Prediction and validation of cell alignment alongmicrovessels as order principle to restore tissuearchitecture in liver regenerationStefan Hoehmea,1, Marc Brulportb,1, Alexander Bauerb, Essam Bedawyb, Wiebke Schormannb, Matthias Hermesb,Verena Puppeb, Rolf Gebhardtc, Sebastian Zellmerc, Michael Schwarzd, Ernesto Bockampe, Tobias Timmelf,Jan G. Hengstlerb,2, and Dirk Drasdoa,g,2

aInterdisciplinary Centre for Bioinformatics (IZBI), University of Leipzig, Härtelstrasse 16-18, D-04107 Leipzig, Germany; bLeibniz Research Centre forWorking Environment and Human Factors (IfADo); University of Dortmund, Ardeystrasse 67, D-44139 Dortmund, Germany; gInstitut National deRecherche en Informatique et en Automatique (INRIA), Unit Rocquencourt B.P. 105, 78153, Le Chesnay Cedex, France; dInstitute of Experimentaland Clinical Pharmacology and Toxicology, Department of Toxicology, University of Tübingen, Wilhelmstrasse 56, 72074 Tübingen, Germany; cInstitute ofBiochemistry, Medical Faculty, University of Leipzig, Johannisallee 30, 04103, Leipzig, Germany; eClinical School of the Johannes Gutenberg–UniversityMainz Institute for Toxicology, Obere Zahlbacher Strasse 67, 55131 Mainz, Germany; and fBiofluidmechanics Laboratory, Charite–UniversitätsmedizinBerlin, Berlin, Germany

Edited* by Manfred Eigen, Max Planck Institute for Biophysical Chemistry, Gottingen-Nikolausberg, Germany, and approved February 23, 2010 (received forreview August 18, 2009)

Only little is known about how cells coordinately behave to estab-lish functional tissue structure and restore microarchitecture duringregeneration. Research in this field is hampered by a lack of tech-niques that allow quantification of tissue architecture and itsdevelopment. To bridge this gap, we have established a procedurebased on confocal laser scans, image processing, and three-dimen-sional tissue reconstruction, as well as quantitative mathematicalmodeling. As a proof of principle, we reconstructed and modeledliver regeneration in mice after damage by CCl4, a prototypical in-ducer of pericentral liver damage.Wehave chosen the regeneratingliver as an example because of the tight link between liver architec-ture and function: the complex microarchitecture formed by hepa-tocytes and microvessels, i.e. sinusoids, ensures optimal exchangeof metabolites between blood and hepatocytes. Our model cap-tures all hepatocytes and sinusoids of a liver lobule during a 16 daysregeneration process. The model unambiguously predicted a so-farunrecognizedmechanismas essential for liver regeneration,where-by daughter hepatocytes align along the orientation of the closestsinusoid, a process which we named “hepatocyte-sinusoid align-ment” (HSA). The simulated tissue architecture was only in agree-ment with the experimentally obtained data when HSA wasincluded into the model and, moreover, no other likely mechanismcould replace it. In order to experimentally validate the model ofprediction of HSA, we analyzed the three-dimensional orientationof daughter hepatocytes in relation to the sinusoids. The results ofthis analysis clearly confirmed themodel prediction.We believe ourprocedure is widely applicable in the systems biology of tissues.

agent based model ∣ image processing and analysis ∣mathematical tissue modeling ∣ systems biology ∣ morphogenesis

The liver is the main metabolic organ which removes drugs andtoxins from the blood. One of the outstanding features of the

liver is its capacity to regenerate hepatocyte loss of up to 70% ofits mass within a relatively short period of time (1). Hepatic pa-renchyma is organized in repetitive functional units called liverlobules, which besides its main constituents, hepatocytes, consistsof sinusoidal endothelial cells, Kupffer, stellate, and bile ductcells. Branches of the hepatic artery and portal vein guide bloodto the periportal regions of the lobules (Fig. 1A). From there, itflows through microvessels, the sinusoids, along hepatocyte col-umns that are lined with endothelial cells (generally known assinusoidal cells), and drains into the central vein. This complexlobule architecture ensures a maximal exchange area betweenblood and hepatocytes in healthy liver. In liver disease, such ashepatocellular cancer, the contact surface between hepatocytesand sinusoidal cells decreases and contributes to compromised

