In
pharmacology
Pharmacology is a branch of medicine, biology and pharmaceutical sciences concerned with drug or medication action, where a drug may be defined as any artificial, natural, or endogenous (from within the body) molecule which exerts a biochemica ...
, clearance is a
pharmacokinetic measurement of the volume of
plasma from which a substance is completely removed per unit time. Usually, clearance is measured in L/h or mL/min.
The quantity reflects the rate of drug elimination divided by plasma concentration.
Excretion
Excretion is a process in which metabolic waste
is eliminated from an organism. In vertebrates this is primarily carried out by the lungs, kidneys, and skin. This is in contrast with secretion, where the substance may have specific tasks after ...
, 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 by
Thomas Addis
Thomas Addis Jr. (July 27, 1881 – June 4, 1949) was a Scottish physician-scientist from Edinburgh who made important contributions to the understanding of how blood clots work. He was a pioneer in the field of nephrology, the branch of internal ...
, a graduate of the
University 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 + lung clearance = total body clearance). For many drugs, however, clearance is solely a function of renal excretion. In these cases, clearance is almost synonymous with renal clearance or renal plasma clearance. Each substance has a specific clearance that depends on how the substance is ''handled'' by the nephron. Clearance is a function of 1)
glomerular filtration, 2) secretion from the
peritubular capillaries to the
nephron, and 3) reabsorption from the
nephron back to the
peritubular capillaries. Clearance is variable in
zero-order kinetics because a constant amount of the drug is eliminated per unit time, but it is constant in
first-order kinetics, because the amount of drug eliminated per unit time changes with the concentration of drug in the blood.
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.
Definition
When referring to the function of the
kidney
The kidneys are two reddish-brown bean-shaped organs found in vertebrates. They are located on the left and right in the retroperitoneal space, and in adult humans are about in length. They receive blood from the paired renal arteries; blo ...
, clearance is considered to be the ''amount of liquid filtered out of the blood that gets processed by the
kidney
The kidneys are two reddish-brown bean-shaped organs found in vertebrates. They are located on the left and right in the retroperitoneal space, and in adult humans are about in length. They receive blood from the paired renal arteries; blo ...
s'' or ''the amount of blood cleaned per time'' because it has the units of a
volumetric flow rate volume_per_unit_time.html"_;"title="volume.html"_;"title="volume">volume_per_unit_time">volume.html"_;"title="volume">volume_per_unit_time_.html" ;"title="volume">volume_per_unit_time.html" ;"title="volume.html" ;"title="volume">volume per unit time">volume.html" ;"title="volume">volume per unit time ">volume">volume_per_unit_time.html" ;"title="volume.html" ;"title="volume">volume per unit time">volume.html" ;"title="volume">volume per unit time However, it does not refer to a real value; "the kidney does not completely remove a substance from the total renal plasma flow." From a mass transfer perspective and physiology, physiologically, 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 the
mass transfer coefficient, dialysate flow and dialysate recirculation flow for hemodialysis, and the
glomerular filtration rate and the
tubular reabsorption rate, for the kidney. A physiologic interpretation of clearance (at steady-state) is that clearance is ''a ratio of the mass generation and blood (or
plasma) concentration''.
Its definition follows from the
differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, ...
that describes
exponential decay
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and (lambda) is a positive rate ...
and is used to model kidney function and
hemodialysis machine function:
Where:
*
is the mass generation rate of the substance - assumed to be a constant, i.e. not a function of time (equal to zero for foreign substances/drugs)
mol/minor
ol/s* t is dialysis time or time since injection of the substance/drug
inor
* V is the
volume of distribution
In pharmacology, the volume of distribution (VD, also known as apparent volume of distribution, literally, ''volume of dilution'') is the theoretical volume that would be necessary to contain the total amount of an administered drug at the same c ...
or total
body water
In physiology, body water is the water content of an animal body that is contained in the tissues, the blood, the bones and elsewhere. The percentages of body water contained in various fluid compartments add up to total body water (TBW). This ...
or
3">3* K is the clearance
L/minor
3/s">3/s* C is the concentration
mol/Lor
3">ol/m3(in the United States often
g/mL
From the above definitions it follows that
is the first
derivative
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. ...
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 the
time constant that describes its removal rate from the body divided by its
volume of distribution
In pharmacology, the volume of distribution (VD, also known as apparent volume of distribution, literally, ''volume of dilution'') is the theoretical volume that would be necessary to contain the total amount of an administered drug at the same c ...
