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Abstract

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results
  5. Discussion
  6. Acknowledgment
  7. References
  8. Supporting Information

The impairment of hepatic metabolism due to liver injury has high systemic relevance. However, it is difficult to calculate the impairment of metabolic capacity from a specific pattern of liver damage with conventional techniques. We established an integrated metabolic spatial-temporal model (IM) using hepatic ammonia detoxification as a paradigm. First, a metabolic model (MM) based on mass balancing and mouse liver perfusion data was established to describe ammonia detoxification and its zonation. Next, the MM was combined with a spatial-temporal model simulating liver tissue damage and regeneration after CCl4 intoxication. The resulting IM simulated and visualized whether, where, and to what extent liver damage compromised ammonia detoxification. It allowed us to enter the extent and spatial patterns of liver damage and then calculate the outflow concentrations of ammonia, glutamine, and urea in the hepatic vein. The model was validated through comparisons with (1) published data for isolated, perfused livers with and without CCl4 intoxication and (2) a set of in vivo experiments. Using the experimentally determined portal concentrations of ammonia, the model adequately predicted metabolite concentrations over time in the hepatic vein during toxin-induced liver damage and regeneration in rodents. Further simulations, especially in combination with a simplified model of blood circulation with three ammonia-detoxifying compartments, indicated a yet unidentified process of ammonia consumption during liver regeneration and revealed unexpected concomitant changes in amino acid metabolism in the liver and at extrahepatic sites. Conclusion: The IM of hepatic ammonia detoxification considerably improves our understanding of the metabolic impact of liver disease and highlights the importance of integrated modeling approaches on the way toward virtual organisms. (Hepatology 2014;;60:2039–2050)

Abbreviations
Arg

arginine

Asp

aspartate

CA(t)

concentration at position A

CAB(t)

concentration at a given point in space between A and B

CAC(t)

concentration at a given point in space between A and C

CB(t)

concentration at position B

CBC(t)

concentration at a given point in space between B and C

CC(t)

concentration at position C

cj,k

measured output concentrations for j = {glutamine, NH4, urea} and k = 1, …, 13 experiments

ĉj,k

simulated parameter-dependent output concentrations for j = {glutamine, NH4, urea} and k = 1, …, 13 experiments

cGln

concentration of glutamine

cGln,in

inflow concentration of glutamine

cGln,out

outflow concentration of glutamine

cGln,pc

concentration of glutamine in the pericentral compartment

cGln,pp

concentration of glutamine in the periportal compartment

cNH4

concentration of NH4+

cNH4,in

inflow concentration of NH4+

cNH4,out

outflow concentration of NH4+

cNH4,pc

concentration of NH4+ in the pericentral compartment

cNH4,pp

concentration of NH4+ in the periportal compartment

CPS

carbamoyl phosphate synthetase

cUrea

concentration of urea

cUrea,in

inflow concentration of urea

cUrea,out

outflow concentration of urea

cUrea,pc

concentration of urea in the pericentral compartment

cUrea,pp

concentration of urea in the periportal compartment

F

transported volume per unit of time

FmL

perfusion volume flow rate per liver mass

Gln

glutamine

GLNase

glutaminase

Glu

glutamate

GS

glutamine synthetase

h

approximate average height of a lobule

IM

integrated metabolic spatial-temporal model

KAG,Gln

dissociation constant of glutaminase glutamine

Ki,GS,Gln

inhibition constant of GS glutamine

Km,C,NH4

Michaelis constant of carbamoyl phosphate synthetase ammonia

Km,G,NH4

Michaelis constant of glutaminase ammonia

Km,GS,NH4

Michaelis constant of glutamine synthetase ammonia

L

average hepatocyte diameter

MM

metabolic model

n

Hill coefficient

N

number of hepatocytes per unit of area within a liver lobule

Npc

pericentral number of hepatocytes in a cross-section of a liver lobule

Npp

periportal number of hepatocytes in a cross-section of a liver lobule

q

least squares

SD

standard deviation

STM

spatial-temporal model

ti,i+1

given point in time between ti and ti+1

vC

synthesis rate of urea

vG

glutaminase-catalyzed glutamine degradation rate

vGS

glutamine synthesis rate

vH

hepatocyte volume

vmax,C

maximal synthesis rate of urea

vmax,G

maximal rate of glutamine degradation

vmax,GS

maximal rate of glutamine synthesis

vNH4,endo

production rate of released endogenous ammonia

Vpc

volume of the pericentral region

Vpp

volume of the periportal region

Vx

volume of compartment x

xA

minimal distance of that point to A

xB

minimal distance of a point to B

xC

minimal distance of a point to C.

