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Clearance (pharmacology)

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Pharmacokinetic measurement

Inpharmacology,clearance ( $Cl_{\text{tot}}$ ) is apharmacokinetic parameter representing theefficiency of drug elimination. This is the rate of elimination of a substance divided by its concentration.^[1] The parameter also indicates the theoretical volume ofplasma from which a substance would be completely removed per unit time. Usually, clearance is measured in L/h or mL/min.^[2]Excretion, on the other hand, is a measurement of the amount of a substance removed from the body per unit time (e.g., mg/min, μg/min, etc.). While clearance and excretion of a substance are related, they are not the same thing. The concept of clearance was described byThomas Addis, a graduate of theUniversity of Edinburgh Medical School.

Substances in the body can be cleared by various organs, including the kidneys, liver, lungs, etc. Thus, total body clearance is equal to the sum clearance of the substance by each organ (e.g., renal clearance + hepatic clearance + pulmonary clearance = total body clearance). For many drugs, however, clearance is solely a function of renal excretion. In these cases, clearance is almost synonymous withrenal clearance orrenal plasma clearance. Each substance has a specific clearance that depends on how the substance ishandled by the nephron. Clearance is a function of 1)glomerular filtration, 2) secretion from theperitubular capillaries to thenephron, and 3) reabsorption from thenephron back to theperitubular capillaries. Clearance is variable inzero-order kinetics because a constant amount of the drug is eliminated per unit time, but it is constant infirst-order kinetics, because the amount of drug eliminated per unit time changes with the concentration of drug in the blood.^[3]^[4]

Clearance can refer to the volume of plasma from which the substance is removed (i.e.,cleared) per unit time or, in some cases, inter-compartmental clearances can be discussed when referring to redistribution between body compartments such as plasma, muscle, and fat.^[2]

Definition

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Diagram showing the basic physiologic mechanisms of the kidney

The clearance of a substance is the volume of plasma that contains the same amount of the substance as has been removed from the plasma per unit time.^[5]^: 228

When referring to the function of thekidney, clearance is considered to be theamount of liquid filtered out of the blood that gets processed by thekidneys orthe amount of blood cleaned per time because it has the units of avolumetric flow rate [volume per unittime ]. However, it does not refer to a real value; "the kidney does not completely remove a substance from the total renal plasma flow."^[6] From amass transfer perspective^[7] andphysiologically, volumetric blood flow (to the dialysis machine and/or kidney) is only one of several factors that determine blood concentration and removal of a substance from the body. Other factors include themass transfer coefficient, dialysate flow and dialysate recirculation flow for hemodialysis, and theglomerular filtration rate and thetubular reabsorption rate, for the kidney. A physiologic interpretation of clearance (at steady-state) is that clearance isa ratio of the mass generation and blood (orplasma) concentration.

Its definition follows from thedifferential equation that describesexponential decay and is used to model kidney function andhemodialysis machine function:

V{\frac {dC}{dt}}=-K\cdot C+{\dot {m}}

Where:

${\dot {m}}$ is the mass generation rate of the substance - assumed to be a constant, i.e. not a function of time (equal to zero for exogenous (foreign) substances/drugs) [mmol/min] or [mol/s]
t is dialysis time or time since injection of the substance/drug [min] or [s]
V is thevolume of distribution or totalbody water [L] or [m³]
K is the clearance [mL/min] or [m³/s]
C is the concentration [mmol/L] or [mol/m³] (in the United States often [mg/mL])

From the above definitions it follows that ${\frac {dC}{dt}}$ is the firstderivative of concentration with respect to time, i.e. the change in concentration with time.

It is derived from a mass balance.

Clearance of a substance is sometimes expressed as the inverse of thetime constant that describes its removal rate from the body divided by its volume of distribution (or total body water).

In steady-state, it is defined as the mass generation rate of a substance (which equals the mass removal rate) divided by itsconcentration in theblood.

