Metabolic Brain Disease

, Volume 25, Issue 1, pp 57–63

No oxygen delivery limitation in hepatic encephalopathy


    • Pathophysiology and Experimental Tomography CenterAarhus Hospital, Aarhus University Hospitals
    • Department of Neuroscience and PharmacologyUniversity of Copenhagen
    • Department of Neurology and NeurosurgeryMcGill University
  • Susanne Keiding
    • Pathophysiology and Experimental Tomography CenterAarhus Hospital, Aarhus University Hospitals
    • Department of Hepatology VAarhus Hospital, Aarhus University Hospitals
  • Hendrik Vilstrup
    • Department of Hepatology VAarhus Hospital, Aarhus University Hospitals
  • Peter Iversen
    • Pathophysiology and Experimental Tomography CenterAarhus Hospital, Aarhus University Hospitals
Original Paper

DOI: 10.1007/s11011-010-9179-9

Cite this article as:
Gjedde, A., Keiding, S., Vilstrup, H. et al. Metab Brain Dis (2010) 25: 57. doi:10.1007/s11011-010-9179-9


Hepatic encephalopathy is a condition of reduced brain functioning in which both blood flow and brain energy metabolism declined. It is not known whether blood flow or metabolism is the primary limiting factor of brain function in this condition. We used calculations of mitochondrial oxygen tension to choose between cause and effect in three groups of volunteers, including healthy control subjects (HC), patients with cirrhosis of the liver without hepatic encephalopathy (CL), and patients with cirrhosis with acute hepatic encephalopathy. Compared to HC subjects, blood flow and energy metabolism had declined in all gray matter regions of the brain in patients with HE but not significantly in patients with CL. Analysis of flow-metabolism coupling indicated that blood flow declined in HE as a consequence of reduced brain energy metabolism implied by the calculation of increased mitochondrial oxygen tensions that patients with HE were unable to utilize. We ascribe the inability to use the delivered oxygen of patients with HE to a specific inhibition associated with oxidative metabolism in mitochondria.


Brain energy metabolismCerebral blood flowCerebral metabolic rate for oxygenHepatic encephalopathy


Hepatic Encephalopathy (HE) is a frequent complication to cirrhosis of the liver, which seriously interferes with the health of the patient. It is not known whether the main cause is a primary deficiency of blood supply (oligemia), which secondarily impairs brain energy metabolism, or a primary inhibition of metabolism to which blood flow responds normally. Based on the observations reported by Iversen et al. (2008), we tested the hypothesis that the primary perturbation of brain energy metabolism in patients with cirrhosis and hepatic encephalopathy is an interference with oxidative metabolism and not a reduction of cerebral blood flow.

The link between oxygen delivery and oxidative metabolism in brain tissue is the tension of oxygen at the sites of oxygen metabolism. Oxygen metabolism is the linked reactions of oxidation of glucose to CO2 and reduction of oxygen to water. The site of the oxygen reduction is the cytochrome c oxidase protein in mitochondria, with which the oxygen reaction obeys a simple Michaelis-Menten formalism. Two processes are balanced: One is the oxygen transport from capillaries to mitochondria and the other is the net oxygen consumption in mitochondria. By relating these two processes, it is possible to determine the oxygen tension that links the oxygen metabolism to the diffusion of oxygen from capillaries. The change of this tension then indicates whether metabolism or delivery is the limiting factor.