liver function (Fig. 1F). Recent research on liver regenerationhas focused on molecular pathways and the mechanisms involved(2). Little is known about how cells coordinately behave to re-store the complex functional lobule architecture. What are thefundamental mechanisms underlying this complex regenerationprocess? In the present study, we analyzed liver regenerationin mice after intoxication with CCl4. CCl4 causes hepatocytesclose to the central vein to die (Fig. 2B) since only these cellsexpress CYP2E1, which metabolically activates CCl4 to the toxicentity (3). This pattern of toxicity is similar to that caused in hu-mans by an overdose of acetaminophen. Nevertheless, after onlyabout 10 d this central necrotic lesion is closed and the lobulearchitecture is completely restored (Fig. 2D). To shed light onthe underlying processes, we established a three-step procedurebased on confocal laser scans visualizing hepatocytes and sinusoi-dal cells (Fig. 1B), image processing and 3D tissue reconstruction(Fig. 1 C–E), and quantitative mathematical modeling (Fig. 3 andMovies S1, S2, S3, S4, S5, and S6). Our procedure uses threeparameter types: (lobule) architectural parameters to quantifythe static liver lobule, (regeneration) process parameters to quan-tify the regeneration process, and (mathematical) modeling para-meters to characterize the mathematical simulation model. Wecombined architectural and process parameters to set up a de-tailed mathematical computer model of liver lobule regenerationafter toxic damage. For determination of the process parameters,we complemented conventional techniques, such as BrdU incor-poration, with techniques of processing and analyzing experimen-tally obtained 3D confocal images. This enabled us to extractquantitative information that would otherwise be inaccessible,such as the 3D spatial-temporal proliferation pattern of hepato-cytes and the contact area between hepatocytes and sinusoidalcells during the regeneration process (Fig. 3F). We identified pos-sible mechanisms underlying the observed regeneration processby analyzing a wide range of mathematical model variants within

Author contributions: S.H., R.G., J.G.H., and D.D. designed research; S.H., M.B., A.B.,E. Bedawy, W.S., M.H., V.P., R.G., S.Z., M.S., E. Bockamp, T.T., J.G.H., and D.D. performedresearch; S.H., J.G.H., and D.D. contributed new reagents/analytic tools; S.H., J.G.H.,and D.D. analyzed data; and S.H., J.G.H., and D.D. wrote the paper.

The authors declare no conflict of interest.

*This Direct Submission article had a prearranged editor.

Freely available online through the PNAS open access option.1S.H. and M.B. contributed equally to this work.2To whom correspondence may be addressed. E-mail: hengstler@ifado.de (experiment) ordirk.drasdo@inria.fr (modeling, image processing).

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.0909374107/-/DCSupplemental/.

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plausible physiological model parameter ranges, followed by aquantitative comparison of the simulation results with the experi-mental observations, using the same process parameters for bothexperiments and simulations. Finally, we used the mathematicalmodel to guide further experiments by predicting the most infor-mative experiments to select the most appropriate mechanisms

underlying regeneration. Using this strategy, we identified amechanism, “hepatocyte-sinusoid alignment” (HSA), wherebydaughter cells from hepatocyte division align along the closestsinusoid. Model simulations and experiments demonstrated thatHSA is a key mechanism necessary for the regeneration of thefunctional architecture of the liver lobule that cannot be replacedby alternative mechanisms. Quantitative spatio-temporal mathe-matical modeling of tissue organization represents a generic wayto merge information from different sources to synergistically ob-tain quantitative and qualitative insights into tissue organizationprocesses.

ResultsThree-Dimensional Reconstruction of the Liver Lobule. In order to es-tablish a quantitative spatial-temporal model of the regeneratingliver lobule, we first reconstructed and quantitatively described itsarchitecture. For this purpose, we used confocal laser scans ofapproximately 150 μm thick liver tissue slices. Sinusoidal cellsappear red after staining with ICAM (intercellular adhesion mo-lecule) antibodies; whereas the apical side of hepatocytes ap-pears green after staining with DPPIV (Dipeptidylpeptidase IV)antibodies (Fig. 1B). Based on the confocal laser scans(SI Appendix), the full 3D structure of the sinusoidal networkwas reconstructed using filtering, segmentation, and morphologi-cal restoration steps (Fig. 1 C–E and SI Appendix). The same con-focal laser scans have been used to determine the position ofhepatocyte nuclei after staining with DAPI (Fig. 1E). From theimage processing and analysis steps, we obtained statistical dis-tributions for the architectural parameters. These were the aver-age vessel diameter and density (including branching lengths thatquantify the sinusoidal network and the position), volume, den-sity, and shape of the hepatocytes (SI Appendix). In order tocapture variations among different liver lobules, we studied 26lobules from different mice. Additionally, the results were vali-dated using transgenic mice in which differentiation betweenhepatocytes and sinusoidal cells was based on EGFP expres-sion under the control of an albumin/alpha-fetoprotein (Alfp)-promoter, and sinusoidal cells were visualized by CD31 immunos-taining (SI Appendix). From the obtained architectural parameter

Fig. 1. (A) Concrete liver lobule inferred from experimental data by the im-age processing chain shown in (B)–(E) and successive image analysis. Recon-structed lobules served as an initial state for the mathematical model. (B) Atypical image obtained by confocal microscopy after adaptive histogramequalization filtering. Blue: DAPI (hepatocyte nuclei); yellow: ICAMþ DPPIV(sinusoids); red: ICAM; green: DPPIV. (C) Effect of generalized erosion filtering(all red pixels will be removed). (D) Effect of generalized dilatation filtering(all green pixels are added). (E) Result of image processing chain in three di-mensions. Blue: Hepatocyte nuclei; white: sinusoids. Note the complex archi-tecture that links the periportal zone with the central vein in the middle ofthe lobule. (F) Fraction of the surface area of hepatocytes in contact with si-nusoids (orange) and other hepatocytes (gray) in normal liver tissue and livercarcinomas. Details in SI Appendix.

