The Pythagorean theorem reveals the inherent companion of cardiac ejection fraction

Coronary Flow Evaluation in Heart Transplant Patients Compared to Healthy Controls Documents the Superiority of Coronary Flow Velocity Reserve Companion as Diagnostic and Prognostic Tool

Background

Distinct contributions by functional or structural alterations of coronary microcirculation in heart transplantation (HT) and their prognostic role have not been fully elucidated. We aimed to identify the mechanisms of coronary microvascular dysfunction (CMD) in HT and their prognostic implications.

Methods

134 patients, surviving at least 5 years after HT, without evidence of angiographic vasculopathy or symptoms/signs of rejection were included. 50 healthy volunteers served as controls. All underwent the assessment of rest and hyperemic coronary diastolic peak flow velocity (DPVr and DPVh) and coronary flow velocity reserve (CFVR) and its inherent companion that is based on the adjusted quadratic mean: CCFVR = √{(DPVr)2 + (DPVh)2}. Additionally, basal and hyperemic coronary microvascular resistance (BMR and HMR) were estimated.

Results

Based on CFVR and DPVh, HT patients can be assigned to four endotypes: endotype 1, discordant with preserved CFVR (3.1 ± 0.4); endotype 2, concordant with preserved CFVR (3.4 ± 0.5); endotype 3, concordant with impaired CFVR (1.8 ± 0.3) and endotype 4, discordant with impaired CFVR (2.0 ± 0.2). Intriguingly, endotype 1 showed lower DPVr (p < 0.0001) and lower DPVh (p < 0.0001) than controls with lower CFVR (p < 0.0001) and lower CCFVR (p < 0.0001) than controls. Moreover, both BMR and HMR were higher in endotype 1 than in controls (p = 0.001 and p < 0.0001, respectively), suggesting structural microvascular remodeling. Conversely, endotype 2 was comparable to controls. A 13/32 (41%) patients in endotype 1 died in a follow up of 28 years and mortality rate was comparable to endotype 3 (14/31, 45%). However, CCFVR was < 80 cm/s in all 13 deaths of endotype 1 (characterized by preserved CFVR). At multivariable analysis, CMD, DPVh < 75 cm/s and CCFVR < 80 cm/s were independent predictors of mortality. The inclusion of CCFVR < 80 cm/s to models with clinical indicators of mortality better predicted survival, compared to only adding CMD or DPVh < 75 cm/s (p < 0.0001 and p = 0.03, respectively).

Conclusion

A normal CFVR could hide detection of microvasculopathy with high flow resistance and low flow velocities at rest. This microvasculopathy seems to be secondary to factors unrelated to HT (less rejections and more often diabetes). The combined use of CFVR and CCFVR provides more complete clinical and prognostic information on coronary microvasculopathy in HT.

Case report on the importance of longitudinal analysis of left ventricular end-systolic volume, rather than ejection fraction, in a heart transplant patient

Background

Sequential determinations of left ventricular (LV) volume constitute a cornerstone in the mechanical performance evaluation of any heart transplant (HTX) patient. A comprehensive analysis of volumetric data offers unique insight into adaptation and pathophysiology.

Case summary

With a focus on eight sequential biplane angiocardiographic LV end-systolic volume (ESV) determinations, we evaluate the clinical course of a male patient following HTX (female donor) at the age of 61 years. This former smoker had a history of chronic obstructive pulmonary disease, hypertension, and hypercholesterolaemia refractory to treatment, and presented with multivessel coronary artery disease. The later course was complicated by pulmonary hypertension, an abdominal aortic aneurysm, and secondary chronic kidney disease. After an additional episode of pulmonary embolism, the patient died at the age of 79. At one point, the ESV was > 700% higher than the starting value, and actually by far exceeded the relative change of any other volume-based metric evaluated, including ejection fraction (EF).

Discussion

The longitudinal study of LV volumetric data in HTX patients offers a unique window to the pathophysiology of remodelling and sex-specific adaptation processes. The present case documents that proper analysis of serial findings form a rich source of clinically relevant information regarding disease progression. End-systolic volume is the primary indicator, in contrast to the popular metric EF. This finding is supported by population-based studies reported in the literature. We conclude that comprehensive analysis of volumetric data, particularly ESV, contributes to personalized medicine and enhances insight into LV (reverse) remodelling, while also informing about prognosis.

Sex-Specific Interpretation of Coronary Flow Reserve and Fractional Flow Reserve Metrics, Including Their Companions

BACKGROUND

Impairment of coronary flow is usually evaluated by considering the ratio of two measurements. Fractional flow reserve (FFR) estimates impact on an epicardial artery by taking mean post-stenotic pressure divided by mean aortic pressure, both obtained during adenosine induced hyperemia. Coronary flow reserve (CFR) compares hyperemic flow or velocity with the baseline situation, also as a ratio. As severity of underlying pathology may differ for men and women, we investigate the impact of these differences on relevant metrics.

METHODS

As sex associated differences may cancel out in a ratio, this weakness of a ratio can be compensated by analyzing the intrinsic companion (C) and consider polar coordinates. Thus, besides the familiar ratio based metrics, we also analyze FFRC and CFRC. Outcomes of in silico studies are employed to extrapolate actual patient data and predict consequences. For FFR 129 patients (38 women) were invasively studied using pressure wires. CFR was measured noninvasively for the left anterior descending coronary artery by recording ultrasound based Doppler velocity in 114 individuals (28 women).