Materials and methods

This report is an extension of data presented in part by Iversen et al. (2008). We completed dynamic PET acquisitions for each subject of the regional uptake of specific tracer as functions of time, including i.v. administration of 15O-water for determination of regional cerebral blood flow (CBF) (Ohta et al. 1996), and inhalation of 15O-oxygen gas for determination of regional cerebral oxygen consumption (CMRO2) (Ohta et al. 1992), accompanied by arterial blood sampling of arterial tracer input functions. We then co- registered the PET data to T1-weighted MR images. The co-registration allowed parametric image determination of initial clearances of the tracers from the arterial input functions by means of non-linear three-weighted regression. We calculated the cerebral blood flow rate from the initial clearance of radioactive water from the general relationship between clearance, blood flow, and extraction fraction:
$$ {K_1} = F\,E(0) $$
where K1 is the unidirectional clearance, i.e., the clearance in the absence of backflux, F is the blood flow rate, and E(0) is the fraction of substance that “initially” undergoes extraction as measured in the theoretical absence of backflux and reflecting the permeability of the substance. In the case of tracer water, we calculated the flow rate by assuming a known fraction of initial extraction of 85%:
$$ F = \frac{{K_1^{{{\rm{H}}_2}{\rm{O}}}}}{{0.85}} $$
which has the unit of ml blood (ml brain tissue)−1 min−1. We similarly calculated the cerebral oxygen consumption rate from the product of the initial clearance and the concentration of oxygen in arterial blood:
$$ R = K_1^{{{\rm{O}}_2}}{C_a} $$
where R is the oxygen metabolic rate with unit of μmol oxygen (ml brain tissue)−1 min−1. From these two measures, we subsequently calculated the fraction of initially extracted oxygen as reflected in the ratio of initial clearances:
$$ {E_{{{\rm{O}}_2}}} = \frac{R}{{F\,{C_a}}} = 0.85\left( {\frac{{K_1^{{{\rm{O}}_2}}}}{{K_1^{{{\rm{H}}_2}{\rm{O}}}}}} \right) $$
We completed statistical parametric mapping of variables in predefined brain regions or volumes-of-interest (VOIs), and voxel-based statistical analysis of regions with significantly altered CBF or CMRO2 or both. Calculation of the average oxygen tension in brain capillaries proceeded from the kinetics of oxygen dissociation from hemoglobin as previously described (Gjedde et al. 2005):
$$ P_{{{\rm{O}}_2}}^{\rm{cap}} = {P_{50}}\sqrt[h]{{\frac{2}{{{E_{{{\rm{O}}_2}}}}} - 1}} = {P_{50}}\sqrt[h]{{\frac{{{S_a} + {S_v}}}{{{S_a} - {S_v}}}}} $$
where \( P_{{{\rm{O}}_2}}^{\rm{cap}} \) is the average capillary oxygen tension, P50 is the hemoglobin half-saturation tension of oxygen, h is the Hill-coefficient of oxygen binding to hemoglobin, Sa and Sv are the arterial and cerebral oxygen saturations of hemoglobin. Calculation of the average oxygen tension at mitochondria proceeded from the diffusion of oxygen from the capillary to the mitochondria, driven by the pressure difference as dictated by the diffusion coefficient or hydraulic conductivity of the tissue, also as previously described (Gjedde et al. 2005):
$$ P_{{{\rm{O}}_2}}^{\rm{mit}} = P_{{{\rm{O}}_2}}^{\rm{cap}} - \frac{R}{L} $$
where \( P_{{{\rm{O}}_2}}^{\rm{mit}} \) is the average mitochondrial oxygen tension, and L is the tissue conductivity. When oxygen tensions are plotted versus 1/L, Eq. 6 defines a line with a slope of R, the oxygen consumption rate, and an ordinate intercept of \( P_{{{\rm{O}}_2}}^{\rm{cap}} \). The mitochondrial oxygen tension can then be calculated when L is known. The flow-metabolism couple can then be derived by solving Eqs. 46 for the dependence of flow on the variables known to influence the delivery of oxygen (Gjedde et al. 2005),
$$ F = \left( {\frac{R}{{2{C_a}}}} \right)\left( {1 + {{\left[ {\frac{{R + LP_{{{\rm{O}}_2}}^{\rm{mit}}}}{{L{P_{50}}}}} \right]}^h}} \right) $$
where the symbols have the definitions mentioned above. In the present study, we regarded the oxygen diffusibility (L = 4.4 μmol/hg/min), hemoglobin oxygen binding affinity (P50 = 27 mmHg), and Hill coefficient (h = 2.7), as constants (Gjedde et al. 2005). In Eq. 7, the oxygen tension is the result of the two processes of metabolism and delivery, which in turn is related to the maximum reaction rate (Vmax) and affinity for oxygen (Km) of the cytochrome c oxidase reaction, such that
$$ R = {V_{\max }}\left( {\frac{{P_{{{\rm{O}}_2}}^{\rm{mit}}}}{{{K_m} + P_{{{\rm{O}}_2}}^{\rm{mit}}}}} \right) $$
from which relationship follows the dependence of the mitochondrial oxygen tension on the enzyme kinetic properties of cytochrome c oxidase,
$$ P_{{{\rm{O}}_2}}^{\rm{mit}} = \frac{{R{K_m}}}{{{V_{\max }} - R}} $$
and the extended flow-metabolism couple when the kinetic properties are entered in place of the mitochondrial oxygen tension (Gjedde et al. 2005),
$$ F = \left( {\frac{R}{{2{C_a}}}} \right)\left( {1 + {{\left\{ {\left( {\frac{R}{{L{P_{50}}}}} \right)\left( {1 + \frac{{L{K_m}}}{{{V_{\max }} - R}}} \right)} \right\}}^h}} \right) $$
where the expression enclosed in curly brackets is a lumped variable (LV), the variability of which when lifted to the power of dictates the degree of curvature of the flow-metabolism couple. The value of the LV depends on the interrelations between the individual variables, which are not known.
The three groups of volunteers included 6 patients suffering from cirrhosis of the liver with overt type C hepatic encephalopathy (HE), 6 patients with cirrhosis without HE (CL), and 7 healthy control subjects (HC) without known disease. All subjects gave written informed consent to participation according to the protocol approved by the official regional research ethics committee. Details of these groups are given by Iversen et al. (2008). The main characteristics are given in Table 1.
Table 1

