Assessment of the hepatic circulation in humans: New concepts based on evidence derived from a D-sorbitol clearance method

I EV EW AI TfCLES Assessment of the hepatic circulation in humans: New concepts based on evidence derived from a D-sorbitol clearance method GIANPAOLO MOLINO, PAOLO AVAGNINA, GUSTAVO BELFORTE,and JOHANNES BIRCHER TURIN,ITALY,and HERDECKE,GERMANY

D-Sorbitol (SOR) is safe, is easy to measure, and has an exceptionally high extraction ratio in the normal liver of 0.93 _+0.05 (mean _+$D). Together with the general interest in hepatic hemodynamics, these facts motivated us to review the usefulness of this compound for the assessment of liver plasma flow in humans. We concluded that in subjects without liver disease the nonrenal clearance of SOR--measured noninvasively--very closely approximates hepatic plasma flow. Because of its lower and more variable extraction ratio, indocyanine green should no longer be used without hepatic vein catheterization. Even in patients with cirrhosis, SOR exhibits higher hepatic extraction ratios than indocyanine green. To fully explore the potential of SOR in the evaluation of such patients attention needs to be paid to the complex changes in architecture and function occurring in this disease. In cirrhotics the noninvasively measured nonrenal clearance of SOR presumably approximates the flow through intact and capillarized sinusoids (functional flow) and reflects the amount of blood having functional contact with hepatocytes. The theoretic background of the method, its accuracy, further research needs, and potentials of various approaches are discussed in detail. (J Lab Clin Med 1998; 131:393-405)

Abbreviations: BSP =

b r o m o s u l p h t a l e i n ; ETH = e t h a n o l ; G A L = g a l a c t o s e ; ICG = i n d o c y a n i n e g r e e n ; SOR = D-sorbitol; for terms used t o d e s c r i b e h e p a t i c circulation, s e e Table I

R

ecent advances in techniques to measure hepatic perfusion in humans have reopened the question of how such measurements should be performed and what their results really mean.l, 2 It is timely, therefore, to review the available methods and the concepts used for interpretation of From Divisione di Medicina Generale, A Azienda Ospedaliera San Giovanni Battista, Torino; Dipartimento di Scienze Cliniche e Biologiche, Universit~i di Torino; Dipartimento di Automatica ed Informatica, Politecnico di Torino; and Medizinische Fakultgt, Universit~itWitten/Herdecke. Submitted for publication February4, 1997; revision submittedJuly 15, 1997; acceptedAugust 12, 1997. Reprint requests: Gianpaolo Molino, MD, Divisioue di Medicina Generale A, Azienda Ospedaliera San Giovanni Battista, Corso Bramante 88, 10126 Torino, Italia. Copyright © 1998 by Mosby,Inc. 0022-2143198 $5.00 + O 5/1/88742

their results in healthy persons and in patients with liver diseases. It is now well established that endobiotics and xenobiotics with high hepatic extraction are to a large measure cleared by a flow-dependent regime. 1-4 Available knowledge regarding hepatic blood flow in healthy humans during ordinary and unusual stresses of life and in patients with various disease conditions is quite limited and heterogeneous. 5-11 However, it is important to assess and describe liver patients with physiologically meaningful terms in regard to their leading abnormalities, including hepatic perfusion. In discussions about measurements of hepatic perfusion the following two fundamental issues usually remain controversial: (1) Can liver blood flow be measured noninvasively in normal subjects and in cirrhotics with the clearance technique? (2) In patients with cirrhosis can we learn more than total hepatic blood flow with the infusion and extraction technique of Bradley?

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In order to approach these questions, we review the definitions used to describe aspects of liver perfusion and evaluate how they relate to the various methods. In addition, we compare potentials and limitations of current techniques in relation to possible scientific questions. DEFINITION OF TERMS

reduce the complexity by conceptualizing flow as occurring via three different channels (see Fig. 1, bottom): (1) fenestrated sinusoids, which are surrounded by hepatocytes, allowing hepatocellular function to occur]2 (Qfs); (2) capillarized sinusoids, where the exchange of macromolecules, but not of small solutes, is impeded]6,17 (Qcs); and (3) intrahepatic shunts, channels that do not permit exchange with hepatocytes 16,17

In the normal liver the relations and schemes used to describe liver circulation are relatively simple (Fig. 1, top). Total flow (QtotaI, physical flow) is the sum of arterial flow (Qa) and portal flow (Qp) and is equal to hepatic venous flow (Qhv). All blood passes through intact sinusoidal units, allowing a "normal" exchange of substances between blood and hepatocytes or Kupffer cells. Under these circumstances, Qtotal equals the flow through functioning sinusoids (Qfs), implying exchange of compounds between blood and hepatocytes in a manner specific for the liver and for each molecular species considered. In the absence of extrahepatic portosystemic collateral circulation, Qp equals the portal flow that reaches the liver (Qpl) 12 (Table I). In patients with cirrhosis the situation is more complicated. Although all the blood flowing through the hepatic artery is considered to reach the liver, a significant fraction of the blood entering the portal system (Qp) may flow to the systemic circulation through extrahepatic shunts (Qehs). 13 The architectural changes of the cirrhotic liver are so variable, heterogeneous, and complex that it is impossible to construct a simple model that truly reflects these complexities.14j 5 From a functional point of view, it appears justifiable to

(Qihs). In principle, fenestrated and capillarized sinusoids are fed in variable proportion from both the hepatic artery and the portal vein. The idea of these channels makes it possible to refer physiologic measurements made with specific test compounds to respective model concepts, even though in reality no sinusoid may be completely functioning or completely capillarized. The relations between these various terms are given in Table I. A new concept, related to the functional interpretation of circulatory parameters, may now be introduced: blood flow measured by dynamic tests using molecules removed by liver cells reflects the amount of blood having "functional contact" with hepatocytes, which is different from the physical (total) flow. Capillarization (i.e., reduction in fenestration of sinusoids and collagen deposition within the space of Disse) impedes the exchange of blood plasma with hepatocytes, thereby altering the exchange of protein-bound molecules. 15 This implies that the hepatic removal of substances such as indocyanine green does not reflect the function of liver cells, because access to hepatocytes is affected by variable "physical" limitations which do not apply to the same extent for

