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Lautt WW. Hepatic Circulation: Physiology and Pathophysiology. San Rafael (CA): Morgan & Claypool Life Sciences; 2009.

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Hepatic Circulation: Physiology and Pathophysiology.

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Chapter 8In Vivo Pharmacodynamic Approaches

To study any phenomenon, it is useful to have a quantifiable index. The index must have a direct relevance to the studied phenomenon and the measured index should be expressed in a useful manner. The vascular resistance of blood vessels has been the subject of speculation and investigation at least since Laplace described a mathematical expression for vascular resistance. Vascular resistance is defined as the pressure gradient across the vascular bed, divided by the flow through the bed. I will discuss the merits of quantifying arterial vascular tone using resistance or, more appropriately, conductance (flow divided by pressure gradient).

The vascular tone in blood vessels is affected by both active and passive forces. Constriction of vascular smooth muscle results in an active increase in vascular resistance to blood flow. An increase in blood pressure will result in a passive elastic stretch of the resistance vessels. In this chapter, I also discuss the use of an index of contractility that finds major utility in describing the active and passive elastic forces that influence venous resistance sites. These concepts have been developed for the liver, but use of the index of contractility also found utility in elegantly describing the cardiovascular system of the octopus [2]. The differentiation between venous resistance and the index of contractility has also been applied to portacaval shunts that form in response to chronic elevation in intrahepatic venous resistance [143]. With the use of these two indices of vascular tone, I will then describe general procedural approaches for establishing the experimental setup to permit in vivo pharmacodynamic studies to be carried out.


Traditionally, vascular tone has been expressed in units of vascular resistance. Stark [351] and Robard [317] argued for the use of vascular conductance, the inverse of resistance, to quantitate vascular tone. In my first studies on the hepatic artery, I adopted the use of vascular resistance [230], ignoring the wise council of my colleague Ron Stark. But I thereafter used conductance to represent arterial tone [184]. At that point, there did not appear to be an obvious advantage to using conductance over resistance except for the theoretical points raised by Stark.

Pharmacodynamic relationships cannot be described from arterial resistance responses, whereas vascular responses, expressed as conductance, are readily quantitated. The most obvious example is pharmacodynamic studies related to a potent vasoconstrictor. As the intensity of the constriction increases, blood flow decreases and may actually cease. As blood flow approaches zero, calculated resistance approaches infinity, a quantitative value that is useless. Arterial conductance, however, falls along with blood flow, and at zero flow, conductance is zero. At constant perfusion pressure, conductance is linearly related to blood flow. Local changes in vascular tone produce primarily changes in blood flow rather than systemic pressure. Both the pressure and flow parameters must be considered when expressing vascular tone because both parameters change simultaneously. However, changes in regional arterial vascular tone largely result in changes in blood flow; therefore, blood flow should be in the numerator of the equation in order that the parameter and the index reflecting the parameter change similarly. Using vascular conductance, pharmacodynamic calculations can be done using enzyme kinetic mathematics.

The data analyzed in Figures 8.1 and 8.2 were obtained from the superior mesenteric artery. Electrical stimulation of the periarterial nerve bundle at 1, 3, and 9 Hz was carried out in the presence and absence of two doses of intra-arterial adenosine. Both resistance and conductance curves show clearly that adenosine antagonizes the nerve-induced vasoconstriction. Attempts to quantitate the degree and type of antagonism, however, are highly dependent on the means of data expression. When the data are plotted using a standard Lineweaver–Burke (1/response vs 1/stimulus) or Eadie–Hofstee plot (response vs response/stimulus), kinetic parameters of the responses come clear only if conductance is used. Figure 8.2 shows a classic Eadie–Hofstee plot of response (as percentage change in vascular conductance) against response divided by the frequency of stimulation. The intercept on the ordinate indicates the Rmax, that is, the maximal mean vasoconstriction attainable, which is seen to be equivalent to reduction of conductance of 80%. The Km, or frequency of stimulation that procures 50% of Rmax, is seen as the negative slope of the line or can be calculated from the intercept of the abscissa (Rmax/Km). In the presence of adenosine, the curve is shifted in parallel, indicating that adenosine produces noncompetitive antagonism of nerve-induced constriction. That is, Rmax is reduced by adenosine but Km is unchanged (competitive antagonism would be indicated by constant Rmax but changing Km). A clear dose-related effect is seen, as a higher dose of adenosine shifts the curve further. Similar plots of changes in resistance from the same data produced uninterpretable results. The control Km is calculated as 25.6 Hz, a value clearly not representing the biological reality because maximal vascular responses occur at 6–10 Hz [213]. In addition, both Rmax and Km undergo dramatic decreases as the adenosine is added. The kinetics of stimulus antagonism are rendered meaningless by the use of vascular resistance. Similar types of kinetic calculations using the Lineweaver–Burke transformation have been used to show that 8-phenyltheophylline competitively antagonizes adenosine-induced vasodilation in the hepatic artery when vascular tone is assessed using conductance [216].