Patient material


Cirrhosis with acute HE (HE)

Cirrhosis without HE (CL)

Healthy volunteers (HC)

Number of subjects








Age [years]

58 (48–62)

56 (47–63)

53 (46–65)

Body weight [kg]

75 (45–103)

87 (62–107)

85 (69–90)

MAP [mmHg]

87 (81–92)

92 (73–107)

105 (100–112)

New Haven coma grade

I:3; II:1; III:2


Child-Pugh class

A:0; B:1; C:5

A:2; B:3; C:1

GEC# [Patient/reference]

0.51* (0.40–0.61)

0.56* (0.45–0.68)

1.00 (0.85–1.15)

Continuous reaction time [index]

0.8 (0.3–1.9)

2.1 (1.0–3.0)

2.4 (2.0–2.8)

This table was originally reported by Iversen et al. (2008).


The arterial blood samples obtained from the three groups revealed low carbon dioxide tensions, and elevated ammonia concentrations in both groups of cirrhotics compared to the healthy control subjects. The samples further revealed alkalosis in the group of cirrhotics with acute hepatic encephalopathy in whom the ammonia concentration was four-fold higher than in the healthy controls and two-fold higher than in the cirrhotics without acute hepatic encephalopathy. The main differences between the two groups of cirrhotics therefore included the degree of alkalosis and the degree of elevation of the arterial ammonia concentration as shown in Table 2.
Table 2

Arterial blood samples

Patient Group

Ammonia (µmol/L)


PaCO2 (mmHg)

PaO2 (mmHg)

SBC (mmol/L)

CaO2 (mmol/L)

SaO2 (%)

Cirrhosis with acute HE (n = 6)

129 ± 26*

7.48 ± 0.01*

33 ± 2*

82 ± 3

25.9 ± 1.1

7.1 ± 1.0

96 ± 1

Cirrhosis w/o HE (n = 6)

69 ± 7*

7.45 ± 0.01

36 ± 1

73 ± 5

26.3 ± 0.9

6.8 ± 0.7

95 ± 1

Healthy controls (n = 7)

26 ± 5

7.43 ± 0.01

39 ± 1

77 ± 2

25.7 ± 0.7

8.2 ± 0.9

96 ± 1

This table was in part reported by Iversen et al. (2008).

The measures of brain energy metabolism revealed significantly lowered oxygen consumption in the group of cirrhotics with acute hepatic encephalopathy compared to the two groups without encephalopathy, as listed in Table 3. In the cirrhotics with acute hepatic encephalopathy, blood flow measures were reduced to a degree appropriate to the reduction of carbon dioxide tension in arterial blood, suggesting that the reduction of CO2 and the reduction of brain energy metabolism had similar origins and relied on related mechanisms.
Table 3

Main outcome measures of PET study

Variable ± Std. Deviation




CMRO2 (μmol hg−1 min−1)*

100 ± 20

143 ± 23

145 ± 16

CBF (ml hg−1 min−1)*

26 ± 3

43 ± 5

46 ± 7

EO2 (ratio)

0.50 ± 0.11

0.44 ± 0.07

0.35 ± 0.06

\( P_{{{\rm{O}}_2}}^{\rm{cap}} \) (mmHg)

37 ± 4

38 ± 3

42 ± 3

\( P_{{{\rm{O}}_2}}^{\rm{mit}} \) (mmHg) (from individuals)

14 ± 8

5 ± 6

9 ± 6

\( P_{{{\rm{O}}_2}}^{\rm{mit}} \) (mmHg) (from means)

16 ± 1

9 ± 1

13 ± 1

Vmax (μmol hg−1 min−1) (Km = 3.5 mmHg)

122 ± 2

200 ± 6


*originally reported by Iversen et al. (2008)

The oxygen extraction fractions calculated by means of Eq. 4 were elevated in the two groups of cirrhotics and the calculated average oxygen tensions in capillaries commensurately reduced. All measures therefore indicated more severe cerebral metabolic and circulatory depression in the cirrhotics with the acute hepatic encephalopathy but only calculation of the mitochondrial oxygen tensions of the three groups indicated whether metabolic depression preceded circulatory depression or vice versa.