The impairment of hepatic ammonia detoxification in the diseased liver is a key event in the pathogenesis of hepatic encephalopathy.[1] Hepatic ammonia consumption by the synthesis of both urea and glutamine (Gln) is critical for keeping systemic ammonia levels low. In the intact liver lobule, urea synthesis and Gln synthesis are anatomically arranged in series[2-8] (Fig. 1A). Through the use of bidirectional (antegrade and retrograde) rat liver perfusion, the concept of intercellular Gln cycling [i.e., the glutaminase (GLNase)-catalyzed deamidation of Gln in periportal hepatocytes and the glutamine synthetase (GS)–catalyzed resynthesis of Gln in pericentral scavenger cells] has been established.[2, 9] Under normal conditions, periportal Gln breakdown and pericentral Gln synthesis are well balanced. Under pathological conditions such as sepsis, liver cirrhosis, and CCl4 or acetaminophen intoxication, a scavenger cell defect essentially contributes to the development of hyperammonemia,[1, 4-6, 10] which is potentially life-threatening.[11]

image

Figure 1. Acinar compartmentation of ammonia detoxification in the intact liver. (A) Gln cycling. Periportal GLNase and pericentral GS are simultaneously active, and this results in periportal breakdown and pericentral resynthesis of Gln. CPS functions as a low-affinity but high-capacity system for ammonia detoxification. In the pericentral compartment, ammonia escaping the periportal compartment is used for Gln synthesis (a high-affinity but low-capacity system). Adapted with permission from European Journal of Biochemistry[2] and Frontiers in Bioscience.[9] (B) Metabolic reactions and compartment volumes considered in the MM. Gln, ammonia (NH4+), and urea enter the MM (cGln,in, cNH4,in, and cUrea,in). Metabolites can be taken up or released by both the periportal and pericentral compartments as indicated by arrows. The volumes of the periportal and pericentral compartments are defined as Vpp and Vpc, respectively. NH4+,endo represents endogenous ammonia sources not considered in detail here. C-bm-P, carbamoyl phosphate.

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Modeling of hepatic urea metabolism started more than 30 years ago,[12] but it remained limited because acinar compartmentation had not yet been elucidated. Later, acinar compartmentalization of ammonia metabolism was integrated into the modeling of the hepatic contribution to systemic acid-base homeostasis.[13] Recently, spatial-temporal models (STMs) of liver tissue have been developed.[14-16] These models consider hepatocytes and sinusoids of a liver lobule as well as the principles of how individual cells interact in order to establish functional tissue microarchitecture. They can be used to simulate, for example, the destruction and regeneration process of a liver lobule after the administration of CCl4, but they lack the ability to simulate spatial-temporal profiles of metabolites.

To bridge this gap, a two-compartment metabolic model (MM) of ammonia, urea, and Gln metabolism was developed (Fig. 1B), and it was integrated into an STM of liver regeneration.[15] Moreover, the published version of the STM, comprising only a single liver lobule, was extended to a group of seven lobules. To achieve this goal, the following strategy was applied (Fig. 2):

  1. Mouse liver perfusion experiments were performed with different concentrations of ammonia and Gln in antegrade and retrograde directions of both intact and impaired tissue, and the effluent concentrations of ammonia, Gln, and urea were thereby monitored. The resulting perfusion data, complemented by available biological knowledge (e.g., the stoichiometry of metabolic reactions), were used to establish an MM of ammonia detoxification in the intact murine liver.
  2. The recently established STM for liver regeneration after CCl4-induced damage in mice[15] was applied to simulate the volumes of GS-active, GS-inactive, and necrotic compartments after CCl4 intoxication and during regeneration.
  3. The MM and the STM were coupled to form an integrated metabolic spatial-temporal model (IM), which allowed the prediction of ammonia detoxification in damaged and regenerating livers.
  4. For validation, the simulation results of the IM were compared to in vivo data for rats and mice. This resulted in good agreement between experimental and simulated data.
  5. The investigation was completed with a simplified model of blood circulation with three ammonia-detoxifying compartments in order to estimate the contributions of the (damaged) liver and extrahepatic tissues to ammonia metabolism in vivo.
image

Figure 2. Work flow for setting up the experiments and models. First, the MM was established on the basis of biological knowledge. Parameters of the model were identified with data from perfusion experiments with isolated livers from healthy and in vivo CCl4-intoxicated mice. With image analysis, the necrotic zones following CCl4-induced damage and during subsequent liver regeneration were quantified in order to apply the STM.[15] The volume and architectural information allowed the generation of data for the necrotic zone for all time points during damage and regeneration. Combining both models led to the IM for ammonia detoxification of the intact, damaged, and regenerating liver. Finally, the model was validated with published data for ammonia detoxification in isolated, perfused rat livers[5] and with in vivo measured liver metabolite concentrations of mice.