FIGURE 8.1. Frequency–response relationships of sympathetic nerve stimulation in the superior mesenteric artery expressed as percentage change in resistance (% SMAR) or conductance (% SMAC) in the control state and during intra-arterial infusion of two doses of adenosine (0.


Frequency–response relationships of sympathetic nerve stimulation in the superior mesenteric artery expressed as percentage change in resistance (% SMAR) or conductance (% SMAC) in the control state and during intra-arterial infusion of two doses (more...)

FIGURE 8.2. Data from Figure 8.


Data from Figure 8.1 linearized by Eadie–Hofstee plots using vascular responses expressed as percentage change in resistance (% SMAR) or conductance (% SMAC) showing calculated values of the maximal vasoconstriction (Rmax) and Km (or more appropriately (more...)

Although the linear conversion provided by the Lineweaver–Burke or Eadie–Hofstee transformations provides interpretable data, the smallest responses have a large impact on the slope of the relationship. Small errors in the smallest responses can distort the slope. In contrast, computer-assisted iterative solution of the nonlinear rectangular hyperbolic shape of a dose–response curve or nerve response curve allows for calculation of Rmax and ED50 values with as few as three measured data points. The expression of the X-axis on a linear scale rather than a log scale demonstrates that the point of highest confidence in defining the mathematical relationship of these curves is with the zero value. The use of log transferred data loses the zero data point. Ideally, a second response would be approximately 50% of the maximal response and there should be two other stimuli, preferably producing a maximal or near maximal effect. The advantage of being able to use the zero value cannot be overstated. The utility of calculated vascular conductance to provide valid data is demonstrated by the ability to extract pharmacodynamic data using all three methods of estimating Rmax and ED50.

The ability to carry out studies deriving multiple data points for pharmacodynamic calculations are shown in Figures 8.3 and 8.4. Intraportal adenosine was infused and the response of the hepatic artery was determined to four incremental doses of infusion of adenosine tested against progressively increasing doses of an adenosine receptor antagonist, 8-phenyltheophylline. Figure 8.4 shows the data from Figure 8.3 plotted according to the Lineweaver–Burke double reciprocal plot of the data.

FIGURE 8.3. Dose–response curves for intraportal adenosine infusion in the absence of antagonist (control) and in the presence of stepwise increases in dose (i.


Dose–response curves for intraportal adenosine infusion in the absence of antagonist (control) and in the presence of stepwise increases in dose (i.a.) of 8-phenyltheophylline (dose is expressed in milligrams per kilogram; by use of cumulative (more...)

FIGURE 8.4. Double reciprocal Lineweaver–Burke plot from Figure 8.


Double reciprocal Lineweaver–Burke plot from Figure 8.3. Maximal dilation seen is rated as 1, and if a vasodilation of 86% of the maximal response was seen, it would be entered at 1/(0.86). The y-intercept estimates maximal vasodilation and, converted (more...)

The hepatic capacitance responses can also be analyzed using the nonlinear regression of the rectangular hyperbolic dose–response curve (GraphPad, ISI Software). The Hz50 (nerve frequency stimulation required to produce 50% of the maximal response) in the cat liver was 3.4 Hz. Both adenosine and glucagon produced modulation of sympathetic nerve-induced capacitance responses, although neither compound had significant effects on basal blood volume. Adenosine did not affect the Hz50 but produced a modest suppression of the Rmax. In contrast, glucagon produced a modest decrease in Rmax and an increase in the Hz50 [214].


The concept of the index of contractility (IC) has been described in Chapter 6. The IC is useful for differentiating changes in venous resistance as active or passive responses. Note that in the case of the hepatic venous resistance sites, changes in venous tone result in changes in venous pressure and not in flow. The pressure should therefore be in the numerator of the equation, and vascular tone in the venous system is best represented using calculations of vascular resistance rather than vascular conductance.

The differentiation between resistance and IC is also a useful tool for hemodynamic studies of vascular control of portacaval shunts that form in portal hypertension. The vascular preparation used for this approach uses a chronic portal venous occlusion model using a vascular constrictor that absorbs fluid and gradually swells shut over a 4-week period. With all portal flow going through the shunts into the vena cava, the pressure gradient acting on these blood vessels can be calculated as the mean of upstream (portal venous) and downstream (IVC) pressures and, if other arterial inputs to the portal vein are ligated (inferior mesenteric artery, gastric, and splenic arteries), the only blood flow is through the superior mesenteric artery, which can be readily quantified [142]. In this preparation the spleen is removed. The areas normally supplied by the occluded arteries have anastomotic connections to the superior mesenteric artery. All flow in the shunts is derived from the superior mesenteric artery.