Clearance, half-life and volume of distribution

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There is an important relationship between clearance, elimination half-life and distribution volume.The elimination rate constant of a drug $K_{\text{el}}$ is equivalent to total clearance divided by the distribution volume

$K_{\text{el}}={\dfrac {Cl_{\text{tot}}}{V_{\text{d}}}}$

(note the usage of Cl and not Κ, not to confuse with $K_{\text{el}}$ ). But $K_{\text{el}}$ is also equivalent to $\ln 2$ divided by elimination rate half-life $t_{1/2}$ , $K_{\text{el}}={\dfrac {\ln 2}{t_{1/2}}}$ . Thus, $Cl_{\text{tot}}={\dfrac {\ln 2\cdot V_{\text{d}}}{t_{1/2}}}$ . This means, for example, that an increase in total clearance results in a decrease in elimination rate half-life, provided distribution volume is constant.^[8]

Effect of plasma protein binding

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For substances that exhibit substantialplasma protein binding, clearance is generally dependent on the total concentration (free + protein-bound) and not the free concentration.^[9]

Most plasma substances have primarily their free concentrations regulated, which thus remains the same, so extensive protein binding increases total plasma concentration (free + protein-bound). This decreases clearance compared to what would have been the case if the substance did not bind to protein.^[9] However, the mass removal rate is the same,^[9] because it depends only on concentration of free substance, and is independent on plasma protein binding, even with the fact that plasma proteins increase in concentration in the distalrenal glomerulus as plasma is filtered into Bowman's capsule, because the relative increases in concentrations of substance-protein and non-occupied protein are equal and therefore give no net binding or dissociation of substances from plasma proteins, thus giving a constant plasma concentration of free substance throughout the glomerulus, which also would have been the case without any plasma protein binding.

In other sites than the kidneys, however, where clearance is made bymembrane transport proteins rather than filtration, extensive plasma protein binding may increase clearance by keeping concentration of free substance fairly constant throughout the capillary bed, inhibiting a decrease in clearance caused by decreased concentration of free substance through the capillary.

Derivation of equation

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Equation1 is derived from amass balance:

\Delta m_{\text{body}}=(-{\dot {m}}_{\text{out}}+{\dot {m}}_{\text{in}}+{\dot {m}}_{\text{gen.}})\Delta t

where:

$\Delta t$ is a period of time
$\Delta m_{\text{body}}$ the change in mass of the toxin in the body during $\Delta t$
${\dot {m}}_{\text{in}}$ is the toxin intake rate
${\dot {m}}_{\text{out}}$ is the toxin removal rate
${\dot {m}}_{\text{gen.}}$ is the toxin generation rate

In words, the above equation states:

The change in the mass of a toxin within the body ( $\Delta m$ ) during some time $\Delta t$ is equal to the toxin intake plus the toxin generation minus the toxin removal.

Since

m_{\text{body}}=C\cdot V

and

{\dot {m}}_{\text{out}}=K\cdot C

Equation A1 can be rewritten as:

\Delta (C\cdot V)=\left(-K\cdot C+{\dot {m}}_{\text{in}}+{\dot {m}}_{\text{gen.}}\right)\Delta t

If one lumps thein andgen. terms together, i.e. ${\dot {m}}={\dot {m}}_{\text{in}}+{\dot {m}}_{\text{gen.}}$ and divides by $\Delta t$ the result is adifference equation:

{\frac {\Delta (C\cdot V)}{\Delta t}}=-K\cdot C+{\dot {m}}

If one applies thelimit $\Delta t\to 0$ one obtains a differential equation:

{\frac {d(C\cdot V)}{dt}}=-K\cdot C+{\dot {m}}

Using theproduct rule this can be rewritten as:

C{\frac {dV}{dt}}+V{\frac {dC}{dt}}=-K\cdot C+{\dot {m}}

If one assumes that the volume change is not significant, i.e. $C{\frac {dV}{dt}}=0$ , the result is Equation1:

