Glomerular filtration rate

Creatinine

In clinical practice, however, creatinine clearance or estimates of creatinine clearance based on the serum creatinine level are used to measure GFR. Creatinine is produced naturally by the body (creatinine is a breakdown 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% to 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. However, creatinine estimates of GFR have their limitations. All of the estimating equations depend on a prediction of the 24-hour creatinine excretion rate, which is a function of muscle mass which is quite variable. One of the equations, the Cockcroft and Gault equation (see below) does not correct for race. With a higher muscle mass, serum creatinine will be higher for any given rate of clearance.

Inulin

The GFR can be determined by injecting inulin or the inulin-analog sinistrin into the blood stream. Since both inulin and sinistrin are neither reabsorbed nor secreted by the kidney after glomerular filtration, their rate of excretion is directly proportional to the rate of filtration of water and solutes across the glomerular filter. Incomplete urine collection is an important source of error in inulin clearance measurement.^[5] Using inulin to measure kidney function is the "gold standard" for comparison with other means of estimating glomerular filtration rate.^[6]

Radioactive tracers

GFR can be accurately measured using radioactive substances, in particular chromium-51 and technetium-99m. These come close to the ideal properties of inulin (undergoing only glomerular filtration) but can be measured more practically with only a few urine or blood samples.^[7] Measurement of renal or plasma clearance of ⁵¹Cr-EDTA is widely used in Europe but not available in the United States, where ^99mTc-DTPA may be used instead.^[8] Renal and plasma clearance ⁵¹Cr-EDTA has been shown to be accurate in comparison with the gold standard, inulin.^[9][10][11] Use of ⁵¹Cr‑EDTA is considered a reference standard measure in UK guidance.^[12]

Cystatin C

Problems with creatinine (varying muscle mass, recent meat ingestion (much less dependent on the diet than urea), etc.) have led to evaluation of alternative agents for estimation of GFR. One of these is cystatin C, a ubiquitous protein secreted by most cells in the body (it is an inhibitor of cysteine protease).

Cystatin C is freely filtered at the glomerulus. After filtration, Cystatin C is reabsorbed and catabolized by the tubular epithelial cells, with only small amounts excreted in the urine. Cystatin C levels are therefore measured not in the urine, but in the bloodstream.

Equations have been developed linking estimated GFR to serum cystatin C levels. Most recently, some proposed equations have combined (sex, age and race) adjusted cystatin C and creatinine. The most accurate is (sex, age and race) adjusted cystatin C, followed by (sex, age and race) adjusted creatinine and then cystatine C alone in slightly different with adjusted creatinine.^[13]

K_f

Because this constant is a measurement of hydraulic conductivity multiplied by the capillary surface area, it is almost impossible to measure physically. However, it can be determined experimentally. Methods of determining the GFR are listed in the above and below sections and it is clear from our equation that ${\displaystyle K_{f}}$ can be found by dividing the experimental GFR by the net filtration pressure:^[14]

${\displaystyle K_{f}={\frac {\textrm {GFR}}{\text{Net Filt. Pressure}}}={\frac {\textrm {GFR}}{(P_{G}-P_{B}-\Pi _{G}+\Pi _{B})}}}$

P_G

The hydrostatic pressure within the glomerular capillaries is determined by the pressure difference between the fluid entering immediately from the afferent arteriole and leaving through the efferent arteriole. The pressure difference is approximated by the product of the total resistance of the respective arteriole and the flux of blood through it:^[15]

${\displaystyle P_{a}-P_{G}=R_{a}\times Q_{a}}$

${\displaystyle P_{G}-P_{e}=R_{e}\times Q_{e}}$

Where:

• ${\displaystyle P_{a}}$ is the afferent arteriole pressure.
• ${\displaystyle P_{G}}$ is the hydrostatic pressure within the glomerular capillaries.
• ${\displaystyle P_{e}}$ is the efferent arteriole pressure.
• ${\displaystyle R_{a}}$ is the afferent arteriole resistance.
• ${\displaystyle R_{e}}$ is the efferent arteriole resistance.
• ${\displaystyle Q_{a}}$ is the afferent arteriole flux.
• And, ${\displaystyle Q_{e}}$ is the efferent arteriole flux.

P_B

The pressure in the Bowman's capsule and proximal tubule can be determined by the difference between the pressure in the Bowman's capsule and the descending tubule:^[15]

${\displaystyle P_{B}-P_{d}=R_{d}\times (Q_{a}-Q_{e})}$

Where:

• ${\displaystyle P_{d}}$ is the pressure in the descending tubule.
• And, ${\displaystyle R_{d}}$ is the resistance of the descending tubule.

