Definitions

# Renal function

Renal function, in nephrology, is an indication of the state of the kidney and its role in renal physiology. Glomerular filtration rate (GFR) describes the flow rate of filtered fluid through the kidney. Creatinine clearance rate (CCr) is the volume of blood plasma that is cleared of creatinine per unit time and is a useful measure for approximating the GFR. Both GFR and CCr may be accurately calculated by comparative measurements of substances in the blood and urine, or estimated by formulas using just a blood test result (eGFR and eCCr).

The results of these tests are important in assessing the excretory function of the kidneys. For example, grading of chronic renal insufficiency and dosage of drugs that are primarily excreted via urine are based on GFR (or creatinine clearance).

It is commonly believed to be the amount of liquid filtered out of the blood that gets processed by the kidneys. Physiologically, these quantities (volumetric blood flow and mass removal) are only related loosely. Clearance is a ratio of the mass generation and concentration at a steady state.

## Indirect markers

Most doctors use the plasma concentrations of the waste substances of creatinine and urea, as well as electrolytes to determine renal function. These measures are adequate to determine whether a patient is suffering from kidney disease.

Unfortunately, blood urea nitrogen (BUN) and creatinine will not be raised above the normal range until 60% of total kidney function is lost. Hence, the more accurate Glomerular filtration rate or its approximation of the creatinine clearance are measured whenever renal disease is suspected or careful dosing of nephrotoxic drugs is required.

Another prognostic marker for kidney disease is Microalbuminuria; the measurement of small amounts of albumin in the urine that cannot be detected by urine dipstick methods.

## Glomerular filtration rate

Glomerular filtration rate (GFR) is the volume of fluid filtered from the renal (kidney) glomerular capillaries into the Bowman's capsule per unit time.

Glomerular filtration rate (GFR) can be calculated by measuring any chemical that has a steady level in the blood, and is freely filtered but neither reabsorbed nor secreted by the kidneys. The rate therefore measured is the quantity of the substance in the urine that originated from a calculable volume of blood. The GFR is typically recorded in units of volume per time, e.g. milliliters per minute ml/min. Compare to filtration fraction.

$GFR = frac \left\{ mbox\left\{Urine Concentration\right\} times mbox\left\{Urine Flow\right\} \right\}\left\{ mbox\left\{Plasma Concentration\right\} \right\}$

There are several different techniques used to calculate or estimate the glomerular filtration rate (GFR or eGFR).

### Measurement using inulin

The GFR can be determined by injecting inulin (not insulin) into the plasma. Since inulin is neither reabsorbed nor secreted by the kidney after glomerular filtration, its rate of excretion is directly proportional to the rate of filtration of water and solutes across the glomerular filter.

## Creatinine clearance approximation of GFR

In clinical practice, however, creatinine clearance is used to measure GFR. Creatinine is produced naturally by the body (creatinine is a metabolite of creatine, which is found in muscle). It is freely filtered by the glomerulus, but also actively secreted by the renal tubules in very small amounts such that creatinine clearance overestimates actual GFR by 10-20%. This margin of error is acceptable considering the ease with which creatinine clearance is measured. Unlike precise GFR measurements involving constant infusions of inulin, creatinine is already at a steady-state concentration in the blood and so measuring creatinine clearance is much less cumbersome.

### Calculation of CCr

Creatinine clearance (CCr) can be calculated if values for creatinine's urine concentration (UCr), urine flow rate (V), and creatinine's plasma concentration (PCr) are known. Since the product of urine concentration and urine flow rate yields creatinine's excretion rate, creatinine clearance is also said to be its excretion rate (UCr×V) divided by its plasma concentration. This is commonly represented mathematically as

$C_\left\{Cr\right\} = frac \left\{ U_\left\{Cr\right\} times V \right\}\left\{ P_\left\{Cr\right\} \right\}$

Example: A person has a plasma creatinine concentration of 0.01 mg/ml and in 1 hour produces 60ml of urine with a creatinine concentration of 1.25 mg/ml.

