**4. Is it necessary to index GFR?**

6 Basic Nephrology and Acute Kidney Injury

For the determination of the body surface area of Indians, Banerjee et al. updated the constant C of the formula of DuBois & DuBois. (Banerjee & Bhattacharya, 1961; Banerjee & Sen, 1955) Nwoye et al. computed new variables for height and weight formulas that accurately predict the surface area of Africans and Saudi males. (Nwoye, 1989; Nwoye & Al-Shehri, 2003) The formula of Fujimoto et al. was developed to calculate the BSA in the Japanese population (Fujimoto et al., 1968), while Stevenson developed a formula to estimate the BSA in Chinese people. (Stevenson, 1937) Interesting is that recently, a new 3Dscanning method for measuring BSA is introduced and used to propose new BSA formulas. (Tikuisis et al., 2001; Yu et al., 2010) An overview of a non exhaustive list of BSA formulas is

**AUTHOR FORMULA** 

Stevenson (1937) BSA = 0.0128 \* weight + 0.0061 \* height - 0.1529 Banerjee & Sen (1955) BSA = 0.007466 \* weight 0.425 \* height 0.725 Banerjee & Bhattacharya (1961) BSA = 0.0070 \* weight 0.425 \* height 0.725 Fujimoto et al. (1968) BSA = 0.008883 \* weight 0.444 \* height 0.663 Gehan & George (1970) BSA = 0.0235 \* weight 0.51456 \* height 0.42246 Haycock et al. (1978) BSA = 0.02465 \* weight 0.5378 \* height 0.3964

DuBois & DuBois (1916) BSA = 0.007184 \* weight 0.425 \* height 0.725 Faber & Melcher (1921) BSA = 0.007850 \* weight 0.425 \* height 0.725 Boyd (1935) BSA = 0.017827 \* weight 0.4838 \* height 0.5

Mosteller (1987) BSA = (weight 0.5 \* height 0.5)/60

Livingston & Lee (2001) BSA = 0.1173 \* weight 0.6466

Nwoye (1989) BSA = 0.001315 \* weight 0.2620 \* height 1.2139 Shuter & Aslani (2000) BSA = 0.00949 \* weight 0.441 \* height 0.655

The GFR of a healthy person can vary from 1 ml/min for neonates to 200 ml/min for large adults. White et al. stated that this makes the interpretation of a GFR measurement not easy for the physician unless the physician is familiar with the expected normal value for the particular patient. (White & Strydom, 1991) Therefore, it would be worth considering to

In 1928, renal function was for the first time corrected for BSA by McIntosh et al. (McIntosh et al., 1928) McIntosh et al. built their indexation theory on the experience of the research of Taylor et al., which assumed a correlation between urea excretion and the weight of the kidneys in rabbits. Taylor et al. also showed that there exists a better correlation between kidney weight and BSA, than between kidney weight and animal's weight. (Taylor et al., 1923) When McIntosh et al. on their turn corrected urea clearances of 18 adults and 8 children for BSA, the data from the small children yielded the same normal values as for adults. In the footsteps of Taylor et al., MacKay illustrated a direct correlation between BSA

Tikuisis for men (2001) BSA = 0.01281\* weight 0.44 \* height 0.60 Tikuisis for women (2001) BSA = 0.01474 \* weight 0.47 \* height 0.55 Nwoye & Al-Sheri (2003) BSA = 0.02036 \* weight 0.427 \* height 0.516 Yu et al. (2010) BSA = 0.00713989 \* weight 0.4040 \* height 0.7437 Table 1. Overview of BSA formulas. BSA is expressed in m², weight in kg, height in cm.

normalize GFR in such a way that the influence of patient variables is minimal.

Meeh (1879) BSA = 0.1053 weight 2/3

given in Table 1.

**3. Indexing GFR for BSA** 

In 1928, McIntosh et al. already noticed that indexing is not necessary for 'normally built' people. McIntosh stated: "*The nature of the standard clearance formula is such that correction for body size in persons between 62 and 71 inches in height does not exceed 5 per cent, and in tests of renal function may be neglected.*" (McIntosh et al., 1928) It follows that in longitudinal studies, the absolute GFR should be used for evaluating the kidney function, avoiding the use of BSA-indexed GFR which is affected by weight changes. On the other hand, indexation seems to be necessary to compare different patient values and to allow comparison with fixed reference values. Three cases will here be studied to illustrate these statements: (1) the GFR of a small and heavy person will be compared with each other, (2) the GFR evolution during childhood will be presented and (3) the GFR of two adult men, one with a stable weight and one with a weight that increases with age, will be followed.

#### **4.1 Case 1: Comparison of the GFR of a small and heavy person**

Imagine the body of a small and heavy person as a small and big pond with the kidneys as a pump and filter combination to clear the dirt out of the pond. The dirt is equally present in the pond and the pump sends a constant flow through the filter which is here assumed to have the same clearing efficiency, after which the cleared water is drained off in the pond again. Repeated cycles will diminish the concentration of dirt in the water. If the small and the big pond both have an equally working pump and filter combination of 60 ml/min, it will take much longer for the big pond to be cleared than it will take for the small pond. Or the pump of the big pond will have to work at a higher rate than the pump of the small one to clear all the dirt out of the water in the same time. This indicates that the function of the pumps must be corrected for a value that describes the size of the ponds in a certain way.