J Lab Clin M e d Volume 131, N u m b e r 5

small molecules.18 Indeed, the reduction of the indocyanine green extraction ratio that occurs in liver cirrhosis is at least partially related to a prehepatocellular alteration and cannot reflect liver function quantitatively. STRENGTHS AND WEAKNESSES OF CURRENTLY AVAILABLE TECHNIQUES

The potentials and limitations of various methods used to assess hepatic perfusion are summarized in Table II). Procedures apart from clearance methods.. Direct measurements of flow through the hepatic artery and the portal vein have been achieved with electromagnetic flow probes. 19-23This method has the advantage that short-term changes in either of the two vessels can be monitored, but the technique is applicable only during surgical procedures, which severely limits its usefulness. Further disadvantages of this device include cumbersome design, baseline or zero instability, and unsuitability for small blood vessels, low flow states, and long-term preparations. Doppler sonography is noninvasive and in principle allows separate assessment of portal venous and arterial flows at frequent intervals, so that instantaneous and average flows with both short and long intervals can be evaluated. 24 Based on the Doppler effect, the echoDoppler, test yields information derived from the movement of red blood cells. It measures the direction and velocity of flow. 25,26 Portal vein measurements are not very reliable owing to wide variations in blood flow and vessel diameter under physiologic conditions (e.g., respiration, Valsalva maneuver, even in recumbent subjects). 27,28 However, the superior mesenteric artery provides 75% of all blood flow entering the portal system, and experimental studies have shown that changes in mesenteric blood flow are a reliable indicator of blood flow changes in the portal vein. 29 Practical limitations of the Doppler technique are the dependency of the measurements on the angle of insonafion, the difficulty of estimating the cross-sectional area of the vein, and the high interobserver variability.30-32 A relatively new, noninvasive technique for blood flow measurement is magnetic resonance velocity mapping. This method provides temporal and spatial information on flow during the cardiac cycle and has been shown to be accurate. 33,34 The technique can be used to measure absolute flow values with low variability in several splanchnic vessels simultaneously. The examination is not hindered by bowel gases or patient habitus. However, the relatively long data acquisition time makes the method less suitable for the study of shortlasting changes in flow. 35,36 Assessment of intrahepatic and extrahepatic shunting has been achieved by scintiscanning of liver and

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Table I. Description a n d definition o f terms

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arterial flow portal flow portal flow to the liver hepatic venous outflow flow through functioning sinusoids flow through capillarized sinusoids flow through intrahepatic shunts flow through extrahepatic shuns total hepatic flow (= physical flow) functional hepatic flow concentration in inflow to liver concentration in outflow from the liver (= hepatic vein) extraction ratio of D-sorbitol extraction ratio of ICG extraction ratio = (Cf - Co) + C i clearance = etotal " E steady state concentration infusion rate intrinsic clearance

In health:

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= =

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= =

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Qp

=

Qpt + Qehs

Qfs + Qcs for small molecules (e.g., SOR) Qfs for large molecules (e.g., proteinbound ICG)

lung after injection of microspheres into various sites of the portal system. 37-39 The technique is limited to animal studies. It measures the radioactivity in the organs (radioactive counts per minute) after sacrifice of the animal. In the absence of portosystemic shunts, the microspheres are retained in the liver, whereas shunting transports them to the lungs. The radioactive microsphere method yields a reliable and detailed evaluation of the systemic and splanchnic circulation in animals with or without portal hypertension; however, it provides only instantaneous hemodynamic information and is unsuitable for the study of changes in blood flow over time. Porchet and Bircher4° tried to measure port0systemic shunting (Qehs + Qihs) by comparing the systemic availability of simultaneous oral and intravenous doses of glyceryl trinitrate as measured by digital plethysmography. Although this method is noninvasive and is valid in principle, it is limited by an undefined intestinal firstpass elimination of glyceryl trinitrate and by possibly false calibrations caused by absorption of the drug in polyvinyl tubing.

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Table II. M e t h o d s for the assessment of h e p a t i c perfusion Techniques

Potentials

Electromagnetic flow probes Doppler sonography Magnetic resonance velocity mapping Scintiscanning after microsphere injection Bioavailability of glyceryl trinitrate Scintiangiography

Main limitations

Separate assessment of Qa and Qp; observation of rapid changes Separate assessment of Qa and Qp; noninvasive; repeatable Temporal and spatial assessment of Qa and Qp simultaneously Separate measurements of Qehs and Qihs Measures sum of eehs + eihs Assessment of Qa/Qpl ratio

AUC-method after oral and intravenous dosing

Noninvasive assessment of Qtotal

Infusion and extraction technique of Bradley

Measurements of Qtotal

Clearance techniques

Assessment of Qfs with protein-bound molecule, or Qfs + Qcs with small solutes, or Kupffer cell function with colloids

Possible only in anesthetized patients with opened abdomen Accuracy and reproducibility open to question Low suitability for short-lasting changes of flow Access to splenic or portal veins requires invasive procedures, radioactivity No absolute values; not validated in another laboratory Accuracy and reproducibility open to question; radioactivity Requires many hours and application of isotopes Requires hepatic vein catheter; impossible to sample mixed hepatic venous blood Inaccuracy due to incomplete extraction; radioactive labeling of colloids

References

19-23 24-32 33-36 37-39 40 41-43 44-46 47,48

49-68

AUC, Area under the curve.

Scintiangiography with technetium 99-labeled compounds may be used to visualize the temporal pattern of arterial and portal inflow of the label into the liver and thereby to measure the ratio of Qa to Qpl. 41,42 However, interpretation of the resulting curves over the area of interest either depends on arbitrary assumptions or is subject to significant inter-observer variations. The validity of the results has therefore been questioned. 43 A pharmacokinetic, noninvasive method of measuring total liver flow (Qtotal) is based on simultaneous oral and intravenous dosing (one dose being radiolabeled) of a highly extracted drug that is completely absorbed by the gastrointestinal tract and metabolized only by the liver. 44 Propranolol has been used for this purpose. 45,46 The measurements, derived by assessing the areas under the respective plasma concentration-time curves, yield an integral of Qtotal over the period of investigation but necessitate the use of an appropriate radioactive label, require many hours, and are based on a number of assumptions to be verified for each test compound under consideration. Clearance techniques. The most widely used procedures to assess hepatic perfusion are based on the clearance technique. 47-64 Its rationale may be shown by the following relation: C1 = Qtotal • E

(1)

where C1 is the clearance and E is the extraction ratio.