$C_\left\{Cr\right\} = frac \left\{1.25 mg/ml times frac\left\{60ml\right\}\left\{60min\right\}\right\}\left\{0.01 mg/ml\right\} = frac \left\{ \left\{1.25 mg/ml\right\} times \left\{1 ml/min\right\}\right\}\left\{0.01 mg/ml\right\} = frac \left\{1.25 mg/min\right\}\left\{0.01 mg/ml\right\} = \left\{125 ml/min\right\}$

Commonly a 24 hour urine collection is undertaken, from empty-bladder one morning to the contents of the bladder the following morning, with a comparative blood test then taken. The urinary flow rate is still calculated per minute, hence:

$C_\left\{Cr\right\} = frac \left\{ U_\left\{Cr\right\} times mbox\left\{24-hour volume\right\} \right\}\left\{P_\left\{Cr\right\} times 24 times 60 mins\right\}$

To allow comparison of results between people of different sizes, the CCr is often corrected for the body surface area (BSA) and expressed compared to the average sized man as ml/min/1.73 m2. While most adults have a BSA that approaches 1.7 (1.6-1.9), extremely obese or slim patients should have their CCr corrected for their actual BSA.

$C_\left\{Cr-corrected\right\} = frac times \left\{1.73\right\}\right\} \left\{BSA\right\}$
BSA can be calculated on the basis of weight and height.

## Estimated values

A number of formulae have been devised to estimate GFR or Ccr values on the basis of serum creatinine levels.

### Estimated creatinine clearance rate (eCcr) using Cockcroft-Gault formula

A commonly used surrogate marker for actual creatinine clearance is the Cockcroft-Gault formula, which may be used to calculate an Estimated Creatinine Clearance, which in turn estimates GFR: It is named after the scientists who first published the formula, and it employs creatinine measurements and a patient's weight to predict the Creatinine clearance. The formula, as originally published, is:
$eC_\left\{Cr\right\} = frac \left\{ mbox\left\{\left(140 - Age\right)\right\} times mbox\left\{Mass \left(in kilograms\right)\right\} times \left[\left\{0.85 if Female\right\}\right]\right\} \left\{mbox\left\{72\right\} times mbox\left\{Serum Creatinine \left(in mg/dL\right)\right\}\right\}$
This formula expects weight to be measured in kilograms and creatinine to be measured in mg/dL, as is standard in the USA. The resulting value is multiplied by a constant of 0.85 if the patient is female. This formula is useful because the calculations are relatively simple and can often be performed without the aid of a calculator.

For creatinine in µmol/L:

$eC_\left\{Cr\right\} = frac \left\{ mbox\left\{\left(140 - Age\right)\right\} times mbox\left\{Mass \left(in kilograms\right)\right\} times \left\{Constant\right\} \right\} \left\{mbox\left\{Serum Creatinine \left(in \right\} mu mbox\left\{mol/L\right)\right\}\right\}$
Where Constant is 1.23 for men and 1.04 for women.

### Estimated GFR (eGFR) using Modification of Diet in Renal Disease (MDRD) formula

The most recently advocated formula for calculating the GFR is the one that was developed by the Modification of Diet in Renal Disease Study Group. Most laboratories in Australia, and The United Kingdom now calculate and report the MDRD estimated GFR along with creatinine measurements and this forms the basis of Chronic kidney disease#Staging. The adoption of the automatic reporting of MDRD-eGFR has been widely criticised.

The most commonly used formula is the "4-variable MDRD" which estimates GFR using four variables: serum creatinine, age, race, and gender. The original MDRD used six variables with the additional variables being the blood urea nitrogen and albumin levels. The equations have been validated in patients with chronic kidney disease; however both versions underestimate the GFR in healthy patients with GFRs over 60 mL/min. The equations have not been validated in acute renal failure.

For creatinine in mg/dL:

$mbox\left\{eGFR\right\} = mbox\left\{186\right\} times mbox\left\{Serum Creatinine\right\}^\left\{-1.154\right\} times mbox\left\{Age\right\}^\left\{-0.203\right\} times \left\{\left[1.21 if Black\right]\right\} times \left\{\left[0.742 if Female\right]\right\}$

For creatinine in µmol/L:

$mbox\left\{eGFR\right\} = mbox\left\{32788\right\} times mbox\left\{Serum Creatinine\right\}^\left\{-1.154\right\} times mbox\left\{Age\right\}^\left\{-0.203\right\} times \left\{\left[1.21 if Black\right]\right\} times \left\{\left[0.742 if Female\right]\right\}$
Creatinine levels in µmol/L can be converted to mg/dL by dividing them by 88.4. The 32788 number above is equal to 186×88.41.154.

