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| In [[medicine]], the '''clearance''' is a [[pharmacokinetics|pharmacokinetic]] measurement of the renal [[excretion]] ability. Although clearance may also involve other organs than the kidney, it 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 reabsorption from the [[nephron]] back to the [[peritubular capillaries]]. Clearance is constant in [[first-order kinetics]] because a constant fraction of the drug is eliminated per unit time, but it is variable in [[First-order kinetics#Zeroth-order reactions|zero-order kinetics]], because the amount of drug eliminated per unit time changes with the concentration of drug in the blood.<ref>{{cite web|url=http://www.pharmacology2000.com/General/Pharmacokinetics/kinobj1.htm |title=Pharmacokinetics objectives |publisher=Pharmacology2000.com |date=2006-12-27 |accessdate=2013-05-06}}</ref><ref>Kaplan Step1 Pharmacology 2010, page 14</ref>
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| ==Definition==
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| [[File:Physiology of Nephron.png|300px|thumb|right|Diagram showing the basic physiologic mechanisms of the kidney]]
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| 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 [[kidney]]s'' 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."<ref>{{cite journal |author=Seldin DW |title=The development of the clearance concept |journal=J. Nephrol. |volume=17 |issue=1 |pages=166–71 |year=2004 |pmid=15151274}} Available at: [http://www.sin-italy.org/jnonline/Vol17n1/166.html http://www.sin-italy.org/jnonline/Vol17n1/166.html]. Accessed on: Sept 2, 2007.</ref> From a [[mass transfer]] perspective<ref>{{cite journal |author=Babb AL, Popovich RP, Christopher TG, Scribner BH |title=The genesis of the square meter-hour hypothesis |journal=Transactions - American Society for Artificial Internal Organs |volume=17 |issue= |pages=81–91 |year=1971 |pmid=5158139}}</ref> and [[physiology|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 [[nephron|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 [[blood plasma|plasma]]) concentration''.
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| Its definition follows from the [[differential equation]] that describes [[exponential decay]] and is used to model kidney function and [[hemodialysis]] machine function:
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| <math>V \frac{dC}{dt} = -K \cdot C + \dot{m} \qquad (1)</math>
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| Where:
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| *<math>\dot{m}</math> 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]
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| *t is dialysis time or time since injection of the substance/drug [min] or [s]
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| *V is the [[volume of distribution]] or total [[body water]] [L] or [m³]
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| *K is the clearance [mL/min] or [m³/s]
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| *C is the concentration [mmol/L] or [mol/m³] (in the [[USA]] often [mg/mL])
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| From the above definitions it follows that <math>\frac{dC}{dt}</math> is the first [[derivative]] of concentration with respect to time, i.e. the change in concentration with time.
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| It is derived from a mass balance.
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| 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]] (or total [[body water]]).
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| 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]].
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| ==Effect of plasma protein binding==
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| For substances that exhibit substantial [[plasma protein binding]], clearance is generally defined as the total concentration (free + protein-bound) and not the free concentration.<ref name=Winter>Basic clinical pharmacokinetics, [http://books.google.dk/books?id=JIajn4ebtq0C&pg=PA32&lpg=PA32&dq=Plasma+Protein+Binding Page 32: Plasma protein binding] | |
| By Michael E. Winter
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| Edition: 4, illustrated
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| Published by Lippincott Williams & Wilkins, 2003
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| ISBN 0-7817-4147-5, ISBN 978-0-7817-4147-7
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| 511 pages</ref>
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| 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 gives a decreased clearance than what would have been the case with no protein binding.<ref name=Winter/> However, the mass removal rate is the same,<ref name=Winter/> 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 [[Glomerulus|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.
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| In other sites than the kidneys, however, where clearance is made by [[membrane transport protein]]s 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.
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| ==Derivation of equation==
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| Equation ''1'' is derived from a [[mass balance]]:
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| :<math>\Delta m_{body}=(-\dot m_{out}+ \dot m_{in} +\dot m_{gen.})\Delta t \qquad (2)</math>
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| where:
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| *<math>\Delta t</math> is a period of time
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| *<math>\Delta m_{body}</math> the change in mass of the toxin in the body during <math>\Delta t</math>
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| *<math>\dot m_{in}</math> is the toxin intake rate
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| *<math>\dot m_{out}</math> is the toxin removal rate
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| *<math>\dot m_{gen.}</math> is the toxin generation rate
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| In words, the above equation states:
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| :''The change in the mass of a toxin within the body (<math>\Delta m</math>) during some time <math>\Delta t</math> is equal to the toxin intake plus the toxin generation minus the toxin removal.