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Materials and Methods

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results
  5. Discussion
  6. Acknowledgment
  7. References
  8. Supporting Information

Bidirectional Liver Perfusion and Biochemical Assays

All experiments were approved by the responsible local authorities. Male C57BL/6N mice (8-12 weeks old, body weight = 20-25 g, n = 43) were allowed the Ssniff R/M-H diet (Ssniff, Soest, Germany) and water ad libitum. Isolated livers were perfused (69 perfusions) without recirculation of the perfusate[17, 18] (see also the Supporting Information). In some experiments, a single dose of CCl4 (1.6 g/kg of body weight) was administered intraperitoneally in corn oil.

Quantification of Metabolites in Mouse Blood for Model Validation

Ammonia, urea, and Gln were measured in plasma obtained from portal and hepatic veins of mice 0 to 12 days after CCl4 administration. Three mice were used per time point. Ammonia and urea were quantified with kits from Sigma-Aldrich (Taufkirchen, Germany) and BioAssay Systems (Hayward, CA), respectively. Gln was measured with high-performance liquid chromatography at Laborärztliche Arbeitsgemeinschaft für Diagnostik und Rationalisierung Medizinisches Versorgungszentrum (Dortmund, Germany). At each time point, the liver was fixed in 4% paraformaldehyde (Carl-Roth, Karlsruhe, Germany) for 48 hours, and it was used for hematoxylin/eosin staining.

Quantification of Liver Compartment Volumes

The MM uses the volumes of the periportal and pericentral regions (Vpp and Vpc, respectively) in the lobule in which the ammonia-catabolizing reactions take place. These volumes were estimated with the following relations: VNvHh/L, VppNppvHh/L, and VpcNpcvHh/L. Here, vH is the hepatocyte volume (vH ≈ 1.26 × 10−5 mm3), h is the approximate average height of a lobule (h ≈ 279.6 μm), and L is the average hepatocyte diameter (L ≈ 23.3 μm).[15] N is the number of hepatocytes within a liver lobule (determined from confocal laser scanning micrographs).[15] Npp and Npc are the periportal and pericentral numbers of hepatocytes in a cross-section of a liver lobule, respectively. They were determined from GS-stained bright-field micrographs. In the intact liver, N = Npp + Npc held. We found Vpp ≈ 12V/13 and NpcV/13. The compartment volumes of healthy livers and livers during regeneration were taken from Hoehme et al.[15]

Calculation of the Perfusion Volume Flow

The perfusion volume flow rate per liver mass, FmL = F/mL (where F is the transported volume per unit of time), was experimentally determined and was, on average, 6 mL·min−1·g−1. It could be used to calculate the term F/Vx for the MM, that is, the ratio of flow F and the volume of compartment x [Vx; x = pp (periportal) or pc (pericentral)]. See also Supporting Equations 1 to 5.

Endogenous Ammonia From Balancing Measured Concentrations

The production rate of released endogenous ammonia (vNH4,endo) was assumed to be equally distributed over all cells along the acinus. It could be calculated from the nitrogen balance of the perfusion experiment concentrations (Table 1). The residual concentrations of endogenous ammonia (ΔcNH4,endo) resulted in mean values of 0.0395 mM for perfusion experiments without added ammonia and −0.0495 mM for experiments with ammonia. vNH4,endo was calculated as follows:

  • display math(1)
Table 1. Summary of 69 Mouse Liver Perfusion Experiments
ExperimentPerfusion DirectioncGln,in (mM)cNH4,in (mM)CCl4cGln,out (mM)SD for cGln,outcNH4,out (mM)SD for cNH4,outcUrea,out (mM)SD for cUrea,out
  1. The table shows the perfusion direction (either antegrade or retrograde), the mean steady-state inflow concentrations of Gln (cGln,in) and ammonia (cNH4,in) in the perfusion medium, and the measured mean steady-state outflow concentrations of Gln (cGln,out), ammonia (cNH4,out), and urea (cUrea,out) with the standard deviations (SDs).

1Antegrade00No0.01690.01450.00260.00450.01750.0051
2Antegrade00.2No0.05000.01740.03840.01210.04670.0102
3Retrograde00No0.00400.01550.03000.01150.01740.0073
4Retrograde00.2No0.05570.01410.06990.00920.03280.0090
5Antegrade0.1250No0.11960.02100.00630.00420.02860.0037
6Antegrade0.250No0.23870.02510.01080.00550.02560.003
7Antegrade0.50No0.49120.09650.01650.00550.02770.0027
8Antegrade0.1250.2No0.18670.03940.03910.01010.05990.0208
9Antegrade0.250.2No0.30890.06560.04360.00840.05920.0191
10Antegrade0.50.2No0.48480.05260.05680.00830.12400.0415
11Antegrade00.2Yes0.00000.00260.10100.04070.04940.0188
12Antegrade0.1250.2Yes0.11560.03730.10750.04010.05120.0234
13Antegrade0.1250Yes0.12560.04560.02690.00560.01820.0102

This resulted in vNH4,endo = 0.237 mM/min for all experiments without added ammonia and vNH4,endo = −0.297 mM/min for experiments with ammonia, respectively.

