In medicine, the clearance is a pharmacokinetic measurement of the
volume of plasma that is completely cleared off of a substance per unit
time. The usual units are ml/min The total body clearance will be equal
to the renal clearance + hepatic clearance + lung clearance. Although for
many drugs the clearance is simply considered as the renal excretion
ability, that is, the rate at which waste substances are cleared from the
blood by the kidney. In these cases clearance 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 re-absorption from the nephron back to the peritubular
capillaries. Clearance is variable in zero-order kinetics because a constant
fraction 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. The concept of clearance was
described by Thomas Addis, a graduate of the University of Edinburgh Medical
School. It can refer to the amount of drug
removed from the whole body per unit time, or in some cases the
inter-compartmental clearances can be discussed referring to redistribution
between body compartments such as plasma, muscle, fat.
Definition When referring to the function of the
kidney, clearance is considered to be the amount of liquid filtered out of the
blood that gets processed by the kidneys 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; "the kidney does not completely remove a
substance from the total renal plasma flow." From a mass transfer perspective
and physiologically, volumetric blood flow 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 is that clearance is a ratio of the mass
generation and blood concentration. Its definition follows from the
differential equation that describes exponential decay 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 [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 distribution or total body water [L] or [m³]
K is the clearance [mL/min] or [m³/s] C is the concentration [mmol/L] or
[mol/m³] 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. In steady-state, it is defined as the
mass generation rate of a substance divided by its concentration in the
blood. Effect of plasma protein binding
For substances that exhibit substantial plasma protein binding, clearance is
generally defined as the total concentration 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. 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 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 balance:
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 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: Solution to the differential equation
The general solution of the above differential equation is:
Where: Co is the concentration at the beginning
of dialysis or the initial concentration of the substance/drug [mmol/L] or
[mol/m³] e is the base of the natural logarithm
= Steady-state solution= The solution to the above differential
equation at time infinity is: The above equation can be rewritten as:
The above equation makes clear the relationship between mass removal and
clearance. It states that the concentration and clearance vary
inversely with one another. If applied to creatinine, 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 and an analysis of its composition with the aid
of the following equation): Where:
K is the clearance [mL/min] CU is the urine concentration [mmol/L]
Q is the urine flow [mL/min] CB is the plasma concentration [mmol/L]
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 is valid only
for the steady-state condition. If the substance being cleared is not at a
constant plasma concentration K must be obtained from the solution of the
differential equation. See also
Table of medication secreted in kidney Sieving coefficient
Creatinine clearance Kt/V
Pharmacokinetics Renal clearance ratio
Standardized Kt/V Urea reduction ratio
References