The latter value corresponds to the arteriohepaticvenous concentration difference divided by the arterial concentration. The relation in equation (1) implies that clearance is equal to Qtotal when E equals 1--that is, if the test compound is removed completely from the blood in a single passage through the liver. When a steady-state infusion technique is employed, measurements fulfill the following equation: C1 = I + Css

(2)

where I is the infusion rate and Css is the steady-state plasma concentration. Obviously, the test compound must not be eliminated by any organ other than the liver (or suitable compensation must be introduced), and it must not re-enter the circulation once it has been eliminated (e.g., by enterohepatic circulation). To date, no compound has fulfilled these requirements completely (Table III). The highest extraction ratios are seen with SOR, 51-53 GAL, 54-57 and ETH. 58,59 The latter two compounds must be given in low doses to avoid saturation effects, whereas for SOR first-order kinetics have been demonstrated over a wide range of safe doses. 51 Lidocaine, 6°,61 propranolol, 45,46 ICG, 62,63 and BSP 64 have intermediate rather than high hepatic extraction ratios. The renal output of SOR or of GAL does not intro-

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duce significant errors in the assessment of the hepatic clearance, when it is measured and corrected for. Extrahepatic and extrarenal elimination may be pertinent sources of inaccuracy for GAL and ETH but not for SOR. The high level of protein binding for ICG and BSP limits their distribution principally to the intravascular volume, whereas unbound solutes such as SOR, GAL, and ETH distribute themselves rapidly into the extravascular space or body water. Consequently, the small volumes of distribution of ICG and BSP are associated with very short half-lives (3 to 6 minutes in norreal subjects) and a relatively short period required to achieve steady-state conditions. These periods are much longer for SOR, GAL, and ETH. Lidocaine and propranolol have virtual volumes of distribution that are larger than body water and are potentially modified by variable concentration-related binding to plasma proteins. Macroaggregated albumin labeled with isotopes of iodine and labeled colloidal gold (198Au) have in the past been used for clearance measurements that were thought to reflect liver perfusion. 65-68 Both are eliminated not by hepatocytes but by the reticuloendothelial system. The limitations for the application of macroaggregated albumin lie in the splenic elimination of the test compound and the poor reproducibility of the distribution of particle sizes: For 198Au particles the long physical half-life of the tracer is also a severe constraint. It would be informative to compare measurements of blood flow made by different methods; however, such comparisons would be cumbersome and questionable for several reasons: different methods measure different fluxes (see Table II); all methods are affected by not negligible errors69; and practical (and sometimes ethical) reasons prevent measurements based on different methods. The "gold standard" for the measurement of total hepatic plasma flow (Qtotal) is the infusion and extraction technique of Bradley, 47,48 which is an application of the Fick principle to the liver. In addition to the clearance, the hepatic extraction ratio is measured, and Qtotal is obtained from equation (1). The method requires hepatic vein catheterization, which limits its application because of ethical considerations. For anatomic reasons it is not possible to obtain mixed hepatic venous blood. Indeed, sampling usually occurs in the periphery of a hepatic vein, and the question whether the specimens are representative for mixed hepatic venous blood cannot be answered. For this reason Bradley called such measurements "estimated" hepatic blood flOW.47

INTERPRETATIONOF CLEARANCEDATAIN SUBJECTS WITHHEALTHYLIVERS Until recently it was generally accepted that hepatic blood flow cannot be measured with the clearance tech-

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Fig. 2. Model-based computations of the modifications of EIc G (top) and Eso ~ (bottom) as a function of changes in liver function (i.e., metabolic capacity of the liver or sinusoidal units). The normal mean value is taken as 1.0. The curves indicate predictable changes in extraction ratios taken from experimental data (means and ranges). The method of computation is detailed in the Appendix (for more explanations see the text). , 0 data from Zeeh et al.52; 0 , data from Molino et al. 53

nique alone, because uncertainty about changes in the hepatic extraction ratio renders the relation between clearance and blood flow unpredictable. Consequently, a critical attitude toward ICG clearance values has prevailed. 63 The introduction of SOR as a test compound offers new and interesting opportunities. When considering the data derived from Zeeh et al.52 and Molino et al.53 in normal subjects, the intrinsic clearance of SOR (measured as the ratio of hepatic removal to the calculated mean sinusoidal plasma concentration) is about five times larger than the intrinsic clearance of ICG. For this reason, the mean SOR hepatic extraction ratio (EsoR) in normal volunteers is higher than the ratio for ICG (EIc6) (0.93 versus 0.58, respectively), and changes in metabolic function have a smaller influence on Eso R than on Em6 (see Fig. 2). For example, application of a simulation procedure (Appendix) to these data makes it possible to predict that, if the metabolic capacity of the liver is reduced to 50%, Eso R will fall from 0.93 to 0.73 and EIc~ will fall from 0.58 to 0.35. In contrast, if the metabolic capacity is doubled, Eso R increases only slightly to 0.99, whereas E~c~ increases markedly from 0.58 to 0.82. Predictions by simulation

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Table III. P h a r m a c o k i n e t i c Test substance SOR GAL ETH Lidocaine Propranolol ICG BSP ALB-MA COLL-198Au

Average E in normal liver 0.93 0.91 0.82 0.75 0.73 0.61 0.60 0.8011 0.9511

features of test compounds Renal elimination (%) 10 8 1 5 <1 -Trace ---

Extrahepatic extrarenal elimination -Some Some ----RES RES

u s e d t o assess h e p a t i c Volumes of distribution 0.22 0.30 0.66 1.48 4.00 0.04 0.04 0.04 0.04

L/kg L/kg* L/kg L/kg L/kg L/kg L/kg !_/kg L/kg

Protein binding ---70% 93% ++ + ---

perfusion Adverse reactions* Safet Safe§ Safe Drug-related Drug-related Rare anaphyiactic Rare anaphylactic Radioactivity Radioactivity

References 51-53 54-57 58,59 60,61 45,46 62,63 64 66,68 65,67

ALB-MA, Macroaggregated albumin; COLL-t98Au, radiolabeled colloidal gold; tIES, reticuloendothelia[ system. *With established dose. tAdverse reactions may be expected only in subjects with fructose intolerance. *Variable amounts of galactose may enter cells. ~Adverse reactions may be expected only in subjects with galactosemia. JJAffected by particle size.

