Statistics at high-altitudes: Relevance for the interpretation of metrics that reveal cardiac morphology and performance.

Survey of four ratio-based metrics, commonly used to evaluate left ventricular performance. The numerator of each ratio is plotted against the corresponding denominator, implying that the slope of the colored line reflects the value of the ratio.9,11 Similar graphs can be constructed for the other cardiac compartments. Data sets obtained at various altitudes and defined with reference to sea level, based on Rao et al.6 Acronyms: E/A unitless ratio of the early (E) and late (A) diastolic wave peak velocities (cm/s); EDD, end-diastolic diameter (mm); EDV, end-diastolic volume (mL); EF, ejection fraction (%); ESD, end-systolic diameter (mm); ESV, end-systolic volume (mL); FS, fractional shortening (%).

Pulse Pressure is Sex-Specifically Associated with the Ratio of Diastolic and Systolic Arterial Pressure in Healthy Children, and Differently During Night Versus Daytime Recordings.

Noninvasive blood pressure recordings typically focus on systolic blood pressure (SBP) and diastolic pressure (DBP). Derived metrics are often analyzed, e.g. pulse pressure (PP), defined as SBP minus DBP. As the metric PP is not unique, we introduced the PP companion (PPC), calculated using the Pythagorean theorem. PPC is associated with mean arterial pressure (MAP). Another mathematical construct frequently used in hemodynamic studies refers to the ratio of DBP and SBP, denoted as Prat. PP and Prat share the same companion (C). The association between PratC and MAP, as well as the connection between PP and Prat has not been studied in healthy children. We analyzed a large set of daytime (DT) and nighttime (NT) data (N=949, age 5 to 16 years, including 485 girls), published in the literature. Average PP increases with age (in 0.5 year increments), while Prat decreases. Prat vs PP yields R2>0.985 for both DT and NT data, when stratified for boys and girls. PPC is significantly lower (P<0.0001) during the night for both sexes. We conclude that Prat carries no substantial incremental value beyond PP, in contrast to PPC which points to DT/NT, age-dependent and sex-specific differences in these children.Clinical Relevance- Various derived metrics based on blood pressure have been introduced in hemodynamic studies, but not all of them are fully independent. The diastolic to systolic pressure ratio in healthy children is inversely associated with pulse pressure, showing partial sex-specific overlap, but substantial daytime versus night differences.

Sex-specific Evaluation of Ventricular Ejection Fraction and End-Systolic Volume Applied to Cardiac Resynchronization Therapy.

Cardiac resynchronization therapy (CRT) can decrease the risk of heart failure (HF) events in relatively asymptomatic patients with a reduced ejection fraction (EF) and wide QRS complex. However, individual response to this type of therapy varies widely. Often based on either EF increase or end-systolic volume (ESV) decrease as criterion, a subgroup of super-responders has been described. Therefore, it is important to determine factors that can predict a favorable response and identify those patients who may benefit from CRT. With this goal in mind we explored the possible role of ESV.To improve insight in ventricular pump function we previously introduced the volume regulation graph (VRG), relating ESV to end-diastolic volume (EDV). An individual patient is uniquely defined by the prevailing working point in the volume domain. The traditional metric EF can be graphically derived for each working point. The nonlinear association between EF and ESV is given by EF = 1 + γ {ESV / (δ - ESV)}, with empirical constants γ and δ. The impact of CRT super-responders on EF can be evaluated, taking into account sex-specific ESV values. Based on available regression equations we modeled the impact on EF (as percent points) resulting from CRT-induced fractional ESV changes expressed as % of baseline ESV. Our analysis confirms clinical findings, indicating that CRT super-responders are likely to be women, and clarify why a specific reduction of ESV cannot be directly translated into EF improvement. We propose that the EF as CRT criterion should be abandoned and replaced by sex-specific ESV evaluations.Clinical Relevance- Response to CRT should be evaluated in a sex-specific manner. The smaller heart size in women has implications for the interpretation of percentwise reductions of ESV and their translation into an associated increase of EF.

Ventricular Ejection Fraction and Global Strains in Connection with the Volume Regulation Graph.