Fig. 2. Representative examples of mouse liver lobules visualized under light microscopy. (A) Control, (B) 2 d, (C) 4 d, and (D) 8 d after administration of CCl4,illustrating the emergence and regeneration of the central dead cell area. The examples shown in (A)–(D), employing a suboptimal peroxidase block, allowedan automated differentiation between the paler central dead cell area (B2, green striped area) and the darker surviving hepatocytes, while, at larger mag-nification, BrdU-positive and BrdU-negative cells could still be clearly distinguished. Hand-drawn lines in (A)–(D), (A2) and (B2) show the approximate extensionof the liver lobules. (A2) Central veins were identified by immunostaining for GS. The process parameters for quantification of the regeneration process were(E) distribution of BrdU-positive cells in a liver lobule. Three mice were used per time point, namely, 0, 1, 2, 3, 4, 8, and 16 d after administration of CCl4. At leasttwo liver lobules were analyzed per mouse: (F) average hepatocyte density, (G) area of central necrosis, and (H) hepatocyte-sinusoid contact area over time.

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distributions, we generated a representative liver lobule as an in-itial configuration for the mathematical model (Fig. 3C).

Quantification of the Destruction and Regeneration Process.Next, wedefined process parameters to quantify the regeneration process.These were (i) the spatial BrdU incorporation pattern within theliver lobule as a measure for cell proliferation, (ii) the number ofcells in a lobule section as a measure of the lobule mass, (iii) thearea of the central necrosis, and (iv) the hepatocyte-sinusoid con-tact area, defined as the percentage of the hepatocyte surface thatis in contact with an adjacent sinusoid as a measure of lobule ar-chitecture. These process parameters were determined from lightmicroscopy images and confocal laser scans 0, 1, 2, 3, 4, 8, and16 d after intoxication with CCl4 (1.6 g/kg body weight). TheBrdU incorporation pattern was used as an input parameter todetermine the proliferation pattern in our mathematical model.The central necrotic area was clearly distinguished from the sur-viving hepatocytes and was maximal 1–2 d after CCl4 administra-tion (Fig. 2G), at which time the average hepatocyte densitywithin the lobule was minimal (Fig. 2F). BrdU incorporation intohepatocytes peaked 2–3 d after CCl4 administration (Fig. 2E).The distribution of proliferating hepatocytes over the lobulewas not homogeneous and preferentially occurred in the hepato-cyte layers next to the dead cell area (Fig. 2E). The order of celllayers was determined and visualized in Fig. 2B2 (for details, seeSI Appendix). The pericentral hepatocyte marker, glutaminesynthetase (GS), transiently decreased; an effect detected bymRNA expression, immunostaining and enzyme activity analysis(Figs. S1–S3). This demonstrates that the dynamics of destructionand regeneration of the pericentral hepatocytes is in agreementwith previously reported observations (1, 4). The number ofmacrophages increased in the necrotic zone and was concomitantwith an increase in CD68 mRNA (Fig. S4). This may explain therapid disappearance of the dead cell mass. A number of observa-tions were in agreement with a destruction and regenerationprocess. These included a transient decrease of ATP content(Fig. S5), as well as albumin, CYP3A11, and BSEP (ATP bindingcassette, subfamily B, member 11) mRNA expression (factors re-sponsible for differentiated liver functions); a transient increaseof AFP (alphafetoprotein) and ubiquitin mRNA expression(Fig. S1); and also the macroscopic appearance of the analyzedlivers (Fig. S6). Within 8 d, the central necrotic area was closed

(Fig. 2 A–D and G) and the average liver lobule hepatocyte den-sity restored (Fig. 2F). As soon as the central dead cell areas wereregenerated it became difficult to histologically identify the cen-tral veins, which were visible by GS immunostaining in neighbor-ing slices (Fig. 2A2). It is important to note that the structure ofthe sinusoidal network remained essentially unaffected by CCl4(Fig. 4F). In order to quantify the liver lobule microarchitecture,

Fig. 3. Regeneration in the simulation model, starting with a representative liver lobule. (A)–(C) partly show cross sections (compared to Fig. 1A) of modelsimulations: (A) simulation result from model 1 after 10 d, (B) simulation result from model 2 after 10 d, and (C) illustration of the regeneration process (aftert ¼ 0, 1, 2, 4, and 10 d) using model 3 (Movies S1–S3). (D)–(F) A quantitative comparison of experimental data with each model: (D) average hepatocyte density,(E) area of central necrosis, and (F) hepatocyte-sinusoid contact area.

