Injection fraction

In cardiovascular physiology, Injection fraction represents diastolic volume (EDV) divided by end systolic volume (ESV) of the ventricles or IF=EDV/ESV, and is the inverse mathematical operation of the Myocardium Work derived Ejection Fraction.
To the lay reader the ejection fraction of the heart is a time honored ratio between two easily reproducible and measurable volumes of blood within the heart; first when the heart is as full as it can be with blood (End Diastolic Volume) and second after it has emptied as fully as possible (End Systolic Volume). Ejection fraction measures the volume of blood in the heart during the cardiac phase of Systole, inversely; injection fraction is measured during the second phase diastole. Similarly stated, Injection Fraction represents the ratio between the volumes of ESV, when the heart is emptied as fully as possible and EDV, when heart (ventricles) are fully loaded with blood.
"Ejection Fraction" is historically and mathematically derived from Cardiac Output first posited by Adolph Fick 1829-1901. Technical description of mathematic derivation of EF is beyond the scope of this arcticle but can be simplified by stating that it can be derived with many technologies in many ways. Echocardiography is perhaps the most inexpensive, noninvasive and reproducible means to do so. Mathematical and technical approaches to accurate expression of Ejection fraction are abundant and growing. The lay reader may be advised that the simplest expression of Ejection fraction (EF) may be appreciated as the difference between End-systolic volume and End-diastolic volume. EF=ESV/EDV. LVEF may be better appreciated as a basic mathematical construct of the left sided circulation first described by William Harvey 4/1/1578-6/3/1657.
Overview
Simplistically stated the mechanical force of the heart can be compared to a bucket being emptied to a fractional degree 100,000 times per day according to demand from the brain, body and lungs. The "bucket" in terms of accepted mathematical Boundary method is actually four sealed buckets in a cascade divided left and right. Mathematical definition and matching of the ESV and EDV ratios within each of the four chambers provides a more concise picture of volumetrics in both systolic and diastolic function. Computational imaging for these solutions are abundant; the underlying mathematics should remain free sourced.
Mechanical work of the heart is phased into Time intervals. Systole is the time spent emptying the buckets. Pressure required to expel blood from the left and right ventricles is commonly measured in Newtons and Pascals under a Force. Ballistics describes this phase as Coil. Ballistics implies gunpowder to create the force of solid metal against nonviscous air; the heart utilizes Phosphorylation of adenosine triphosphate (ATP) in a similar mechanism to create a force of semisolid muscle against viscous blood. The volumetric term ejection fraction occurs during systole.
Diastole is the opposing force and time spent refilling the ventricles. Ballistics describes this phase as Recoil. Many authorities describe diastole in terms as a passive phase of "relaxation". The opposed volumetric term injection fraction occurs during diastole. Diastolic recoil fills the lungs from the right heart at a much lower pressure gradient than the high pressure gradients in the left heart. Introduction of volumetrics to right sided circulation remains incomplete without inclusion of work by Ibn Al-Nafis 1213-1288 as the first physician to accurately describe the pulmonary circulation.
Mathematical description
Introduction of Time into the mathematics further invites physics. Perhaps the best encyclopedically way to gradually elaborate physics of the heart is the addition of well agreed upon phases and elements of Hooke's Law. Robert Hooke (1635-1703) basically broke down how well and for how long a spring does Work. He was modeling a property called elasticity. It is widely understood that a spring stretches farther when anchored on one end and weighted on the other. The weight straining against the spring can also be understood as Load or more simply, Mass. Robert Hooke likely confirmed the principle of compliance under this theorem. Springs within the myocardium may be stretched in many vectors.
Further appreciation of the phenomena taking place is illuminated by the physics of a bowstring. Cardiomyocytes in a string anchored on opposite sides of a valve ring vaguely resembles archery yet retains the inherent physics. Cardiomyocytes behave like a symphony of bowstrings in a coordinated series with singular purpose. A bowstring may be drawn (displaced) a certain distance to a zenith in vectoring the (blood) mass of the arrow to a target. The point where the arrow rests fully and is ready to be fired (bow fully drawn) may be understood as the Equilibrium Position. When released, the bowstring is again displaced and rapidly moves back to a resting position. All of these contributions can be understood to create a Force where:
x is displacement,
k is the rate or time interval of the displacement, and
F is the Force equal to the product of xk. The heart contains a plurality of springs and bowstrings. Injection fraction occurs during recoil of the springs and bowstrings within the myocardium driving blood into the heart.
The clinical utility of volumetric measurement of systolic function of the heart is now inexpensively replicated and imaged worldwide. Mathematical derivation as stroke volume and minimum volume or MinV similarly apply as determinants of Systole. Ejection Fraction was first, noninvasively and inexpensively reproduced echocardiographically in many languages as EF(EDV-ESV)/EDV. Extrapolated to a single chamber of known dimensions this calculation may be simplified to (LV and RV) yielding EFESV/EDV. Solved as such, this basic mathematical construct of Systole is key to myriad other supporting solutions including right vs. left systole, forward vs. backward systole and pulmonary vs. systemic systole. Q is another evolving attractive mathematical model of Systole.
Volumetric determinants of diastole implies a polemic mathematical approach to the published work of Adolph Fick. Injection fraction as a volumetric determinant of Diastole is the difference between end diastolic volume (EDV) and end systolic volume (ESV)of the left and right ventricles. IFEDV/ESV or (watered down) IF(ESV-EDV)/ESV. Decline of injection fraction implies a measurable volumetric determinant of diastolic dysfunction to the extent that decline of Right and Left EF heralds Systolic dysfunction.
Decline of IF may follow clinically relevant time ratios such as E:A intervals across the mitral valve. E:A ratios are difficult to interpret in a subject 70 or older. Tissue Doppler Echocardiography appears similarly useful in identifying pathologic regional wall motion as a signature of diastolic dysfunction.
It can be measured with a MUGA scan.

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