Abstract
We present a fundamental theoretical framework for analysis of energy dissipation in any component of the circulatory system and formulate the full energy budget for both venous and arterial circulations. New indices allowing disease-specific subject-to-subject comparisons and disease-to-disease hemodynamic evaluation (quantifying the hemodynamic severity of one vascular disease type to the other) are presented based on this formalism. Dimensional analysis of energy dissipation rate with respect to the human circulation shows that the rate of energy dissipation is inversely proportional to the square of the patient body surface area and directly proportional to the cube of cardiac output. This result verified the established formulae for energy loss in aortic stenosis that was solely derived through empirical clinical experience. Three new indices are introduced to evaluate more complex disease states: (1) circulation energy dissipation index (CEDI), (2) aortic valve energy dissipation index (AV-EDI), and (3) total cavopulmonary connection energy dissipation index (TCPC-EDI). CEDI is based on the full energy budget of the circulation and is the proper measure of the work performed by the ventricle relative to the net energy spent in overcoming frictional forces. It is shown to be 4.01+/-0.16 for healthy individuals and above 7.0 for patients with severe aortic stenosis. Application of CEDI index on single-ventricle venous physiology reveals that the surgically created Fontan circulation, which is indeed palliative, progressively degrades in hemodynamic efficiency with growth (p<0.001), with the net dissipation in a typical Fontan patient (Body surface area=1.0 m(2)) being equivalent to that of an average case of severe aortic stenosis. AV-EDI is shown to be the proper index to gauge the hemodynamic severity of stenosed aortic valves as it accurately reflects energy loss. It is about 0.28+/-0.12 for healthy human valves. Moderate aortic stenosis has an AV-EDI one order of magnitude higher while clinically severe aortic stenosis cases always had magnitudes above 3.0. TCPC-EDI represents the efficiency of the TCPC connection and is shown to be negatively correlated to the size of a typical "bottle-neck" region (pulmonary artery) in the surgical TCPC pathway (p<0.05). Energy dissipation in the human circulation has been analyzed theoretically to derive the proper scaling (indexing) factor. CEDI, AV-EDI, and TCPC-EDI are proper measures of the dissipative characteristics of the circulatory system, aortic valve, and the Fontan connection, respectively.
Highlights
Pioneered advances in computational, analytical and experimental cardiovascular fluid dynamics 6,14,27,29,32,42 currently enable patient-specific quantitative hemodynamic analysis of several disease pathologies and for any surgically created pathway, almost routinely.[7,36,39,41] While the current technology allows detailed spatial/temporal prediction of hemodynamic/physiological parameters of interest, such as wall shear stress indices, pressure drops, blood trauma parameters and hydrodynamic energy dissipation, the clinical significance of the absolute values of these parameters, for the patient under consideration is still vague
How can the clinician use detailed information such as pressure drops or raw energy dissipation rate data in a patient and translate it to treatment decisions? Clinical management often relies on “indexing” as a way to establish a threshold number or an acceptable range for a given parameter (e.g. stroke volume is indexed as (1) stroke volume index defined as ratio to body surface area; or (2) Ejection fraction defined as ratio to end diastolic volume)
The scaling of energy dissipation occurring at any component in the circulation system is examined with respect to patient size and cardiac output. This is followed by the formulation of the mean mechanical energy budget of the circulatory system. Based on this formulation, we present three new indices: The first one is a circulatory system level index that is not disease specific, called the circulation energy dissipation index (CEDI), which quantifies the dissipative characteristic of the entire circulatory system as a whole
Summary
Analytical and experimental cardiovascular fluid dynamics 6,14,27,29,32,42 currently enable patient-specific quantitative hemodynamic analysis of several disease pathologies and for any surgically created pathway, almost routinely.[7,36,39,41] While the current technology allows detailed spatial/temporal prediction of hemodynamic/physiological parameters of interest, such as wall shear stress indices, pressure drops, blood trauma parameters and hydrodynamic energy dissipation, the clinical significance of the absolute values of these parameters, for the patient under consideration is still vague. The three new non-dimensional energy dissipation measures of the whole circulatory system (CEDI), aortic stenosis (AV-EDI), and TCPC surgical connection (TCPC-EDI) are introduced.
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