Solution to the differential equation

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The general solution of the above differential equation (1) is:^[10]^[11]

C={\frac {\dot {m}}{K}}+\left(C_{o}-{\frac {\dot {m}}{K}}\right)e^{-{\frac {K\cdot t}{V}}}

Where:

C_o is the concentration at the beginning of dialysisor the initial concentration of the substance/drug (after it has distributed) [mmol/L] or [mol/m³]
e is the base of thenatural logarithm

Steady-state solution

[edit]

The solution to the above differential equation (9) at time infinity (steady state) is:

C_{\infty }={\frac {\dot {m}}{K}}

10a

The above equation (10a) can be rewritten as:

K={\frac {\dot {m}}{C_{\infty }}}

10b

The above equation (10b) makes clear the relationship between mass removal andclearance. It states that (with a constant mass generation) the concentration and clearance varyinversely with one another. If applied to creatinine (i.e.creatinine clearance), it follows from the equation that if theserum creatinine doubles the clearance halves and that if the serum creatinine quadruples the clearance is quartered.

Measurement of renal clearance

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Renal clearance can be measured with a timed collection ofurine and an analysis of its composition with the aid of the following equation (which follows directly from the derivation of (10b)):

K={\frac {C_{U}\cdot Q}{C_{B}}}

Where:

K is the clearance [mL/min]
C_U is the urine concentration [mmol/L] (in the USA often [mg/mL])
Q is the urine flow (volume/time) [mL/min] (often [mL/24 h])
C_B is the plasma concentration [mmol/L] (in the USA often [mg/mL])

When the substance "C" is creatinine, an endogenous chemical that is excreted only by filtration, the clearance is an approximation of theglomerular filtration rate.Inulin clearance is less commonly used to precisely determine glomerular filtration rate.

Note - the above equation (11) is validonly for the steady-state condition. If the substance being cleared isnot at a constant plasma concentration (i.e.not at steady-state)K must be obtained from the (full) solution of the differential equation (9).

References

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^Ma, Guangda (2020)."Non-Linear Elimination"(PDF).clinpharmacol.fmhs.auckland.ac.nz. Retrieved18 September 2023.
^^a ^bRowland M, Tozer TM (2011).Clinical Pharmacokinetics and Pharmacodynamics, Concepts and Applications (4th ed.). Baltimore MD: Lippincott Williams & Wilkins.
^"Pharmacokinetics objectives". Pharmacology2000.com. 2006-12-27. Retrieved2013-05-06.
^Kaplan Step1 Pharmacology 2010, page 14
^Wright, Samson (1972).Samson Wright's applied physiology. Cyril Arthur Keele, Neil Eric (12th ed.). London: English Language Book Society, and Oxford University Press.ISBN 0-19-263321-X.OCLC 396722036.
^Seldin DW (2004)."The development of the clearance concept".Journal of Nephrology.17 (1):166–71.PMID 15151274.
^Babb AL, Popovich RP, Christopher TG, Scribner BH (1971). "The genesis of the square meter-hour hypothesis".Transactions of the American Society for Artificial Internal Organs.17:81–91.PMID 5158139.
^Ritter J, Flower R, Henderson G, Rang H. Rang & Dale's Pharmacology. 8th ed. London. Churchill Livingstone; 2015
^^a ^b ^cWinter ME (2003)."Plasma protein binding".Basic clinical pharmacokinetics (4th ed.). Lippincott Williams & Wilkins. p. 32.ISBN 978-0-7817-4147-7.
^Gotch FA (1998)."The current place of urea kinetic modelling with respect to different dialysis modalities".Nephrology, Dialysis, Transplantation.13 (Suppl 6):10–4.doi:10.1093/ndt/13.suppl_6.10.PMID 9719197.Full Text
^Gotch FA, Sargent JA, Keen ML (August 2000)."Whither goest Kt/V?".Kidney International.76 (Suppl 76): S3-18.doi:10.1046/j.1523-1755.2000.07602.x.PMID 10936795.

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