The calculations revealed no evidence of maladjusted blood flow compared to the measured brain energy metabolism and blood flow in chronic cirrhosis, with or without hepatic encephalopathy. The mitochondrial oxygen tensions calculated by means of Eq. 6 showed a minor increase compared to healthy control subjects, indicating adequate oxygen supply for the magnitude of energy turnover. The absent mismatch suggests a cause of the metabolic depression that is consistent with a primary inhibition of brain energy metabolism and not as a consequence of a limited supply of oxygen associated with a primary reduction of blood flow.

The primary inhibition of brain energy metabolism can be calculated as a reduction of the Vmax of cytochrome c oxidase due to insufficient cytochrome c reduction by electrons from NADH, as suggested by Eq. 10. The Vmax values listed in Table 3 reveal a very substantial reduction in the cirrhotics with acute hepatic encephalopathy compared to the two other groups, determined with the assumption of unchanged affinity.


Flow-metabolism coupling is the elusive mechanism that adjusts blood flow rates to the prevailing energy metabolism of brain tissue. The result of the adjustment is a matching of oxygen delivery to the demand for oxygen. Roy and Sherrington (1890) discussed the mechanism in relation to a series of animal experiments upon which they concluded that “the brain possesses an intrinsic mechanism by which its vascular supply can be varied locally in correspondence with local variations of functional activity.” The nature of this intrinsic mechanism became a popular topic of investigation in the following decades, particularly with respect to the delivery of oxygen, the passive diffusion of which at rest was judged to be inadequate for the supply of oxygen at the highest oxygen delivery rates (Bohr 1909).

Krogh received the Nobel Prize in 1920 for the elucidation of the role of capillary recruitment (Krogh 1919a,b,c) in the adjustment of the oxygen diffusion capacity of capillary beds to the prevailing need for oxygen, except in brain. Thus there is no compelling evidence of capillary recruitment in mammalian brain (Kuschinsky and Paulson 1992; Chen et al. 1994; Hudetz 1997), and the apparent absence of this mechanism would appear to make brain tissue particularly vulnerable to the effects of low blood flow. Hypocapnia nonetheless is known to reduce cerebral blood flow without affecting oxygen consumption, perhaps because of an adjustment of the affinity of cytochrome c oxidase towards oxygen in mitochondria (Gjedde et al. 2005). The role of the cerebral circulation in the maintenance of adequate oxygen delivery therefore remains a mystery, and the effects of low blood flow rates on oxygen consumption, if any, are uncertain.

The main consequence of maintained oxygen consumption in the presence of low blood flow is an increase of the oxygen extraction fraction, which in turn lowers the oxygen tension in the capillaries. This tension defines the pressure head on which the passive oxygen diffusion depends and sets an upper limit of the magnitude to which the extraction can rise at approximately 60% (Gjedde et al. 2005). The rise of the extraction fraction signifies a change of the coupling ratio but it is not clear when the change undergoes transition from physiological to pathological coupling. Change of the coupling ratio in the opposite direction occurs during the increases of blood flow that accompany certain elevations of functional activity in the mammalian brain. During the activation, blood flow commonly is known to rise more than oxygen consumption and hence to cause the oxygen fraction to decline, as recorded by the blood-oxygenation-level dependent (BOLD) magnetic resonance signals from brain tissue. During normal functional activations and deactivations, these changes probably do not represent true uncoupling, despite claims to the contrary (Paulson et al. 2010), but rather reflect a process of non-linear coupling of unknown origin. The function expressing the non-linear coupling is given as Eq. 10 above but its shape and degree of curvature depends on the variability of the constituent terms. Depending on their relationships, any shape in principle is possible. In true linear coupling, the oxygen extraction and average capillary oxygen tension remain constant when blood flow rises to meet additional oxygen requirements but mitochondrial oxygen tension then declines until the pressure difference is large enough to accommodate the increased oxygen flux.