Π_G

Blood plasma has a good many proteins in it and they exert an inward directed force called the osmotic pressure on the water in hypotonic solutions across a membrane, i.e., in the Bowman's capsule. Because plasma proteins are virtually incapable of escaping the glomerular capillaries, this oncotic pressure is defined, simply, by the ideal gas law:^[14][15]

${\displaystyle \Pi _{G}=RTc}$

Where:

• R is the universal gas constant
• T is the temperature.
• And, c is concentration in mol/L of plasma proteins (remember the solutes can freely diffuse through the glomerular capsule).

Π_B

This value is almost always taken to be equal to zero because in a healthy nephron, there should be no proteins in the Bowman's Capsule.^[14]

Filtration fraction

The filtration fraction is the amount of plasma that is actually filtered through the kidney. This can be defined using the equation:

FF=GFR/RPF

• FF is the filtration fraction
• GFR is the glomerular filtration rate
• RPF is the renal plasma flow

Normal human FF is 20%.

Renal clearance

C_x=(U_x)V/P_x

• C_x is the clearance of X (normally in units of mL/min).
• U_x is the urine concentration of X.
• P_x is the plasma concentration of X.
• V is the urine flow rate.

Creatinine clearance C_Cr

One method of determining GFR from creatinine is to collect urine (usually for 24 h) to determine the amount of creatinine that was removed from the blood over a given time interval. If one removes 1440 mg in 24 h, this is equivalent to removing 1 mg/min. If the blood concentration is 0.01 mg/mL (1 mg/dL), then one can say that 100 mL/min of blood is being "cleared" of creatinine, since, to get 1 mg of creatinine, 100 mL of blood containing 0.01 mg/mL would need to have been cleared.

Creatinine clearance (C_Cr) is calculated from the creatinine concentration in the collected urine sample (U_Cr), urine flow rate (Vdt), and the plasma concentration (P_Cr). Since the product of urine concentration and urine flow rate yields creatinine excretion rate, which is the rate of removal from the blood, creatinine clearance is calculated as removal rate per min (U_Cr×Vdt) divided by the plasma creatinine concentration. This is commonly represented mathematically as

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

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

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

The common procedure involves undertaking a 24-hour urine collection, 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:

${\displaystyle C_{Cr}={\frac {U_{Cr}\ \times \ {\text{24-hour volume}}}{\mathrm {P_{Cr}\ \times \ 24\times 60min} }}}$

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 m² (1.6 m² to 1.9 m²), extremely obese or slim patients should have their C_Cr corrected for their actual BSA.

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

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

Twenty-four-hour urine collection to assess creatinine clearance is no longer widely performed, due to difficulty in assuring complete specimen collection. To assess the adequacy of a complete collection, one always calculates the amount of creatinine excreted over a 24-hour period. This amount varies with muscle mass and is higher in young people/old, and in men/women. An unexpectedly low or high 24-hour creatinine excretion rate voids the test. Nevertheless, in cases where estimates of creatinine clearance from serum creatinine are unreliable, creatinine clearance remains a useful test. These cases include "estimation of GFR in individuals with variation in dietary intake (vegetarian diet, creatine supplements) or muscle mass (amputation, malnutrition, muscle wasting), since these factors are not specifically taken into account in prediction equations."^[16]

A number of formulae have been devised to estimate GFR or C_cr values on the basis of serum creatinine levels. Where not otherwise stated serum creatinine is assumed to be stated in mg/dL, not μmol/L—divide by 88.4 to convert from μmol/Lto mg/dL.

Cockcroft-Gault formula

A commonly used surrogate marker for the estimation of creatinine clearance is the Cockcroft-Gault (CG) formula, which in turn estimates GFR in ml/min:^[17] It is named after the scientists, the asthmologist Donald William Cockcroft (b. 1946) and the nephrologist Matthew Henry Gault (1925–2003), who first published the formula in 1976, and it employs serum creatinine measurements and a patient's weight to predict the creatinine clearance.^[18][19] The formula, as originally published, is:

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

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 simple and can often be performed without the aid of a calculator.

When serum creatinine is measured in μmol/L:

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

Where Constant is 1.23 for men and 1.04 for women.

One interesting feature of the Cockcroft and Gault equation is that it shows how dependent the estimation of CCr is based on age. The age term is (140 – age). This means that a 20-year-old person (140 – 20 = 120) will have twice the creatinine clearance as an 80-year-old (140 – 80 = 60) for the same level of serum creatinine. The C-G equation assumes that a woman will have a 15% lower creatinine clearance than a man at the same level of serum creatinine.