have recently been confirmed in acromegaly, where the hepatic clearance of SOR is not significantly increased despite a substantial increase in the galactose elimination capacity.70 Therefore, in subjects with normal livers it appears justifiable to interpret changes in the hepatic clearance of SOR as being predominantly a result of changes in hepatic blood flow; SOR is reasonably reliable for the assessment of hepatic perfusion. In contrast, the use of the ICG clearance may be questionable because of a higher dependence on metabolic changes. Based on these arguments, the SOR clearance technique has now opened the way for the investigation of liver perfusion in subjects with normal livers under various conditions of life, including drug effects, intensive care, and physical exercise. 71-77 The relatively long half-life of SOR and the buffering effect of the large distribution space do not severely limit its use in clinical practice. Ninety percent of the changes toward steady state occur relatively rapidly for SOR (i.e., within 10 to 15 minutes), as shown by Zeeh et al. 52 Consequently, physiologic changes of flow, such as may occur during sleep, after meals, or during exercise, can easily be seen and assessed with acceptable precision. Moreover, hepatic vein catheterization is unnecessary for clinical evaluations, and the errors caused by changes in metabolic capacity appear to be quite acceptable (see Fig. 2). INTERPRETATION OF CLEARANCE DATA IN SUBJECTS WITH CIRRHOSIS

In patients with cirrhosis, Qtotal no longer corresponds to Qa + Qp but rather to Qa + Qp]--that is, to Qfs + Qcs + Qihs (see Fig. 1 and Table I). According to Huet et al., 17 sucrose easily passes across capillarized sinu-

soidal walls in rabbits and in patients with cirrhosis. It is reasonable to assume that SOR passes equally well, although it would be useful to have direct evidence. Accordingly, in our model we assumed that the clearance of SOR occurs in both functioning and capillarized sinusoids, therefore reflecting Qfs + Qcs. Such a speculation needs to be sustained by further experimental data. The concept is complicated by the possibility that sinusoids may not be equipped with a full complement of hepatocytes and therefore may not have normal function. There are several ways to look at this problem: la. Regeneration in cirrhotic livers leads to restoration of intact sinusoidal units (intact sinusoidal unit theory)14; lb. The cirrhotic liver is composed of sinusoidal units having varying functional capacities due to varying numbers of hepatocytes associated with each unit (sick sinusoidal unit theory)14; 2a. Hepatocytes in cirrhotic livers have normal metabolic function (intact hepatocyte theory)v8; 2b. Hepatocytes in cirrhotic livers have reduced metabolic function (sick cell theory).79 At the present time there is neither enough morphologic nor functional evidence to distinguish between alternatives la and lb; both are simplifications. 14 On the other hand, support for the intact hepatocyte theory has been presented in patients with liver cirrhosis, 80-82 and there are good reasons to believe that hepatocytes are sick in cholestasis 79 and during acute and chronic ethanol intoxication, s3 On the basis of these arguments it is not possible at this time to come to a simple pathophysiologic interpretation of hepatic SOR clearance for patients with cirrhosis (e.g., by use of the model shown in Fig. 1).

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Only under hypotheses of intact sinusoidal units and intact hepatocytes (la and 2a) would SOR clearance closely approximate the sum Qfs + Qcs. In other cases, it would have a weaker relation to flow in any of the intrahepatic channels. Nevertheless, hepatic clearance of SOR represents the parenchymal perfusion or flow that is functionally effective and relevant, which may be defined as "functional flow" (Qfunct). Despite the relatively inaccurate definition, this concept has pathophysiologic significance because it presumably predicts rates of hepatic elimination of endobiotics and xenobiotics that have high hepatic extraction ratios and free passage through capillarized sinusoidal walls (e.g., NH 3, GAL, ETH). The concept of functional flow may be extended also to other liver diseases such as hepatitis, cholestasis, and steatosis. However, it does not contribute to an understanding of the details of circulatory and functional pathophysiology which would be needed to predict hepatic elimination of protein-bound compounds such as ICG and BSR The relevance of the concept of functional flow for the elimination of other substrates such as aldosterone and estrogens in patients with cirrhosis needs to be investigated. INTERPRETATION OF RESULTS OF THE INFUSION A N D EXTRACTION TECHNIQUE OF BRADLEY

Bradley's technique assesses Qtotal (physical flow) and therefore, in cirrhotics, also Qfs + Qcs + Qihs" These measures are highly relevant primarily for hemodynamic studies and have been used extensively in the past. When applying ICG as a test compound, it has become customary to calculate also its intrinsic clearance (C1 i = Vmax -2- Kin, where Vmax is maximal velocity and K M is Michaelis-Menten dissociation constant) and to think of it as a flow-independent metabolic capacity.63 In view of the limiting of sinusoidal permeability for ICG by capillarization, the intrinsic clearance of ICG neither reflects the function of liver cells (because its access to hepatocytes is affected by a ,variable "physical" limitation) nor represents the functional capacity of the sum of all hepatocytes. Therefore this parameter is of questionable pathophysiologic significance and should be abandoned. When the Bradley technique is applied in cirrhotic patients with SOR as test compound, the measured Qtotal exceeds the functional flow (see previous discussion). Consequently, in cirrhotic patients, the difference between measures of liver perfusion obtained by the infusion and extraction technique (Qtotal) and by the clearance method (Qfunct) expresses a flow through the liver which is functionally ineffective and therefore may be called "functional intrahepatic shunting" (Qihs). 53 This represents the complement (with respect

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to Qtotal) of the functional flow (Qfunct) and has the corresponding pathophysiologic meaning, indicating the fraction of Qtotal that escapes hepatic elimination through intrahepatic shunts (the flow through capillarized sinusoids being measured as functional flow by the SOR clearance). In the case of intact sinusoidal units and intact hepatocytes (hypotheses la and 2a), the functional intrahepatic shunting approaches an anatomic entity, the actual flow through intrahepatic shunts. In all other cases the expression represents just a pathophysiologic concept. Assuming intact sinusoidal units and intact hepatocytes, the flow through capillarized sinusoids (Qcs) could theoretically be estimated by the difference between the clearance of SOR and the clearance of a very highly protein-bound test compound that has an intrinsic clearance and extraction ratio similar to SOR in normal livers but is affected by capillarization. Although the clearance of SOR includes both Qfs and Qcs, the clearance of such a protein-bound compound would reflect only Qfs. The ideal protein-bound test compound has not yet been found and should be looked for. Available data regarding the measured hepatic extraction ratios of SOR and ICG provide insufficient experimental evidence of the concepts described here. As shown in Fig, 3, which summarizes results by Zeeh et al. 52 and Molino et al., 53 the extraction ratios of SOR and ICG are correlated nonlinearly when patients with varying severities of cirrhosis are considered. This nonlinearity may be explained by capillarization of sinusoids that impedes hepatocellular uptake of ICG or by the difference in intrinsic clearance of the two test compounds, or both. Measurement inaccuracies do not allow us to choose among these speculations.