The IC for portacaval shunts can be calculated in the same manner as done for the hepatic venous resistance sites. Shunt resistance is plotted against 1/distending pressure3. Because R is linearly related to 1/Pd3 and the intercept passes through zero, the IC can be calculated accurately from a single data point. The advantage that the IC calculation offers is that IC changes only in response to active stimuli, whereas calculated changes in resistance incorporate both active and passive responses. This is especially important in considering the effect of drugs used to treat portal hypertension. The one point determination of IC can be validated by demonstrating that IC does not change passively when blood flow (pressure) is changed passively. This type of portacaval surgical preparation can also be done in rats [279].

In the liver, a large active venoconstriction will result in an increased upstream venous pressure which, in turn, will act as a distending pressure on the compliant venous resistance sites, thereby counteracting the active constriction. The vasoconstrictor response to doses of norepinephrine demonstrates the difference in impression provided by the different indices. In response to an intraportal infusion of 1.25 μg/kg/min of norepinephrine, the IC of the portal resistance vessels rose by 89%, whereas the resistance increased by only 26% because the distending pressure had also increased by 14% [143].


For pharmacodynamic studies, accurate dose–response relationships can be obtained by measurements of blood flow in the artery, the inflow and outflow blood pressures, and access to an intra-arterial infusion site (preferably by administration into a side branch such as is possible in the superior mesenteric artery preparation or the hepatic arterial preparation) [184] (Figure 8.5).

FIGURE 8.5. Preparation used to study pharmacological intervention with hepatic arterial buffer response.


Preparation used to study pharmacological intervention with hepatic arterial buffer response. Portal flow to liver is made equal to superior mesenteric arterial flow by removal of the spleen, occlusion of the gastroduodenal artery, inferior mesenteric (more...)

When studying physiological vascular responses, attention must be paid to the biological preparation and related assumptions. For example, many studies attempt to provide data implying regional vascular resistance responses through studies of isolated aorta or other large vessels, which are well recognized to serve a function of conducting blood at low resistance rather than serving as resistance vessels regulating regional blood supply. Adenosine is more active on the small resistance vessels and less on the large conducting vessels, whereas nitric oxide has a greater impact on the larger vessels. Greenway and Stark [122] concluded that vascular data from isolated perfused liver preparations cannot be extrapolated to the intact liver. Even studies carried out in situ must avoid artificial perfusion of the arterial bed. Folkow [80] first reported that a pump inserted into an arterial long-circuit in the hind-limb preparation resulted in significant dilation of the vascular bed, and even minor manipulation of the arterial blood resulted in decreased vascular resistance and reduced reactivity of the vessels. These conclusions have been confirmed and extended to the intestine [73,156] and liver [117]. The response of vascular beds to stimuli, including sympathetic nerve stimulation, vasoactive agents, and myogenic autoregulation, has been shown to be significantly altered in the presence of arterial long-circuits [73,102,117,135]. Whatever substance(s) is released from the manipulated blood appears to be completely cleared during one passage through the lungs because arterial vascular responses appear unaltered in the presence of a venous long-circuit.


The splanchnic vascular interactions are too complex to allow pharmacological responses to be accurately determined using bolus injections of drugs. The hepatic arterial buffer response is a powerful regulator of hepatic circulation. In a situation where portal blood flow increases, either as a result of a normal physiological response or in response to a drug, the increase in portal flow to the liver will activate the buffer response. The competitive effects of the direct vasodilator effect on the hepatic artery and the indirect effect through the change in portal blood flow can result in the hepatic artery showing vasoconstriction to intravenously administered vasodilator drugs [208] (Figure 8.6). When these same drugs are administered directly to the hepatic artery, they demonstrate vasodilator properties typical of other arteries.

FIGURE 8.6. Responses in one cat to intravenous isoproterenol infusion showing the change in superior mesenteric arterial conductance (SMAC) and hepatic arterial conductance (HAC) expressed as a percentage of the maximal vasodilator responses seen with intra-arterial isoproterenol infusions for each artery.


Responses in one cat to intravenous isoproterenol infusion showing the change in superior mesenteric arterial conductance (SMAC) and hepatic arterial conductance (HAC) expressed as a percentage of the maximal vasodilator responses seen with intra-arterial (more...)

Copyright © 2010 by Morgan & Claypool Life Sciences.
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