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CARDIOVASCULAR
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Volume 8, 2003, No 1-2 |
Towards Optimal Control of Blood Flow in
Artificial Hearts
S. Tavoularis, A. Sahrapour, N. U. Ahmed, A. Madrane, R. Vaillancourt
Background: It is well known that high shear stresses and
turbulence can cause hemolysis, while alternating and low-level stresses that
are often encountered in recirculation and stagnation regions may contribute to
platelet activation and thrombus formation. The objective of this study is to
apply the mathematical theory of optimal control to the driving system of
artificial hearts in order to minimize flow-related potential problems.
Methods: Blood flow in large vessels may be approximated by unsteady,
incompressible flow of a Newtonian fluid, which is described by the
Navier-Stokes (momentum) and continuity equations. An optimization problem is
set up such that it selects the optimal variation of flow velocity at a wall
(simulating the motion of a pusher plate or a diaphragm) in order to minimize a
criterion (cost functional) as well as satisfy certain imposed constraints. A
tentative cost functional contains the mean squared shear stress and the mean
squared vorticity in the entire flow domain and the mean squared velocity on the
control boundary. Constraints include matching of the natural flow rate
variation during a cycle and maintaining a zero net displacement of all points
on the control boundary during a cycle. The imposition of optimality results in
an adjoint set of equations, which have to be satisfied simultaneously with the
equations of motion. The solution of all equations is obtained by an iterative
numerical algorithm.
Results: Examples of the application of this method are presented for a
prototype artificial heart, which is an idealized model of sac-type ventricular
assist devices with alternately opening and closing inlet and outlet ports. It
is demonstrated that application of optimal control results in flows with
reduced stresses and recirculation.
Conclusion: The general conclusion of this study is that optimal control
methods are a promising approach for optimizing the design and operation of
artificial hearts and, by inference, other medical devices involving the flow of
fluids.
(CVE. 2003; 8 (1/2): 20-31)
Key words: artificial heart, diaphragm, optimal control,
blood flow
Prof. Stavros Tavoularis
Department of Mechanical Engineering
University of Ottawa, Ottawa, Ontario
Canada K1N 6N5
E-mail: tav@eng.uottawa.ca
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