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Fig. 4. Relative measurement error for Qtotal assessed with SOR assuming steady-state conditions and the parameter values described in the text. The graph, obtained by error analysis as described by Balestra et al. 84 and Molino et al.85 shows that Qtotal has a relative error that increases in proportion to fractional portosystemic shunting (FPS) and its partition between intrahepatic and extrahepatic shunt pathways (IHS/FPS).

ACCURACY OF FLOW PARAMETERS

All the relevant flows discussed previously are measured indirectly. Their accuracy depends both on their relation to some primary quantities directly measured and on the accuracy with which these primary quantities are determined. The relation between flows and primary quantities depends on the model used for describing the real investigated system and can be derived from it. Using the analytic relations described by Balestra et al.84 and Molino et al.,85 derived from the mathematical model formalizing Fig. 1 and Table I, the following error analysis can be performed. Both Qfunctand Qtotalare related to the infusion rate, the systemic and hepatic venous concentrations, the urinary output (as occurs for SOR), and the assumed value of the extraction ratio (E) in normal sinusoids. When these quanrifles are given, Qfunctand Qtotal can be derived. The errors in determining Qfunctand Qtotal, evaluated by standard sensitivity error analysis, depend on the values chosen for these parameters as well as their uncertainty. If SOR as a reference test compound is considered, assuming an infusion rate of 30 mg/min with an error of 1%; an assay precision of 3% in systemic blood, 3% in urine, and 5% in hepatic venous blood; and E = 0.93 in normal livers, results can be summarized as follows: 1. The error of Qfunct is affected neither by fractional portosystemic shunting nor by its partition between intrahepatic and extrahepatic pathways. 2. The measurement errors induce an uncertainty on Qfunct of 5% that does not depend on the value assumed for E. 3. I f E is uncertain and is assumed to be equal to a nominal value plus some percentage error, this same error

must be added to the 5% uncertainty of Qfunct. For example, if E is assumed to be bounded by 0.81 and 0.99 and the nominal value of 0.90 is used together with a 10% uncertainty, the total uncertainty on Qfunct becomes 10% plus 5%, or 15%. 4. Qtotal depends on the systemic and hepatic vein concentration difference, which is influenced by the shunts and by E. As a consequence, the uncertainty of Qtotal is highly dependent on the intrahepatic shunt but only marginally affected by the uncertainty of E. For example, if E is bounded by 0.80 and 1.00, the error on the error induced by this uncertainty is less than 10%. 5. The uncertainty of Qtota] is a function of the fractional portosystemic shunting and of its partitioning between intrahepatic and extrahepatic pathways (Fig. 4). For small intrahepatic shunts, Qtotal and Qfunct have quite the same uncertainties, neglecting the uncertainties of E affecting Qfunct. For high intrahepatic shunts, the uncertainty of Qtotal grows significantly, so that Qtotal is more uncertain than Qfuncteven when the effect of the uncertainty of E is considered. These considerations document a limitation of the Bradley technique which is well known empirically to those who have used it frequently in the past. The differences in accuracy between Qfunct and Qtotal, when measured with SOR, clearly favor a more liberal use of the peripheral clearance measurements of Qfunct and remove some of the attraction of the infusion and extraction method. Yet the Bradley technique remains interesting because of the potential to measure intrahepatic shunts (Qihs). LIMITATIONS OF THE PROPOSED CONCEPTS

The definitions used in this paper mainly refer to morphologic and structural features as detailed in Table I and Fig. 1. Their justification is based on up-to-date concepts regarding the morphologic basis of blood flow within normal and cirrhotic livers. 69 The definitions were chosen in such a way that specific physiologic properties may be associated with each of them, because they were intended to realize the combination of anatomic and functional interpretations of experimental data and to serve as a conceptual framework for the design of new experiments. However, this approach by necessity implies the assumption of a marked simplification of circulatory phenomena in the liver, particularly in disease states. For each experimental protocol the consequences resulting from these simplifications must be examined in detail. Although the definitions supposedly refer to anatomic structures, in the reality of cirrhotic livers there may be no truly anatomic counterparts. Even in the normal

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liver the idea of sinusoidal units of standard size is likely to be wrong; sinusoids probably vary in length within the lobules and perhaps also among different regions of the liver. In the cirrhotic liver there may be some normally functioning sinusoids, some completely capillarized sinusoids, and some true intrahepatic shunts. In addition, an unknown fraction of sinusoids would represent morphologic and functional intermediates. On the other hand, capillarization should probably be viewed as an alteration, depending on uneven pore size and collagen deposition, that causes a varying but substantial impairment of the hepatic uptake of large molecules while affecting to a negligible extent the hepatic removal of small molecules. Furthermore, the architectural changes in sinusoidal interconnections described by Shimizu and Yokoyama 14 must also be accounted for. Although these considerations limit morphologic interpretations of experimental data, they do not invalidate the physiologic conclusion that the overall flowlimited liver function results from three processes simultaneously occurring in parallel, each being associated with specific functional features. Therefore, although the terms refer to anatomic features, they are intended to describe physiologic processes applied to the liver as a whole and to alterations that may be unevenly distributed in the hepatic tissue. Another limitation concerns the assessment of extrahepatic shunting (Qehs)' So far no method has been found that satisfactorily estimates this parameter. A procedure based on the bioavailability of a test compound that is well absorbed and not metabolized in the gastrointestinal tract but highly extracted by the normal liver may be appropriate to assess the fraction of portal blood (Qp) that escapes hepatic elimination (Qihs + Qehs)" Recently an invasive approach has been applied, with direct administration of SOR to exclude any interference by intestinal absorption and metabolism, s6 but because portal (Qp) and hepatic arterial (Qa) flows cannot reliably be measured separately there is no way as yet to combine such information with the clearance measurements detailed previously. RESEARCH NEEDS

A further validation of the concepts discussed in this paper is needed when considering SOR as a test compound. The nonrenal clearance of SOR should be validated by a comparison with simultaneously performed magnetic resonance velocity mapping in subjects with normal livers and in cirrhotics. Although much circumstantial evidence16,87, 8a supports the idea that SOR passes easily through capillarized sinusoids, this assumption has not yet been experimentally documented.