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| Since
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| :<math>m_{body} = C \cdot V \qquad (3)</math>
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| and
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| :<math>\dot m_{out}=K \cdot C \qquad (4)</math>
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| Equation A1 can be rewritten as:
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| :<math>\Delta (C \cdot V)=(-K \cdot C+ \dot m_{in} +\dot m_{gen.})\Delta t \qquad (5)</math>
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| If one lumps the ''in'' and ''gen.'' terms together, i.e. <math>\dot m=\dot m_{in} +\dot m_{gen.}</math> and divides by <math>\Delta t</math> the result is a [[difference equation]]:
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| :<math>\frac{\Delta (C \cdot V)}{\Delta t} = -K \cdot C + \dot{m} \qquad(6)</math>
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| If one applies the [[limit (mathematics)|limit]] <math>\Delta t \rightarrow 0</math> one obtains a differential equation:
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| :<math>\frac{d(C \cdot V)}{dt}= -K \cdot C + \dot{m} \qquad(7)</math>
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| Using the [[Product Rule]] this can be rewritten as:
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| :<math>C \frac{dV}{dt}+V \frac{dC}{dt} = -K \cdot C + \dot{m} \qquad(8)</math>
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| If one assumes that the volume change is not significant, i.e. <math>C \frac{dV}{dt}=0</math>, the result is Equation ''1'':
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| :<math>V \frac{dC}{dt} = -K \cdot C + \dot{m} \qquad(1)</math>
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| ==Solution to the differential equation==
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| The general solution of the above differential equation (''1'') is:
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| <math>C = \frac{\dot{m}}{K} + (C_{o}-\frac{\dot{m}}{K}) e^{-\frac{K \cdot t}{V}} \qquad (9)</math><ref name=gotch1998>{{cite journal |author=Gotch FA |title=The current place of urea kinetic modelling with respect to different dialysis modalities |journal=Nephrol. Dial. Transplant. |volume=13 Suppl 6 |issue= 90006|pages=10–4 |year=1998 |pmid=9719197 |doi=10.1093/ndt/13.suppl_6.10}} [http://ndt.oxfordjournals.org/cgi/reprint/13/suppl_6/10 Full Text]</ref><ref name=gotch2000>{{cite journal |author=Gotch FA, Sargent JA, Keen ML |title=Whither goest Kt/V? |journal=Kidney Int. Suppl. |volume=76 |issue= |pages=S3–18 |year=2000 |pmid=10936795 |doi=10.1046/j.1523-1755.2000.07602.x}}</ref>
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| Where:
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| *C<sub>o</sub> 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]
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| *[[E (mathematical constant)|e]] is the base of the [[natural logarithm]]
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| ===Steady-state solution===
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| The solution to the above differential equation (''9'') at time infinity (steady state) is:
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| <math> C_{\infty} = \frac {\dot{m}}{K} \qquad (10a)</math>
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| The above equation (''10a'') can be rewritten as:
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| <math> K = \frac {\dot{m}}{C_{\infty}} \qquad (10b)</math>
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| 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 proportional|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.
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| ==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 (''10b'')):
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| <math>K = \frac {C_U \cdot Q}{C_B} \qquad (11)</math>
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| Where:
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| *K is the clearance [mL/min]
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| *C<sub>U</sub> is the urine concentration [mmol/L] (in the USA often [mg/mL])
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| *Q is the urine flow (volume/time) [mL/min] (often [mL/24 hours])
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| *C<sub>B</sub> is the plasma concentration [mmol/L] (in the USA often [mg/mL])
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| 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.
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| '''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'').
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| ==See also==
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| *[[Table of medication secreted in kidney]]
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| *[[Sieving coefficient]]
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| *[[Creatinine clearance]]
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| *[[Kt/V]]
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| *[[Pharmacokinetics]]
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| *[[Renal clearance ratio]]
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| *[[Standardized Kt/V]]
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| *[[Urea reduction ratio]]
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| ==References==
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| {{reflist}}
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| {{renal physiology}}
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| {{Pharmacology}}
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| [[Category:Nephrology]]
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| [[Category:Pharmacokinetics]]
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| [[Category:Pharmacology]]
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| [[de:Clearance (Medizin)]]
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Hi there, I am Sophia. Office supervising is exactly where my main earnings comes from but I've always wanted my own business. She is really fond of caving but she doesn't have the time recently. For many years he's been residing in Alaska and he doesn't strategy on changing it.
Also visit my blog post ... certified psychics (http://brazil.amor-amore.com)