Kinetic Parameters Derived From Fitting the Model Outputs to the Measured Data (Nonlinear Optimization)

The remaining kinetic parameters were determined with model fitting, that is, with the least squares (q) between the measured output concentrations (cj,k) and the simulated parameter-dependent output concentrations (ĉj,k) for j = {Gln, NH4, urea} and k = 1, …, 13 experiments weighted by the square of the respective mean concentrations over all experiments ( inline image):

  • display math(2)

Results

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results
  5. Discussion
  6. Acknowledgment
  7. References
  8. Supporting Information

Ammonia Detoxification in the Murine Liver: Bidirectional Liver Perfusion Experiments Illustrate the Acinar Zonation of Ammonia Detoxification

During antegrade perfusion and in the absence of exogenous ammonia, only minor amounts of urea and Gln were released (Fig. 3). Upon an infusion with 0.2 mM ammonia (60 minutes after the start of the experiment), a rapid increase in the release of urea and Gln and a surplus of ammonia were detected, and this achieved effluent steady-state conditions within minutes. After the removal of exogenous ammonia, the system returned to the starting conditions.

image

Figure 3. Impact of the perfusion direction on the involvement of ammonia-detoxifying pathways. Intact, isolated mouse livers were perfused in either the antegrade or retrograde direction throughout the entire perfusion experiment. After 60 minutes of perfusion, 0.2 mM ammonia was added for another 20 minutes to the perfusate. This resulted in an increase in the urea and Gln output. Steady-state conditions were reached within minutes, and these steady-state concentrations were used to fit the parameters of the MM.

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In contrast to antegrade perfusion, small amounts of ammonia were released from the liver during retrograde perfusion (Fig. 3). This can be explained by a net hepatocellular production of ammonia downstream of the GS-containing pericentral scavenger cells.[19]

Accordingly, antegrade ammonia infusion resulted in lower effluent ammonia concentrations in comparison with retrograde infusion (Fig. 3). Similar results were obtained with an intra-experimental change in the perfusion direction (Supporting Fig. 3). Therefore, it can be hypothesized that the two-compartment model of ammonia detoxification, previously established for rats,[2] may also apply to the intact mouse liver.

In antegrade perfusion experiments using intact livers and livers from in vivo CCl4-intoxicated mice, the input concentrations of Gln and ammonia in the perfusion buffer were changed to various combinations. A functional impairment of 100% for the pericentral compartment and a functional impairment of 15% for the periportal compartment were determined experimentally in mouse livers 4 days after CCl4 intoxication. This set of 13 mouse liver perfusion conditions formed the basis of the MM (Table 1).

Establishment of the MM

Model Equations

Hepatic ammonia detoxification is confined to the periportal and pericentral compartments (Fig. 1A). Consequently, the MM considers one periportal compartment and one pericentral compartment (Fig. 1B). It integrates over the transport of metabolites into and out of each compartment as well as the main biochemical pathways/reactions within each compartment (for a summary, see Table 2).

Table 2. Modeled Reactions
 Main EnzymeCompartmentReaction
  1. The symbol, rate limiting enzyme, compartment and overall chemical equation are shown for each of the modeled reactions.

vGGLNasePeriportalGln [RIGHTWARDS ARROW] NH4+ + Glu
vCCPSPeriportalNH4+ + HCO3 + Asp [RIGHTWARDS ARROW] urea + fumarate
vGSGSPericentralNH4+ + Glu [RIGHTWARDS ARROW] Gln

Equation (3) describes GLNase-catalyzed Gln degradation (vG), which includes Hill-type kinetics for Gln and product activation by ammonia[2, 20, 21]:

  • display math(3)

where cGln,pp is the concentration of Gln in the periportal compartment and cNH4,pp is the concentration of NH4+ in the periportal compartment. This rate equation is parameterized by the maximal velocity of Gln degradation (vmax,G), the dissociation constant of Gln (KA,G,Gln), the Michaelis constant of ammonia (Km,G,NH4), and the Hill coefficient (n). Urea synthesis via the urea cycle consists of five reactions that convert two amino groups, one from NH4+ and one from aspartate (Asp), into the excretion product urea. In this work, it is simplified and represented by one of the rate-limiting reactions: carbamoyl phosphate synthetase (CPS). Therefore, the synthesis of urea (vC) is described as follows:

  • display math(4)

where vmax,C represents the maximal synthesis rate of urea and Km,C,NH4 is the Michaelis constant of CPS.

