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Technical Briefs

# Lumped Flow Modeling in Dynamically Loaded Coronary Vessels

[+] Author and Article Information
J. Jacobs, D. Algranati

Faculty of Biomedical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel

Y. Lanir1

Faculty of Biomedical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israelyoram@bm.technion.ac.il

1

Corresponding author.

J Biomech Eng 130(5), 054504 (Sep 17, 2008) (5 pages) doi:10.1115/1.2979877 History: Received January 15, 2008; Revised May 14, 2008; Published September 17, 2008

## Abstract

Most of the myriad (order of $109$) interconnected coronary vessels interact nonlinearly with their embedding contracting myocardium. Their dynamic flow can be simulated based on a nonlinear distributive segmental flow model involving highly nonlinear partial differential equations. Such network flow analysis, although of high accuracy, is computationally excessively complex. On the other hand, a corresponding nonlinear lumped analysis is significantly less demanding since it involves ordinary differential equations. This is, however, at the detriment of accuracy. In the present technical report, a nonlinear lumped representation of coronary segmental flow is presented and tested against predictions of the corresponding distributive analysis. The results suggest that under physiological conditions, the proposed lumped model achieves similar accuracy to the distributive one, yet with considerably higher computational speed.

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## Figures

Figure 1

Electrical nonlinear analog of the segment lumped flow model. The resistances R1 and R2 and capacity C are pressure dependent (Eq. 8).

Figure 2

Left: single bifurcation three vessel network; right: seven vessel network

Figure 3

Predicted nodal pressure distribution for subnetworks A1, A2, and A5. Note the excellent agreement between distributive and lumped models. The normalized time τ equals 0 at early systole and 0.6 at early diastole. Circles in the inset designate predictions of the lumped model.

Figure 4

Predicted nodal exit discharge distribution for subnetworks A1, A2, and A5. Note the excellent agreement between distributive and lumped models. Circles in the inset designate predictions of the lumped model.

Figure 5

Discharge error graph for case A2

Figure 6

Input boundary pressures for network A4. Left, PA, PV pressure distributions; right—PT pressure distribution.

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