CLEARANCE

Clearance

• Clearance is a measure of how rapidly the organ(s) of elimination "clear" drug from the plasma.
• Clearance (CL) can be defined as the volume of plasma completely freed of drug per unit of time (e.g., L/h). It is a "virtual" volume that depends on two major factors for any specific organ of clearance:
  • blood (plasma) flow to the organ
  • fraction of drug extracted from the blood (plasma)
• Extraction ratio
  • Extraction ratio (ER) is the fraction of drug removed in a single pass through the organ of elimination. It can be measured in a single organ by sampling drug concentration in the arterial blood into (Cin) and venous blood from (Cout) the organ.

    ER = [Cin - Cout] / Cin

    Thus if the arterial blood contains 15 mg/L of drug "A" and venous blood from the organ contains 9 mg/L, the ER is (15-9)/15 = 6/15 = 0.4.

  • In the preceding example, an ER of 0.4 means that 40% of the drug in the plasma is removed as it passes through the organ.
  • Extraction ratios for drugs in various organs can range from 0 to 1.0 and may vary depending on the functional capacity of the organ and whether or not the drug concentration is in the "first-order" range of concentrations.
  • Disease conditions and other drugs can change the ER of a drug
  • Extraction ratios can also vary with blood flow if it causes the capacity of the organ to be exceeded.
• Blood flow (often symbolized by Q with a dot on top, but not in these notes because of limitations in the formatting language, html) can be expressed as mL/min, L/h, etc.
  • If an organ of elimination is capable of removing all drug in a single pass, i.e., ER = 1.0, then changes in blood flow to the organ can be very important in determining the elimination rate because blood flow is the rate limiting factor.
  • Conversely, if ER is very low, changes in blood flow are less important.
  • Renal blood flow can vary widely. "Renal shut-down" can dramatically slow elimination of a drug as can slowed renal blood flow due to hypovolemic conditions. For this reason, it is common in clinical medicine to administer fluids to keep renal perfusion high to aid in elimination of some drugs.
• Single organ clearance --

  CL = ER * Flow
  [L/h = frcn x L/h]

  Notice that there are no "mass" terms in the final CL formula. It is the "virtual" volume (in liters) of plasma completely cleared of drug per hour in this case. When the ER is 0.5, the concentration in "twice the CL volume" is lowered by 50%.

• Amount eliminated -- So, how does one find the "amount" of drug actually eliminated during a specific time interval from these computations? Awareness of the difference between "amount" and "fraction" is crucial to understanding clinical pharmacokinetics. Be sure to pay attention to which of these is being used in various equations and terms. In general, when a pharmacokineticist speaks of a "rate", one is referring to a fraction/time.
  • One finds the "amount" eliminated at any instant in time (e.g., one minute) by multiplying the average drug concentration in the plasma "during that minute" by the CL.

    Amount eliminated(t) = CL * Cin(t)
    (mg/min = L/min * mg/L)

    where Cin(t) represents the average concentration of drug in the arterial plasma during the time interval denoted by "t".

  • Amount changes: One should note that this "amount" changes constantly as the concentration of drug in the body changes (increasing while amount absorbed is greater than that eliminated and decreasing when it is less)
  • Fraction stays constant What stays constant when a drug is cleared by first order kinetics is the "fraction" eliminated with each pass of plasma through the organ of clearance.
  • Confused? Try clicking here
    
• Whole body clearance is simply the sum of all organ clearances

  CL(body) = CL(renal) + CL(hepatic) + CL(pulmonary) + CL(etc)

• Relationship between CL(body) and Ke
  • Whole body clearance and the elimination rate constant are related, but emphasize different aspects of the same processes.
  • Elimination Rate constant (Ke) is the FRACTION of drug in the body that is eliminated each unit of time, e.g., "fraction per hour".
  • Calculate Ke from CL & Vd: If one knows the Vd of a drug and the CL(body), one can calculate the FRACTION of the drug in the body that is removed per unit time. This is the same fraction as the fraction of "plasma equivalent" that is completely cleared of drug per unit time. This fraction is the Ke.

    Ke = CL(body) / Vd (fraction/hour)

    CL(body) = Ke x Vd (volume/hour)

  • Diagram of the Relationship among ER, Q, CL, Vd, and Ke.
• Questions / practice

More on "Amounts", Extraction ratios, and Clearance

There may be confusion about how one relates extraction ratio and clearance with how much drug is actually eliminated during any specific time interval. It should be noted that if a drug is cleared by first order kinetics and if blood flow to the organ(s) of elimination is constant, then CL and ER are both constant regardless of how much drug there is in the plasma. However, THE ACTUAL AMOUNT OF DRUG ELIMINATED DURING EACH INTERVAL OF AN HOUR OR A MINUTE IS NOT CONSTANT. If the concentration of drug in the plasma is rising, the amount of drug eliminated (e.g., mg/min) is also rising. Vice versa, if the concentration of drug in the plasma is falling (when drug absorbed per min is less than the amount eliminated), then the amount of drug eliminated each successive minute will also decrease.

To find the actual amount of drug eliminated each minute, one must know the average concentration of drug in the arterial blood to the organ of elimination during that minute. One then multiplies that concentration times the CL to find the amount of drug eliminated during that minute.

Amount of drug eliminated in the minute = Average concentration in incoming plasma x CL

(mg per min (t) = average mg/L in (t) x L/min)

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Questions regarding clearance

• Is it possible to talk about the efficiency of an organ's function in terms of its ability to "clear" a drug from the circulation?
• If one had tests to measure the functional capacity of an organ, e.g., kidney, could one establish relationships that would help one make "predictive dose schedules" for certain drugs?
• Assume that the Clearance of a drug by the kidney is 5 liters/hour and that the Vd is 50 liters. What FRACTION of the Vd is completely "cleared" of drug per hour? Could one point to the specific volume of blood that had been freed of drug in the animal?
• Assume the drug concentration at the beginning was 10 mg/L. How much drug would there be in the animal?
• How much drug would there be in the animal at the end of the first hour? ...the second hour?

Answers to Clearance Questions

• Yes, it IS possible to talk about an organ's function in terms of Clearance
• Yes. In fact it is common to use such measures as Creatinine Clearance as an index of the kidney's filtration capacity. Many formulae have been developed to adjust drug dosage, e.g., of aminoglycosides like gentamicin, based on creatinine clearance.
• If CL = 5 L/h and Vd = 50 L, then 5/50 or 1/10th of the body fluid is cleared of drug per hour (0.1/h).
• Given above parameters and an initial concentration of 10 mg/L, then the animal would contain 10 mg/L * 50 L = 500 mg of drug at the beginning.
• If drug is cleared from 5 L/h, then 5 L * 10 mg/L = 50 mg is eliminated in the first hour. Assuming volume loss was negligible, then the new concentration is 450 mg/50 L = 9 mg/L. Thus 50 /500 or 1/10 of the drug was eliminated. (0.1/h)
• If drug is cleared from 5 L/h, then 5 L * 9 mg/L - 45 mg eliminated in the second hour. This is 45/450 = 1/10 of the drug present was eliminated the second hour (0.1/h). At the same time 1/10th of the Vd was "cleared" of drug in the same hour.
• Note that the FRACTION of drug eliminated in each hour was the same as the FRACTION of the Vd that was "cleared" of drug in each hour. However, the actual amount of drug eliminated decreased as the concentration decreased.
• This leads us to a discussion of elimination rate constants and half-life: Ke & t1/2

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