefore we recommend obtaining at least 20 histological probes per individual. Future studies in the pig would provide important additional information with respect to other quantitative parameters, such as the distribution of intralobular and interlobular connective tissue (Marcos et al. 2015a), as well as the lobular zonality of liver pathologies (e.g. Schwen et al. 2016) and gene expression in hepatocytes (Schwen et al. 2015).

This study has several limitations. Although none of the samples showed histopathological alterations, no liver biochemical tests were done and the liver function was not assessed in this study. Our study was based on one type of simple PAS staining outlining the glycocalyx of the cell membrane. This approach may also represent an advantage when processing archive samples. However, hepatocytes laden with PAS‐positive glycogen granules partially lose contrast between the cytoplasm and cell membrane. For some applications, complex staining protocols enable the interpretation of the morphometry of hepatocytes within the context of the liver tissue (Hoehme et al. 2010; Schwier et al. 2013; Hammad et al. 2014). Moreover, whole‐slide imaging (Hoehme et al. 2010; Schwier et al. 2013; Hammad et al. 2014) is a good choice to handle the variability in the level of more histological sections.

Our study generated a number of more detailed questions that, to our knowledge, have not been addressed to date for the porcine liver:

1. The size, nuclearity and density of hepatocytes will have to be mapped with respect to the position of the hepatocytes within the classical morphological hepatic lobules (Marcos et al. 2016), as well as within the zones of the liver acini. The identification of the lobular and acinar distributions of the stereological characteristics of hepatocytes would contribute to understanding their role in pathological processes that preferentially involve zones of a liver lobule, such as demonstrated during centrilobular necrosis as a result of passive congestion, after poor oxygenation of hepatocytes (Saxena, 2011), in drug‐induced porcine models of liver failure (Newsome et al. 2010), in a porcine model of small‐for‐size syndrome (Kelly et al. 2009) or in a porcine hepatectomy model with a portocaval shunt (Iida et al. 2007). Similarly, periportal necrosis was found to be present in a porcine model of acid aspiration (Heuer et al. 2012) and in toxin‐induced fulminant hepatic failure (Collins et al. 1994).

2. Sexual dimorphism of the hepatocyte size and density (Marcos et al. 2016) examined together with enzyme activity (Bode et al. 2010) may elucidate the regenerative potential of male vs. female porcine livers.

3. It remains unknown how the size, nuclearity and density of hepatocytes are associated with their proliferation rate.

4. From a stereological point of view, the total amounts of hepatocytes within the lobes of the porcine liver remain to be estimated using the fractionator sampling scheme (Marcos et al. 2012). This parameter is not biased by shrinkage and is therefore useful when comparing the functional capacity of the lobes.

Conclusion

The mean number‐weighted volume of porcine mononuclear hepatocytes was 3670 ± 805 μm³ (mean ± SD, corrected for shrinking during histological processing). The mean number‐weighted volume of binuclear hepatocytes was 7050 ± 2550 μm³. The fraction of BnHEP hepatocytes was 4 ± 2%. The numerical density of all hepatocytes was 146 997 ± 15 738 cells mm⁻³. Porcine hepatic lobes contained hepatocytes of a comparable size, nuclearity and density without significant differences between the lobes. Peripheral ROIs of hepatic lobes contained the largest MnHEP with the smallest numerical density. The hepatocyte size and density, as well as the fraction of BnHEP exhibited considerable interindividual differences even in healthy young animals. The distribution of larger MnHEP was correlated with a larger volume of BnHEP and a smaller numerical density of all hepatocytes. The complete primary stereological data in the form of continuous variables have been made available as a supplement to this paper. Practical recommendations for designing studies that involve stereological evaluations of the size, nuclearity and density of hepatocytes in porcine liver are provided. However, a number of biologically relevant parameters remain to be mapped within the porcine liver.

Conflict of interest

The authors declare that they have no conflict of interest.

Author contributions

Khan Lamanero Junatas – review of the literature; histological tissue processing; microscopy and quantification of the sections; data acquisition; illustrations; and manuscript writing. Zbyněk Tonar – idea and concept of the study; literature review; stereological design of the study; conducted pilot study; illustrations; statistics; drafting and writing of the manuscript. Tereza Kubíková – quantification of tissue shrinkage in formalin‐fixed and paraffin‐embedded histological sections. Václav Liška and Richard Pálek – contribution to the study design; animal handling; harvesting the liver; performing the sampling of liver tissue probes from anatomical lobes and regions with different vascular supplies. Patrik Mik – review of the literature on binuclear hepatocytes, contribution to the revised manuscript. Milena Kralickova – critical revision of the manuscript and approval of the article. Kirsti Witter – contribution to the study design and the pilot feasibility study; histological tissue processing; manuscript writing and editing.

Supporting information

Table S1. Primary stereological data on porcine hepatocytes in all samples investigated.