Steven D. Colan1 and Leo Lopez2 1 Harvard Medical School; Boston Children’s Hospital, Boston, MA, USA 2 Stanford University School of Medicine Stanford, CA; Lucile Packard Children’s Hospital Standford, Palo Alto, CA, USA Observations of the developing cardiovascular system date from antiquity, with Aristotle’s description of the beating heart in a chicken egg. However, quantitative description of the cardiovascular system was a key step on the path to modern cardiology. The development of measurement techniques, beginning in the nineteenth century, combined with the ability to treat heart lesions beginning in the mid‐twentieth century, spurred interest in accurate diagnosis and in methods correlating structure and function of the cardiovascular system with clinical outcomes. Determination of the sizes of cardiovascular structures is mandatory for adequate diagnosis and treatment of acquired and congenital cardiac disease [1]. For many cardiac disorders, these quantitative variables are highly predictive of outcome and provide critical information about response to therapy, timing of intervention, and, most importantly, which type of intervention is likely to have the optimum outcome. However, changes in the size and shape of cardiovascular structures can be secondary to factors other than the disease process, and methods are therefore required to differentiate these potential confounders. These issues are particularly evident in children, where somatic growth and maturation can potentially confound detection of disease or treatment effects. Recommendations for standardization of measurements in children were published in 2010 by the American Society of Echocardiography [2]. These recommendations included reporting the size and function of cardiovascular structures as the number of standard deviations from the population mean value (z‐score) relative to age or body size, depending on which of these independent variables is the primary physiologic determinant. Normative values for echocardiographic measurements that are derived from data collected at Boston Children’s Hospital, measured in accordance with the American Society of Echocardiography recommendations are available at https://zscore.chboston.org. The methods of data collection and analysis have been previously published [3,4]. Essential to understanding the reliability of these measurements is documentation of their reproducibility, and the intraobserver, interobserver, and interacquisition variability has also been systematically evaluated [5]. These studies provide the foundation for a recently established normative database of echocardiographic measurements in a large cohort of healthy children in North America as part of the Pediatric Heart Network (PHN) Echo Z‐Score Project [6]. Here we present a general discussion of the issues surrounding adjustment of cardiovascular structures for age and body size and the methods that were used in the derivation of the models in the PHN project. The application and clinical utility of normative data (z‐scores) ultimately depend on the ability to predict outcomes. A severely dilated left ventricle (LV) with a z‐score >4 standard deviations (SD) above the normal mean can be compatible with long‐term survival and normal functional capacity, whereas ventricular hypoplasia with a z‐score <‐4 is not tolerated even in the short term. An additional caveat to the interpretation of z‐score values is that the relationship between degree of abnormality and outcome is highly variable and disease specific, and evolves continuously depending on available therapies. For example, based on data in patients with neonatal critical aortic valvar stenosis, in 1991 we derived an equation based on the sizes of the mitral valve, aortic root, and length of the LV relative to body surface area (BSA) that predicted survival after balloon dilation of the aortic valve with 95% accuracy [7]. However, this predictive capacity was rapidly rendered obsolete due to therapeutic advancements in the field that achieved survival in patients who were previously considered candidates only for single ventricle repair or cardiac transplantation. Ultimately, the statistical degree of abnormality of size and function of a cardiovascular structure is a mathematically determinable, static quantity. In contrast, the implications these abnormalities have for outcomes are disease specific, continuously evolving, and associated with an evolving predictive capacity. The relation of cardiovascular dimensions to body size and age can be observed empirically and analyzed statistically, based on measurements of cardiac and vascular structures derived from imaging data such as echocardiography. The study of the relative growth of a part of an organism in relation to the growth of the entire organism is known as allometry, and therefore here we are concerned with cardiovascular allometry. Although cardiac computed tomography, magnetic resonance imaging, and catheterization also provide quantitative assessment of cardiac structures, these modalities involve greater risk and cost. Therefore, echocardiography remains the primary source of empirical normative pediatric allometric data. Allometric relations can also often be predicted theoretically from basic physiologic principles. These