Modification of Diet in Renal Disease (MDRD) formula

Another formula for calculating the GFR is the one developed by the Modification of Diet in Renal Disease Study Group.^[20] Most laboratories in Australia,^[21] and the United Kingdom now calculate and report the estimated GFR along with creatinine measurements and this forms the basis of diagnosis of chronic kidney disease.^[22][23] The adoption of the automatic reporting of MDRD-eGFR has been widely criticised.^[24][25][26]

The most commonly used formula is the "4-variable MDRD", which estimates GFR using four variables: serum creatinine, age, ethnicity, and gender.^[27] The original MDRD used six variables with the additional variables being the blood urea nitrogen and albumin levels.^[20] 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.^[28][29] The equations have not been validated in acute renal failure.

For creatinine in μmol/L:

${\displaystyle {\text{eGFR}}={\text{32788}}\ \times \ [{\text{Serum Creatinine}}]^{-1.154}\ \times \ {\text{Age}}^{-0.203}\ \times {\text{[1.212 if Black]}}\ \times {\text{[0.742 if Female]}}}$

For creatinine in mg/dL:

${\displaystyle {\text{eGFR}}={\text{186}}\ \times \ [{\text{Serum Creatinine}}]^{-1.154}\ \times \ {\text{Age}}^{-0.203}\ \times {\text{[1.212 if Black]}}\ \times {\text{[0.742 if Female]}}}$

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:

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

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

These MDRD equations are to be used only if the laboratory has NOT calibrated its serum creatinine measurements to isotope dilution mass spectrometry (IDMS). When IDMS-calibrated serum creatinine is used (which is about 6% lower), the above equations should be multiplied by 175/186 or by 0.94086.^[30]

Since these formulae do not adjust for body size, results are given in units of mL/min per 1.73 m², 1.73 m² being the estimated body surface area of an adult with a mass of 63 kg and a height of 1.7m.

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 accurate than the MDRD formula, especially when actual GFR is greater than 60 mL/min per 1.73 m². This is the formula currently recommended by NICE in the UK.^[23]

Researchers pooled data from multiple studies to develop and validate this new equation. They used 10 studies that included 8254 participants, randomly using 2/3 of the data sets for development and the other 1/3 for internal validation. Sixteen 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%. Despite its overall superiority to the MDRD equation, the CKD-EPI equations performed poorly in certain populations, including black women, the elderly and the obese, and was less popular among clinicians than the MDRD estimate.^[31]

The CKD-EPI equation is:

${\displaystyle \mathrm {eGFR} =141\ \times \ \mathrm {\min(SCr/k,1)} ^{a}\ \times \ \mathrm {\max(SCr/k,1)} ^{-1.209}\ \times \ 0.993^{\text{Age}}\ \times {\text{[1.018 if Female]}}\ \times {\text{[1.159 if Black]}}\ }$

where SCr is serum creatinine (mg/dL), k is 0.7 for females and 0.9 for males, a is −0.329 for females and −0.411 for males, min indicates the minimum of SCr/k or 1, and max indicates the maximum of SCr/k or 1.

As separate equations for different populations: For creatinine (IDMS calibrated) in mg/dL:

Male, not black

If serum creatinine (Scr) ≤ 0.9

${\displaystyle \mathrm {eGFR} =141\ \times \ \mathrm {(SCr/0.9)} ^{-0.411}\ \times \ 0.993^{\text{Age}}\ }$

If serum creatinine (Scr) > 0.9

${\displaystyle \mathrm {eGFR} =141\ \times \ \mathrm {(SCr/0.9)} ^{-1.209}\ \times \ 0.993^{\text{Age}}\ }$

Female, not black

If serum creatinine (Scr) ≤ 0.7

${\displaystyle \mathrm {eGFR} =144\ \times \ \mathrm {(SCr/0.7)} ^{-0.329}\ \times \ 0.993^{\text{Age}}\ }$

If serum creatinine (Scr) > 0.7

${\displaystyle \mathrm {eGFR} =144\ \times \ \mathrm {(SCr/0.7)} ^{-1.209}\ \times \ 0.993^{\text{Age}}\ }$

Black male

If serum creatinine (Scr) ≤ 0.9

${\displaystyle \mathrm {eGFR} =163\ \times \ \mathrm {(SCr/0.9)} ^{-0.411}\ \times \ 0.993^{\text{Age}}\ }$

If serum creatinine (Scr) > 0.9

${\displaystyle \mathrm {eGFR} =163\ \times \ \mathrm {(SCr/0.9)} ^{-1.209}\ \times \ 0.993^{\text{Age}}\ }$

Black female

If serum creatinine (Scr) ≤ 0.7

${\displaystyle \mathrm {eGFR} =166\ \times \ \mathrm {(SCr/0.7)} ^{-0.329}\ \times \ 0.993^{\text{Age}}\ }$

