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Encyclopedia > 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). Medicine on the Web NLM (National Library of Medicine, contains resources for patients and healthcare professionals) Virtual Hospital (digital health sciences library by the University of Iowa) Online Medical Information- medical news, links and resources. ... Human kidneys viewed from behind with spine removed The kidneys are bean-shaped excretory organs in vertebrates. ... In physics and engineering, the time constant, usually denoted by the Greek letter Ï„ (tau), characterizes the frequency response of a first-order, linear time-invariant (LTI) system. ... The volume of distribution (VD) is a pharmacological term used to quantify the distribution of a drug throughout the body after oral or intravenous dosing. ... A significant fraction of the human body is 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. Concentration is a very common concept used in chemistry and related fields. ... Red blood cells (erythrocytes) are present in the blood and help carry oxygen to the rest of the cells in the body Blood is a circulating tissue composed of fluid plasma and cells (red blood cells, white blood cells, platelets). ...

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[1] 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. Human kidneys viewed from behind with spine removed The kidneys are bean-shaped excretory organs in vertebrates. ... In fluid dynamics, the volumetric flow rate, also volume flow rate and rate of fluid flow, is the volume of fluid which passes through a given area per unit time. ... Volume, also called capacity, is a quantification of how much space an object occupies. ... A watch Attempting to understand Time has long been a prime occupation for philosophers, scientists and artists. ... Mass transfer is the phrase commonly used in engineering for physical processes which involve molecular and convective transport of atoms and molecules within physical systems. ... Physiology (in Greek physis = nature and logos = word) is the study of the mechanical, physical, and biochemical functions of living organisms. ... Glomerular filtration rate (GFR) is the volume of fluid filtered from the renal glomerular capillaries into Bowmans capsule per unit time. ... Nephron of the kidney A nephron is the basic structural and functional unit of the kidney. ... The word plasma has a Greek root which means to be formed or molded (the word plastic shares this root). ...

Its definition follows from the differential equation that describes exponential decay and is used to model kidney function and hemodialysis machine function: In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ... A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. ... This article is about clinical dialysis; for the laboratory technique, see Dialysis (biochemistry) In medicine, dialysis is a method for removing waste such as urea from the blood when the kidneys are incapable of this, i. ...

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

Where:

• $dot{m}$ 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 $frac{dC}{dt}$ is the first derivative of concentration with respect to time, i.e. the change in concentration with time. The volume of distribution (VD) is a pharmacological term used to quantify the distribution of a drug throughout the body after oral or intravenous dosing. ... A significant fraction of the human body is water. ... In mathematics, the derivative is one of the two central concepts of calculus. ...

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

$C = frac{dot{m}}{K} + (C_{o}-frac{dot{m}}{K}) e^{-frac{K cdot t}{V}} qquad (2)$[2][3]

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

The solution to the above differential equation (2) at time infinity (steady state) is: The mathematical constant e is the base of the natural logarithm function. ... The natural logarithm, invented by John Napier, is the logarithm to the base e, where e is equal to 2. ...

$C_{infty} = frac {dot{m}}{K} qquad (3a)$

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

$K = frac {dot{m}}{C_{infty}} qquad (3b)$

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. This article is about proportionality, the mathematical relation. ... Creatinine clearance is a method that estimates the glomerular filtration rate (GFR) of the kidneys. ... Creatinine is a breakdown product of creatine phosphate in muscle, and is usually produced at a fairly constant rate by the body (depending on muscle mass). ...

## Measurement of renal clearance GA_googleFillSlot("encyclopedia_square");

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)): Urine is liquid waste excreted by the kidneys and is produced by the process of filtration. ...

$K = frac {C_U cdot Q}{C_B} qquad (4)$

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/mL] (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).

Creatinine clearance is a method that estimates the glomerular filtration rate (GFR) of the kidneys. ... Kt/V - a dimensionless number used to quantify hemodialysis and peritoneal dialysis treatment adequacy. ... Pharmacokinetics is a branch of pharmacology dedicated to the study of the time course of substances and their relationship with an organism or system. ... The renal clearance ratio is found with the following equation: X is the analyte substance Cx is the renal plasma clearance of X Cin is the renal plasma clearance of inulin. ... Standardized Kt/V, also std Kt/V, is a way of measuring (renal) dialysis adequacy. ... The urea reduction ratio (URR), is a dimensionless number used to quantify hemodialysis treatment adequacy. ...

## References

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

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