$608 Journal of Biomechanics 2006, Vol. 39 (Suppl 1)

Ventricular work and energy transferred to the aorta were calculated for all the different matching conditions. Ventricular-aortic energy transfer efficiency was calculated as the ratio between transferred work and ventricular work. Ventricular work ranged between 12.2±0.5mJ and 23±1mJ and the energy transferred to the aorta between 3.2±0.1mJ and 13.3±0.5mJ. Efficiency ranged from 64±3% to 23±1%. Optimal mechanical energy transfer was obtained by connecting the ventricle with the highest elastance to the aorta with the lowest elastance while the worst energy transfer was obtained with the lowest ventricular elastance connected to the highest aortic elastance. In all the conditions, ventricular work was proportional to ventricular elastance and showed a limited change by changing the aortic elastance. Energy transfer efficiency was strongly related to the mechanical matching and decreased by increasing the vascular elastance for all the three ventricles. These findings suggest that any mechanical intervention to decrease aortic elastance (i.e. insertion of dampers in the aorta) would have beneficial effects both on the ventricle (no increase in work production) and on the vascular side (increase in work transfer).

References [1] K. Sagawa. The end-systolic pressure-volume relation ofthe ventricle: definition,

modifications and clinical use. Circulation 1981;63(6): 1223-1227.

4433 Mo-Tu, no. 21 (P65) A membrane model for wave f low in the blood vessels M. Hamadiche 1 , N. Kizilova 2 . 1LMFA, Ecole Centrale de Lyon, Eculiy, France, 2Department of Theoretical Mechanics, Kharkov National University, Kharkov, Ukraine

A rational and tractable model for the blood flow in the arteries and veins as viscoelastic cylindrical tubes is presented. The vessel wall is considered as a stretched membrane. The Lagrangian approach is used for description the membrane motion whereas the Euler approach is used for the fluid flow. The waveform generated by the heart contraction in the inlet of the tube and the reflection conditions at the outlet are assigned basing on the Doppler ultrasound measurement data. The formulation leads to highly non-linear partial differential equations describ- ing the coupled fluid flow and wall displacement. Numerical and mathematical analysis of the dynamic equations is carried out in the limit of small defor- mations and small displacements. A set of steady and unsteady solutions of the simplified version of the dynamic equations with increasing complexities is obtained. The functional relationship between the group velocity of the propagating wave and the rheologic parameters is established. Using a linearized model the expression for wave speed is obtained in an- alytical form. The linear analysis shows that the wave speed in the blood vessels depends on both axial and azimuthal tension. However, the speed of the long (short) wave propagation only depends on the axial (azimuthal) tension accordingly. It is found that the arteries will collapse if the azimuthal tension could not balance the pressure fall due to the fluid acceleration and the threshold of the collapse is predicted. It is shown that there is interference between the downstream and upstream propagating waves that leads to complex waveforms depending on the reflection conditions at the outlet of the tube. The results are in qualitative agreement with the flow curves measured in different arteries at various reflection conditions.

14.5 Congenital Cardiovascular Disease Applications 6495 Mo-Tu, no. 22 (P65) Development of a novel system to predict intimal hyperplasia development in an end-to-side distal bypass graft junction S.M. O'Callaghan, T.M. McGIoughlin. Centre for Biomedical Engineering Research Centre, M&AE and MSSI, University of Limerick, Limerick, Ireland

Over 1,000,000 bypass graft procedures have been performed over the past 30 years. Unfortunately 40% of these bypass grafts junctions have failed within 5 years. The primary cause of failure is the development of intimal hyperplasia at the distal bypass graft junction. Intimal hyperplasia is the thickening of the tunica intima. Intimal hyperplasia is thought to develop at the distal bypass graft junction due to the abnormal hemodynamics introduced by the bypass junction. This research presents cell culture and computational results that identified temporal wall shear stress as the hemodynamic variables that most significantly correlates with locations of intimal hyperplasia development. Using computational fluid dynamics software to analysis images of realistic distal bypass graft junction geometry, a program was designed predicting locations of intimal hyperplasia development. This system could be developed into a diagnostic tool where potential sites of disease development could be identify and monitored.