two approaches can be used for purposes of reciprocal verification. A higher level of confidence can be attached to conclusions that are based on concordance of established physiologic principles and empirical methods. We have previously performed such a comprehensive analysis focused primarily on vascular structures [3] and summarize the results here. The development and maintenance of optimum geometric properties of the vascular pathways is essential to provide adequate blood flow over a wide range of body activities, while simultaneously avoiding excess hemodynamic stress. Optimized design of biological structures as a result of the environmental pressure exerted by natural selection is an established principle of biology that explains the curvilinear relation of the weight of a tree and the size of its branches [8], the relation between the diameters of pulmonary bronchi and bronchial air flow, and the shape of eggs [9–11]. Energy efficiency for the vascular system is maximized when the vascular size minimizes the energy required to propel blood through the vascular system by optimizing the relationship between vessel radius and flow rates. Theoretical foundations of the principle of minimum work [12,13] and optimality of the vascular system based on Murray’s law [14–19] have been validated by the quantitative studies of coronary [20] and cerebral arterial dimensions [21]. The theoretical aspects and details of these calculations have been described in detail [14,20,21]. The energy cost of phasic blood flow is determined by two components. Viscous energy loss [22,23] in blood vessels is related to friction between flowing blood and the vessel wall at the endothelial vessel–blood interface. This energy loss decreases with increasing vessel diameter due to the geometric relationship between vascular cross‐sectional area and vascular surface area. The volume of blood within a cylindrical blood vessel increases in proportion to the square of the radius whereas the surface area increases in direct proportion to the radius. Therefore, the proportion of blood in contact with a viscous interface decreases as the radius increases, which means there is proportionally less resistance to flow in large vessels. The second component of energy loss is due to the oscillatory nature of blood flow in the central arterial tree. The oscillatory component of energy loss is related to the need to accelerate flow with every beat (kinetic energy that is lost during the deceleration phase), and this oscillatory component increases in proportion to the volume of blood that undergoes cyclic acceleration and deceleration. The optimal vascular dimension is that at which the sum of these two competing energy costs is minimized (Figure 5.1a). We estimated the viscous energy loss and the inertial energy content of blood flow for the aorta and the main pulmonary artery over the typical range of body surface area (BSA, 0.2–1.8 m2) and over the range of cardiac output (CO) encountered during physical activity (from 3.5 L/min/m2 to 17.5 L/min/m2) in order to determine the optimal vessel size [3]. We found that the size of the aorta that we observed in our normal population corresponded to the theoretical optimal value in terms of energy dissipation for CO up to two times the resting CO in infants, increasing to values that were optimal for three to four times the resting CO for older children (Figure 5.1b). Data obtained from athletes and hypertensive subjects indicate that cardiac structures adapt to peak levels of pressure and volume demand. Heart rate response is the primary determinant of CO increase with exertion, and infants have an approximately twofold magnitude of heart rate reserve, a value that increases to three‐ to fourfold in older children and young adults. Thus, the difference between observed diameters that are optimal in terms of energy dissipation in infants versus children corresponds to the expected difference in CO associated with age‐appropriate physical activity and range of intensity of exertion. Many disease processes result in a change in the size or function of cardiovascular structures, and quantitative assessment of these changes is diagnostically and prognostically useful. However, the usefulness of these measurements is limited by the confounding effects of growth and other factors that influence LV size. In general, cardiovascular structures are highly plastic and are known to remodel in response to variations in the hemodynamic state related to a large number of interacting factors such as growth, development, exercise participation, genetics, body composition, basal metabolic rate, and hematocrit, in addition to many environmental factors such as altitude and ambient temperature. Although many of these factors are difficult to quantify, body size and age are two of the most potent determinants, particularly in children, and are readily quantifiable. Therefore, considerable effort has been devoted to the study of the relationship between the size of cardiovascular structures and both age and body size. Figure 5.1 Optimal aortic valve radius calculated according to the principle of minimal work for two levels of cardiac output. Energy loss per second (erg/s) secondary to viscous friction (descending dashed line) is