If we normalize the absolute GFR of 60 ml/min of the small and heavy person for the BSA (Table 2), then we get a corrected cGFR of 73 ml/min/1.73m² for the small person as opposed to a much smaller cGFR of 46 ml/min/1.73m² for the heavy person. Once the GFR is BSA corrected, it becomes clear that the small person has a better kidney function than the

Is Body Surface Area the Appropriate Index for Glomerular Filtration Rate? 9

GFR. The man with the increasing weight has a GFR which is decreasing with age, but the cGFR is faster decreasing because of his increasing body surface area. There is indeed a double decreasing effect on the corrected cGFR. In Table 4, it is shown that the man with a stable weight has a cGFR of 111 ml/min/1.73m² at the age of 65. However, the man with the increased weight has a cGFR of 95 ml/min/1.73m² at the age of 65 years. This illustrates that weight-changes influence the BSA corrected GFR. Therefore one may wonder whether BSA

**DATA MAN - STABLE WEIGHT MAN - INCREASING WEIGHT Age (years)** 18 35 50 65 18 35 50 65 **Length (cm)** 180 180 180 180 180 180 180 180 **Weight (kg)** 70 70 70 70 70 80 90 100 **BSA (m²)** 1.89 1.89 1.89 1.89 1.89 2.00 2.10 2.20 **GFR (ml/min)** 142 138 133 121 142 138 133 121 **cGFR (ml/min/1.73m²)** 130 126 122 111 130 119 110 95

The cases described above illustrate that indexation is necessary to compare patient values with each other and with reference values. But the question remains whether BSA is the appropriate index for GFR. This has been a subject of debate during the last ten years.

Indexing GFR for BSA goes back to 1928 and it has become so conventional that BSAindexing can be considered as an icon in nephrology. Nevertheless, during the last ten years there is increasing criticism on BSA indexation. According to Tanner, the dispersion of differences between data of children and adults is not a very strong argument for BSA indexing. (Tanner, 1949) Neither is the argument that BSA indexation is necessary because everybody does it and in that way results become comparable. (Kronmal, 1993) BSA indexation is also seriously questioned in populations with unusual anthropometric data such as in children, in obese or lean persons. According to Bird et al. indexing GFR for BSA does not suit children because they naturally have a relatively high BSA simply because of their small size. (Bird et al., 2003) Delanaye et al. studied obese and anorectic patients. (Delanaye et al., 2005, 2009a, 2009b) In those patients, the consequences of indexing for BSA are much more important since the cGFR is influenced by weight-variation and may obscure variations in the absolute GFR. That is why Delanaye et al. recommend using the absolute

**DATA HEALTHY BOY Age (years)** 3.5 7.5 11 15 **Length (cm)** 99 126.5 146 173 **Weight (kg)** 15.5 25 37 58.5 **BSA (m²)** 0.64 0.94 1.24 1.70 **GFR (ml/min)** 44.5 65.0 86.0 118.0 **cGFR (ml/min/1.73m²)** 120 120 120 120

Table 3. Data for GFR evolution during childhood.

is the appropriate index for GFR.

Table 4. Data of an adult man.

**5. Criticism on indexing GFR for BSA** 

**4.4 Conclusion** 


heavy person. We may conclude that indexation of the GFR is necessary to allow comparison between different patients.

Table 2. Data for comparison of the GFR of a small and heavy person.

#### **4.2 Case 2: GFR evolution during childhood**

In this case, we study the evolution of a healthy boy during his childhood. In Table 3 the age, length, weight, BSA, absolute GFR and cGFR of the boy at the age of 3.5, 7.5, 11 and 15 years are listed. For the average healthy boy, the corrected cGFR remains constant during childhood (from 2-3 years till 14 years) (Piepsz et al., 2008, 2009) but the absolute GFR values of the boy at different ages cannot be compared with each other. From the data in Table 3 or by inspection of Figure 2, one may observe an increasing absolute GFR, as well as an increasing BSA as a function of age because the child and his kidneys are still growing. Referring to our pond analogy, one could say that the pump and filter combination of the pond are constantly changing in order to keep the pond clearance at the same rate. Correcting GFR for BSA leads to the same clearance value, independent of age. With the corrected cGFR, the child's kidney function can be followed, regardless of his growth process.

Fig. 2. (A) Absolute GFR as a function of age; (B) BSA as a function of age; (C) cGFR as a function of age.

#### **4.3 Case 3: GFR evolution during adulthood**

It is known that the GFR shows an age-dependent decline for the average healthy person, which may be considered as part of the normal biological process of senescence. The body weight is also often increasing with age. That is why in this case we study the GFR of two adult men, one with a stable weight during adulthood and one with a weight that increases with age (Table 4). The man with a stable weight has a normal age-dependent decreasing


Table 3. Data for GFR evolution during childhood.

GFR. The man with the increasing weight has a GFR which is decreasing with age, but the cGFR is faster decreasing because of his increasing body surface area. There is indeed a double decreasing effect on the corrected cGFR. In Table 4, it is shown that the man with a stable weight has a cGFR of 111 ml/min/1.73m² at the age of 65. However, the man with the increased weight has a cGFR of 95 ml/min/1.73m² at the age of 65 years. This illustrates that weight-changes influence the BSA corrected GFR. Therefore one may wonder whether BSA is the appropriate index for GFR.


Table 4. Data of an adult man.
