The Pythagorean theorem reveals the inherent companion of cardiac ejection fraction

Kerkhof, Peter L. M.; Merillon, J. P.; Yoo, Byung Won; Peace, Richard; Parry, Gareth; Heyndrickx, Guy R.; Kuznetsova, Tatiana; Meijboom, Lilian J.; Sprengers, Ralf W.; Park, Han Ki; Handly, Neal

doi:10.1016/j.ijcard.2018.06.074

Cited by 14 publications

(24 citation statements)

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“…Необходимо выявить недостающий элемент, который обозначается здесь как компаньон (с) и получаемый с математической точки зрения путем примене-ния графических изображений (рис. 2) в сочетании с теоремой Пифагора [2,3,5].…”

Section: Discussionunclassified

“…Важно отметить, что каждую точку на такой линии "iso-ФВ" можно различить, рассчитав расстояние от начала координат {0, 0} до конкретной точки {X, Y}. Длина этого отрезка прямой определяется как гипотенуза соответствующего треугольника и может быть вычислена с использованием теоремы Пифагора [2,3,5]. Значение компаньона ФВ (выраженное в мл) рассчитывается с использованием известной формулы на основе гипотенузы (C) [3]:…”

Section: материал и методыunclassified

“…Однако это означает, что преобразованные данные в лучшем случае предоставляют ту же информацию, что и исходные, и могут даже вводить в заблуждение. Для того, чтобы прояснить этот момент, категорию показателей, основанных на соотношении, таких как ИА, вентрикуло-артериальное сопряжение (ВАС) и ФВ, лучше всего представить в виде полярных координат для давления [2], эластичности и объема, соответ ственно [3]. То же самое относится и к разностям, таким как ПД или УО.…”

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Role of ratio-based metrics in cardiology

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In cardiovascular studies, two related parameters that determine the same physical variable are often recorded. Interpretation of the calculated indicators presented in the form of ratios and differences is difficult, since they can be associated with several combinations of primary data giving the same value.Aim. To find a way to overcome this limitation and take a more comprehensive approach.Material and methods. We analyzed the data on left ventricular volume and blood pressure (BP) in 275 patients (women — 207), obtained using echocardiography and BP monitor. To calculate a lost companion (c) value based on a difference or dimensionless ratio, we applied the Pythagorean theorem. The lost companion isdefined as the hypotenuse in each study area. To calculate the pulse pressure companion (PP), the following formula was used: PP(c)=Ö(SBP2+SBP2). Similar methods were applied to ejection fraction (EF), augmentation pressure (AG) and AG/PP ratio, resulting in the ratio called augmentation index (AIx).Results. 1. Mean blood pressure (MBP) acts as a surrogate for the PP companion (PPc) values (R=0,970, N=257). 2. We have identified correlations between PPc and pulse wave velocity (R=0,397, N=193), and AGc with AIx (75) (R=0,662, N=198). 3. EF has an inverse relationship with the end diastolic volume (EDV) (R=-0,559, N=187), and the ventricular-arterial coupling (VAC) correlates with ESV (r=-0,627, N=180). 4. Comparison of EDV and VACc revealed R of 0,949.Conclusion. Companions calculated from the available data can have significant additional diagnostic value without the need for additional measurements. It is important to note that the combination of traditional ratio-based and suggested companions allows for more accurate data on individual patients.

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Role of ratio-based metrics in cardiology

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“…To compensate for the incompleteness of the ratio, a corresponding companion (C) is identified that covers the missing information. 4 , 5 The necessity to introduce C can be readily understood from a graphical representation as in Figure 1 , based on the patient discussed. Ejection fraction is an algebraic composite of the variables on the two axes, namely ESV ( y- axis) and EDV ( x- axis).…”

Section: Introductionmentioning

confidence: 99%

“…distance from the origin (labelled S) to point A or B] is defined by EF companion (EFC) = √{ESV 2 +EDV 2 }, following the familiar Pythagorean theorem. 4 , 5 …”

Section: Introductionmentioning

confidence: 99%

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

Kerkhof

Heyndrickx

2021

European Heart Journal - Case Reports

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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.

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In search for the optimal ventricular systolic dysfunction metric that associates with reduced exercise capacity

Kerkhof

Handly

2022

J of Clinical Ultrasound

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The Pythagorean theorem reveals the inherent companion of cardiac ejection fraction

Abstract: The EFC is a neglected companion, containing information which is additive to EF. Analysis based on ESV and EDV is preferred over the use of EF.

Cited by 14 publications

References 17 publications

Role of ratio-based metrics in cardiology

Role of ratio-based metrics in cardiology

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

In search for the optimal ventricular systolic dysfunction metric that associates with reduced exercise capacity

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