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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 .

It is commonly ''and incorrectly'' believed 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 ]. From a Mass Transfer perspective 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.

Its definition follows from the Differential Equation that describes Exponential Decay and is used to model kidney function and Hemodialysis machine function:

V rac{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) or [mol/s

  • t is dialysis time or time since injection of the substance/drug or [s

  • V is the Volume Of Distribution or total Body Water or [m3

  • K is the clearance or [m3/s

  • C is the concentration or [mol/m3 (in the USA often [mg/mL])

    • From the above definitions it follows that rac{dC}{dt} is the first Derivative of concentration with respect to time, i.e. the change in concentration with time.


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

C = rac{\dot{m}}{K} + (C_{o}- rac{\dot{m}}{K}) e^{- rac{K \cdot t}{V}} \qquad (2)

Where:
  • Co is the concentration at the beginning of dialysis ''or'' the initial concentration of the substance/drug (after it has distributed) 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:

C_{\infty} = rac {\dot{m}}{K} \qquad (3a)

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

K = rac {\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.


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 (''3b'')):

K = rac {C_U \cdot Q}{C_B} \qquad (4)

Where:

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'').


SEE ALSO



REFERENCES