plotted against the radius of the aortic valve (cm). On the same scale, the inertial energy content of blood (ascending dashed line) and the total energy loss calculated as the sum of viscous energy loss and inertial energy content loss (continuous red line) are plotted for theoretical cardiac outputs (QS) of 3.5 L/min (a) and 17.5 L/min (b), representing the theoretical cardiac output at rest and at maximal exercise of a normal subject with a body surface area (BSA) of 1 m2. The least amount of total energy loss per unit time corresponds to the minimum of the total energy loss curve. The corresponding radius for 3.5 L/min flow is 0.45 cm and for 17.5 L/min it is 0.8 cm. These values represent the theoretical range of normal optimal aortic valve radius for this BSA. Source: Sluysmans T, Colan SD. Theoretical and empirical derivation of cardiovascular allometric relationships in children. J Appl Physiol 2005;99:445–57. The American Physiological Society. In addition to the implications of allometry for patient care, adjustment for the effects of changes in body size also has important implications for clinical research. Although clinical investigators attempt to avoid potential confounders by selection of a properly matched control group, if the disease or the therapeutic intervention can impact growth, detection of beneficial effects due to the therapeutic intervention can be confounded by differences in somatic growth between the intervention and control groups. For example, consider a study undertaken to determine if a novel medical therapy can favorably alter the severity of LV dilation in infants with dilated cardiomyopathy. We know that treatments may have different effects on somatic growth, either directly or secondary to improved cardiovascular status. Even if active and placebo treated cohorts are matched for age and BSA at the time of study enrollment, the differential impact of somatic growth on LV size could confound the interpretation of the direct effects of disease treatment on LV size if the proportion of change in LV size attributable to somatic growth cannot be quantified. Thus, adjusting for the effects of somatic size is critical to evaluating therapeutic benefit. Historically, the most common approach to adjusting cardiovascular structures for body size has been to calculate their ratio relative to BSA. For example, “cardiac index” is calculated as CO divided by BSA, and “left ventricular mass index” is frequently calculated as LV mass (LVM) divided by BSA, although alternative methods of adjusting LVM for body size have been recommended. Because the term “left ventricular mass index” is ambiguous, it is not used in this chapter and the specific formula is shown, such as LVM/BSA, LVM/BSA1.33, LVM/height2.7, etc. Current recommendations in the adult guidelines published by the American Society of Echocardiography are to adjust LV mass and volumes in adults using these “per‐surface area standards” [24] despite their demonstrated lack of validity [25–28]. For “indexing” to be successful, the indexed variable must be invariant with changes in the indexing variable. The genesis of the “per‐BSA” approach is the observation that in numerous intra‐ and inter‐species studies, body heat production and CO are linearly related to BSA over a broad range of body sizes [29,30]. Consequently, cardiac index has been adopted as a reasonably valid method of comparing the CO of individuals of varying BSA. Next, based on regression models that found a nearly linear relationship between CO and the size of other cardiac and vascular structures in adults, the per‐BSA method was extrapolated and adopted by many as a general method for adjusting for the effects of body size on all cardiovascular structures. Unfortunately, although the relationship between two variables can often be described as nearly linear, this does not mean that this is the best descriptor of their relationship. The mathematical inadequacy of this method can be readily recognized by a simple example. There are many studies documenting a statistically significant linear relationship between LV volume and BSA, and a statistically significant linear relationship between LV short‐axis dimension and BSA. However, volume and dimension are related by a cubic function, and it is therefore mathematically impossible for both volume and dimension to have a true linear relationship to BSA. The delusion that the per‐BSA method is adequate in adjusting for the effects of body size is based on excess reliance on simple linear regression analysis performed over short ranges of the independent variable (BSA) in the absence of critical examination of how well the mathematical model actually describes the data and whether these results align with physiological underpinnings [31,32]. It is reasonably straightforward to statistically test whether an allometric model provides an adequate description of the relationship between body size and the size of the body part. The intent of “indexing” or “normalizing” a variable such as CO for BSA is to permit valid comparisons between individuals of differing BSA by eliminating any residual dependence of the indexed variable on BSA. Therefore, if the method of indexing or adjusting for body size fully accounts for the effect of body size