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The hypothesis that the hepatic extraction ratio of SOR is almost 100% in all subjects with a normal liver needs to be substantiated under all physiologic conditions (e.g., when liver blood flow increases after a meal or decreases during exercise or sleep), and extrapolations from the concept of functional flow (Qfunct) measured with SOR to other compounds require further appropriate experiments. The technique used to measure intrahepatic shunt flow (Qihs) should be validated by other independent methods. When the microsphere method is used as a standard of reference, it must be remembered that complete agreement cannot be expected, because microspheres assess pore size, whereas the clearance method, as proposed here, is based on hepatocellular function. The approach proposed to assess flow separately through functioning sinusoids (Qfs) and through capillarized sinusoids (Qcs) requires evaluation of test compounds other than ICG that have a very high degree of protein binding and an intrinsic clearance in the normal liver similar to that of SOR. POTENTIAL APPLICATIONS

Some conclusive theses are now allowed according to the above analysis. First, in subjects with normal livers S O R i s the first test compound suitable for assessment of hepatic plasma flow (Qtotal) by noninvasive clearance techniques. As shown in Fig. 2, the extraction ratio in normal livers is so high that it is only marginally affected by minor changes in metabolic capacity of the liver. Consequently, in contrast to all other test compounds, it is not necessary to document the extraction ratio in each individual case to obtain "clinically useful" information. When SOR is applied as an infusion, the main limitation of the method consists in the requirement for steady-state conditions; in addition, when SOR is given as a bolus, extravascular distribution leads to a double exponential elimination which empirically is difficult to follow for a sufficient period. The potential for noninvasive measurement of liver blood flow in humans should now be used to explore hepatic perfusion under ordinary and extraordinary conditions of life and to investigate in more depth the effects of extrahepatic disease on liver plasma flow. Second, in patients with cirrhosis the nonrenal clearance of SOR represents functional flow (Qfunct), a term to which a specific physiologic meaning can be attached--that is, in a first approximation, the sum of flow through functioning and capillarized sinusoids (Qfs and Qcs, respectively). This is thought to be representative for compounds that may pass through capillarized sinusoids, such as SOR, and to express the maximum the liver still can do. On the other hand, it can-

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not serve as a model for liver function in respect to highly protein-bound molecules. The validity and relevance of these concepts deserve further investigation. Third, when SOR is used to measure total hepatic flow (Qtotal) with the infusion and extraction technique of Bradley in patients with cirrhosis, the difference between Qtotal and Qfunct may be regarded as intrahepatic shunt flow (Qihs). This conclusion depends entirely on an acceptance of the definitions given in Table I and Fig. 1 and obviously is affected by the limitations in accuracy of Qtotal outlined in this paper (see Fig. 4). The possibility of measuring Qihs adds a new dimension to the Bradley technique and justifies further research to evaluate its physiologic and clinical significance in more detail. Finally, the combination of SOR with an equally well extracted but highly protein-bound compound may have the potential to differentiate between Qfs and Qcs. For this approach ICG is not optimal. Therefore, highly protein-bound test compounds with an intrinsic clearance similar to that of SOR should be looked for, and the method should be carefully re-evaluated.

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13. Blei AT. Pharmacokinetic-hemodynamic interactions in cirrhosis. Semin Liver Dis 1986;6:299-308. 14. Shimizu H, Yokoyama T. Three-dimensional structural changes of hepatic sinusoids in cirrhosis providing an increase in vascular resistance of portal hypertension. Acta Pathol Jpn 1993;43:625-34. 15. Bunchet E, Fujieda K. Capillarization and venularization of hepatic sinusoids in porcine serum-induced rat liver fibrosis: a mechanism to maintain liver blood flow. Hepatology 1993;18:1450-8. 16. Schaffner F, Popper H. Capillarization of hepatic sinusoids in man. Gastroenterology 1963;44:239-42. 17. Huet P-M, Goresky CA, Villeneuve J-P, Marlean D, Lough JO. Assessment of liver microcirculation in human cirrhosis. J Clin Invest 1982;70:1234-44. 18. Keiding S. Dynamic aspect of hepatic removal of circulating substances. In: Mclntyre N, Benhamou JP, Bircher J, Rizzetto M, Rodes J, editors. Oxford Textbook of Clinical Hepatology. Oxford: Oxford University Press, 1991:78-87. 19. Kolin A. An electromagnetic flowmeter: principle of the method and its application to blood flow measurements. Proc Soc Exp Biol Med 1936;35:43-56. 20. Von Wetterer E. Eine neue methode zur registrierung der blutstroemungs-geschwindigkeit am uneroeffneten gefaess. Z Biol 1938;98:26-36. 21. Kolin A. An AC induction flowmeter for measurement of blood flow in intact blood vessels. Proc Soc Exp Biol Med 1941;46:235-9. 22. Levy ML, Palazzi HM, Nardi GL, Bunker JR Hepatic blood flow variations during surgical anesthesia in man measured by radioactive colloid. Surg Gynecol Obstet 1961;112: 289-94. 23. Shenk WG, McDonald JC, McDonald K, Drapanas T. Direct measurement of hepatic blood flow in surgical patients: with related observations on hepatic blood flow dynamics in experimental animals. Ann Surg 1962;156:463-71. 24. Horn JR, Zierler B, Bauer LA, Reiss W, Strandness DE Jr. Estimation of hepatic blood flow in branches of hepatic vessels utilizing a noninvasive, duplex Doppler method. J Clin Pharmacol 1990;30:922-9. 25. Franklin DL, Baker DW, Ellis RM. A pulsed ultrasonic flowmeter. IRE Trans Med Electron 1959;ME6:294-6. 26. Aulick LH, Baze WB, McLeod CG, Wilmore DW. Control of blood flow in a large surface wound. Ann Surg 1980;191:249-58. 27. Smith H-J, GrCttum P, Simonsen S. Ultrasonic assessment of abdominal venous return. I. Effect of cardiac action and respiration on mean velocity pattern, cross-sectional area and flow in the inferior vena cava and portal vein. Acta Radiol Diagn 1985;26:581-8. 28. Anderson MF. Pulsed Doppler ultrasonic flowmeter: application to the study of hepatic blood flow. In: Granger DN, Bulkley GB, editors. Measurements of Blood Flow: Application to the Splanchnic Circulation. Baltimore: Williams & Wilkins, 1981:395-8. 29. Kroeger RJ, Groszmann RJ. Increased portal venous resistance hinders portal pressure reduction during the administration of [3-adrenergicblocking agents in a portal hypertensive model. Hepatology 1985;5:97-101. 30. Gill RW. Measurements of blood flow by ultrasound: accuracy and sources of error. Ultrasound Med Biol 1985;11: 625-41. 31. Taylor KJW, Burns PN, Woodcock JP, Wells PNT. Blood flow in deep abdominal and pelvic vessels: ultrasonic pulsedDoppler analysis. Radiology 1985:154:487-93.

