Analysis of Computational Fluid Dynamics and Particle Image Velocimetry Models of Distal-End Side-to-Side and End-to-Side Anastomoses for Coronary Artery Bypass Grafting in a Pulsatile Flow.

BACKGROUND: Intimal hyperplasia (IH) is a major cause of graft failure. Hemodynamic factors such as stagnation and disturbed blood flow are involved in IH formation. The aim of this study is to perform a comparative analysis of distal-end side-to-side (deSTS) and end-to-side (ETS) anastomoses using computational fluid dynamics (CFD) after validating the results via particle image velocimetry (PIV).Methods and Results:We investigated the characteristics of our target flow fields using CFD under steady and pulsatile flows. CFD via PIV under steady flow in a 10-times-actual-size model was validated. The CFD analysis revealed a recirculation zone in the heel region in the deSTS and ETS anastomoses and at the distal end of the graft, and just distal to the toe of the host artery in the deSTS anastomoses. The recirculation zone sizes changed with the phase shift. We found regions of low wall shear stress and high oscillating shear index in the same areas. The PIV and CFD results were similar. CONCLUSIONS: It was demonstrated that the hemodynamic characteristics of CFD and PIV is the difference between the deSTS and ETS anastomoses; that is, the deSTS flow peripheral to the distal end of the graft, at the distal end and just distal to the toe of the host artery is involved in the IH formation.

Transition of velocity distributions in collapsing self-gravitating N-body systems.

By means of N-body simulations, we study the evolution of gravity-dominated systems from an early relaxation to a collapse, focusing on the velocity distributions and thermodynamic properties. To simulate the dynamical evolution, we consider self-gravitating small N-body systems enclosed in a spherical container with adiabatic or semipermeable walls. It is demonstrated that in the early relaxation process, the velocity distribution is non-Gaussian and q-Gaussian, since the system is in quasiequilibrium states (here q is the Tsallis entropic parameter). Thereafter, the velocity distribution undergoes higher non-Gaussian distributions, especially when the core forms rapidly in the collapse process; i.e., q tends to be larger than that for the quasiequilibrium state, since the velocity distribution further deviates from Gaussian. However, after the core forms sufficiently, the velocity distribution gradually relaxes toward a Gaussian-like distribution. Accordingly, the velocity distribution evolves from a non-Gaussian distribution through a higher non-Gaussian distribution to a Gaussian-like distribution; i.e., the velocity distribution does not monotonically relax toward a Gaussian-like distribution in our collapse simulations. We clearly show such a transition of the velocity distribution, based not only on the Tsallis entropic parameter but also on the ratio of velocity moments. We also find that a negative specific heat occurs in a collapse process with mass and energy loss (such as the escape of stars from globular clusters), even if the velocity distribution is Gaussian-like.

Thermodynamic properties of an evaporation process in self-gravitating N -body systems.

By means of N -body simulations, we consider self-gravitating open systems enclosed in a spherical container with semipermeable reflecting walls, in order to investigate the thermodynamics of the evaporation process in self-gravitating N -body systems (such as the escape of stars from globular clusters). To simulate the evaporation process, when the energy of a particle exceeds a certain threshold value, the particle passes through the semipermeable reflecting wall freely. We show that the thermodynamic properties of the evaporation process, such as the dependence of the temperature on energy, agree well with those of stellar polytropes, if the system is in an approximate virial equilibrium state. However, in a lower-energy region or for a rapid evaporation process, the thermodynamic properties deviate from those for the stellar polytrope. Nevertheless, we found that a negative specific heat occurs even in the lower-energy region or for a rapid evaporation process.

Negative specific heat in self-gravitating N-body systems enclosed in a spherical container with reflecting walls.

Gravity-dominated systems have a negative specific heat. We investigate the negative specific heat of self-gravitating systems enclosed in a spherical container with reflecting walls by means of N-body simulations. To simulate nonequilibrium processes, a particle reflected at a nonadiabatic wall is cooled to mimic energy loss by reflecting walls, while an adiabatic wall is employed for microcanonical ensembles. We show that a negative specific heat occurs not only in the microcanonical ensemble but also in certain nonequilibrium processes with the nonadiabatic wall. With increasing cooling rates, the dependence of temperature T on energy epsilon , i.e., the epsilon-T curve, gradually deviates from the microcanonical ensemble and approaches a certain common curve at a low-energy region. The common curve agrees with an epsilon-T curve for stellar polytropes, especially for the polytrope index of n approximately 5 . We show that the stellar polytrope should be related to the present nonequilibrium process appearing in the self-gravitating system with the nonadiabatic wall. In the nonequilibrium process, a rapid change in velocity at the nonadiabatic wall significantly affects the velocity and density profiles. In particular, the greater the cooling rate, the greater the local velocity gradient at a low-energy region.