Research Papers

Nonlinear Dynamics of Dacron Aortic Prostheses Conveying Pulsatile Flow

[+] Author and Article Information
Eleonora Tubaldi

Department of Mechanical Engineering,
McGill University,
Macdonald Engineering Building,
817 Sherbrooke Street West,
Montreal, QC H3A 0C3, Canada
e-mail: eleonora.tubaldi@mail.mcgill.ca

Michael P. Païdoussis

Fellow ASME
Department of Mechanical Engineering,
McGill University,
Macdonald Engineering Building,
817 Sherbrooke Street West,
Montreal, QC H3A 0C3, Canada
e-mail: michael.paidoussis@mcgill.ca

Marco Amabili

Fellow ASME
Department of Mechanical Engineering,
McGill University,
Macdonald Engineering Building,
817 Sherbrooke Street West,
Montreal, QC H3A 0C3 Canada
e-mail: marco.amabili@mcgill.ca

Manuscript received August 15, 2017; final manuscript received December 31, 2017; published online March 19, 2018. Assoc. Editor: Jonathan Vande Geest.

J Biomech Eng 140(6), 061004 (Mar 19, 2018) (12 pages) Paper No: BIO-17-1365; doi: 10.1115/1.4039284 History: Received August 15, 2017; Revised December 31, 2017

This study addresses the dynamic response to pulsatile physiological blood flow and pressure of a woven Dacron graft currently used in thoracic aortic surgery. The model of the prosthesis assumes a cylindrical orthotropic shell described by means of nonlinear Novozhilov shell theory. The blood flow is modeled as Newtonian pulsatile flow, and unsteady viscous effects are included. Coupled fluid–structure Lagrange equations for open systems with wave propagation subject to pulsatile flow are applied. Physiological waveforms of blood pressure and velocity are approximated with the first eight harmonics of the corresponding Fourier series. Time responses of the prosthetic wall radial displacement are considered for two physiological conditions: at rest (60 bpm) and at high heart rate (180 bpm). While the response at 60 bpm reproduces the behavior of the pulsatile pressure, higher harmonics frequency contributions are observed at 180 bpm altering the shape of the time response. Frequency-responses show resonance peaks for heart rates between 130 bpm and 200 bpm due to higher harmonics of the pulsatile flow excitation. These resonant peaks correspond to unwanted high-frequency radial oscillations of the vessel wall that can compromise the long-term functioning of the prosthesis in case of significant physical activity. Thanks to this study, the dynamic response of Dacron prostheses to pulsatile flow can be understood as well as some possible complications in case of significant physical activity.

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Grahic Jump Location
Fig. 1

Schematic of the shell conveying pulsatile flow with boundary conditions at the shell ends

Grahic Jump Location
Fig. 2

(a) Flow velocity at rest (blue line) and during exercise (green line), (b) transmural pressure values in the aortic segment; dotted line: physiological data [62], continuous line: Fourier series with N = 8

Grahic Jump Location
Fig. 3

Computed time response of the nondimensionalized radial displacement w/h of the Dacron prosthesis, ζ = 0.04, (a) at rest (HR = 60 bpm) and (b) during exercise (HR = 180 bpm); dotted line: x = L/4, dashed line: x = L/2, continuous line: x = 3L/4

Grahic Jump Location
Fig. 4

Computed time response of the Dacron prosthesis under physiological pulsatile pressure and velocity at rest conditions, ζ = 0.04, HR = 60 bpm; (a) w1,0, (b) w2,0, (c) w3,0, and (d) w4,0

Grahic Jump Location
Fig. 5

Computed time response of the Dacron prosthesis under physiological pulsatile pressure and velocity during exercise, ζ = 0.04, HR = 180 bpm; (a) w1,0, (b) w2,0, (c) w3,0, and (d) w4,0

Grahic Jump Location
Fig. 6

Frequency spectrum of the response of the Dacron prosthesis to physiological pulsatile pressure and velocity at rest conditions, ζ = 0.04, HR = 60 bpm; (a) w1,0, (b) w2,0, (c) w3,0, and (d) w4,0

Grahic Jump Location
Fig. 7

Frequency spectrum of the response of the Dacron prosthesis to physiological pulsatile pressure and velocity during exercise, ζ = 0.04, HR = 180 bpm; (a) w1,0, (b) w2,0, (c) w3,0, and (d) w4,0

Grahic Jump Location
Fig. 8

Frequency response curves of the axisymmetric modes: (a) w1,0, (b) w2,0, (c) w3,0, and (d) w4,0 obtained by varying the HR; ζ = 0.01 (black line), ζ = 0.02 (green line), ζ = 0.03 (red line), ζ = 0.04 (blue line), ζ = 0.05 (magenta line)

Grahic Jump Location
Fig. 9

Maximum (continuous line) and minimum (dashed line) frequency response curves of the axisymmetric modes, ζ = 0.04; (a) w1,0, (b) w2,0, (c) w3,0, and (d) w4,0

Grahic Jump Location
Fig. 10

Bifurcation diagrams for the asymmetric modes, ζ = 0.01; (a) w1,2, (b) w2,2, (c) w3,2, and (d) w4,2; T and 2T stand for periodic response with the excitation period and twice the excitation period, respectively



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