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Abstract:
Simple least square regression analysis, major axis regression, and reduced major axis regression have been advocated for straight line fitting to the logarithmically transformed data pairs in bivariate allometric studies. As all these techniques are based on rigid a priori assumptions on the error structure, their application may lead to considerable biases in slope estimation if these requirements are not met. A different mathematical model, the linear functional relationship, allows to remove the bias by estimating the error structure from grouped empirical data. The model is applicable to interspecific and cross-sectional growth allometric studies where natural grouping criteria are available (species, age). The technique is illustrated by growth allometry of myocardial cells and capillaries in the late postnatal period (after weaning) in 33 normal male Wistar rats (group 1: 5 weeks, group 2: 7 weeks, group 3: 13 weeks, group 4: 52 weeks). In left ventricular myocardium fixed by vascular perfusion, length and volume densities of myocardial cells and capillaries were estimated by stereological techniques at the light and electron microscopic level. Total capillary length and total myocardial cell volume were scaled to total myocardial cell length. A comparison of the scaling methods showed an underestimation of the slope and its confidence interval by all regression techniques, which would have led to the erroneous conclusion that the myocardial cell does not remain geometrically similar throughout the normal growth process. Linear functional relationship and the technique of instrumental variables led to nearly identical results and were both compatible with geometric similarity of the myocardial cell during growth. Positive allometry of total capillary length to total myocardial cell length (b = 1.674) demonstrates continuous neoformation of capillaries. The intensity of capillary proliferative activity during growth was intermediate between the reactions observed in myocardial hypertrophy due to pressure overload and that due to physical training. This agrees with the fact that both systemic arterial pressure and cardiac output increase during maturation. The study is designed as a worked example which should enable the practicing researcher to treat data from cross-sectional growth allometric studies with a simple and unbiased statistical method.