Clearance (medicine)
Encyclopedia
In medicine
, the clearance is a measurement of the renal excretion
ability. Although clearance may also involve other organs than the kidney, it is almost synonymous with renal clearance or renal plasma clearance. Each substance has a specific clearance that depends on its filtration characteristics. Clearance is a function of glomerular filtration, secretion from the peritubular capillaries
to the nephron
, and reabsorption from the nephron
back to the peritubular capillaries
. Clearance
is constant in first-order kinetics because a constant fraction of the drug is eliminated per unit time, but it is variable in zero-order kinetics, because a constant amount of drug is eliminated per unit time.
, clearance is considered to be the amount of liquid filtered out of the blood that gets processed by the kidney
s or the amount of blood cleaned per time because it has the units of a volumetric flow rate
[ volume
/ time
]. However, it does not refer to a real value; "[t]he kidney does not completely remove a substance from the total renal plasma flow." From a mass transfer
perspective and 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
that describes exponential decay and is used to model kidney function and hemodialysis
machine function:
Where:
From the above definitions it follows that
is the first derivative
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
(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 its concentration
in the blood
.
, clearance is generally defined as 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 gives a decreased clearance than what would have been the case with no protein binding. 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 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.
:
where:
In words, the above equation states:
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:
If one applies the limit
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 1:
Where:
The above equation (10a) can be rewritten as:
The above equation (10b) 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.
and an analysis of its composition with the aid of the following equation (which follows directly from the derivation of (10b)):
Where:
When the substance "C" is creatinine, an endogenous chemical that is excreted only by filtration, the calculated clearance is equivalent to the glomerular filtration rate. Inulin
clearance is also used to estimate glomerular filtration rate.
Note - the above equation (11) 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 (9).
Medicine
Medicine is the science and art of healing. It encompasses a variety of health care practices evolved to maintain and restore health by the prevention and treatment of illness....
, the clearance is a measurement of the renal excretion
Excretion
Excretion is the process by which waste products of metabolism and other non-useful materials are eliminated from an organism. 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 leaving the cell...
ability. Although clearance may also involve other organs than the kidney, it is almost synonymous with renal clearance or renal plasma clearance. Each substance has a specific clearance that depends on its filtration characteristics. Clearance is a function of glomerular filtration, secretion from the peritubular capillaries
Peritubular capillaries
In the renal system, peritubular capillaries are tiny blood vessels that travel alongside nephrons allowing reabsorption and secretion between blood and the inner lumen of the nephron....
to the nephron
Nephron
The renal tubule is the portion of the nephron containing the tubular fluid filtered through the glomerulus. After passing through the renal tubule, the filtrate continues to the collecting duct system, which is not part of the nephron....
, and reabsorption from the nephron
Nephron
The renal tubule is the portion of the nephron containing the tubular fluid filtered through the glomerulus. After passing through the renal tubule, the filtrate continues to the collecting duct system, which is not part of the nephron....
back to the peritubular capillaries
Peritubular capillaries
In the renal system, peritubular capillaries are tiny blood vessels that travel alongside nephrons allowing reabsorption and secretion between blood and the inner lumen of the nephron....
. Clearance
Clearance
A clearance can refer to:* in chess, A positional move, where a player moves a piece occupying a certain square away, replacing it with an allied piece that will strengthen the player's position....
is constant in first-order kinetics because a constant fraction of the drug is eliminated per unit time, but it is variable in zero-order kinetics, because a constant amount of drug is eliminated per unit time.
Definition
When referring to the function of the kidneyKidney
The kidneys, organs with several functions, serve essential regulatory roles in most animals, including vertebrates and some invertebrates. They are essential in the urinary system and also serve homeostatic functions such as the regulation of electrolytes, maintenance of acid–base balance, and...
, clearance is considered to be the amount of liquid filtered out of the blood that gets processed by the kidney
Kidney
The kidneys, organs with several functions, serve essential regulatory roles in most animals, including vertebrates and some invertebrates. They are essential in the urinary system and also serve homeostatic functions such as the regulation of electrolytes, maintenance of acid–base balance, and...
s or the amount of blood cleaned per time because it has the units of a volumetric flow rate
Volumetric flow rate
The volumetric flow rate in fluid dynamics and hydrometry, is the volume of fluid which passes through a given surface per unit time...
[ volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....
/ time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
]. However, it does not refer to a real value; "[t]he kidney does not completely remove a substance from the total renal plasma flow." From a mass transfer
Mass transfer
Mass transfer is the net movement of mass from one location, usually meaning a stream, phase, fraction or component, to another. Mass transfer occurs in many processes, such as absorption, evaporation, adsorption, drying, precipitation, membrane filtration, and distillation. Mass transfer is used...
perspective and physiologically
Physiology
Physiology is the science of the function of living systems. This includes how organisms, organ systems, organs, cells, and bio-molecules carry out the chemical or physical functions that exist in a living system. The highest honor awarded in physiology is the Nobel Prize in Physiology or...
, 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
Nephron
The renal tubule is the portion of the nephron containing the tubular fluid filtered through the glomerulus. After passing through the renal tubule, the filtrate continues to the collecting duct system, which is not part of the nephron....
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
Blood plasma
Blood plasma is the straw-colored liquid component of blood in which the blood cells in whole blood are normally suspended. It makes up about 55% of the total blood volume. It is the intravascular fluid part of extracellular fluid...
) concentration.
Its definition follows from the differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
that describes exponential decay and is used to model kidney function and hemodialysis
Hemodialysis
In medicine, hemodialysis is a method for removing waste products such as creatinine and urea, as well as free water from the blood when the kidneys are in renal failure. Hemodialysis is one of three renal replacement therapies .Hemodialysis can be an outpatient or inpatient therapy...
