The purpose of scaling organ dimensions is motivated by the possibility of comparing individuals of different body sizes, a potent determinant of organ size. This is useful in comparative physiology, to understand differences among species, as well as in human pathophysiology, to explore changes induced both by body growth during childhood and by diseases during adulthood and maturity. In human studies, scaling meets the necessity of understanding when a physiologic or pathologic process influences organ development, function, or simply dimension, in the attempt to capture diseased conditions even when not clinically evident.
Human heart size has been a major target for studies of this type. The attempt to normalize left ventricular (LV) mass (LVM) for body size is not merely an academic exercise but has strong clinical implications, because, with the exception of age, LV hypertrophy (LVH) is the most potent (and reversible) marker of cardiovascular risk. The awareness of this power is increasing, and the computation of LVM index is increasingly included in echocardiography reports, despite the technical problems related to correct ultrasound orientation and the identification of interfaces.
All types of anthropometric parameters present substantial limitations, especially when normalizing cardiac structural parameters during childhood. Nevertheless, by strong tradition, body surface area (BSA) is the indexing variable most often used to normalize for body size LVM, LV dimensions, and LV volumes in adults. The most popular formula was developed by Du Bois and Du Bois more than a century ago but has never been validated in obesity. BSA has been used ratiometrically to normalize LVM (i.e., assuming that LVM values are linearly proportional to BSA values). Human growth, however, is not isometric (meaning that changes in body size due to growth or other physiologic processes do not lead to proportional changes in organ size), and therefore, that assumption does not fit with physiology.
In addition, on the basis of geometric considerations, a three-dimensional parameter (such as LVM) cannot be a linear function of a two-dimensional measure (such as BSA). This geometric mismatch was nicely represented in a simulation, demonstrating that the power regulating the relation between LVM and BSA is not 1 (linear) but 1.5 (exponential), as would be expected. In other words, to make linear the relation between LVM and BSA, BSA needs to be raised to the power of 1.5, resulting in a cubic function, compatible with the three-dimensionally shaped LVM (i.e., m 2 raised to the power of 1.5 = m 2×1.5 = m 3 ).
The Body Weight Issue
Following historical studies, the great comparative physiologist Knut Schmidt-Nielsen spent a substantial part of his life working on scaling, demonstrating that the relations between body size and organ size are in fact allometric (i.e., changes in organ size are not proportional to changes in body size induced by growth or other physiologic processes) and not isometric. This means that they are regulated by power regressions of the type Y = a × X b , where the coefficient of regression b is the allometric scaling factor Schmidt-Nielsen called the “allometric signal.”
The most practical procedure for scaling, therefore, would be to normalize organ size using the allometric signal of body weight (kilograms). This is what has been done for heart weight in a series of 104 mammalian species. As described by Prothero, the allometric regression regulating this relation across the species was the following:
As expected, the allometric signal of body weight was very close to 1 (both terms of the equation share a common three-dimensional shape). Because the normal left ventricle represents 40% to 45% of the total weight of the normal heart, this equation indicates that LV weight in a healthy man of 80 kg should be 170 to 190 g.
Taking the opportunity of the large range of body sizes in our laboratory’s database, as an example, we tested Prothero’s equation in three random subjects with very different body weights. In a normotensive, normal-weight man with a perfect body mass index ( Table 1 ), the equation was accurate in predicting the observed LVM. However, when applied in a class III obese patient, the true LVM was overestimated by 62%. Even more surprising, in a very small girl with anorexia nervosa, the degree of overestimation was even greater (93%).
| Variable | Normal | Obesity | Anorexia nervosa |
|---|---|---|---|
| Sex | Male | Male | Female |
| Age (y) | 39 | 48 | 17 |
| Weight (kg) | 81 | 151 | 34 |
| Height (m) | 1.80 | 1.72 | 1.58 |
| BMI (kg/m 2 ) | 25 | 51 | 14 |
| Blood pressure (mm Hg) | 118/64 | 126/82 | 92/60 |
| Observed LVM (echocardiography) (g) | 188 | 220 | 43 |
| Predicted LVM (based on BW) (g) | 194 | 356 | 83 |
| LVM, difference from observed (g [%]) | 6 (3) | 136 (62) | 40 (93) |
The reason for this overestimation in conditions of abnormal body size lies in the different body compositions of the three subjects. Both the obese and the anorectic patients have deficits of fat-free mass, relative in the obese patient and absolute in the presence of anorexia. The alteration in body composition explains the impossibility of reliably predicting LVM from weight in individuals who substantially deviate from a “normal” body shape and poses doubts regarding variables derived using weight, such as BSA. And, in fact, the use of normalization to BSA substantially underestimated the prevalence of LVH and the population risk attributable to LVH, when applied in a population with high prevalence of obesity.
Ideally, because the left ventricle is a muscle, LVM should be normalized for fat-free muscle mass. An easily measured surrogate of fat-free mass is body height. In mammals, height (or length) is a measure of the skeletal size, the architecture supporting the muscle mass. The skeleton, therefore, is genetically linked to given amounts of muscle, and skeletal length (or height) is biologically linked to a genetically programmed (“ideal”) fat-free body mass.
Thus, body height is an acceptable surrogate of what should be fat-free mass in normal conditions. Because of the geometric disproportion between height (a linear measure) and LVM (a three-dimensional variable generated by a cubic function), the relation cannot be linear, because LVM should approach a cubic function of height. And, in fact, when examining a very large range of body sizes, encompassing nearly the entire life span (between 3 months and 70 years of age) and maintaining normal proportions between weight and height (i.e., in normal-weight individuals), the allometric signal found to linearize the relation between LVM and height is 2.7, close to 3.
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