In the present study, the elevated oxygen extraction to brain tissue in hepatic encephalopathy in principle is evidence of non-linear coupling of oxygen consumption to blood flow, normally known as a form of “deactivation”. The question is whether the deactivation is a true pathological uncoupling with consequences for brain energy metabolism and cognition, or whether it is a physiological adjustment to a pathologically low oxygen consumption rate? The two possibilities are, either 1) reduction of oxygen supply in relation to demand (elevated oxygen consumption without a corresponding increase of blood flow, or a reduction of blood flow without a corresponding decline of oxygen consumption) lowers mitochondrial oxygen tension, or 2) inhibition of oxygen consumption with a corresponding decline of blood flow according to the physiologically non-linear flow-metabolism coupling that maintains the oxygen tension of mitochondria Fig. 1. When individual gray matter blood flow rates are plotted versus oxygen consumption rates in the same regions, as shown in Fig. 2, an apparently linear coupling function is obtained, with a slope of 0.3 ml/μmol. With basis in Eq. 4, the linearity suggests that the main correlation of the extraction fraction in this investigation is the arterial oxygen concentration, as illustrated very significantly in Fig. 3.
Fig. 1

Oxygen Gradients in Brain in Hepatic Encephalopathy. Oxygen gradient diagrams in three groups of subjects. Abscissa: Diffusion capacity measure in units of reciprocal conductivity (hg min mmHg mmol−1), assumed to be a constant because of absence of capillary recruitment in brain tissue. Ordinate: Partial pressure of oxygen (mmHg). Slope is oxygen consumption. End points then represent oxygen tensions at end of diffusion path
Fig. 2

Flow-Metabolism Coupling in Brain in Hepatic Encephalopathy. Flow-metabolism coupling in combined group of subjects, indicated by the color-coded symbols. Abscissa: Oxygen consumption in units of metabolic rate. Ordinate: Cerebral blood flow in conventional units. The line is the linear regression to the 19 points
Fig. 3

Effect of Arterial Oxygen Concentrations. Correlation between oxygen extraction fraction and arterial oxygen concentration, suggesting role of capillary oxygen in regulation of blood flow. Abscissa: Arterial oxygen concentration (mM). Ordinate: Cerebral oxygen extraction fraction (ratio)

In the present study, we used previously reported absolute values of blood flow and oxygen consumption (Iversen et al. 2008). These measures are not common. In contrast, relative changes are the only measures available when the more popular blood-oxygenation-level dependent (BOLD) signals are used to obtain functional magnetic resonance images (fMRI). The relative changes of oxygen consumption and blood flow in human brain appear to belong to either one of only two general categories, one in which the change of oxygen consumption is very low compared to the change of blood flow, and one in which the change of oxygen consumption is substantial relative to the change of blood flow (Gjedde et al. 2002). The two categories are thought to reflect the differential energy demands of changes of less demanding and more demanding cognitive processes. When the activation or deactivation involves significant perturbation of cognition, the average relative change of oxygen consumption is 60–75% of the change of blood flow. When the activation or deactivation involves little apparent change of cognition, the change of oxygen consumption is no more than 5–10% of the change of blood flow (Gjedde et al. 2002). Hepatic encephalopathy is a disorder with massive cognitive disruption. To test whether this disruption is associated with the expected substantial relative change of oxygen consumption, we calculated the changes of all subjects by normalization to the oxygen consumption and blood flow averages of the healthy control subjects, as shown in Fig. 4. The average relative change of oxygen consumption in all subjects represented 67% of the change of blood flow, consistent with a very large perturbation of energy demanding processes in the human brain.
Fig. 4

Relative Changes of Metabolism. Magnitude of change of relative oxygen metabolic rate, in relation to magnitude of change of relative blood flow. Abscissa: Gray matter blood flow, relative to average gray matter blood flow in healthy control subjects. Ordinate: Gray matter oxygen consumption rate, relative to average gray matter oxygen consumption rate in healthy control subjects. The slope of the linear regression indicates that the relative change of oxygen consumption is 67% of the relative change of blood flow


In conclusion, we find that the calculation of mitochondrial oxygen tensions shows that HE is accompanied by a primary inhibition of oxygen consumption with a corresponding decline of cerebral blood flow according to the expected practically linear flow-metabolism coupling associated with substantial perturbations of cognition.


The authors thank the staff of the Pathophysiology and Experimental Tomography Center of Aarhus University Hospitals. This study was supported by the Danish Medical Research Council.

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