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) [mmol/min] or [mol/s]- t is dialysis time or time since injection of the substance/drug [min] or [s]
- V is the volume of distributionVolume of distributionThe volume of distribution , also known as apparent volume of distribution, is a pharmacological term used to quantify the distribution of a medication between plasma and the rest of the body after oral or parenteral dosing...
or total body waterBody waterIn medicine, body water is the water content of the human body. A significant fraction of the human body is water. Arthur Guyton 's Textbook of Medical Physiology states that "the total amount of water in a man of average weight is approximately 40 litres, averaging 57 percent of his total body...
[L] or [m³] - K is the clearance [mL/min] or [m³/s]
- C is the concentration [mmol/L] or [mol/m³] (in the USA often [mg/mL])
From the above definitions it follows that
is the first derivativeDerivative
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...
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
Time constant
In physics and engineering, the time constant, usually denoted by the Greek letter \tau , is the risetime characterizing the response to a time-varying input of a first-order, linear time-invariant system.Concretely, a first-order LTI system is a system that can be modeled by a single first order...
that describes its removal rate from the body divided by its volume of distribution
Volume of distribution
The volume of distribution , also known as apparent volume of distribution, is a pharmacological term used to quantify the distribution of a medication between plasma and the rest of the body after oral or parenteral dosing...
(or total body water
Body water
In medicine, body water is the water content of the human body. A significant fraction of the human body is water. Arthur Guyton 's Textbook of Medical Physiology states that "the total amount of water in a man of average weight is approximately 40 litres, averaging 57 percent of his total body...
).
In steady-state, it is defined as the mass generation rate of a substance (which equals the mass removal rate) divided by its concentration
Concentration
In chemistry, concentration is defined as the abundance of a constituent divided by the total volume of a mixture. Four types can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration...
in the blood
Blood
Blood is a specialized bodily fluid in animals that delivers necessary substances such as nutrients and oxygen to the cells and transports metabolic waste products away from those same cells....
.
Effect of plasma protein binding
For substances that exhibit substantial plasma protein bindingPlasma protein binding
A drug's efficiency may be affected by the degree to which it binds to the proteins within blood plasma. The less bound a drug is, the more efficiently it can traverse cell membranes or diffuse. Common blood proteins that drugs bind to are human serum albumin, lipoprotein, glycoprotein, α, β‚ and γ...
, clearance is generally defined as 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 gives a decreased clearance than what would have been the case with no protein binding. 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
Glomerulus
A glomerulus is a capillary tuft that is involved in the first step of filtering blood to form urine.A glomerulus is surrounded by Bowman's capsule, the beginning component of nephrons in the vertebrate kidney. A glomerulus receives its blood supply from an afferent arteriole of the renal...
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 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
Equation 1 is derived from a mass balanceMass balance
A mass 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 been unknown, or difficult to measure without this technique...
:
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:If one applies the limit
Limit (mathematics)
In mathematics, the concept of a "limit" is used to describe the value that a function or sequence "approaches" as the input or index approaches some value. The concept of limit allows mathematicians to define a new point from a Cauchy sequence of previously defined points within a complete metric...
one obtains a differential equation:Using the Product Rule
Product rule
In calculus, the product rule is a formula used to find the derivatives of products of two or more functions. It may be stated thus:'=f'\cdot g+f\cdot g' \,\! or in the Leibniz notation thus:...
this can be rewritten as:
If one assumes that the volume change is not significant, i.e.
, the result is Equation 1:Solution to the differential equation
The general solution of the above differential equation (1) is:Where:
- Co is the concentration at the beginning of dialysis or the initial concentration of the substance/drug (after it has distributed) [mmol/L] or [mol/m³]
- eE (mathematical constant)The mathematical constant ' is the unique real number such that the value of the derivative of the function at the point is equal to 1. The function so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base...
is the base of the natural logarithmNatural logarithmThe natural logarithm is the logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828...
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 (10b) 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 urineUrine
Urine is a typically sterile liquid by-product of the body that is secreted by the kidneys through a process called urination and excreted through the urethra. Cellular metabolism generates numerous by-products, many rich in nitrogen, that require elimination from the bloodstream...
and an analysis of its composition with the aid of the following equation (which follows directly from the derivation of (10b)):
Where:
- K is the clearance [mL/min]
- CU is the urine concentration [mmol/L] (in the USA often [mg/mL])
- Q is the urine flow (volume/time) [mL/min] (often [mL/24 hours])
- CB 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 calculated clearance is equivalent to the glomerular filtration rate. Inulin
Inulin
Inulins are a group of naturally occurring polysaccharides produced by many types of plants. They belong to a class of fibers known as fructans. Inulin is used by some plants as a means of storing energy and is typically found in roots or rhizomes...
clearance is also used to estimate glomerular filtration rate.
Note - the above equation (11) 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 (9).
See also
- Table of medication secreted in kidney
- Sieving coefficient
- Creatinine clearance
- Kt/VKt/VIn medicine, Kt/V is a number used to quantify hemodialysis and peritoneal dialysis treatment adequacy.*K - dialyzer clearance of urea*t - dialysis time*V - volume of distribution of urea, approximately equal to patient's total body water...
- PharmacokineticsPharmacokineticsPharmacokinetics, sometimes abbreviated as PK, is a branch of pharmacology dedicated to the determination of the fate of substances administered externally to a living organism...
- Renal clearance ratio
- Standardized Kt/VStandardized Kt/VStandardized Kt/V, also std Kt/V, is a way of measuring dialysis adequacy. It was developed by Frank Gotch and is used in the USA to measure dialysis. Despite the name, it is quite different from Kt/V...
- Urea reduction ratio