Correspondingly, Equation (5) represents the reaction kinetics of Gln synthesis (vGS), which includes activation by ammonia and noncompetitive inhibition by Gln[22]:

  • display math(5)

where vmax,GS is the maximal rate of Gln synthesis, Km,GS,NH4 is the Michaelis constant of GS, Ki,GS,Gln is the inhibition constant, cGln,pc is the concentration of Gln in the pericentral compartment, and cNH4,pc is the concentration of NH4+ in the pericentral compartment. On the basis of these rate equations, cGln,pp, cNH4,pp, and the concentration of urea of the periportal compartment (cUrea,pp) can be described by 3 differential equations that reflect the mass balance:

  • display math(6)
  • display math(7)
  • display math(8)

where Vpp is the volume of the periportal compartment in the intact liver (Vpp ≈ 12Vpc), cGln,in is the inflow concentration of Gln, cNH4,in is the inflow concentration of NH4+, and cUrea,in is the inflow concentration of urea. During regeneration, the volume changes with time: V = V(t), Vpp = Vpp(t), and Vpc = Vpc(t). The volume changes occur much more slowly than the changes in the metabolite concentrations. Hence, the volume can be considered to be quasi-stationary during changes in the metabolite concentration. F denotes the volumetric perfusion flow rate (i.e., the transported volume per unit of time). Because transport processes are assumed to occur instantaneously in this model, F drives the transport of input metabolites (e.g., incoming blood with cGln,in) and periportal output metabolites (e.g., cGln,pp). For ammonia (Equation (7)), there is an additional term representing the endogenous ammonium production rate: vNH4,endo (see Equation (1)). It is located inside the compartment (Fig. 1B) and represents further ammonia fluxes such as intercellular protein degradation[19] and nonmodeled reactions. Similarly, there are 3 differential equations for the pericentral compartment:

  • display math(9)
  • display math(10)
  • display math(11)

where cUrea,pc is the concentration of urea in the pericentral compartment. In addition, the model allows us to simulate retrograde perfusion with the following substitutions (Fig. 1B): (1) cGln,pp, cNH4,pp, and cUrea,pp in Equations 9-11 become cGln,in, cNH4,in, and cUrea,in, respectively, and (2) cGln,in, cNH4,in, and cUrea,in in Equations 6-8 become cGln,pc, cNH4,pc, and cUrea,pc, respectively.

Theoretically, in impaired liver tissue, a third compartment comprising the necrotic tissue could be added. This compartment is metabolically not active and, for reasons of simplicity, was neglected for the calculation of metabolites (Supporting Equations 6-8).

Determination of the Parameter Values

The volumes and the flow parameters as well as the endogenous ammonia rates were calculated from measured data (Equation (1) and Table 1). The Hill coefficient of GLNase (n) was set to the reported value of 2.[21] The remaining kinetic parameters were determined by the least squares (q; Equation (2)) between the measured (Table 1) and simulated steady-state concentrations of Gln, ammonia, and urea. Supporting Table 1 shows the resulting fitted parameter. It is noticeable that the Km,C,NH4 value of the CPS reaction is more than 100-fold higher than the Km,GS,NH4 value of the GS reaction; this reflects the high-capacity/low-affinity and low-capacity/high-affinity compartments originally described by Häussinger.[2]

Model Simulations of Experimental Perfusion Data

With the fitted parameters derived from the perfusion experiments, the Gln, ammonia, and urea concentrations were calculated with the MM. The simulated and experimentally determined concentrations were in good quantitative and qualitative agreement (Fig. 4). Besides simulation of antegrade perfusion, the model also allows simulation of retrograde perfusion (Supporting Fig. 4) as well as perfusion experiments with CCl4-intoxicated livers (Supporting Fig. 5).

image

Figure 4. Measured and simulated steady-state outflow concentrations of Gln, ammonia, and urea show good agreement between the MM predictions and the experimental data from intact mouse liver perfusions in the antegrade direction. The white bars show the measured outflow concentrations and the standard deviations. The black bars represent the simulation results. The inflow concentrations of Gln (Glnin) and ammonia (NH4+in) in the perfusion medium are given at the top of each plot. Numbers in the boxes refer to the experiments listed in Table 1.

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A strength of the MM is its ability to calculate not only the output concentrations of NH4+, Gln, and urea at any given input concentration but also the concentrations of the metabolites at the border between the periportal and pericentral compartments (Supporting Table 2).

In summary, despite its simplicity, the MM with two compartments is capable of explaining the experimental findings of hepatic ammonia detoxification.

Development of an IM

Compartment modeling, as described in the previous paragraph, does not consider the complex spatial-temporal changes in cellular tissue architecture after liver damage and during regeneration. In particular, it does not explain volume changes in the subcompartments occurring after CCl4-induced damage. In order to circumvent these limitations, an integrated mathematical model (IM), based on the STM[15] in combination with the previously described MM, was developed.