(or total
body water
In physiology, body water is the water content of an animal body that is contained in the tissues, the blood, the bones and elsewhere. The percentages of body water contained in various fluid compartments add up to total body water (TBW). This ...
).
In steady-state, it is defined as the mass generation rate of a substance (which equals the mass removal rate) divided by its
concentration
In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', '' molar concentration'', ''number concentration'', ...
in the
blood
Blood is a body fluid in the circulatory system of humans and other vertebrates that delivers necessary substances such as nutrients and oxygen to the cells, and transports metabolic waste products away from those same cells. Blood in the cir ...
.
Clearance, half-life and distribution volume
There is an important relationship between clearance, elimination half-life and distribution volume.
The elimination rate constant of a drug
is equivalent to total clearance divided by the distribution volume
(note the usage of Cl and not Κ, not to confuse with
). But
is also equivalent to
divided by elimination rate half-life
,
. Thus,
. This means, for example, that an increase in total clearance results in a decrease in elimination rate half-life, provided distribution volume is constant. Derivation of these equations can be found in e.g. Rang and Dale's Pharmacology
[Ritter J, Flower R, Henderson G, Rang H. Rang & Dale's Pharmacology. 8th ed. London. Churchill Livingstone; 2015]
Effect of plasma protein binding
For substances that exhibit substantial
plasma protein binding, clearance is generally dependent on the total concentration (free + protein-bound) and not the free concentration.
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.
[ However, the mass removal rate is the same,][ 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 distal renal 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 by ]membrane transport protein
A membrane transport protein (or simply transporter) is a membrane protein involved in the movement of ions, small molecules, and macromolecules, such as another protein, across a biological membrane. Transport proteins are integral transmemb ...
s 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
Equation is derived from a mass balance
In physics, a mass balance, also called a material balance, is an application of conservation of mass to the analysis of physical systems. By accounting for material entering and leaving a system, mass flows can be identified which might have b ...
:
where:
* is a period of time
* the change in mass of the toxin in the body during
* is the toxin intake rate
* is the toxin removal rate
* is the toxin generation rate
In words, the above equation states:
:''The change in the mass of a toxin within the body () during some time is equal to the toxin intake plus the toxin generation minus the toxin removal.
Since
and
Equation A1 can be rewritten as:
If one lumps the ''in'' and ''gen.'' terms together, i.e. and divides by the result is a difference equation
In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter ...
:
If one applies the limit
Limit or Limits may refer to:
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* ''Limit'' (film), a South Korean film
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* "Limit" (song), a 2016 single by Luna Sea
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one obtains a differential equation:
Using the Product Rule this can be rewritten as:
If one assumes that the volume change is not significant, i.e. , the result is Equation :
Solution to the differential equation
The general solution of the above differential equation (1) is:[Full Text]
/ref>
Where:
* ''C''o is the concentration at the beginning of dialysis ''or'' the initial concentration of the substance/drug (after it has distributed) mol/Lor 3">ol/m3* ''e'' is the base of the natural logarithm
Steady-state solution
The solution to the above differential equation (''9'') at time infinity (steady state) is:
The above equation (''10a'') can be rewritten as:
The above equation () makes clear the relationship between mass removal and ''clearance''. It states that (with a constant mass generation) the concentration and clearance vary inversely with one another. If applied to creatinine (i.e. creatinine clearance), it follows from the equation that if the serum creatinine doubles the clearance halves and that if the serum creatinine quadruples the clearance is quartered.
Measurement of renal clearance
Renal clearance can be measured with a timed collection of urine
Urine is a liquid by-product of metabolism in humans and in many other animals. Urine flows from the kidneys through the ureters to the urinary bladder. Urination results in urine being excreted from the body through the urethra.
Cellul ...
and an analysis of its composition with the aid of the following equation (which follows directly from the derivation of ()):
Where:
* K is the clearance L/min* CU is the urine concentration mol/L(in the USA often g/mL
* Q is the urine flow (volume/time) L/min(often L/24 h
* CB is the plasma concentration mol/L(in the USA often g/mL
When the substance "C" is creatinine, an endogenous chemical that is excreted only by filtration, the clearance is an approximation of the glomerular filtration rate. Inulin clearance is less commonly used to precisely determine glomerular filtration rate.
Note - the above equation () is valid ''only'' for the steady-state condition. If the substance being cleared is ''not'' at a constant plasma concentration (i.e. ''not'' at steady-state) ''K'' must be obtained from the (full) solution of the differential equation ().
See also
References
Further reading
*
{{Pharmacology
Nephrology
Pharmacokinetic metrics
Temporal rates
de:Clearance (Medizin)