A mathematical reason for FEV1/FVC dependence on age

Abstract

Background: Recent studies have showed that FEV1/FVC describing correspondence between the forced expiratory volume in one second (FEV1) and forced vital capacity (FVC) depends significantly on age. However, the nature of this dependence is uncertain. The study aim is to analyze mathematically the relationship between FEV1 and FVC to find a cause of the FEV1/FVC dependence on age in healthy subjects.

Methods: The relationship was examined for 1,120 males and 1,625 females--Polish (Caucasian) population, healthy, never-smoking, aged 18 - 85 years, who performed a technically adequate spirometry maneuver. Lung functions were measured using the LungTest1000 (MES, Poland) with maximal effort according to the ATS/ERS guidelines.

Results: A very strong, age-independent linear relationship between FEV1 and FVC was found in healthy individuals (the correlation coefficient r = 0.96). It can be described with the equation FEV1 = A x FVC + C, where A = 0.84 and C = -0.23 (-0.36) for females (males). As C is different from zero, FEV1/FVC depends on FVC because FEV1/FVC = A + C/FVC, in average. And thus, since FVC is significantly age-dependent, FEV1/FVC has to be also age-dependent because of the term C/FVC. In particular, the smaller the FVC value because of advanced age, the more significant the fall of FEV1/FVC.

Conclusions: FEV1/FVC dependence on age in healthy individuals is of mathematical rather than biological nature. Due to the strong correlation between FEV1 and FVC in healthy subjects, the difference between patient's FEV1 and the FEV1 value expected for patient's FVC seems to be a more natural, age-independent description of the correspondence between patient's FEV1 and FVC.

Figure 1

Forced expiratory volume in one second (FEV1) versus forced vital capacity (FVC) in females and males. Light gray dots – the studied material; thin lines – the linear regression; bold points creating curves – the moving 50th percentile of FEV1 for particular values of FVC calculated separately in three ranges of age (blue- 18–40, black- 41–65, and red- 66–85 years).

Figure 2

A graphical interpretation of FEV1/FVC decline with age in healthy subjects. FEV1 and FVC for an individual can be represented by one point on the plane determined by the coordinate system: FVC and FEV1. The ratio FEV1 to FVC is equal to the tangent of the angle α contained between the horizontal axis (FVC-axis) and the vector leading out to that point from the coordinate system origin. Thus, the lower value of the angle, the smaller the FEV1/FVC value.

Figure 3

Predicted forced expiratory volume in one second (FEV1) versus forced vital capacity (FVC) for females. Light gray dots – the studied material. Bold curves – the mean values of FEV1 and FVC predicted for females aged 20 to 80 year (height = 160, 165, and 170 cm) with equations of various authors: ECSC [11], Lubinski and Golczewski [7], Brandli et al. [12], Langhammer et al. [13], Hankinson et al. [14], Falaschetti et al. [8]. The red parts of the curves correspond to data for females younger than 35 years (they are partly covered by the black parts).

Figure 4

Standardized Spirometric Aberration Index (SAI) plotted against age. Gray dots - the studied material, the bold line - the predicted value (equal to SAI = 0), the thin line - the lower limit of normal (equal to SAI= −1).