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## Clearance (medicine)In medicine, the ## Additional recommended knowledge
## DefinitionWhen referring to the function of the kidney, clearance 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 considered to be the 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 (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 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] (in the USA often [mg/mL])
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. ## Derivation of equationEquation where: - Δ
*t*is a period of time - Δ
*m*_{body}the change in mass of the toxin in the body during Δ*t* - 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 (Δ**m*) during some time Δ*t*is equal to the toxin intake plus the toxin generation minus the toxin removal.
Since and Equation A1 can be re-written as: If one lumps the If one applies the limit one obtains a differential equation: Using the chain rule this can be re-written as: If one assumes that the volume change is not significant, i.e. , the result is Equation ## Solution to the differential equationThe general solution of the above differential equation (
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
## Steady-state solutionThe solution to the above differential equation (
The above equation (
The above equation ( ## Measurement of renal clearanceRenal 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 (
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 hours])
- C
_{B}is the plasma concentration [mmol/L] (in the USA often [mg/mL])
## 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**^**Seldin DW (2004). "The development of the clearance concept".*J. Nephrol.***17**(1): 166-71. PMID 15151274. Available at: http://www.sin-italy.org/jnonline/Vol17n1/166.html. Accessed on: Sept 2, 2007.**^**Babb AL, Popovich RP, Christopher TG, Scribner BH (1971). "The genesis of the square meter-hour hypothesis".*Transactions - American Society for Artificial Internal Organs***17**: 81-91. PMID 5158139.**^**Gotch FA (1998). "The current place of urea kinetic modelling with respect to different dialysis modalities".*Nephrol. Dial. Transplant.***13 Suppl 6**: 10-4. PMID 9719197. Full Text**^**Gotch FA, Sargent JA, Keen ML (2000). "Whither goest Kt/V?".*Kidney Int. Suppl.***76**: S3-18. PMID 10936795.
Categories: Pharmacokinetics | Pharmacology |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Clearance_(medicine)". A list of authors is available in Wikipedia. |