Clearance (medicine)

Jump to: navigation, search

WikiDoc Resources for Clearance (medicine)

Articles

Most recent articles on Clearance (medicine)

Most cited articles on Clearance (medicine)

Review articles on Clearance (medicine)

Articles on Clearance (medicine) in N Eng J Med, Lancet, BMJ

Media

Powerpoint slides on Clearance (medicine)

Images of Clearance (medicine)

Photos of Clearance (medicine)

Podcasts & MP3s on Clearance (medicine)

Videos on Clearance (medicine)

Evidence Based Medicine

Cochrane Collaboration on Clearance (medicine)

Bandolier on Clearance (medicine)

TRIP on Clearance (medicine)

Clinical Trials

Ongoing Trials on Clearance (medicine) at Clinical Trials.gov

Trial results on Clearance (medicine)

Clinical Trials on Clearance (medicine) at Google

Guidelines / Policies / Govt

US National Guidelines Clearinghouse on Clearance (medicine)

NICE Guidance on Clearance (medicine)

NHS PRODIGY Guidance

FDA on Clearance (medicine)

CDC on Clearance (medicine)

Books

Books on Clearance (medicine)

News

Clearance (medicine) in the news

Be alerted to news on Clearance (medicine)

News trends on Clearance (medicine)

Commentary

Blogs on Clearance (medicine)

Definitions

Definitions of Clearance (medicine)

Patient Resources / Community

Patient resources on Clearance (medicine)

Discussion groups on Clearance (medicine)

Patient Handouts on Clearance (medicine)

Directions to Hospitals Treating Clearance (medicine)

Risk calculators and risk factors for Clearance (medicine)

Healthcare Provider Resources

Symptoms of Clearance (medicine)

Causes & Risk Factors for Clearance (medicine)

Diagnostic studies for Clearance (medicine)

Treatment of Clearance (medicine)

Continuing Medical Education (CME)

CME Programs on Clearance (medicine)

International

Clearance (medicine) en Espanol

Clearance (medicine) en Francais

Business

Clearance (medicine) in the Marketplace

Patents on Clearance (medicine)

Experimental / Informatics

List of terms related to Clearance (medicine)


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 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; "[t]he kidney does not completely remove a substance from the total renal plasma flow."[1] From a mass transfer perspective[2] 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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): V \frac{dC}{dt} = -K \cdot C + \dot{m} \qquad (1)

Where:

  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \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) [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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \frac{dC}{dt} 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 equation

Equation 1 is derived from a mass balance:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \Delta m_{body}=(-\dot m_{out}+ \dot m_{in} +\dot m_{gen.})\Delta t \qquad (2)

where:

  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \Delta t is a period of time
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \Delta m_{body} the change in mass of the toxin in the body during Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \Delta t
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \dot m_{in} is the toxin intake rate
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \dot m_{out} is the toxin removal rate
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \dot m_{gen.} is the toxin generation rate

In words, the above equation states:

The change in the mass of a toxin within the body (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \Delta m ) during some time Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \Delta t is equal to the toxin intake plus the toxin generation minus the toxin removal.

Since

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): m_{body} = C \cdot V \qquad (3)

and

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \dot m_{out}=K \cdot C \qquad (4)

Equation A1 can be re-written as:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \Delta (C \cdot V)=(-K \cdot C+ \dot m_{in} +\dot m_{gen.})\Delta t \qquad (5)

If one lumps the in and gen. terms together, i.e. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \dot m=\dot m_{in} +\dot m_{gen.} and divides by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \Delta t the result is a difference equation:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \frac{\Delta (C \cdot V)}{\Delta t} = -K \cdot C + \dot{m} \qquad(6)

If one applies the limit Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \Delta t \rightarrow 0 one obtains a differential equation:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \frac{d(C \cdot V)}{dt}= -K \cdot C + \dot{m} \qquad(7)

Using the chain rule this can be re-written as:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): C \frac{dV}{dt}+V \frac{dC}{dt} = -K \cdot C + \dot{m} \qquad(8)

If one assumes that the volume change is not significant, i.e. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): C \frac{dV}{dt}=0 , the result is Equation 1:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): V \frac{dC}{dt} = -K \cdot C + \dot{m} \qquad(1)

Solution to the differential equation

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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): C = \frac{\dot{m}}{K} + (C_{o}-\frac{\dot{m}}{K}) e^{-\frac{K \cdot t}{V}} \qquad (9) [3][4]

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]
  • e is the base of the natural logarithm

Steady-state solution

The solution to the above differential equation (9) at time infinity (steady state) is:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): C_{\infty} = \frac {\dot{m}}{K} \qquad (10a)

The above equation (10a) can be re-written as:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): K = \frac {\dot{m}}{C_{\infty}} \qquad (10b)

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 urine and an analysis of its composition with the aid of the following equation (which follows directly from the derivation of (10b)):

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): K = \frac {C_U \cdot Q}{C_B} \qquad (11)

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])

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

References

  1. 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.
  2. 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. 
  3. 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
  4. Gotch FA, Sargent JA, Keen ML (2000). "Whither goest Kt/V?". Kidney Int. Suppl. 76: S3–18. PMID 10936795. 

de:Renale Clearance it:Clearance nl:Klaring (medisch) no:Clearance sv:Clearance



Linked-in.jpg