Ejection fraction (EF) is traditionally considered useful to infer ventricular function. Newer metrics such as global function index (GFI) and various strains add supplemental diagnostic or prognostic value. All these candidates refer to dimensionless ratios, rather than to the characteristics of the underlying components. Therefore, we introduced the volume regulation graph (VRG), relating end-systolic volume (ESV) to end-diastolic volume (EDV). An individual patient is then uniquely defined by the prevailing working point in the volume domain. Alternatively, the combination of EF=(1-ESV/EDV) and any suitable companion (denoted as C) metric (e.g. the Pythagorean mean) specifies this working point.An expression relates EF to global longitudinal (GLS) and circumferential strain (GCS): ESV/EDV = (GLS+1) (GCS+1)2, resembling the empirical regression equation for the VRG. However, the latter has a non-zero intercept (mL). The discrepancy can be solved by the introduction of one or more pertinent companion metrics.We studied 96 patients by cardiac magnetic resonance imaging and calculated EF, EFC, GFI, GLS and GCS. The GFI is inversely related to GLS (R2=0.26). For regression we found: ESV=0.74 EDV-27.0 with R2=0.81 for N=96. Similar results were obtained for echocardiography data (N=25). Graphs relating EF to GLS and GCS indicate that EFC can distinguish patients with nearly identical values for these 3 metrics.Thus, the VRG offers a unifying framework that visualizes the association between ESV and EDV, while documenting iso-EF and iso-EFC trajectories. Newer metrics including GFI, GLS and GCS require consideration of a companion variable such as EFC to permit a comprehensive analysis.Clinical Relevance- The VRG allows insight into ventricular functioning and illustrates the working point concept. Companion metrics (having a physical dimension) should be considered in conjunction with any traditional ratio-based index.

Ventricular and Atrial Ejection Fractions are Associated with Mean Compartmental Cavity Volume in Cardiac Disease.

Ejection fraction (EF) is considered to provide clinically useful information. Despite its enormous popularity, with more than 75,000 citations in PubMed, only few studies have traced the origin(s) of its foundation. This fact is surprising, as there are perhaps more papers published that criticize EF, than the number of publications that actually provide a solid (mathematical) basis for its alleged applicability. EF depends on two volume determinations, namely end-systolic volume (ESV) and end-diastolic volume (EDV). EF is defined as 1-ESV/EDV, yielding a metric without physical units. Previously we formulated a robust analytical expression for the nonlinear connection between EF and ESV. Here we extend that approach by providing a formula to illustrate that EF is strongly associated with half the sum (HS) of ESV and EDV. HS is not new, but forms a major component in the recently introduced Global Function Index. For 420 heart failure (HF) patients we found for left ventricular angio data: R(ESV, eDv) = 0.92, R(EF, ESV) = -0.90, and R(EF, HS) = -0.65. For echo (33 HF patients stages A, B, C and D): R(EF, HS) = -0.82. For the right atrium (CMRI in 21 acute myocardial infarction patients): R(EF, HS)=-0.65. For the left atrium (N=86) R (EF, hS)=-0.46. ESV indicates the level to which the ventricle is able to squeeze blood out of the cavity via pressure build-up. In contrast, EF refers to relative volume changes, not to the mechanism of pumping action. We conclude that for each cardiac compartment EF borrows its acclaimed attractiveness from the fact that for a wide patient spectrum the ESVand EDV correlate in a fairly linear manner. Attractiveness of EF features a straightforward mathematical derivation, rather than reflecting underlying physiology. Clinical Relevance - Ejection fraction (EF) is found to reflect (mean) ventricular / atrial size, and is primarily associated with end-systolic volume, which variable in turn highly correlates with diastolic volume. As a mathematical construct, EF has little affinity with "function", which is a central concept in physiology.

The Ratio of Diastolic and Systolic Arterial Pressure is Associated with Pulse Pressure.

Pulse pressure (PP) is defined as the difference between systolic blood pressure (SBP) and diastolic blood pressure (DBP). The metric PP is not unique, as numerous combinations of SBP and DBP yield the same value for PP. Therefore, we introduced the PP companion (PPC) which is calculated using the Pythagorean theorem. Only the combination of PP and PPC offers unique characterization. Interestingly, PPCwas found to be associated with mean arterial pressure (MAP). Another mathematical construct frequently used in hemodynamic studies refers to the ratio of DBP and SBP, or DBP/SBP, denoted as Prat. As Prat and PP share the same companion (C), we investigated the association between PratC and MAP, as well as the connection between PP and Prat. Various patient cohorts were included: A) 52 heart failure patients (16 women), B) 88 patients (11 women) with acute cardiac syndromes, C) 257 patients (68 men) diagnosed with atherosclerosis or any of various types of autoimmune disease, and D) 106 hypertensives (51 men). Linear regression analysis resulted in the following correlations: A: R (PratC, MAP) = 0.94, R (PP, Prat) = -0.91 B: R (PratC, MAP) = 0.98, R (PP, Prat) = -0.85 C: R (PratC, MAP) = 0.97, R (PP, Prat) = -0.86 D: R (PratC, MAP) = 0.92, R (PP, Prat) = -0.82 We conclude that Prat carries no substantial incremental value beyond PP, while both Prat and PP are incomplete metrics, requiring simultaneous consideration of MAP. Clinical Relevance- Various ratio-based metrics have been introduced in hemodynamic studies without paying attention to missing components or even redundant candidates. Here we present a uniform method to provide comprehensive insight.

[A critical analysis of ejection fraction]. / La serendipia en torno la fracción de eyección: una revisión de la historia, la casualidad y la cuasi-funcionalidad de una métrica aplaudida.