Fig. 4. Sinusoidal cells survive in the central dead cell area of the liver lobuleafter CCl4 poisoning and activate the tie-2 promoter. (A) Constructs of thetriple transgenic tie-2-reporter mice. (B) Liver tissue of an untreated tie-2-re-porter mouse. Green fluorescence (EGFP) indicates positive tie-2 promoteractivity in the endothelial cells of a vein (white arrow in upper right image).Sinusoidal cells are visualized by CD31 immunostaining (light red in the lowerleft image) and nuclei by DAPI (blue in the lower right image). The mergedpicture (upper left image) demonstrates that endothelial cells of the vein, butnot the sinusoidal cells, express EGFP (yellow). (C) and (D) Two days after CCl4administration, some of the sinusoidal cells start to express EGFP. (C) EGFPgreen fluorescence and (D) green, red, and blue merged fluorescence. Thecentral dead cell area is characterized by loss of nuclei and increased redbackground fluorescence. A substantial fraction of the sinusoidal cells withinthe central dead hepatocyte area survives and starts to express EGFP as areporter of tie-2-promoter activity. 3D reconstructed lobule (E) before and(F) after CCl4 administration. As hepatocytes (blue) die, the sinusoids (gray)remain largely intact.

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we measured the hepatocyte-sinusoid and the hepatocyte-hepa-tocyte contact areas. This measurement was validated by compar-ing healthy liver and liver carcinoma tissues (Fig. 1F). In normalliver, 35.8� 2.3% (mean� standard deviation) of the hepatocytesurface was in contact with other hepatocytes and 48.5� 2.5%with sinusoids. In liver carcinomas, the contact areas were 48.1�3.6% (with hepatocytes) and 39.1� 2.3% (with sinusoids), illus-trating the significant (unpaired t-test: p ¼ 0.0015) decrease inhepatocyte-sinusoid contact and a corresponding increase of he-patocyte-hepatocyte-contact in liver tumors. Since both measuresare complementary, we considered only the hepatocyte-sinusoidcontact area at which the exchange of metabolites between bloodand hepatocytes occurred. Also, during the regeneration processafter CCl4 damage, the hepatocyte-sinusoid contact transientlydecreased with a minimum at day 2 and subsequent recoveryup to day 16 (Fig. 2H).

Establishment of the Spatial-Temporal Simulation Model. Havingmeasured 3D changes in liver structure during and after liverdamage, we established a mathematical model of a single liverlobule simulating the 16 d process after treatment with CCl4. Thebasic units of the model are the single hepatocytes and the sinu-soids. We modeled each hepatocyte as an individual homo-geneous, isotropic elastic and adhesive object capable of migra-tion, growth, division, and death. The interactions amonghepatocytes, between hepatocytes and sinusoids, and hepatocytesand extra-cellular matrix were modeled using a previously vali-dated force model (5). It includes central forces between cellsresulting from adhesion by cell surface receptors and repulsionfrom cell compression and deformation. The hepatocyte move-ment was modeled by a stochastic equation of motion for theposition of each hepatocyte. The equation included all forces ex-erted on that hepatocyte at each point in time as well as a randomterm mimicking the hepatocyte micromotility. Each sinusoid ofthe sinusoidal network was modeled as a chain of linked spherescharacterized by its extensibility. The ends of the sinusoidal net-work were fixed at the central vein and the periportal field. Itsmovement was modeled similarly as for hepatocytes but withno micromotility. Our mathematical model was parameterizedby measurable biophysical and cell-biological parameters (for de-tails, see SI Appendix). Moreover, we considered a possible influ-ence of morphogenes transported either via blood into the liverlobules or secreted by the necrotic cells close to the central vein.We iteratively developed our final model which was driven by di-rect comparisons with the process parameters in Fig. 3 D–F. Adetailed description of the spatial-temporal simulation model,the used variants, and the model parameters can be found inSI Appendix. We considered two starting configurations: (i) a re-presentative liver lobule generated by averaging the architecturalparameters of 26 liver lobules, and (ii) a concrete liver lobulereconstructed from a specific confocal dataset to avoid possibleartifacts that may arise from averaging. For the representativeinitial configuration shown in Fig. 3C, the hepatocyte-sinusoidcontact area was 51� 1.2% of the hepatocyte surface which wasclose to the experimental value of 48.5� 2.5%. Note that theseparameters cannot be directly tuned as they are fully determinedby the architectural parameters.