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32. de Vries PJ, van Hattum J, Hoekstra JBL, de Hoodge R Duplex Doppler measurement of portal venous flow in normal subjects: inter- and intra-observer variability. J Hepatol 1991;13:358-63. 33. van Rossum AC, Sprender M, Visser FC, Peels KH, Valk J, Roos JR An in vivo validation of quantitative blood flow imaging in arteries and veins using magnetic resonarLce phase-shift techniques. Eur Heart J 1991; 12:117-26. 34. Rebergen SA, Chin JGJ, Ottenkamo J, van der Wall EE, de Roos A. Magnetic resonance measurements of blood flow: principles and clinical applications. Cardiovasc Imag 1992; 4:175-81. 35. Burkart DJ, Johnson CD, Mortom MJ, Wolf RL, Ehrman RL. Volumetric flow rates in the portal venous system: measurement with cine phase-contrast MR imaging. AJR Am J Roengtenol 1993; 160:1113-8. 36. Lycklama ~t Nijeholt GJ, Burggraaf K, Wasse MNJM, et al. Variability of splanchnic blood flow measurements using MR velocity mapping under fasting and post-prandial conditions: comparison with echo-Doppler. J Hepatol 1997;26:298-304. 37. Sapirstein LA. Regional blood flow by fractional distribution of indicators. Am J Physiol 1958;193:161-8. 38. Gurll NJ, Reynolds DC, Shirazi SS. Acute and chronic splanchnic blood flow responses to porta caval shunt in normal dog. Gastroenterology 1980;78:1432-6. 39. Groszmann RJ, Vorobioff J, Riley E. Splanchnic hemodynamics in portal hypertensive rats: measurements with y-labelled microspheres. Am J Physiol 1982;242:G156-60. 40. Porchet H, Bircher J. Noninvasive assessment of portal-systemic shunting: evaluation of a method to investigate sys= temic availability of oral glyceryl trinitrate by digital plethysmography. Gastroenterology 1982;82:629-37. 41. Biersack HJ, Torres J, Thelen M, Monzon O, Winkler C. Determination of liver and spleen perfusion by quantitative sequential scintigraphy: results in normal subjects and in patients with portal hypertension. Clin Nucl Med 1981; 6:218-20. 42. Tindale WB, Barber DC. The effect of methodology and tracer identity on a non-invasive index of liver blood flow. Nucl Med Commun 1987;8:973-81. 43. Molino G, Baccega M, Squadrone E, Magnani C. Assessment of liver circulation by quantitative scintiangiography: evaluation of the relative contribution of the hepatic arterial and portal venous blood flows to liver perfusion. Eur J Nucl Med 1989;15:211-6. 44. Perrier D, Gibaldi M. Clearance and biologic half-life as indices of intrinsic hepatic metabolism. J Pharmacol Exp Ther 1974;191:17-24. 45. Branch RA, Shand DG. Propranolol disposition in chronic liver diseases: a physiological approach. Clin Pharmacokinet 1976;1:264-79. 46. Kornhauser DN, Wood AJJ, Vestal RE, Wilkinson GR, Branch RA, Shand DG. Biological determinants of propranolol disposition in man. Clin Pharmacol Ther 1978;23: 165-74. 47. Bradley SE, Ingelfinger FJ, Bradley GR Curry JJ. The estimation of hepatic blood flow in man. J Clin Invest 1945; 24:890-7. 48. Bradley SE. The hepatic circulation. In: American Physiologic Society, editors. Handbook of Physiology: Circulation (vol. 3). Washington, DC: 1962:1387-438. 49. Bass L, Keiding S, Winkler K, Tygstrup N. Enzymatic elimination of substrates flowing through the intact liver. J Theor Biol 1976;61:392-409.

