In medicine, the clearance, also renal clearance or renal plasma clearance (when referring to the function of the kidney), of a substance is 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.

It is commonly and incorrectly believed 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 . 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. The proper 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:

$V\; \backslash frac\{dC\}\{dt\}\; =\; -K\; \backslash cdot\; C\; +\; \backslash dot\{m\}\; \backslash qquad\; (1)$

Where:

• $\backslash dot\{m\}$ is the mass generation rate of the substance - assumed to be a constant, i.e. not a function of time (equal to zero for foreign substances/drugs) or [mol/s
• t is dialysis time or time since injection of the substance/drug or [s
• V is the volume of distribution or total body water or [m³
• K is the clearance or [m³/s
• C is the concentration or USA often [mg/mL" target="_blank" >^*)

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

The solution of the above differential equation (1) is:

$C\; =\; \backslash frac\{\backslash dot\{m\}\}\{K\}\; +\; (C\_\{o\}-\backslash frac\{\backslash dot\{m\}\}\{K\})\; e^\{-\backslash frac\{K\; \backslash cdot\; t\}\{V\}\}\; \backslash qquad\; (2)$

Where:

• C_o is the concentration at the beginning of dialysis or the initial concentration of the substance/drug (after it has distributed) or [mol/m³
• e is the base of the natural logarithm

The solution to the above differential equation (2) at time infinity (steady state) is:

$C\_\{\backslash infty\}\; =\; \backslash frac\; \{\backslash dot\{m\}\}\{K\}\; \backslash qquad\; (3a)$

The above equation (3a) can be re-written as:

$K\; =\; \backslash frac\; \{\backslash dot\{m\}\}\{C\_\{\backslash infty\}\}\; \backslash qquad\; (3b)$

The above equation (3b) 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

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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 (3b)):

$K\; =\; \backslash frac\; \{C\_U\; \backslash cdot\; Q\}\{C\_B\}\; \backslash qquad\; (4)$

Where:

• K is the clearance ^*
• C_U is the urine concentration (in the USA often [mg/mL)
• Q is the urine flow (volume/time) (often [mL/24 hours)
• C_B is the plasma concentration (in the USA often [mg/mL)

Note - the above equation (4) 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 (2).

See also

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• Creatinine clearance
• Kt/V
• Pharmacokinetics
• Renal clearance ratio
• Standardized Kt/V
• Urea reduction ratio

References

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1. Babb AL, Popovich RP, Christopher TG, Scribner BH. The genesis of the square meter-hour hypothesis. Trans Am Soc Artif Intern Organs. 1971;17:81-91. PMID 5158139
2. Gotch FA. The current place of urea kinetic modelling with respect to different dialysis modalities. Nephrol Dial Transplant. 1998;13 Suppl 6:10-4. PMID 9719197 Full Text
3. Gotch FA, Sargent JA, Keen ML. Whither goest Kt/V? Kidney Int Suppl. 2000 Aug;76:S3-18. PMID 10936795

nephrology | pharmacokinetics | pharmacology

Clearance (Medizin)