Initial analyses started with a model variant (model 1) that wassuccessfully used in previous studies to quantitatively mimic thegrowth dynamics of growing cell populations in vitro (6). Inmodel 1, we assumed random orientation of cell division, an ab-sence of morphogen influencing the direction of cell movement,and an unspecific homogeneous isotropic adhesion of hepa-tocytes to other hepatocytes (Fig. 3A and Movie S1). Despitethe fact that this model was in agreement with the experimentalfindings regarding the average hepatocyte density (Fig. 3D), it didnot explain the experimentally observed dynamics of the rege-neration process, since closure of the central necrotic lesion

was too slow (Fig. 3E). Furthermore, the hepatocyte-sinusoidcontact area did not agree with the experimental data (Fig. 3F).We verified this finding by running simulations over a wide rangeof physiological parameters modifying cellular micromotility, he-patocyte-hepatocyte and hepatocyte-sinusoid adhesion, hepato-cyte-hepatocyte and hepatocyte-matrix friction, and changedthe biophysical properties of hepatocytes and sinusoids. For ex-ample, strongly increased micromotility resulted in detachmentof hepatocytes migrating individually into the necrotic lesion(SI Appendix). However, a detachment of single cells from theregeneration front was not observed in our experiments. There-fore, the micromotility must not exceed a threshold value beyondwhich hepatocytes detach and migrate individually into the le-sion. We concluded that the lesion cannot be closed at the neces-sary speed without leading to this detachment of singlehepatocytes, in the absence of a mechanism that directs hepato-cyte migration into the necrotic zone. We tested the ability ofmorphogen and mechanical force gradients to direct migrationof the hepatocytes towards the necrotic area.

In addition, we introduced anisotropic cell-cell adhesion ef-fects since hepatocytes are polar, with an apical or bile canalicularside oriented towards neighboring hepatocytes and a basolateralblood side oriented towards sinusoids. We modified cell-celladhesion in the model such that adjacent polar hepatocytes onlyformed adhesive bonds at their apical sides (SI Appendix). Thebest data fit was obtained with a model (model 2) that integratedpolar hepatocytes with a micromotility that was biased in thedirection of the necrotic area and thereby directed cell migration.Model 2 (Fig. 3B and Movie S2) was in agreement with the ex-perimental observations regarding hepatocyte density (Fig. 3D)and successfully mimicked the regeneration dynamics (Fig. 3E).A bias in the micromotility may be caused by a local mechanicalor morphogen gradient, as long as both affect a layer thickness ofonly 2–5 cells at the edge of the necrotic lesion. We found that ifall hepatocytes in a lobule were affected, the lobule architecturewould be distorted. We modeled the influence of gradientscaused by cytokine secretion by dead or dying hepatocytes fromthe central necrotic region, or cytokine transport via the blood.However, none of those model variations was able to successfullyrestore the lobule microarchitecture (Fig. 3F). After 16 d, therepresentative model 2 showed a hepatocyte-sinusoid contactarea of only 37.1� 1.1% which was significantly lower than theexperimental situation (48.5� 2.5%).

Hepatocyte Alignment Along Sinusoidal Cells Is a Key Mechanism toRestore Liver Microarchitecture. Because neither model 1 nor mod-el 2 were able to fully explain the experimentally observed data,we incorporated a further mechanism into our model, namely,HSA. As already mentioned, in the process of HSA, daughter he-patocytes from cell division align themselves along the closest si-nusoid, such that the line connecting the centers of the twodaughter cells is parallel to the local orientation of the closestsinusoid. The first experimental evidence that sinusoids may serveas an aid to orientation of regenerating hepatocytes came fromour tie-2-reporter mice. Sinusoidal cells survive after administra-tion of CCl4, even in the central region of the lobule where almostall hepatocytes die. However, since sinusoidal cells are very thinthey may easily be overlooked in the central dead cell mass whenparaffin slices are prepared and stained by conventional techni-ques (Fig. S7). We first noticed their presence in the central deadcell mass using tie-2-reporter mice where EGFP is expressed un-der control of a tie-2 promoter (Fig. 4A and SI Appendix). A re-latively high fraction of sinusoidal cells, especially in the dead cellarea, expressed EGFP (Fig. 4 C and D and Fig. S8). This resultshows that the sinusoidal cells in the dead hepatocyte area sur-vive, but may be stressed and begin to show tie-2 promoter activ-ity, which is known to be involved in vessel remodeling (7). Inorder to visualize the state of the sinusoidal network, we

