Clearance (pharmacology)

In pharmacology, clearance (${\displaystyle Cl_{\text{tot}}}$) is a pharmacokinetic parameter representing the efficiency of drug elimination. This is the rate of elimination of a substance divided by its concentration.^[1] The parameter also indicates the theoretical volume of plasma 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 by Thomas Addis, 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 + pulmonary 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.^[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]

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

Cuando se hace referencia a la función del riñón , la depuración se considera la cantidad de líquido filtrado de la sangre que es procesada por los riñones o la cantidad de sangre limpiada por unidad de tiempo porque tiene unidades de un caudal volumétrico [ volumen por unidad de tiempo ]. Sin embargo, no se refiere a un valor real; "el riñón no elimina completamente una sustancia del flujo plasmático renal total". ^{[ 6 ]} Desde una perspectiva de transferencia de masa ^{[ 7 ]} y fisiológicamente , el flujo sanguíneo volumétrico (hacia la máquina de diálisis y/o el riñón) es solo uno de varios factores que determinan la concentración sanguínea y la eliminación de una sustancia del cuerpo. Otros factores incluyen el coeficiente de transferencia de masa , el flujo de dializado y el flujo de recirculación del dializado para la hemodiálisis, y la tasa de filtración glomerular y la tasa de reabsorción tubular , para el riñón. Una interpretación fisiológica de la depuración (en estado estacionario) es que la depuración es una relación entre la generación de masa y la concentración sanguínea (o plasmática ) .

Su definición se deriva de la ecuación diferencial que describe el decaimiento exponencial y se utiliza para modelar la función renal y el funcionamiento de la máquina de hemodiálisis :

Dónde:

• ${\displaystyle {\dot {m}}}$es la tasa de generación de masa de la sustancia, que se supone constante, es decir, no es una función del tiempo (igual a cero para sustancias/fármacos exógenos (extraños)) [mmol/min] o [mol/s]
• t es el tiempo de diálisis o el tiempo transcurrido desde la inyección de la sustancia/fármaco [min] o [s].
• V es el volumen de distribución o agua corporal total [L] o [m ³ ].
• K es la depuración [mL/min] o [m ³ /s]
• C es la concentración [mmol/L] o [mol/m ³ ] (en Estados Unidos a menudo [mg/mL])

De las definiciones anteriores se deduce que${\displaystyle {\frac {dC}{dt}}}$es la primera derivada de la concentración con respecto al tiempo, es decir, el cambio en la concentración con el tiempo.

Se deriva de un balance de masas.

La eliminación de una sustancia se expresa a veces como el inverso de la constante de tiempo que describe su tasa de eliminación del organismo, dividido por su volumen de distribución (o agua corporal total).

En estado estacionario, se define como la tasa de generación de masa de una sustancia (que es igual a la tasa de eliminación de masa) dividida por su concentración en la sangre .

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

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

(note the usage of Cl and not Κ, not to confuse with ${\displaystyle K_{\text{el}}}$). But ${\displaystyle K_{\text{el}}}$ is also equivalent to ${\displaystyle \ln 2}$ divided by elimination rate half-life ${\displaystyle t_{1/2}}$, ${\displaystyle K_{\text{el}}={\dfrac {\ln 2}{t_{1/2}}}}$. Thus, ${\displaystyle Cl_{\text{tot}}={\dfrac {\ln 2\cdot V_{\text{d}}}{t_{1/2}}}}$ . 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]

For substances that exhibit substantial plasma 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 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.

Equation 1 is derived from a mass balance:

where:

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

In words, the above equation states: "The change in the mass of a toxin within the body (${\displaystyle \Delta m}$) during some time ${\displaystyle \Delta t}$ 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. ${\displaystyle {\dot {m}}={\dot {m}}_{\text{in}}+{\dot {m}}_{\text{gen.}}}$ and divides by ${\displaystyle \Delta t}$ the result is a difference equation:

If one applies the limit${\displaystyle \Delta t\to 0}$ 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. ${\displaystyle C{\frac {dV}{dt}}=0}$, the result is Equation 1:

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

Where:

• C_o 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]
• e is the base of the natural logarithm

Renal clearance can be measured with a timed collection of urine 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]
• 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 the glomerular filtration rate. Inulin clearance is less commonly used to precisely determine 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).