Briefly, the STM model is a center-based (single cell–based) model[23] based on the following model assumptions (for details, see Hoehme et al.[15]):

  1. Hepatocytes can be mimicked as homogeneous, isotropic, elastic and adhesive, intrinsically spherical objects capable of migration, growth, division, and death.
  2. The migration of each hepatocyte can be calculated with an equation of motion. This equation permits us to investigate the position and orientation of each hepatocyte at each instant of time by summing up all physical forces, including active force components such as micromotility. The physical forces include friction forces of hepatocytes with the extracellular matrix, the sinusoids, and other hepatocytes as well as repulsion and adhesion forces of a hepatocyte within its environment.
  3. Cell orientation changes can be mimicked by an optimization principle with the Metropolis algorithm for the energy change occurring in case of a cell orientation change.[24] Alternatively, an equation for the angular momentum[25] can be used, but such an equation is much more complicated and computationally more expensive.
  4. The hepatocytes have been assumed to divide along the closest sinusoid. This order principle ensures the regeneration of liver architecture.[15]
  5. The model considers only sinusoids and hepatocytes, the main constituents of a liver lobule. Other cell types are neglected. The sinusoidal network is mimicked through chains of spheres linked by springs, and each sphere is again modeled by an equation of motion. In this way, the interaction forces between hepatocytes and sinusoids can be efficiently modeled.

The STM quantitatively mimics the regeneration of the liver mass and architecture after CCl4-induced pericentral damage.[15] The volumes of the periportal and pericentral compartments were calculated with the STM and were subsequently inserted into the MM. Thus, the two models were coupled.

Moreover, in order to visualize the metabolism calculated with the MM and the STM in time and space, the concentrations of Gln, ammonia, and urea at any given point in time and space were approximated with a mathematical interpolation approach. The MM provided the concentrations of ammonia, urea, and Gln at (A) the central vein, (B) an intermediate region at the border between the GS-positive and GS-negative parts of the lobule, and (C) the portal triads during the entire regeneration process after CCl4 intoxication. With these data, we performed a two-stage, n-linear interpolation in space, which is a direct extension of bilinear interpolation, within a two-dimensional hexagonal polygon aligned orthogonally to the central vein in order to interpolate the concentration values at any point in space (see Equations (12) and 13) and time (see Equation (14)) within a liver lobule:

  • display math(12)
  • display math(13)
  • display math(14)

where CA(t), CB(t), and CC(t) are the concentrations at positions A, B, and C, respectively. CAB(t) is the concentration at a given point in space between A and B. CBC(t) and CAC(t) are defined accordingly. In Equations 12 and 13, which represent the spatial interpolation, xA is the minimal distance of that point to A, and xB and xC are defined accordingly. In equation (14), which represents the temporal interpolation, ti,i+1 is a given point in time between ti and ti+1.

The IM simulates the concentrations of ammonia, urea, and Gln in the liver vein after CCl4-induced tissue destruction and the regeneration process. Figure 5A summarizes the destruction and regeneration of the two compartments and the corresponding changes in the metabolites. For this simulated liver perfusion during regeneration, the input concentrations were kept constant at cGln,in = 0.125 mM and cNH4,in = 0.2 mM (Fig. 5A), and a flow rate of 6 mL·min−1·g−1 was applied.

image

Figure 5. (A) Simulation of the acinar compartment volumes and metabolite concentrations over time during the damage and regeneration of livers from CCl4-intoxicated mice. The time courses of the periportal fractions (eppVpp) and pericentral fractions (epcVpc) of the intact volume after in vivo CCl4 intoxication of mice (top left) with the corresponding changes in cGln, cNH4, and cUrea (top right) are shown. Metabolite concentrations were calculated via the MM with the impaired volumes as quantified by the STM. (B) Simulated damage and regeneration scenario with the IM. The individual figures show seven neighboring liver lobules over time under intact, damaged, and regenerating conditions. Vessels are denoted by red elements. The left three lobules show normal hepatocytes (light brown), GS-positive hepatocytes (dark brown), proliferating hepatocytes (red, pink-like color), and the necrotic zone (empty pericentral space). The right four lobules show the local ammonia concentration according to the color legend. The visualization of the ammonia concentration was calculated with an interpolation algorithm using the metabolic compartment model: (i) intact liver lobules, (ii) necrosis in progress after CCl4 intoxication, (iii) maximum necrosis, (iv) onset of regeneration, (v) beginning of the regeneration of the pericentral compartment, and (vi) final stages of regeneration. A video sequence of this process and the corresponding concentrations of ammonia, Gln, and urea is provided as Supporting Information.

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Notice that the previously established model comprising only one liver lobule[15] was extended in Fig. 5B to a group of seven lobules. The seven-lobule configuration reduced boundary artifacts that emerged if only a single lobule was considered (data not shown). Each lobule was created on the basis of statistical data obtained from an analysis of 26 confocal volume data sets. Therefore, Fig. 5B represents statistical lobules with average properties. This novel IM allowed us to (1) calculate the development of the total volume of hepatocytes in the periportal and pericentral compartments at any time during the tissue destruction and regeneration process and (2) calculate and visualize the concentrations of ammonia, urea, and Gln for each individual cell (see the video in the Supporting Information).

