Medical decision making for 5D cardiac model: Template matching technique and simulation of the fifth dimension

Abstract

The purpose of this paper is to develop a 5D cardiac model which is inspired from the 5D model for the lungs. This model depends on five variables: the anatomical structure of the 3D heart, temporal dimension and the function of blood flow as the fifth dimension. To test this hypothesis, we took the same mathematical modeling as a reference for the fifth dimension of pulmonary flow where r→_ρ(t)=r→_v(t)+r_f→(t) wherer→_v(t) is the displacement vectors with approximate magnitudes by linear functions of the tidal volume and r_f→(t) is the blood flow. The scans were acquired for 10 patients,in the 404 series for a total of 18,483 images studied in three cases: healthy patient, case of heart failure and aortic stenosis. Where r→_vand r→_f are the unit vectors along the volume of ejection and the blood flow axes, indicating the direction of motion of the object due to heart volume ejection and blood flow variations, respectively. The quantities of α and β coefficients are determined from real-time patient image data. The alpha and beta coefficients are derived from the following dimension equations[mm / ml] [mm*ms / ml] . Since the cardiac system has two diastolic and systolic phases, we have calculated α₁ and β₁ for telediatolic volume and α₂ and β₂ for telesystolic volume throughout the cardiac cycle as a function of the location of the cuts chosen randomly. Fifth-dimensional experiments are used to track, simulate the behavior of blood flow to detect preliminary indications for the identification of stenosis or valve leakage. The average discrepancy was tabulated as the global fraction of systolic ejection. The results shown in Fig. 3 detect a correspondence between the hunting chamber cut and the flow sequence through the orifice of aorta for this patient with suspicious of having an aortic stenosis disease and an ejection fraction about 71% with a maximum of velocity (Vmax) detected=250 (cm / ms) = 2.5 (m / 10-3 s). In this case this patient has a minor stenosis in the aorta. It should be referred that the normalization of this measures is classified such as : Minor stenosis: area 1.5 cm2, Vmax <3 m / moderate stenosis: area 1.0 - 1.5 cm2, Vmax 3 - 4 m / severe stenosis: area <1.0 cm2, Vmax> 4 m / s. For a patient who has an aortic stenosis the cloud of the points is accumulated comparing to the origin of the axis while the patient with a symptom of insufficiency the points are widened with a remarkable gap in the trajectory. To solve the issue of the bad prediction, the inaccuracy of the clouds points of the model 5D, the lack of the exact measurements to estimate the degree of cardiac insufficiency (leakage or stenosis), a solution of 5D imagery was depicted. Our main contribution is to test the validity of the template-matching algorithm and the fifth dimension simulation to provide more clues to detect the aortic stenosis and cardiac insufficiency in the context of medical decision support.

Keywords: 5D model; Blood flow, Prognosis; Cardiac pathologies; Valvulopathies.