BMI and body surface area

Clinical background

BMI and body surface area (BSA) are two anthropometric measures that serve different purposes. BMI classifies weight status and is used for risk stratification of metabolic and cardiovascular disease. BSA indexes haemodynamic variables, for example cardiac output (cardiac index = cardiac output/BSA), and forms the basis of dosing for drugs with a narrow therapeutic window, above all cytotoxic agents.

Both measures rest on weight and height alone. What makes them practical — that they require neither laboratory analysis nor sophisticated measuring equipment — is also their weakness: they reduce body composition to two external dimensions and do not separate fat mass from muscle mass.

Calculating BMI and body surface area

BMI is calculated as weight divided by height squared:

$$\text{BMI} = \frac{\text{weight (kg)}}{\text{height (m)}^2}$$

Body surface area is calculated with empirically derived formulae. The calculator reports three:

Mosteller [1]: $$\text{BSA} = \sqrt{\frac{\text{height (cm)} \times \text{weight (kg)}}{3600}}$$

Du Bois: $$\text{BSA} = 0{.}007184 \times \text{height (cm)}^{0{.}725} \times \text{weight (kg)}^{0{.}425}$$

Haycock: $$\text{BSA} = 0{.}024265 \times \text{height (cm)}^{0{.}3964} \times \text{weight (kg)}^{0{.}5378}$$

Mosteller's formula was published in 1987 as a simplification of earlier formulae, above all the Du Bois equation, and spread rapidly because of its simplicity [1]. The Du Bois equation was derived in 1916 from nine subjects, several of them infants, and despite its narrow derivation base has been the most widely used body surface area formula for a century [2]. Haycock's formula was validated in 1978 in infants, children and adults and is often preferred in paediatrics [2].

Interpretation in practice

BMI is classified by the WHO into four main categories:

The thresholds of 25 and 30 were chosen on the basis of the association between BMI and mortality in large cohort studies and have been retained by the WHO since 1997. Where the BMI is borderline, particularly between 24 and 26, the measure should be interpreted together with abdominal adiposity and the metabolic risk profile rather than as a classifier on its own.

BSA has no classification bands. The value is used as a continuous variable: cytotoxic doses are adjusted to BSA (mg/m²), and cardiac output is indexed as cardiac output divided by BSA (L/min/m²). A normal cardiac index is around 2.5–4.0 L/min/m². In adult patients in routine practice, the BSA usually lies between 1.5 and 2.2 m².

When several BSA formulae are compared in the same patient, the results usually differ by a few per cent. In marked obesity the difference can be greater, which is important to bear in mind when dosing cytotoxic drugs with a narrow therapeutic window.

Validation and performance

The ability of BMI to identify obesity, defined as a raised body fat percentage by bioelectrical impedance, was evaluated in the NHANES III cohort of 13,601 adult participants aged 20–80 years [3]. At the threshold of BMI ≥30, specificity was high: 95 per cent in men and 99 per cent in women. Sensitivity was, by contrast, low: 36 per cent in men and 49 per cent in women. BMI correlated moderately with fat percentage (R² = 0.44 in men, 0.71 in women) but equally well with fat-free mass (R² = 0.50 and 0.55 respectively), confirming that the measure does not separate fat from muscle mass. Diagnostic performance declined with increasing age, and in the intermediate BMI range of 25–30 the tool was at its weakest.

For the BSA formulae, Verbraecken et al. [2] compared Mosteller, Du Bois and six other formulae in 1,868 adult patients across normal weight, overweight and obesity. All the formulae correlated highly with one another. The Du Bois equation underestimated body surface area in patients with obesity compared with a 3D-based reference method, and Mosteller was recommended for adult patients on the basis of its simplicity and satisfactory agreement.

Fancher et al. [4] compared the Du Bois and Mosteller formulae at extremes of height and weight and found that the difference could produce clinically significant differences in cytotoxic dose, particularly in patients in the upper percentiles for height and weight.

Limitations

BMI rests on the assumption that weight and height capture body composition, which is only partly true. Well-trained individuals with a large muscle mass may have a BMI in the obese range without a raised fat percentage. Conversely, older patients with sarcopenia and a relatively higher fat percentage may have a normal BMI and still carry metabolic risk. In patients with ascites or oedema, weight reflects fluid retention rather than body mass.

The BSA formulae share a common weakness: they are empirically derived from small and not always representative cohorts. The Du Bois equation rests on nine subjects, several of them children. None of the formulae has been validated against modern 3D scanning in patients with marked obesity, and agreement between them is poorest precisely in this group.

For cytotoxic dosing, the question has been raised whether BSA-based dosing is rational at all, since pharmacokinetics vary independently of body surface area. Some protocols have therefore moved to fixed doses or dosing per kg body weight rather than per BSA.

References

1. Mosteller RD. Simplified calculation of body-surface area. N Engl J Med. 1987;317(17):1098. PMID: 3657876
2. Verbraecken J et al. Body surface area in normal-weight, overweight, and obese adults. A comparison study. Metabolism. 2006;55(4):515–524. PMID: 16546483
3. Romero-Corral A et al. Accuracy of body mass index in diagnosing obesity in the adult general population. Int J Obes (Lond). 2008;32(6):959–966. PMID: 18283284
4. Fancher KM et al. Comparison of two different formulas for body surface area in adults at extremes of height and weight. J Oncol Pharm Pract. 2016;22(5):690–695. PMID: 26385906