Comparison of the Model Predictions to Experimental Data and Implications

Results simulated by the IM were validated with experimental data from both rats and mice. First, data published by Häussinger and Gerok[5] showed that the perfusion of isolated intact rat livers with increasing ammonia concentrations resulted in increasing ammonia release, an increase in released Gln, and a linear increase in urea (Fig. 6A-C). In isolated, perfused livers from CCl4-intoxicated rats, the concentration of released ammonia was higher than that in livers from control animals. Almost no Gln synthesis occurred because of the destroyed pericentral compartment, whereas urea synthesis remained largely unaffected. Even though the model parameters were calibrated with perfusion data from isolated mouse livers, the MM was able to correctly simulate the metabolic changes after CCl4 administration (Fig. 6D-F). Furthermore, this indicates that the underlying mechanisms governing ammonia detoxification are highly comparable in mice and rats.

image

Figure 6. Model results versus published data for perfusion experiments using isolated livers from CCl4-intoxicated rats. In the top row, published data show that CCl4 intoxication of rat livers results in (A) increased ammonia release, (B) a strong decrease in Gln synthesis, and (C) essentially no effects on urea synthesis. Reprinted with permission from Chemico-Biological Interactions.[5] Copyright 1984, Elsevier. The bottom row presents a simulation of these experiments with the MM. A comparison of the top row and the bottom row shows good qualitative agreement despite calibration of the model based on data from mouse livers. This demonstrates the general validity of the model at least for the rodent liver.

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Second, mice were intoxicated in vivo with CCl4 to induce severe liver damage. Blood was taken from the portal vein (representing the liver inflow) and the liver vein (representing the liver outflow) at different time points after CCl4 intoxication (Fig. 7). Assuming that the ratio of arterial blood to venous blood at the portal site was 3:726 and that the concentrations of ammonia and Gln in the right heart chamber were similar to those in the hepatic artery, we were able to calculate the input concentrations of the liver on the basis of the concentrations determined in vivo for the right heart chamber (Supporting Fig. 6) and the portal vein. These concentrations were used as input parameters (meas,in, measured liver input values). For the simulations with the MM, the profiles depicted in Fig. 5A were used at a physiological flow rate of 4 mL·min−1·g−1.[27] The concentrations in the hepatic vein were predicted for two different rates of endogenous ammonia and were compared with experimental in vivo data (Fig. 7). Although the predicted and experimentally determined concentrations of ammonia and Gln almost perfectly matched in the normal and fully regenerated mice and nicely followed the strong changes after damage and during regeneration, the quantitative fit during this period was slightly less. This may indicate so far unknown aspects of ammonia detoxification in damaged livers.

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Figure 7. In vivo model validation using in vivo ammonia and Gln concentrations during liver regeneration after CCl4 intoxication of mice. Experimentally determined liver input concentrations (meas,in), composed of arterial and portal blood in a 3:7 ratio[26] of Gln (top) and ammonia (bottom) were used to predict the respective output concentrations in the hepatic vein (sim,out,1) and were compared with the experimentally measured concentrations (meas,out). For these experiments, no endogenous ammonia source was considered, i.e. vNH4,endo = 0 mM/min. On days 0 and 12, a very good quantitative prediction can be made, particularly for ammonia. In necrotic tissue and during regeneration (days 2-6), the predicted values (sim,out,1) closely mimic the observed changes. However, the simulated concentrations of ammonia are slightly higher than those determined experimentally. Taking into account an ammonia sink by setting vNH4,endo to −0.297 mM/min improves the simulation (sim,out,2) for the regeneration phase (days 2-6), and this indicates that additional, yet unidentified mechanisms of ammonia removal might play a role during regeneration. Meas,in, measured liver input values; meas,out, measure liver output values; sim,out,1, simulated liver output values for vNH4,endo= 0 mM/min; sim,out,2, simulated liver output values for vNH4,endo=−0.297 mM/min.

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It is well known that extrahepatic organs such as the skeletal muscles, brain, and kidneys may contribute to ammonia metabolism.[28] To understand the influence of these extrahepatic compartments, we used the previously described mouse hepatotoxicity protocol with CCl4. Ammonia and Gln were analyzed in the portal and liver veins and additionally in mixed venous blood from the right heart chamber (Supporting Fig. 6). With the data, the extrahepatic contribution was calculated on the basis of a three-compartment model (Supporting Fig. 7) consisting of (1) the liver, (2) organs in series with the liver (e.g., the gastrointestinal tract, including the gut and splanchnic organs; extrahepatic 2), and (3) extrahepatic organs parallel to the liver (e.g., skeletal muscles, kidneys, and brain; extrahepatic 1). The model showed that the extrahepatic 1 compartment switched from a neutral state to extrahepatic ammonia detoxification during days 2 to 4 after CCl4 administration with a maximal rate of 0.24 μmol/min (Supporting Fig. 8). Correspondingly, extrahepatic Gln formation increased during the same period. In contrast, the compartment of the gastrointestinal tract (extrahepatic 2) did not show any significant changes after CCl4 intoxication.