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immunostained sinusoidal cells with ICAM antibodies and recon-structed the network in healthy livers 2 d after CCl4 administra-tion. Although the sinusoidal network showed some degree ofdestruction, the basic network structure remained intact (Fig. 4E and F). Analysis of the numbers of hepatocytes and sinusoidalcells showed that the majority of sinusoidal cells survived, even inthe central area where almost all hepatocytes were destroyed byCCl4 (Fig. S9). This prompted us to study the hypothesis that si-nusoidal cells may play a role during the regeneration process andto include the HSA mechanism into our model. As a result, wefound model 3 (Fig. 3C and Movie S3) to be in excellent agree-ment with all experimental observations, including hepatocytedensity (Fig. 3D) and regeneration dynamics (Fig. 3E). Further-more, the lobule architecture was restored after 16 d and the he-patocyte-sinusoid contact area was 50.4%, corresponding to theexperimental situation (48.5� 2.5%) (Fig. 3F). Fig. 3C illustratesa typical computer simulation with model 3. In summary, ourmodel simulations strongly suggested that HSA may be thekey mechanism in regeneration of the liver architecture. Froma sensitivity analysis, our model predicts that the alignment ofdaughter cells along the closest sinusoid must occur within a max-imum of 2 h after cell division.

Experimental Validation of Hepatocyte-Sinusoid Alignment. To fur-ther enhance our model, we experimentally tested the predictionof the mathematical model by determining the degree of align-ment of hepatocytes after cell division along sinusoids. For thispurpose, we reconstructed the 3D sinusoidal network for restinghepatocytes (BrdU-negative) and hepatocytes after cell division(BrdU-positive) using confocal laser scans (Fig. 5D). BrdU-positive nuclei appeared as green fluorescence; whereas, cell bor-ders appeared red due to phalloidine staining. We applied an ex-perimental design whereby BrdU was injected 48 h after CCl4administration, when hepatocyte proliferation was close to itsmaximum. Livers were prepared at time intervals between 8 hand 14 d after BrdU injection (for detailed design, see Fig. S10).Two-dimensional analysis of paraffin slices suggested that daugh-ter cells were aligned in the direction of the sinusoid (Fig. 5 A–C).

However, in 2D analyses, the result may be compromised by thechoice of the cutting plane. Therefore, we reconstructed and ana-lyzed the full 3D structure of the lobules and identified all pairs ofBrdU-positive neighboring hepatocytes. For each of these pairs,we calculated the line connecting the cell centers and determinedthe angle between that line and the tangent to the adjacent sinu-soid. The closer this angle is to zero, the better the alignment.Eight hours after BrdU injection (the earliest analyzed timeperiod), the majority of daughter cells showed a good alignmentwith the neighboring sinusoid (Fig. 5E and Fig. S11). The simula-tion result with model 3 showed an excellent agreement with theexperimentally observed angle distribution, while in models 1 and2, the orientation angle was uniformly distributed in ½0; π∕2�(Fig. 5E).

DiscussionDevelopment, architecture and function of tissues depend on in-teractions between cells that can vary in time and space (8). Suchinteractions occur primarily by direct contact or secretion ofsoluble factors. In particular, liver function and dysfunction de-pends on its microarchitecture. Blood flows through the sinusoidsthereby coming into contact with hepatocytes before it flows outinto the central vein (Fig. 1A). Quantitative analysis of the liverlobule microarchitecture suggests that, during evolution, an opti-mal sinusoidal architecture has formed to ensure an efficient ex-change between blood and hepatocytes. Liver function iscompromised if the hepatocyte-sinusoid contact area decreases.Obviously, the two most abundant cell types of the liver, hepato-cytes and sinusoidal cells, are crucial for the maintenance of livermicroarchitecture. However, analysis of hepatocyte-sinusoid in-teractions and their influence on liver microarchitecture is experi-mentally challenging. Conventional techniques are insufficient indescribing 3D spatial-temporal processes; therefore, there wereno techniques available to quantify liver microarchitecture. Asan alternative, we established a process chain that utilized the sy-nergies from combined experimental assays, image analysis, anddirect spatial-temporalmodeling.As a starting point formodeling,we reconstructed liver lobules from confocal laser scans such thatthe position of all individual hepatocytes and sinusoidal cells, aswell as all further relevant information on lobule architecture,were correctly captured. We introduced architectural parametersto quantify lobule mass and structure. The architectural para-meters served to define the initial state of our mathematicalmodel. In order to quantify the regeneration process after CCl4induced necrosis of hepatocytes close to the central vein, and topermit a quantitative comparison with the simulation results ofourmathematicalmodel, we introduced a number of process para-meters. These parameters were experimentally determined in re-generating mouse liver, covering a period of 0.5–16 d aftertreatmentwithCCl4, and included ameasureof (i) the spatial-tem-poral pattern of cell proliferation, (ii) the average liver lobule he-patocyte density, (iii) the area of the necrotic lesion, and (iv) theliver lobule microarchitecture, namely, the hepatocyte-sinusoidcontact area reflecting liver function. Using model simulations,we have demonstrated that if any of these parameters had not beentaken into account, we would have failed to correctly identify thekey mechanisms involved in liver regeneration after CCl4 intoxi-cation. The first parameter (i) served as an input parameter and—together with our abstract but still realistic description of a cell—ensured that the average lobule hepatocyte density was restored[parameter (ii)]. However, if cell migration was completely dic-tated by physical interaction forces, the cells would accumulatein the periportal zone and the lesion would not be closed(Movie S1). The lesion is only closed if hepatocytes actively mi-grate towards the necrotic zone [parameter (iii)]. Indeed, severallines of evidence suggested that dead or dying hepatocytes causedsurviving hepatocytes to migrate in their direction: (I) Time-lapsevideos of cultured mouse hepatocytes demonstrated that viable