on the cardiovascular measurement, then the indexed variable will have the same mean value regardless of body size. It is worth considering a concrete example of how easily one can be misled by a high correlation coefficient obtained by linear regression. Figure 5.2a presents the strong linear relationship (R2 = 0.88) between the diameter of the aortic valve annulus (AVD) and BSA in 1365 normal children evaluated at Boston Children’s Hospital varying in age from newborn to 18 years of age and varying in BSA from 0.18 to 2.3 m2. Such observations, in the absence of careful testing for whether this linear model eliminates residual dependence of AVD on BSA, have led to the common method of a per‐BSA approach with “indexed aortic valve diameter” calculated as AVD divided by BSA. However, Figure 5.2b demonstrates the inadequacy of the per‐BSA method for this variable because a curvilinear (power) function provides a significantly better correlation for the AVD diameter versus BSA relationship. Figure 5.2c illustrates the mathematically equivalent form of the relation in Figure 5.2b as the regression of AVD versus BSA0.5, which results in a linear fit with the intercept passing through the origin. The aortic valve dimensions are seen to have a progressive increase in the residuals (the distance of the points from the regression line). When AVD/BSA0.5 is regressed against BSA (Figure 5.2d), there is no significant residual relation between the “indexed” AV dimension and BSA (that is, the slope of the regression line is not significantly different from zero), and there is also no significant relation between the residuals and BSA, indicating that heteroscedasticity (variability of the predicted variable) across the range of BSA has also been eliminated. This is the goal for a correctly “indexed” variable – the mean and standard deviation are constant over the data range. Figure 5.2 (a) The linear regression line for aortic valve dimension (AVD) versus body surface area (BSA) in normal children shows a high correlation with a non‐zero intercept. (b) The regression for AVD versus BSA is optimal for the nonlinear function AVD = a × BSA0.5. (c) The regression of AVD versus BSA0.5 is linear with a zero intercept. (d) The regression of AVD/BSA0.5 versus BSA demonstrates a constant mean and standard deviation. The inadequacy of the per‐BSA method has led investigators to evaluate other approaches to adjusting for the effect of body size on the size of cardiovascular structures. The first and simplest is to attempt to linearize the relationship by mathematically transforming either the cardiovascular structure, BSA, or both. The observation that the cross‐sectional areas of vascular structures relate linearly to BSA predicts that their diameters should relate linearly to the square root of BSA (BSA0.5). It has also been suggested that this approach can be generalized [3] such that linear measurements should be normalized to BSA0.5, area measurements should be normalized to BSA1.0, and volume measurements should be normalized to BSA1.5. Although this approach fails with cardiac chamber measurements (as discussed in the section “Adjustment of cardiac chamber size and LV mass for somatic growth”), the relationships of the central arterial dimensions follow this paradigm for dimensions and cross‐sectional areas. As shown in Figure 5.2c, AVD versus BSA0.5 is indeed highly linear with a zero intercept, and the graph of AVD/BSA0.5 versus BSA (Figure 5.2d) shows that indexing AVD to BSA0.5 eliminates residual dependence of the aortic valve diameter on BSA. Although vascular and valvar dimensions scale to BSA0.5 and vascular and valvar cross‐sectional areas scale to BSA1.0, chamber sizes, specifically atrial and ventricular volumes and ventricular mass, do not scale to BSA1.5, which would be the anticipated result if all normalized variables were dimensionless (cm/m, cm2/m2, and cm3/m3) [4]. However, despite the assertion by some investigators [33] that the relation between BSA and both LV mass (LVM) and volume must be BSA1.5, in fact the empirically observed relation documented by numerous investigators is that LV end‐diastolic volume (EDV) and LVM relate most closely to BSAb where mean b ~1.33 (range 1.25–1.35) [3,6]. For 1436 normal children evaluated at Boston Children’s Hospital, we found BSA1.33 to be the optimum scaling transform for left ventricular EDV (Figure 5.3), which is in close agreement to the exponent (1.3) identified in the larger multicenter PHN study [6]. The explanation for this failure to follow the same scaling paradigm is the nonlinear decrease in heart rate associated with increasing BSA and age. In the normal population the relations of age and BSA to heart rate are similar, although BSA is likely the more important physiologic determinant based on the impact of height on pulse wave reflections [34]
CHAPTER 5
Structural Measurements and Adjustments for Growth
Introduction
Physiologic principles underlying cardiovascular dimensions
The principle of minimum work
Allometric modeling
The fallacy of indexing for body surface area (BSA): the so‐called “per‐BSA method”
Alternative “indexing” methods
Adjustment of cardiac chamber size and left ventricular mass for somatic growth
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