PHAR 4634 - Chapter 17 Page 4

## Hepatic clearance

The systemic clearance, CL, is a measure of the efficiency with which a drug is irreversibly removed from the body. Under first order conditions, clearance can be calculated as:-

Single dose

Equation XVII-1 Clearance after a Single Dose

During multiple dose regimens, clearance can be calculated under steady state conditions as:-

Equation XVII-2 Clearance at Steady State

where Cpss is the steady state plasma concentration and Cp is the average plasma concentration during the dosing interval .

### Venous equilibration model equation

The above equations apply to the overall clearance of drug from the body. We can also consider the organ clearance as it may be measured in an isolated organ system. Here we would have for example an isolated liver, perfused with blood containing the drug of interest. By measuring the drug concentration in the blood entering and leaving the organ at steady state, the organ clearance can be measured for the drug.

Diagram XVII-1 Blood Flow through the Liver

where Q is the blood flow rate to the organ, Ca is the concentration of drug in the blood entering the organ, and Cv is the concentration of drug in the blood leaving the organ. The term E is the steady state extraction ratio. High E values mean high clearance by the liver and thus extensive metabolism.

The sum of the individual organ clearance values are equal to the systemic clearance, CL. For a drug which is eliminated entirely via the liver, the hepatic clearance is equal to the systemic or total body clearance. From the equation above we can see that the organ clearance is a function of the liver blood flow and the extraction ratio of the drug. The liver blood flow is a physiological parameter which may be altered in disease states. The extraction ratio, we shall see shortly is a parameter dependent not only of the condition of the liver but also the drug.

Both the hepatic clearance and the extraction ratio are empirical parameters which can be used as measures of the efficiency of the elimination process. They are dependent on three independent variables:-

i) total hepatic blood flow (Q),

ii) fraction unbound (fu) or the extent of drug binding to blood constituents. This may be saturable with high dose, polar compounds, and

iii) the free intrinsic clearance (CLint) or the rate-limiting step in drug uptake from blood, intracellular transport, metabolism, and where necessary biliary secretion. The free intrinsic clearance may be thought of as the clearance of drug from liver plasma water, devoid of the influence of blood flow or binding. Since a major part of this parameter is metabolism which is typically enzyme mediated this parameter may be saturated at higher doses, for some drugs.

The equation describing hepatic clearance in terms of these parameters using the venous equilibration model can be defined as[1]:-

Equation XVII-3 Clearance

CL = Q * E

With this equation it is possible to look at the influence of free intrinsic clearance, drug binding, and liver blood flow on the overall hepatic clearance of a drug. Drugs can be classified into three types depending on the intrinsic clearance and binding. Flow limited, capacity limited, and others.

### Flow limited drugs

High fu * CLint ( ) value. [fu*CLint >> Q]. For drugs with high total intrinsic clearance the extraction ratio, E, approaches 100%, the hepatic clearance approximates and is dependent of hepatic blood flow. Hepatic clearance is said to be FLOW LIMITED. Also, we can note that the hepatic clearance is not dependent on moderate changes in free intrinsic clearance or binding to blood constituents.

Examples include:- lidocaine, propranolol, morphine.

### Capacity limited drugs

Very low total intrinsic clearance. [fu * CLint << Q]. With drugs having very low intrinsic clearance, hepatic extraction is inefficient and hepatic clearance becomes independent of hepatic blood flow. Now changes in free intrinsic clearance and/or binding to blood constituents becomes very important in determination of the overall hepatic clearance. Hepatic clearance is said to be CAPACITY LIMITED as the intrinsic capacity of the liver controls the drug clearance.

Examples include:- phenytoin, warfarin, and quinidine. For such drugs it is possible that liver disease will cause a decrease in CLint but also an increase in fu. In this case the overall hepatic clearance doesn't reflect just the hepatic metabolic activity but also the drug binding. This is illustrated with tolbutamide. In patients with hepatitis there is an increase in fu but no change in CLint. As a result CL is increased and the elimination half-life decreases. The change in elimination half-life reflects changes in binding and not changes in drug metabolizing activity.

### Other drugs

Between these two extremes. Capacity-limited but binding-insensitive drugs. The three parameters; Q, fu, and CLint are important determinants of drug elimination.

Examples include:- theophylline, antipyrine