Analyzing the concentrations of 13 amino acids in the portal and hepatic liver veins and the right heart chamber, we observed a rather complex situation. For example, 2 days after CCl4 intoxication, the serum concentration of aspartic acid increased, and liver aspartic acid metabolism seemed to be impaired. In contrast, only minor changes in histidine were observed, whereas arginine (Arg) disappeared completely from the circulation (Supporting Figs. 9 and 10).

Discussion

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results
  5. Discussion
  6. Acknowledgment
  7. References
  8. Supporting Information

In this study, an MM of hepatic ammonia metabolism was developed and combined with an STM[15] into an IM simulating the impact of liver damage and regeneration after intoxication on ammonia detoxification. The MM represents the main reactions of ammonia detoxification and their zonal distribution in liver lobules. Numerical model fitting resulted in excellent agreement between the model outputs and the experimental data from antegrade and retrograde isolated, perfused mouse livers. The IM allows us for the first time to simulate and visualize whether, where, and to what extent liver damage compromises ammonia detoxification. Although established for CCl4, the model can be easily adapted to other hepatotoxins known to induce zonal liver damage. Thus, the user can choose a certain extent and spatial pattern of liver damage in order to calculate the concentrations of ammonia, Gln, and urea in the hepatic vein (liver outflow) for given concentrations of the three metabolites in the portal vein (liver inflow).

The model calculations were compared with corresponding data from two experimental scenarios. The first scenario (Fig. 6) was related to data from isolated, perfused livers of rats with and without pretreatment with hepatotoxic doses of CCl4.[5] The model simulations were in good agreement with the experimental data. This is remarkable because the model established here was calibrated with mouse livers and demonstrated its general validity at least for rodent livers.

The second experimental scenario was related to data from CCl4-intoxicated mice in vivo over a period of 12 days (Fig. 7). The concentrations of ammonia, Gln, and urea were analyzed in the portal and hepatic veins of the mice at different time periods after intoxication. Assuming that the compartment volume changes during damage and regeneration were much slower than the concentration changes in vivo, we found that the data simulated by the IM closely followed the experimentally observed changes in the outflow concentrations during tissue damage and regeneration, although the match was not as perfect as that for a normal liver.

Differences between simulated and experimental data offer us the opportunity to identify still unknown physiological mechanisms. The model allows the testing of hypothetical reactions and whether they improve simulation accuracy. If an additional (yet unknown) sink of ammonia in damaged and regenerating livers is simulated by the setting of vNH4,endo to −0.297 mM/min, the agreement between experimental and simulated data considerably improves (Fig. 7). A possible ammonia sink might be the de novo synthesis of amino acids (and proteins). An increase in the latter during liver regeneration is well known.

Furthermore, the incorporation of the IM into a simplified model of blood circulation with three ammonia-detoxifying compartments allowed the estimation of the relative contributions of the (damaged) liver and extrahepatic tissues to amino acid and ammonia metabolism in vivo. Interestingly, this resulted in a demonstration of increased extrahepatic ammonia detoxification and the discovery of an altered amino acid metabolism [e.g., Arg (cf. Supporting Fig. 9) or Asp (cf. Supporting Fig. 10)] during regeneration after CCl4.

These examples illustrate how the model may help us to distinguish realistic hypotheses from unrealistic ones and to better interpret changes in altered serum amino acid levels in diseased states.

In conclusion, an MM of ammonia detoxification was successfully merged with an STM of tissue damage and regeneration. The resulting integrated model nicely predicted ammonia detoxification in the intact or toxin-damaged and regenerating liver. The integrated liver model is programmed so that it can be easily coupled to models of other body compartments and thus represents a valuable step on the path to virtual organisms.

Acknowledgment

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results
  5. Discussion
  6. Acknowledgment
  7. References
  8. Supporting Information

The authors thank N. Eichhorst, F. Struck, and D. Mahn for their excellent technical assistance and S. Töpfer and I. Vignon-Clementel for valuable discussions. The administrative support of G. Miczka and E. Stüttgen at the Projektträger Jülich is also gratefully acknowledged.

References

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results
  5. Discussion
  6. Acknowledgment
  7. References
  8. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results
  5. Discussion
  6. Acknowledgment
  7. References
  8. Supporting Information

Additional Supporting Information may be found at onlinelibrary.wiley.com/doi/10.1002/hep.27136/suppinfo.

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hep27136-sup-0001-suppinfo.pdf668KSupplementary Information
hep27136-sup-0002-suppvideo.avi8044KSupplementary Information Video

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