Nonlinear pulsatile flows

466

Abstracts

RELATIOS

OF TURBULENT

BLOOD

PAUL D. STEIS (Department

FLOW TO CARDIOVASCULAR

PATHOPHYSIOLOCl

of Medicine. Henry Ford Hospital, Detroit, MI 48202, U.S.A.)

Disturbances of flow, particularly turbulence, are clinically important in relation to cardiac murmurs and to the configuration of some aspects of the arterial pulse. Regarding disease processes, it is likely that turbulence may relate to post stenotic dilatations, and aneurysms. It is also likely that hemolysis in the region of prosthetic and natural stenotic valves relates to turbulence and/or high shear stresses. Thrombosis in the region of prosthetic valves and microthrombi on natural stenotic valves perhaps also may partially relate to turbulence and/or wall shear. There is a possibility that continued narrowing of congenitally stenotic valves may relate to such disturbances, through the process of a repetitive deposition and organization of microthrombi. Regarding atherosclerosis, once plaques have developed, there is a possibility that disturbances distal to the plaques may accelerate the disease process. It is unlikely that turbulence participates in the initiation of atherosclerosis. The role, if any, of fluid dynamic factors in atherosclerosis is speculative, but recent data suggest that sites of low shear show the earliest atherosclerotic changes. NONLINEAR

TIN-KAN HUNG (Departments

PULSATILE

FLOWS

of Civil Engineering and Neurosurgery, Pittsburgh, PA 15261, U.S.A.)

University of Pittsburgh,

Blood flows in arteries are dominated by cardiac pumping, the curvature and the changes in cross-sections. The nonlinear characteristics of the pulsatile flows are further complicated by the distensibility of the arterial wall. Without experimental data as input, a mathematical approach to the problem becomes difficult. Simplification has to be made with minimal artifacts in computational Bow simulation. Formulation of the dimensionless form of the Navier-Stokes equations is vital to the convergence of numerical solution. For flows in curved or stenotic vessels, the time-dependent boundary conditions are cast in the differential equations, making the computational algorithms simpler and effective for solving the moving boundary value problems. The instantaneous pressure drop between two points of the upstream and downstream end-sections is prescribed as the input dynamic condition along with the dilation and contraction of the wall. The pressure and velocity profiles at these two endsections became part of the numerical solutions for the pulsatile blood flow simulation by digital computer. This approach, however, is not suitable when the geometry outside of the computational domain has a significant effect on the velocity profiles at both end-sections.

FLUID-DYNAMICS

ASPECTS

WEN-JEI YANG (Department

OF ATHEROGENESIS

IN CARDIOVASCULAR

SYSTEMS

of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109, U.S.A.)

Circumstantial evidence is abundant, stating that the origin and development of arterial disease are related to hydrodynamic variables. The geometric features of blood vessels affect the flow profile, shear stress, and pressure drop. It is, therefore, natural to suspect that the location and rate ofatherosclerosis vary with vascular geometry. A computational technique is developed to predict unsteady two-dimensional blood ffow in human aortic bifurcations. Cubic splines or polynomials are fitted to the digitized contours of the vascular walls to generate the computational region. The area is then mapped onto a rectangle with a slip which is the image of the inner walls. The Navier-Stokes equations are transformed by the mapping into the new plane. The velocity profiles and the vorticity are in terms of the stream function. Wall shear distributions are calculated for pulsatile flows. The velocity profiles at the bifurcation of the human descending aorta are validated against the experimental results obtained by a laser Doppler anemometer. The wall shear distributions are used to determine geometric risk factors in atherosclerosis. MECHANICS

OF BLOOD

SUCKING

INSECTS:

DEVELOPMENT

OF MODEL

EQUATIONS

NARENDERP. REDDY (Biomechanics Laboratory,

Department of Biomedical Engineering, University of Akron, Akron, OH 44325, U.S.A.)

The domain of insect biomechanics, to a large extent, remains unexplored. An understanding of the mechanics of blood sucking and nectar feeding is important in studying the optimal feeding and foraging strategies in the blood