Ejection fraction (EF) is defined by the ratio of end-systolic volume (ESV) and end-diastolic volume (EDV). The resulting fraction is a dimensionless number whose interpretation is ambiguous and most likely misleading. Despite this limitation, EF is widely accepted as a clinical marker of cardiac function. In this article we analyze the role of ESV, a fundamental variable of ventricular mechanics, compared with the popular EF. Common physiology-based mathematics can explain a simple association between EF and ESV. This concept is illustrated by a detailed analysis of the information obtained from angiocardiography, echocardiography and cardiac magnetic resonance studies. EF versus ESV produces a non-linear curve. For a small ESV, the EF approaches 100%, while for a large ESV, the EF gradually decreases toward zero. This elemental relationship is commonly observed in innervated natural hearts. Thus, the popularity of EF mostly derives from a fortuitous connection with the pivotal variable ESV. Alongside this finding, we unfold historical events that facilitated the emergence of EF as a result of serendipity. Our physiology-based approach denounces the circumstantial theories invoked to justify the importance of EF as an index of cardiac function, which are critically discussed. EF appears to be nothing more than a blessing in disguise. For this reason, we propose the ESV as a more logical metric for the analysis of ventricular function.

Various Approaches to Define the Volume Intercept of the Ventricular End-Systolic Pressure-Volume Relationship: Implications for Statistical Analysis.

Ventricular pump function is often characterized by the (non)linear end-systolic pressure-volume relationship (ESPVR). For each working point on that curve the tangent along with the intercept (Vo) reflect contractile state. Vo on the abscissa is an extrapolated point without physiological meaning, and may be negative. To obtain positive values for the intercept, investigators often choose a non-zero pressure level. Although this preference is mathematically sound, we demonstrate that statistical evaluations may yield different results, depending on the pressure level selected. Published data on 17 cardiac patients representing three diagnostic groups were analyzed, showing dicrotic notch pressure based values -14

La serendipia en torno la fracción de eyección: una revisión de la historia, la casualidad y la cuasi-funcionalidad de una métrica aplaudida / A critical analysis of ejection fraction

Ejection fraction (EF) is defined by the ratio of end-systolic volume (ESV) and end-diastolic volume (EDV). The resulting fraction is a dimensionless number whose interpretation is ambiguous and most likely misleading. Despite this limitation, EF is widely accepted as a clinical marker of cardiac function. In this article we analyze the role of ESV, a fundamental variable of ventricular mechanics, compared with the popular EF. Common physiology-based mathematics can explain a simple association between EF and ESV. This concept is illustrated by a detailed analysis of the information obtained from angiocardiography, echocardiography and cardiac magnetic resonance studies. EF versus ESV produces a non-linear curve. For a small ESV, the EF approaches 100%, while for a large ESV, the EF gradually decreases toward zero. This elemental relationship is commonly observed in innervated natural hearts. Thus, the popularity of EF mostly derives from a fortuitous connection with the pivotal variable ESV. Alongside this finding, we unfold historical events that facilitated the emergence of EF as a result of serendipity. Our physiology-based approach denounces the circumstantial theories invoked to justify the importance of EF as an index of cardiac function, which are critically discussed. EF appears to be nothing more than a blessing in disguise. For this reason, we propose the ESV as a more logical metric for the analysis of ventricular function.

Ratiology and a Complementary Class of Metrics for Cardiovascular Investigations.

Cardiovascular investigations often involve ratio-based metrics or differences: ejection fraction, arterial pressure augmentation index, coronary fractional flow reserve, pulse pressure. Focusing on a single number (ratio or difference) implies that information is lost. The lost companions constitute a well-defined but thus far unrecognized class, having additive value, a physical dimension, and often a physiological meaning. Physiologists should play a prominent role in exploring these complementary avenues and also define alternatives.

Polar Coordinate Description of Blood Pressure Measurements and Implications for Sex-Specific and Personalized Analysis.

Vascular properties and their associated impact on cardiovascular risk factors are often evaluated by metrics such as pulse pressure (PP) and the augmentation index (AIx). All derived metrics are essentially based on the combination of blood pressure recordings. These clinically used metrics typically concern a difference (as in PP) or a ratio (as in AIx). A polar coordinate description reveals the companion (C) of the traditional metric. The aim of this study is to evaluate the impact of PPC and AIxC by analyzing both patient data and a detailed data set on healthy children derived from the literature.Companions are calculated using the Pythagorean theorem, and show that PPC is related to mean arterial pressure, thus complementing the biomarker PP. Also, inflection pressure is tied to systolic pressure, implying a possible simplification of obtaining the numerical value of AIx. Outcomes for adults and children are comparable. We conclude that derived metrics such as PP and AIx are incomplete. The associated companion metrics PPC and AIxC can easily be calculated. They add clinically relevant information without the need to perform additional measurements. Combination of traditional and the newly described companion metrics permits more precise characterization of individual patients.