Poster Presentations

7147 Mo-Tu, no. 23 (P65) Analysis of radial crushing strength of cardiovascular stents using finite element method K. Jayavenkateshwaran, J. Raamachandran. Solid Mechanics Group, Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, Tamlinadu, India

The importance of the cardiovascular stents is well understood because of their effectiveness in preventing restenosis. The stents are deployed in the coronary blood vessel generally through the arteries using the catheter with balloon. The stents which are crimped initially over the balloon are deployed by inflating the balloon and the deflated balloon with the catheter are removed after the deployment. Once the balloon is deflated, the stent structure will carry the radial crushing force exerted by the artery. The stent should be suitably designed to carry this radial crushing force otherwise the stent may buckle and take a noncircular cross sectional lumen or may even collapse radially. The present day stents consist of two parts namely (i) corrugated rings (ii) links. Corrugated rings essentially carry the radial crushing force whereas the links impart flexibility to the stent geometry. This paper studies the buckling strength and the radial collapse strength of four different corrugated ring geometries, using the finite element method. The effect of the number of folds per ring and the strut dimensions over these mechanical properties were studied through a parametric analysis.

References [1] Domulin C, Cochelin B. Mechanical behavior modeling of balloon expandable

stents. Journal of Biomechanics 2000; 33: 1461-1470. [2] Tan LB, Webb DC, Kormi K, AI-Hassain STS. A method for investigating the

mechanical properties of intra-coronary stents using finite element numerical simulation. International Journal of Cardiology 2001 ; 78: 51-67.

4164 Mo-Tu, no. 24 (P65) Pulse wave propagation in the intraorgan arterial beds and diagnostic analysis of pressure and flow curves N. Kizilova. Department of Theoretical Mechanics, Kharkov National University, Kharkov, Ukraine

Wave propagation and reflection in the intraorgan vasculatures is determined by their geometry, reflection conditions and wall properties. Important diag- nostic information about the inner organ state can be obtained by analysis of the pressure P(t) and flow U(t) curves measured non-invasively by ultrasound devices [1]. Due to significant individual variations the influence of geometry of the vasculature and pathological conditions has to be separated for the correct analysis of the curves. Here wave propagation in the systems of viscoelastic tubes is investigated. Geometrical parameters of the systems are obtained by measurements on vascular plastic casts. Basing on the model of the wave propagation in the viscoelastic tube and the pressure and flow continuity conditions at the bifurcations the input wave admittance is calculated for both tree-like systems and systems with loops. Different pathology is modelled as increasing rigidity of the wall, occlusion of separate tubes and variations in the reflection conditions at the terminuses. Some regularity in the structure and wave admittance of the vasculatures is obtained. The resonance characteristics [2] of the systems are computed. It is shown that negative wave reflection which amplifies the blood inflow due to the sucking effect is proper to the intraorgan vasculatures. Analysis of the intensities dl(t)=dP*dU of the forward and backward waves gives the estimations of the distances to the occluded vessels. The area and the slope of the P(U) loop are significantly defined by the resistance and compliance of the terminuses. Non-invasive measurements of the pressure-flow curves in the feeding artery of an inner organ is proposed for recognition the pathological variations and separation the influence of the altered wall properties, vessel occlusions and microcirculation state.

References [1] Kizilova N. Wave propagation and reflection in systems of compliant tubes. Int.

J. Fluid Mech. Res. 2004; 31(6): 608~20. [2] Kizilova N. Pulse wave reflections in branching arterial networks and pulse

diagnosis methods. J. Chinese Inst. Eng 2003; 26(6): 869~80.

7148 Mo-Tu, no. 25 (P65) Study of effects of balloon dimensions and its property in cardiovascular stenting using finite element technique K. Jayavenkateshwaran, J. Raamachandran. Solid Mechanics Group, Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, Tamlinadu, India

Balloon expandable stents are commonly employed to resume the blood flow in clogged coronary arteries after Percutaneous Transluminal Coronary Angioplasty. The effect of presence of the balloon in the deployment system on the efficacy of the procedure got less attention in the literature. Actually