Abstract
A theoretical fluid mechanical model is proposed for the investigation of myocardial perfusion in healthy and stenotic conditions. The model hinges on Terzaghi’s consolidation theory and reformulates the related unsteady flow equation for the simulation of the swelling–drainage alternation characterizing the diastolic–systolic phases. When compared with the outcome of experimental in vivo observations in terms of left ventricle transmural perfusion ratio (T.P.R.), the analytical solution provided by the present study for the time-dependent blood pressure and flow rate across the ventricle wall proves to consistently reproduce the basic mechanisms of both healthy and ischemic perfusion. Therefore, it could constitute a useful interpretative support to improve the comprehension of the basic hemodynamic mechanisms leading to the most common cardiac diseases. Additionally, it could represent the mathematical basis for the application of inverse methods aimed at estimating the characteristic parameters of ischemic perfusion (i.e., location and severity of coronary stenoses) via downstream ventricular measurements, possibly inspiring their assessment via non-invasive myocardial imaging techniques.
Highlights
The factors that are usually responsible for triggering ischemic heart diseases can be identified in the reduction in coronary reserve below a lower limit, and/or in the increase in myocardial oxygen consumption above an upper physiological threshold.An arteriosclerotic lesion located within an epicardial vessel determines a downstream pressure drop that increases with decreasing vessel’s free diameter
The solid phase is represented by myocardial fibers and walls of vessels; The interstitial fluid is represented by the blood filling the myocardial vessels; The arterial network is responsible for the diastolic circumferential swelling process; The external overloading consists in a rhythmic vertical contraction of the heart muscle; σ indicates the vertical stress absorbed by the muscular fibers; p is the so-called transmural pressure; σ is the total vertical stress within the ventricle wall; The systolic circumferential drainage takes place through the venous network
It should be emphasized that, if stenosis were not removed, even the ischemic analytical model is forbythe first time proposed for the interpretation the fluidzones,An which are characterized a pathologic though non-immediately criticalofreduction mechanical processes governing left ventricle wall perfusion in healthy and in pressure and oxygen supply as compared to healthy conditions, would be atischemic risk of conditions
Summary
The factors that are usually responsible for triggering ischemic heart diseases can be identified in the reduction in coronary reserve below a lower limit, and/or in the increase in myocardial oxygen consumption above an upper physiological threshold. Bioengineering 2021, 8, 64 features of myocardial wall perfusion in normal conditions and in the presence of coronary occlusions that determine a reduced blood inflow towards a more or less extended ventricle sector. The model provides pressure and flow rate distribution in the ventricular occlusions that determine a reduced blood inflowfor towards a more orcirculation less extended large- and medium-scale arterial network and accounts the microscale Tion for the local time-dependent myocardial pressure and flow rate, it may be since the proposed model is fully analytical and yields an exact solution for the local useful for the application of inverse methods [20,21] aimed at estimating the ischemic pertime-dependent myocardial pressure and flow rate, it may be useful for fusion parameters that better fit downstream ventricular measurements. Detection of exact location and severity of coronary stenoses via myocardial imaging techniques [22,23,24,25,26,27]
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