Acoustic measurements obtained from sensitive microphones placed on the chest are used in a procedure to noninvasively diagnose coronary artery disease. Utilizing specially developed signal processing techniques, the spectral content of isolated diastolic heart sounds has been estimated, and these sounds usually show an increase in high-frequency components in patients with occlusive coronary arteries. In order to establish a theory for the origin of these spectral features, a sound source model has been developed which combines an incremental network model of the left coronary artery tree with a transfer function model describing arterial chamber resonant characteristics. The network model predicts flow in both normal and stenosed coronary arteries. From this flow information, the arterial chamber transfer function model predicts the development of acoustic signals from the chamber resonant characteristics. The transfer function of a segment of coronary artery demonstrates two resonance frequencies. These resonance frequencies depend on the length and diameter of the chamber segment, as well as on the distal hydraulic impedance loading the segment. >

Modeling sound generation in stenosed coronary arteries

A lumped parameter model to evaluate the fluid dynamics of different coronary bypasses

A new lumped-parameter model for coronary hemodynamics is developed. This model is developed for the whole coronary network based on CT scans of a patient-specific geometry including the right coronary tree, which is absent in many previous mathematical models. The model adopts the structured tree model boundary conditions similar to the work of Olufsen et al., thus avoiding the necessity of invasive perfusion measurements. In addition, we also incorporated the effects of the head loss at the two inlets of the large coronary arteries for the first time. The head loss could explain the phenomenon of a sudden increase of the resistance at the inlet of coronary vessel. The estimated blood pressure and flow rate results from the model agree well with the clinical measurements. The computed impedances also match the experimental perfusion measurement. The effects of coronary arterial stenosis are considered and the fractional flow reserve and relative flow in the coronary vessels for a stenotic vessel computed in this model show good agreement with published experimental data. It is believed that the approach could be readily translated to clinical practice to facilitate real time clinical diagnosis.

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A patient-specific lumped-parameter model of coronary circulation.

This work reviews the main aspects of cardiovascular system dynamics with an emphasis on modeling hemodynamic characteristics by the use of a lumped parameter approach. The methodological and physiological aspects of the circulation dynamics are summarized with the help of existing mathematical models. The main characteristics of the hemodynamic elements, such as the heart and arterial and venous systems, are first described. Distributed models of an arterial network are introduced, and their characteristics are compared with those of lumped parameter models. We also discuss the nonlinear characteristics of the pressure-volume relationship in veins. Then the control pathways that participate in feedback mechanisms (baroreceptors and cardiopulmonary receptors) are described to explain the interaction between hemodynamics and autonomic nerve control in the circulation. Based on a set-point model, the computational aspects of reflex control are explained.

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Mathematical modeling of cardiovascular system dynamics using a lumped parameter method.

In this work, we propose a model of the coronary circulation based on hydraulic/electric analogy. This model aims to provide quantitative estimations of the distribution of flows and pressures across the coro-nary network for patients with stenoses of the left main coronary artery (LMCA), left anterior de-scending artery (LAD) and left circumflex branch (LCx), and chronic occlusion of the right coronary artery (RCA), undergoing off-pump coronary sur-gery. The results of the simulations are presented for 10 patients with various stenoses grades and collat-eral supply. For each patient, the four revasculariza-tion situations (no graft operating, pathological situa-tion (0G); right graft only (1G), left grafts only (2G), complete revascularization (3G)) are considered. It is shown that: 1) the complete revascularization is fully justified for these patients because neither the right graft alone, nor the left grafts alone can ensure a suf-ficient perfusion improvement for the heart; 2) the capillary and collateral resistances (and the propor-tion between them) have a major impact on the flows and pressures everywhere in the network; 3) in the presence of the left grafts, the flows in the native stenosed arteries become low and this could promote the development of the native disease in these branches.

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Patients' specific simulations of coronary fluxes in case of three-vessel disease

From Newton's equation and the continuity equation, an equivalent analogue circuit model can be derived for each small segment of the coronary arteries. Sapoznikov divided the coronary artery tree into 116 segments. By replacing each segment with its analogue circuit model, a final incremental network model was derived. The model was tested using typical physical parameters under normal conditions, as well as in the presence of coronary artery stenosis. In the case of stenosis, the arteriolar flow with and without autoregulation were compared. The model shows good agreement with the reported effects of stenoses and heart rate on coronary blood flow.

Jin Zhao Wang

Papers

Incremental network analogue model of the coronary artery.