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50. Keiding S. Hepatic clearance and liver blood flow. J Hepatol 1987;4:393-8. 51. Molino G, Cavanna A, Avagnina R Ballar~ M, Torchio M. Hepatic clearance of D-sorbitol: noninvasive test for evaluating functional liver plasma flow. Dig Dis Sci 1987;32: 753-78. 52. Zeeh J, Lange H, Bosch J, et al. Steady-state extrarenal sorbitol clearance as a measure of hepatic plasma flow. Gastroenterology 1988;95:749-59. 53. Molino G, Avagnina R Ballarb M, et al. Combined evaluation of total and functional liver plasma flow and intrahepatic shunting. Dig Dis Sci 1991;36:1189-96. 54. Tygstrup N, Winkler K. Galactose blood clearance as a measure of hepatic blood flow. Clin Sci 1958; 17:1-9. 55. Henderson JM, Kutner MH, Baln RE First-order clearance of plasma galactose: the effect of liver disease. Gastroenterology 1982;83:1090-6. 56. Keiding S, Bass L. Galactose clearance as a measure of hepatic blood flow. Gastroenterology 1983;85:986-7. 57. Keiding S. Galactose clearance measurements and liver blood flow. Gastroenterology 1988;94:477-81. 58. Keiding S, Johansen S, Midtbol I, Christiansen I. Ethanol elimination kinetics in human liver and in pig liver in vivo. Am J Physiol 1979;237:316-24. 59. Greenway CV, Lautt WW. Hepatic blood flow: estimation from clearances of very low dose infusions of ethanol in cats. Can J Physiol Pharmacol 1988;66:1192-7. 60. Boyes RN, Scott DB, Jebson PJ, Godman MJ, Julian DG. Pharmacokinetics of lidocalne in man. Clin Pharmacol Ther 1971;12:105-16. 61. Benowitz NL, Meister W. Clinical pharmacokinetics of lignocaine. Clin Pharmacokinet 1978;3:177-201. 62. Caesar J, Shaldon S, Chiandussi L, Guevara L, Sherlock S. The use of indocyanine green in the measurement of hepatic blood flow as a test of hepatic function. Clin Sci 1961; 21:43-7. 63. Skak C, Keiding S. Methodological problems in the use of indocyanine green to estimate hepatic blood flow and ICG clearance in man. Liver 1987;7:155-62. 64. Hacki W, Bircher J, Preisig R. A new look at the plasma disappearance of sulphobromophtalein (BSP): Correlation with the BSP transport maximum and the hepatic plasma flow in man. J Lab Clin Med 1976;88:1019-31. 65. Dobson EL, Jones HB. The behaviour of intravenously injected particulate: its rate of disappearance from the bloodstream as a measure of liver blood flow. Acta Med Scand Suppl 1952;273:1-71. 66. Groszmann RJ, Dubin M, Royer M. Study of indirect method for measuring hepatic blood flow in the isolated perfused dog liver. Digestion 1975;13:220-31. 67. Vetter H, Falkner R, Neumayr A. The disappearance of Colloidal radiogold from the circulation and its application to the estimation of liver blood flow in normal and cirrhotic subjects. J Clin Invest 1954;33:1594-602. 68. Halpern BN, Biozzi G, Benacerraf B. Cin6tique de la phagocytose d'une serum-albumine humaine spdcialement raitde et radiomarqude et son application 5 l'6tude de la circulation h6patique chez l'homme. Compt Rend Soc Biol 1956; 150:1307-11. 69. Balestra G, Belforte G, Molino G. Analysis of a protocol for the evaluation of liver function: reliability of circulatory parameter estimation. In: Proceedings of the Conference, Medical Informatics '88: Computers in Clinical Medicine. London: British Medical Informatics Society, 1988:191-7. 70. Avagnina R Martini M, Terzolo M, et al. Assessment of func-

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APPENDIX Relation between extraction ratio and alterations in

liver function. The relation between the extraction ratio

and changes in liver function has been derived according to the following assumptions: • The functioning liver (in which uptake occurs) is d e s c r i b e d by a single sinusoidal tube that can be regarded as the sum of many tubes in parallel; • Uptake is distributed and is a linear function of the local concentration (there is no saturation or other nonlinearity); • Blood flow along the sinusoidal tube is constant and the exchange with hepatocytes is immediate; • B l o o d transit time (in sinusoid) is n e g l i g i b l e with respect to the variation in the rate of the input concentration. U n d e r such assumptions the concentration profile along the sinusoidal tube is given b y the following equation: C(1) = Cie-M

(1)

where C i is the input concentration, 1 is the distance from the input, and )~ is an uptake parameter that is specific for a given substance. The equation for output concentration (Co) is C O = Ci e-~L

(2)

where L is the total length of the sinusoidal tube. W h e n a pathologic condition occurs, it is assumed to uniformly reduce the uptake capability of all cells (sick cell theory) or to reduce the number of functioning cells (intact cell theory). To analyze the effect of such conditions on the output concentration, let us denote with ~1, a value between 0 and 1, an impairment index that expresses the uptake c a p a c i t y o f sick cells relative to normal cells. Then, C O = Cie-(Cq)~)L

(3)

W h e n the subject is normal, c~1 equals 1, and equation (3) equals equation (2). Similarly, let us introduce a second coefficient tx2, also b e t w e e n 0 and 1, that r e p r e s e n t s the r e l a t i v e n u m b e r o f f u n c t i o n i n g cells w h e n d e a l i n g w i t h the i n t a c t c e l l a s s u m p t i o n . B e c a u s e w e a s s u m e d a line a r s y s t e m , the l o c a t i o n a l o n g the t u b e o f the nonw o r k i n g cells is irrelevant for the output c o n c e n t r a tion. T h e r e f o r e , a r e d u c t i o n o f the f u n c t i o n i n g c e l l n u m b e r is equivalent to a r e d u c t i o n o f the s i n u s o i d a l tube length. In this c a s e the o u t p u t c o n c e n t r a t i o n is given b y the f o l l o w i n g equation: C O = Cie-~(°~2L)

(4)

F r o m e q u a t i o n s (3) a n d (4) it a p p e a r s that b o t h m e c h a n i s m s have i n f l u e n c e on the o u t p u t c o n c e n tration. In fact, both conditions could be present s i m u l t a n e o u s l y . In that case, the i m p a i r m e n t i n d e x

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Molino et al,

w o u l d b e cz = CXl(X2 a n d t h e e q u a t i o n become Co = Cie-(c~lX)(a2L)= Cie-c~lc~2)~L= Ci e -c&L

would (5)

It appears that the intact cell and sick cell theories are i n d i s t i n g u i s h a b l e in this m o d e l in regard to their influence on the variation in output concentration. In the following discussion we refer to the i m p a i r m e n t index cz only. The extraction ratio is defined as Ci-C o E=

Ci

(6)

F r o m equation (5), E : E ( ~ ) - C i - Cie-C&L- 1 - e -a~L = 1 - (e-~'L)c~ (7) Ci and then 1 - E (cz) = (e -ZL)cz

(8)

405

Denote with E n the extraction ratio in the normal subject when cz = 1; from equation (8), e -xL = 1 - E n

(9)

Then, substituting equation (9) in equation (7), E(cz) = 1 - (1 - En) c~

(10)

If the extraction ratio in a normal liver is known, it is p o s s i b l e to obtain the extraction ratio E(c0 for any alteration of liver function, that is, for any value o f cz. Examples are shown in Fig. 2 for SOR and ICG.