A more elaborate version of the MDRD equation also includes serum albumin and blood urea nitrogen (BUN) levels:

$mbox\left\{eGFR\right\} = mbox\left\{170\right\} times mbox\left\{Serum Creatinine\right\}^\left\{-0.999\right\} times mbox\left\{Age\right\}^\left\{-0.176\right\} times \left\{\left[0.762 if Female\right]\right\} times \left\{\left[1.180 if Black\right]\right\} times mbox\left\{BUN\right\}^\left\{-0.170\right\} times mbox\left\{Albumin\right\}^\left\{+0.318\right\}$
Where the creatinine and blood urea nitrogen concentrations are both in mg/dL. The albumin concentration is in g/dL.

### Estimated GFR for Children using Schwartz formula

In children, the Schwartz formula is used. This employs the serum creatinine (mg/dl), the child's height (cm) and a constant to estimate the glomerular filtration rate:
$mbox\left\{eGFR\right\} = frac\left\{ \left\{k\right\} times \left\{Height\right\} \right\}\left\{Serum Creatinine\right\}$
Where k is a constant that depends on muscle mass, which itself varies with a child's age:
In first year of life, for pre-term babies K=0.33 and for full-term infants K=0.45
For infants between ages of 1 and 12 years, K=0.55.

The method of selection of the K-constant value has been questioned as being dependent upon the gold-standard of renal function used (i.e. creatinine clearance, inulin clearance etc) and also may be dependent upon the urinary flow rate at the time of measurement.

### Calculation using Starling equation

It is also theoretically possible to calculate GFR using the Starling equation.

$J_v = K_f \left(\left[P_c - P_i\right] - sigma\left[pi_c - pi_i\right] \right)$

The equation is used both in a general sense for all capillary flow, and in a specific sense for the glomerulus:

 General usage Glomerular usage Meaning of variable Relationship to GFR Description Pc Pgc Capillary hydrostatic pressure Direct Increased by dilation of afferent arteriole or constriction of efferent arteriole Pi Pbs Interstitial hydrostatic pressure Inverse πc πgc Capillary oncotic pressure Inverse Decreased by nephrotic syndrome πi πbs Interstitial oncotic pressure Direct Kf Kf Filtration coefficient Direct Increased by inflammation σ σ Reflection coefficient Inverse Jv GFR net filtration n/a

Note that $\left(\left[P_c - P_i\right] - sigma\left[pi_c - pi_i\right] \right)$ is the net driving force, and therefore the net filtration is proportional to the net driving force.

In practice, it is not possible to identify the needed values for this equation, but the equation is still useful for understanding the factors that affect GFR, and providing a theoretical underpinning for the above calculations.

## Normal ranges

For most patients, a GFR over 60 ml/min is adequate. But, if the GFR has significantly declined from a previous test result, this can be an early indicator of kidney disease requiring medical intervention. The sooner kidney dysfunction is diagnosed and treated, the greater odds of preserving remaining nephrons, and preventing the need for dialysis.

The normal ranges of GFR, adjusted for body surface area, are:

• Males: 70 ± 14 mL/min/m2
• Females: 60 ± 10 mL/min/m2

Normal reference ranges for creatinine clearance are:

 Gender Low High Units male 55 146 ml/minute/1.73 m2 female 52 134 ml/minute/1.73m2

Risk factors for kidney disease include diabetes, high blood pressure, family history, older age, ethnic group.

GFR can increase due to hypoproteinemia because of the reduction in plasma oncotic pressure. GFR can also increase due to constriction of the efferent arteriole but decreases due to constriction of the afferent arteriole.

### Chronic Kidney Disease stages

The severity of chronic kidney disease (CKD) is described by 6 stages, the most severe three are defined by the MDRD-eGFR value, and first three also depend whether there is other evidence of kidney disease (e.g. proteinuria):
0) Normal kidney function – GFR above 90ml/min/1.73m2 and no proteinuria
1) CKD1 – GFR above 90ml/min/1.73m2 with evidence of kidney damage
2) CKD2 (Mild) – GFR of 60 to 89 ml/min/1.73m2 with evidence of kidney damage
3) CKD3 (Moderate) – GFR of 30 to 59 ml/min/1.73m2
4) CKD4 (Severe) – GFR of 15 to 29 ml/min/1.73m2
5) CKD5 Kidney failure (dialysis or kidney transplant needed) – GFR less than 15 ml/min/1.73m2