If serum creatinine (Scr) > 0.7

${\displaystyle \mathrm {eGFR} =166\ \times \ \mathrm {(SCr/0.7)} ^{-1.209}\ \times \ 0.993^{\text{Age}}\ }$

This formula was developed by Levey et al.^[32]

The formula CKD-EPI may provide improved cardiovascular risk prediction over the MDRD Study formula in a middle-age population.^[33]

Mayo Quadratic formula

Another estimation tool to calculate GFR is the Mayo Quadratic formula. This formula was developed by Rule et al.,^[28] 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. Studies in 2008 found that the Mayo Clinic Quadratic Equation compared moderately well with radionuclide GFR, but had inferior bias and accuracy than the MDRD equation in a clinical setting.^[34][35]

The equation is:

${\displaystyle {\text{eGFR}}={\text{exp}}{(1.911+5.249/[{\text{Serum Creatinine}}]-2.114/[{\text{Serum Creatinine}}]^{2}-0.00686\ \times \ {\text{Age}}-{\text{[0.205 if Female]}})}}$^[35]

If Serum Creatinine < 0.8 mg/dL, use 0.8 mg/dL for Serum Creatinine.

Schwartz formula

In children, the Schwartz formula is used.^[36][37] This employs the serum creatinine (mg/dL), the child's height (cm) and a constant to estimate the glomerular filtration rate:

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

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^[38] and for full-term infants k=0.45^[37]

For infants and children of age 1 to 12 years, k=0.55.^[36]

The method of selection of the constant k has been questioned as being dependent upon the gold-standard of renal function used (i.e. inulin clearance, creatinine clearance, etc.) and also may be dependent upon the urinary flow rate at the time of measurement.^[39]

In 2009 the formula was updated to use standardized serum creatinine (recommend k=0.413) and additional formulas that allow improved precision were derived if serum cystatin C is measured in addition to serum creatinine.^[40]

IDMS standardization effort

One problem with any creatinine-based equation for GFR is that the methods used to assay creatinine in the blood differ widely in their susceptibility to non-specific chromogens, which cause the creatinine value to be overestimated. In particular, the MDRD equation was derived using serum creatinine measurements that had this problem. The NKDEP program in the United States has attempted to solve this problem by trying to get all laboratories to calibrate their measures of creatinine to a "gold standard", which in this case is isotope dilution mass spectrometry (IDMS). In late 2009 not all labs in the U.S. had changed over to the new system. There are two forms of the MDRD equation that are available, depending on whether or not creatinine was measured by an IDMS-calibrated assay. The CKD-EPI equation is designed to be used with IDMS-calibrated serum creatinine values only.

Chronic kidney disease stages

Risk factors for kidney disease include diabetes, high blood pressure, family history, older age, ethnic group and smoking. For most patients, a GFR over 60 mL/min/1.73m² is adequate. But significant decline of the GFR from a previous test result 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 severity of chronic kidney disease (CKD) is described by six stages; the most severe three are defined by the MDRD-eGFR value, and first three also depend on whether there is other evidence of kidney disease (e.g., proteinuria):

0) Normal kidney function – GFR above 90 mL/min/1.73 m² and no proteinuria

1) CKD1 – GFR above 90 mL/min/1.73 m² with evidence of kidney damage

2) CKD2 (mild) – GFR of 60 to 89 mL/min/1.73 m² with evidence of kidney damage

3) CKD3 (moderate) – GFR of 30 to 59 mL/min/1.73 m²

4) CKD4 (severe) – GFR of 15 to 29 mL/min/1.73 m²

5) CKD5 kidney failure – GFR less than 15 mL/min/1.73 m² Some people add CKD5D for those stage 5 patients requiring dialysis; many patients in CKD5 are not yet on dialysis.

Note: others add a "T" to patients who have had a transplant regardless of stage.

Not all clinicians agree with the above classification, suggesting that it may mislabel patients with mildly reduced kidney function, especially the elderly, as having a disease.^[41][42] A conference was held in 2009 regarding these controversies by Kidney Disease: Improving Global Outcomes (KDIGO) on CKD: Definition, Classification and Prognosis, gathering data on CKD prognosis to refine the definition and staging of CKD.^[43]

Online calculators

• Online GFR Calculator
• Schwartz formula for estimating pediatric renal function
• Creatinine clearance calculator (Cockcroft-Gault Equation)- by MDCalc
• MDRD GFR Equation
• GFR calculator using Cystatin C

Reference links

• National Kidney Disease Education Program website. Includes professional references and GFR calculators
• eGFR at Lab Tests Online