Assessment of kidney 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 (C_Cr) 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 C_Cr 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 eC_Cr).

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.

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.

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

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 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. Compared to the MDRD formula, the inulin clearance slightly overestimates the glomerular function. In early stage renal disease, the inulin clearance may remain normal due to hyperfiltration in the remaining nephrons. Incomplete urine collection is an important source of error in inulin clearance measurement.

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 break-down product of creatine phosphate, which is found in muscle). It is freely filtered by the glomerulus, but also actively secreted by the peritubular capillaries 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 C_Cr

Creatinine clearance (C_Cr) can be calculated if values for creatinine's urine concentration (U_Cr), urine flow rate (V), and creatinine's plasma concentration (P_Cr) 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 (U_Cr×V) divided by its plasma concentration. This is commonly represented mathematically as

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

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.

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

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:

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

To allow comparison of results between people of different sizes, the C_Cr 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 C_Cr corrected for their actual BSA.

$C_{Cr-corrected}={\frac {{C_{Cr}}\ \times \ {1.73}}{BSA}}$

BSA can be calculated on the basis of weight and height.

Estimated values

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

Estimated creatinine clearance rate (eC_Cr) 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:

$eC_{Cr}={\frac {{\mbox{(140 - Age)}}\ \times \ {\mbox{Mass (in kilograms)}}\ \times \ [{0.85\ if\ Female}]}{{\mbox{72}}\ \times \ {\mbox{Serum Creatinine (in mg/dL)}}}}$

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:

$eC_{Cr}={\frac {{\mbox{(140 - Age)}}\ \times \ {\mbox{Mass (in kilograms)}}\ \times \ {Constant}}{{\mbox{Serum Creatinine (in }}\mu {\mbox{mol/L)}}}}$

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:

${\mbox{eGFR}}={\mbox{186}}\ \times \ {\mbox{Serum Creatinine}}^{-1.154}\ \times \ {\mbox{Age}}^{-0.203}\ \times \ {[1.210\ if\ Black]}\ \times \ {[0.742\ if\ Female]}$

For creatinine in µmol/L:

${\mbox{eGFR}}={\mbox{32788}}\ \times \ {\mbox{Serum Creatinine}}^{-1.154}\ \times \ {\mbox{Age}}^{-0.203}\ \times \ {[1.210\ if\ Black]}\ \times \ {[0.742\ if\ Female]}$

Creatinine levels in µmol/L can be converted to mg/dL by dividing them by 88.4. The 32788 number above is equal to 186×88.4^1.154.

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

${\mbox{eGFR}}={\mbox{170}}\ \times \ {\mbox{Serum Creatinine}}^{-0.999}\ \times \ {\mbox{Age}}^{-0.176}\ \times \ {[0.762\ if\ Female]}\ \times \ {[1.180\ if\ Black]}\ \times \ {\mbox{BUN}}^{-0.170}\ \times \ {\mbox{Albumin}}^{+0.318}$

Where the creatinine and blood urea nitrogen concentrations are both in mg/dL. The albumin concentration is in g/dL.

Since these formulae do not adjust for body mass, they (relative to the Cockcroft-Gault formula) underestimate eGFR for heavy people and overestimate it for underweight people. (see Cockcroft-Gault formula above).

Estimated GFR (eGFR) using the CKD-EPI formula

The CKD-EPI (Chronic Kidney Disease Epidemiology Collaboration) formula was published in May 2009. It was developed in an effort to create a formula more precise than the MDRD formula, especially when actual GFR is >60 mL/min per 1.73 m2.

Researchers pooled data from multiple studies to develop and validate this new equation. They randomly divided 10 studies which included 8254 participants, into separate data sets for development and internal validation. 16 additional studies, which included 3896 participants, were used for external validation.

The CKD-EPI equation performed better than the MDRD (Modification of Diet in Renal Disease Study) equation, especially at higher GFR, with less bias and greater accuracy. When looking at NHANES (National Health and Nutrition Examination Survey) data, the median estimated GFR was 94.5 mL/min per 1.73 m2 vs. 85.0 mL/min per 1.73 m2, and the prevalence of chronic kidney disease was 11.5% versus 13.1%.

The CKD-EPI equation, expressed as a single equation, is:

GFR = 141 X min(Scr/κ,1)α X max(Scr/κ, 1)-1.209 X 0.993Age X 1.018 [if female] X 1.159 [if black]

where Scr is serum creatinine (mg/dL), κ is 0.7 for females and 0.9 for males, α is -0.329 for females and -0.411 for males, min indicates the minimum of Scr/κ or 1, and max indicates the maximum of Scr/κ or 1.

This formula was developed by Levey et al.

Estimated GFR (eGFR) using the Mayo Quadratic formula

Another estimation tool to calculate GFR is the Mayo Quadratic formula. This formula was developed by Rule et al. in an attempt to better estimate GFR in patients with preserved kidney function. It is well recognized that the MDRD formula tends to underestimate GFR in patients with preserved kidney function.

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:

${\mbox{eGFR}}={\frac {{k}\times {Height}}{Serum\ Creatinine}}$

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.

$J_{v}=K_{f}([P_{c}-P_{i}]-\sigma [\pi _{c}-\pi _{i}])$

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 $([P_{c}-P_{i}]-\sigma [\pi _{c}-\pi _{i}])$ 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/1.73m2
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. Non-steroidal anti-inflammatory drugs (NSAIDs) prevent the production of prostaglandins, molecules which dilate the afferent arteriole. NSAIDs could therefore worsen kidney function by decreasing afferent blood flow to the Bowman's capsule.

Chronic Kidney Disease stages

Main article: Chronic kidney disease

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

See also

• Clearance
• Dialysis
• filtration fraction
• Kt/V
• Pharmacokinetics
• Renal clearance ratio
• Renal failure
• Standardized Kt/V
• Tubuloglomerular feedback
• Urea reduction ratio

External links

Cockcroft-Gault calculators

• Online GFR Calculator using MDRD and Cockcroft formulas Includes background information about calculations and inulin clearance.
• Online GFR Calculator (Cockcroft-Gault Formula)
• Online GFR Calculator using MDRD, Gault, and Combo Also shows GFR expected for age and current GFR percentage of expected.
• Online calculator for Cockcroft-Gault and MDRD formulae.

MDRD Calculators

• Online Calculator for Cockcroft-Gault and sMDRD Equations.
• Online eGFR Calculator using sMDRD, Cockcroft-Gault and Combined Equations Also shows eGFR expected for age and current eGFR percentage of expected.
• Online eGFR Calculator using sMDRD and Cockcroft-Gault Equations Includes background information about calculations and inulin clearance.
• Online eGFR Calculator
• Online eGFR Calculator Calculator for the "Estimated Glomerular Filtration Rate (eGFR)" from Serum Creatinine, using the "Simplified Modification of Diet in Renal Disease (sMDRD) Study Group Equation".

Other formulas calculators

• Online CKD-EPI eGFR calculator
• Online Mayo Quadratic eGFR calculator
• Schwartz formula - cornell.edu

Reference links

• National Kidney Disease Education Program website. Includes professional references and GFR calculators