Fig. 5. Experimental validationofHSA. (A) Immunohistochemistry staining inlightmicroscopy. BrdU-positivenuclei aredarkbrown. (B) Confocalmicroscopyimage, green: BrdU-positive cells; blue: nonproliferating hepatocytes; red: lec-tin (cell boundaries; sinusoids).Note thepair of BrdU-positive cells indicatedbythewhite arrow is oriented inparallel to theneighboring sinusoid indicatedbya yellowarrow. (C) 3D reconstructionof twodaughter cells that areoriented inthe direction of the neighboring sinusoid. (D) 3D distribution of BrdU-positivecells and sinusoids. The inset shows the connecting line of daughter hepato-cytes (red) and their orientation (angle α) with regard to the closest sinusoid(blue line). (E) Density-distribution for α in experiments and models 1–3.

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hepatocytes were attracted by dead hepatocytes (Movie S1 andS2), (II) filopodia extended several micrometers in front of thehepatocytes at the edge of the dead cell area (SI Appendix),and (III) some hepatocytes show stress fiber formation, as evi-denced by phalloidine staining, similar to hepatocytes in vitroshowing a high scattering activity (Fig. S12). We also includedthe known polarity of hepatocytes into the model by assuming po-lar hepatocyte-hepatocyte adhesion and considered no adhesionwith sinusoids as adhesion was found to slow down regeneration.However, none of the mechanisms resulted in correct hepatocytealignment. They formed local double-cell, instead of single-cell,columns by pushing apart adjacent sinusoids, thereby increasingthe hepatocyte-hepatocyte contact area at the expense of the he-patocyte-sinusoid contact area.

The simulated tissue architecture was in agreement with theexperimentally obtained data only when we introduced a uniquemechanism i.e. the alignment of daughter hepatocytes in thedirection of the closest sinusoid (HSA) a so-far unrecognized pro-cess. Importantly, by using a model parameter sensitivity analysiswithin all model variants, we could show that HSA could not besubstituted by including any other likely mechanisms into themodel. Therefore, the model unambiguously predicted that HSAmust take place and that complete regeneration is not possiblewithout HSA. In order to experimentally validate the model pre-diction of HSA, we reconstructed and analyzed the 3D orienta-tion of daughter hepatocytes in relation to the sinusoids. Theresults of this analysis (Fig. 5E) confirmed the model prediction.

As previously already recognized, sinusoidal cells are central totriggering hepatocyte proliferation (9–12). An important me-chanism of CCl4 toxicity is that it causes a greater than 5-foldincrease of hepatocyte growth factor (HGF) in sinusoidal cells,leading to increased proliferation of hepatocytes (10). In additionto HGF, IL-6 and TNF-alpha are also secreted by sinusoidal cellsand contribute to the proliferative stimulus (12). The same cellsalso secrete the mito-inhibitor, transforming growth factor-beta1,which, after a spectacular phase of hepatocyte proliferation, ter-minates liver regeneration (1). Because of the influence of sinu-soidal cells on hepatocyte proliferation, we speculated whethercytokines secreted by sinusoidal cells might also explain HSA.Some explorative experiments did indeed support this hypothesis.When hepatocytes and sinusoidal cells were cocultured under thetime-lapse microscope, hepatocytes were attracted by sinusoidalcells and tended to maximize the hepatocyte-sinusoidal contactarea (Movies S3, S4, S5, and S6 and Fig. S13). This is plausiblebecause HGF does not only induce proliferation but also servesas a chemoattractant for hepatocytes (1) and thus may provide amechanism that contributes to the proposed HSA. In this case,the hepatocyte alignment along the sinusoid should not occurduring but subsequent to cell division. In order to test this hypoth-esis, we performed pilot experiments to study the orientation ofmitotic spindles by staining tubulin in 2D slices from the sameliver samples as those analyzed for daughter cell orientation.In contrast to the above described BrdU-positive daughter cells,the mitotic spindles were not systematically aligned in the direc-tion of the sinusoids (Fig. S14). This data suggests that although