RESULTS

The FFR can be identified as an indicator of the pressure gradient over the stenosis (R=-0.90), while FFRC differs for men compared to women (P=0.04) and correlates (R=0.93) with post-stenotic driving pressure. CFR shows a difference for men versus women (P=0.04) and is best associated with hyperemic flow (R=0.64), whereas CFRC relates to hyperemia recruited velocity (R=0.97). Simulation studies show that FFR may differ for both sexes when considering elderly.

CONCLUSIONS

Analysis of ratios require inclusion of the companion, and sex-specific differences deserve attention.

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.

Fractional Flow Reserve Evaluated as Metric of Coronary Stenosis - A Mathematical Model Study

Introduction: Coronary arterial stenosis may impair myocardial perfusion with myocardial ischemia and associated morbidity and mortality as result. The myocardial fractional flow reserve (FFR) is clinically used as a stenosis-specific index. Aim: This study aims to identify the relation between the FFR and the degree of coronary arterial stenosis using a simple mathematical model of the coronary circulation. Methods: A mathematical model of the coronary circulation, including an arterial stenosis of variable degree, was developed. The relation between the FFR and the degree of stenosis (defined as the fractional cross sectional area narrowing) was investigated, including the influence of the aortic and venous pressures and the capillary resistance. An additional study concerning 22 patients with coronary artery disease permits comparison of clinical data and in silico findings. Results: The FFR shows an S-shaped relationship with the stenosis index. We found a marked influence of venous and aortic pressure and capillary resistance. The FFR is accompanied by a clinically relevant co-metric (FFR C ), defined by the Pythagorean sum of the two pressures in the definition formula for FFR. In the patient group the FFR C is strongly related to the post-stenotic pressure (R = 0.91). The FFR C requires establishment of a validated cut-off point using future trials. Conclusion: The S-shaped dependence of FFR on the severity of the stenosis makes the FFR a measure of the ordinal scale. The marked influences of the aortic and venous pressures and the capillary resistance on the FFR will be interpreted as significant variations in intra- and inter-individual clinical findings. These fluctuations are partly connected to the neglect of considering the FFR C . At otherwise identical conditions the FFR as measured at baseline differs from the value obtained during hyperemic conditions. This expected observation requires further investigation, as the current hyperemia based evaluation fails to take advantage of available baseline data.

Heart Failure Phenotypes Require Sex-Specific Criteria Which Are Based on Ventricular Dimensions

Ejection fraction (EF) is often used as a criterion to establish diagnostic phenotypes of heart failure (HF). Because EF is a derived metric based on end-systolic volume (ESV) and end-diastolic volume (EDV), it is more logical to consider ESV or EDV as cut-off marker. We concentrate on the impact of ESV, which has the advantage of being linearly related to EDV and nonlinearly with EF, both with highly significant correlations. In particular we also analyze if HF classification should distinguish between females and males.ESV and EDV were determined by biplane angiography in 197 HF patients (67 women). As body surface indexed (i) ESVi values for adult healthy females are smaller than for males, we employ classes of ESVi (bins of 10 mL/m²) to group preserved and reduced EF's (cut-off at 50%) for HF. Reference values regarding mean and standard deviation for ESVi are based on a control group (N=155, 65 women) without HF. For interpretation of the findings we use the documented universal relationship connecting EF to ESV: EF = 1 + c₁ {ESV / (c₂ - ESV)}, where c₁ and c₂ are population-based sex-independent constants. In the reference group ESVi (mL/m²) in women (27.4 ± 27.6) is smaller (P=0.0026) than in their male counterparts (43.6 ± 37.5). Similarly, for HF the ESVi in women (45.7 ± 41.4) is smaller (P=0.0033) than in men (64.2 ± 41.4). This signifies (see formula above) that women have higher values for EF, primarily resulting from smaller ventricular size related to their sex, and not exclusively reflecting disease state. Current phenotype classification based on pooled data for males and females may be inappropriate for either sex.The significantly smaller ESVi observed in women has direct consequences for the traditional classification based on EF cutoff values for HF. Sex-specific criteria (regarding ESVi or EF) for HF phenotypes are warranted, and expectedly have substantial consequences for identification, classification, and management of HF patients.

Sex- and Age-Related Reference Values in Cardiology, with Annotations and Guidelines for Interpretation

The definition of "abnormal" in clinical sciences is often based on so-called reference values which point to a range that experts by some sort of consensus consider as normal when looking at biological variables. Such a level is commonly calculated by taking (twice) the standard deviation from the mean, or considering certain percentiles. The suspicion or even confirmation of a disease is then established by demonstrating that the value measured exceeds the upper or lower reference value. As is often the case, the measurement accuracy may depend on the conditions and specific method employed to collect and analyze data. This implies that, for example, data assessed by 2D echocardiography possibly differ from those obtained by MRI and therefore require modality-specific reference values. In this review we summarize reference values for the electrocardiogram, cardiac compartmental volumes, and arterial vessel size in males and females for various age groups. These values may further depend on other variables such as body size, physical training status, and ethnicity. Additional variables relevant for cardiology such as those referring to the microcirculation and biomarkers are only mentioned with reference to the pertinent literature. In general, the sex- and age-specific differences observed are often remarkable and warrant consideration in clinical practice and basic biomedical sciences.