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14-September-2008 18:02:45 - Clearance medicine In medicine, the clearance is a 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. Contents 1 Definition 2 Derivation of equation 3 Solution to the differential equation 3.1 Steady-state solution 4 Measurement of renal clearance 5 See also 6 References Definition When 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 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; the kidney does not completely remove a substance from the total renal plasma flow.1 From a mass transfer perspective2 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: V \fracdCdt = -K \cdot C + \dotm \qquad 1 Where: \dotm 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 \fracdCdt 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: \Delta m_body=-\dot m_out+ \dot m_in +\dot m_gen.\Delta t \qquad 2 where: Δt is a period of time Δmbody the change in mass of the toxin in the body during Δt \dot m_in is the toxin intake rate \dot m_out is the toxin removal rate \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 Δm during some time Δt is equal to the toxin intake plus the toxin generation minus the toxin removal. Since m_body = C \cdot V \qquad 3 and \dot m_out=K \cdot C \qquad 4 Equation A1 can be re-written as: \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. \dot m=\dot m_in +\dot m_gen. and divides by Δt the result is a difference equation: \frac\Delta C \cdot V\Delta t = -K \cdot C + \dotm \qquad6 If one applies the limit \Delta t \rightarrow 0 one obtains a differential equation: \fracdC \cdot Vdt= -K \cdot C + \dotm \qquad7 Using the chain rule this can be re-written as: C \fracdVdt+V \fracdCdt = -K \cdot C + \dotm \qquad8 If one assumes that the volume change is not significant, i.e. C \fracdVdt=0 , the result is Equation 1: V \fracdCdt = -K \cdot C + \dotm \qquad1 Solution to the differential equation The general solution of the above differential equation 1 is: C = \frac\dotmK + C_o-\frac\dotmK e^-\fracK \cdot tV \qquad 9 34 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: C_\infty = \frac \dotmK \qquad 10a The above equation 10a can be re-written as: K = \frac \dotmC_\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: K = \frac C_U \cdot QC_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 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. doi:10.1093/ndt/13.suppl_6.10. PMID 9719197. Full Text ^ Gotch FA, Sargent JA, Keen ML 2000. Whither goest Kt/V?. Kidney Int. Suppl. 76: S3-18. doi:10.1046/j.1523-1755.2000.07602.x. PMID 10936795. v d e Urinary system, physiology: renal physiology and acid base physiology Filtration Renal blood flow - Ultrafiltration - Countercurrent exchange Hormones affecting filtration Antidiuretic hormone ADH - Aldosterone - Atrial natriuretic peptide Secretion/clearance Pharmacokinetics - Clearance of medications Reabsorption Solvent drag - Na+ - Cl- - urea - glucose - oligopeptides - protein Endocrine Renin - Erythropoietin EPO - Calcitriol Active vitamin D - Prostaglandins Assessing Renal function/ Measures of dialysis Glomerular filtration rate - Creatinine clearance - Renal clearance ratio - Urea reduction ratio - Kt/V - Standardized Kt/V - Hemodialysis product - PAH clearance Effective renal plasma flow - Extraction ratio Acid base physiology Fluid balance - Darrow Yannet diagram - Body water - Interstitial fluid - Extracellular fluid - Intracellular fluid/Cytosol - Plasma - Transcellular fluid - Base excess - Davenport diagram - Anion gap - Arterial blood gas Buffering/compensation Bicarbonate buffering system - Respiratory compensation - Renal compensation v d e Medication Pharmacology Pharmacokinetics ADME: Absorption - Distribution - Metabolism - Excretion Clearance Loading dose - Volume of distribution Initial - Rate of infusion Compartment - Bioequivalence - Bioavailability Biological half-life - Plasma protein binding Pharmacodynamics Toxicity Neurotoxicology - Dose-response relationship Efficacy, Potency Other fields pharmacogenetics - pharmacogenomics - Neuropsychopharmacology Neuropharmacology, Psychopharmacology Agonist: Inverse agonist Antagonist: Competitive antagonist Physiological agonism and antagonism Retrieved from http://en..org/wiki/Clearance_medicine Categories: Nephrology | Pharmacokinetics | Pharmacology Views Article Discussion this page History Personal tools Log in / create account Navigation Main page Contents Featured content Current events Random article Search Go Search Interaction Community portal Recent changes Contact Donate to Help Toolbox What links here Related changes Upload file Special pages Printable version Permanent link Cite this page Languages Deutsch Español Français Italiano Nederlands Norsk bokmål Português Svenska This page was last modified on 15 August 2008, at 04:28
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