the orientation of the mitotic spindles of hepatocytes may be ran-dom, the daughter cells still realign themselves in the direction ofthe closest sinusoid within a short period of time. An analysis ofmitotic spindle 3D orientation was challenging and is currentlyunder investigation. However, we were able to mimic the me-chanism in computer simulations by replacing the alignment ofdividing cells along the closest sinusoid in model 3 with thetwo following submechanisms: (1) cell division in a random direc-tion, corresponding to a random orientation of the mitoticspindle, and (2) attraction of hepatocyte cells by a short-rangemorphogen secreted by the sinusoids. We found that morphogen-induced attraction of hepatocytes by sinusoids could explain HSAif it is additionally assumed that the reestablishment of hepato-cyte polarity occurs after cell division. Without reestablishment ofpolarity, hepatocytes formed columns with at least two cell layersbetween the sinusoids, induced by local energy minima.

In conclusion, we have shown that HSA represents a so-far un-recognized mechanism which is essential for the restoration ofliver microarchitecture. It will be interesting to investigate therole of HSA in liver diseases such as cirrhosis and hepatocellularcarcinoma where microarchitecture is also compromised.

Materials and MethodsExperiments. A detailed description of the applied experimental techniques isgiven in the SI Appendix. A standard protocol with CCl4 was applied to induceliver damage in male C57BL/6N mice. Tie-1 and Alfp-Cre transgenic reportermice were used to visualize sinusoidal cells and hepatocytes, respectively.Immunostaining and confocal laser scanning microscopy were performedaccording to published techniques (SI Appendix).

Image Processing and Analysis. In order to reconstruct and analyze the sinu-soidal network from confocal images a complex image processing chain wasapplied. We used adaptive histogram equalization (AHE), morphological op-erators and a medial axis transform-like process to geometrically representthe sinusoidal network as an undirected graph in 3D that allowed us to in-vestigate properties of the sinusoidal network. A similar image processingchain that included AHE, median filtering, and cell shape reconstructionbased on Voronoi space decomposition was shown to lay a solid foundationto investigate hepatocyte properties. For details see SI Appendix.

Mathematical Modeling. Our model included hepatocytes, sinusoids, the cen-tral vein, and the periportal triads, but does not take into account size andmorphology variations between individual hepatocytes, nonparenchymalcell types, such as stellate, Kupffer, and bile duct cells. Cell division is sepa-rated into G1, S, and G2-phases, during which a cell grows and doubles itsvolume, and mitosis where the cell deforms at a constant volume untiltwo daughter cells have emerged. For the diffusion, secretion, and dissocia-tion of the morphogenes, a reaction-diffusion equation was used. For detailssee SI Appendix.

ACKNOWLEDGMENTS. We thank Dr. G. Schütz and Professor U. Deutsch forproviding the Alfp-mice and tie-2 driver mice, respectively. This study wassupported by the BMBF (Federal Ministry of Education and Research)network HepatoSys (projects 0313081A and 0313081F), and the (EuropeanUnion) projects CancerSys (HEALTH-F4-2008-223188) and Passport (No:223894). We dedicate this work to our co-author Alexander Bauer, whopassed away shortly before his PhD-defense, to bear in remembrance hisvaluable contribution.

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the transcriptional regulatory network in the early regenerative response to partialhepatectomy in the rat. BMC Genomics 9:527–541.

3. Gómez MID, et al. (2006) Liver nuclear and microsomal cyp2e1-mediated metabolismof xenobiotics in rats chronically drinking an alcohol-containing liquid diet. Toxicol IndHealth 22:367–374.

4. Hoehme S, et al. (2007) Mathematical modelling of liver regeneration after intoxica-tion with ccl4. Chem Biol Interact 168:74–93.

5. Chu YS, et al. (2005) Johnson-Kendall-Roberts theory applied to living cells. Phys RevLett 94:028102.

6. Drasdo D, et al. (2007) On the role of physics in the growth and pattern formation ofcellular systems: What can we learn from individual-cell-based models?. J Stat Phys128:287–345.

7. Saharinen P, et al. (2008) Angiopoietins assemble distinct tie2 signalling complexes inendothelial cell-cell and cell-matrix contacts. Nat Cell Biol 10:527–537.

8. Hui EE, Bhatia SN (2007) Micromechanical control of cell-cell interactions. Proc NatlAcad Sci USA 104:5722–5726.

9. LeCouter J, et al. (2003) Angiogenesis-independent endothelial protection of liver:Role of vegfr-1. Science 299:890–893.

10. Maher JJ (1993) Cell-specific expression of hepatocyte growth factor in liver.Upregulation in sinusoidal endothelial cells after carbon tetrachloride. J Clin Invest91:2244–2252.

11. Ping C, et al. (2006) Hepatic sinusoidal endothelial cells promote hepatocyte proli-feration early after partial hepatectomy in rats. Arch Med Res 37:576–583.

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