Transient growth, edge states, and repeller in rotating solid and fluid.

For the classical problem of the rotation of a solid, we show a somehow surprising behavior involving large transient growth of perturbation energy that occurs when the moment of inertia associated to the unstable axis approaches the moment of inertia of one of the two stable axes. In that case, small but finite perturbations around this stable axis may induce a total transfer of energy to the unstable axis, leading to relaxation oscillations where the stable and unstable manifolds of the unstable axis play the role of a separatrix, an edge state. For a fluid in solid-body rotation, a similar linear and nonlinear dynamics apply to the transfer of energy between three inertial waves respecting the triadic resonance condition. We show that the existence of large transient energy growth and of relaxation oscillations may be physically interpreted as in the case of a solid by the existence of two quadratic invariants, the energy and the helicity in the case of a rotating fluid. They occur when two waves of the triad have helicities that tend towards each other, when their amplitudes are set such that they have the same energy. We show that this happens when the third wave has a vanishing frequency which corresponds to a nearly horizontal wave vector. An inertial wave, perturbed by a small-amplitude wave with a nearly horizontal wave vector, will then be periodically destroyed, its energy being transferred entirely to the unstable wave, although this perturbation is linearly stable, resulting in relaxation oscillations of wave amplitudes. In the general case we show that the dynamics described for particular triads of inertial waves is valid for a class of triadic interactions of waves in other physical problems, where the physical energy is conserved and is linked to the classical conservation of the so-called pseudomomentum, which singles out the role of waves with vanishing frequency.

Optimization of Drug Delivery by Drug-Eluting Stents.

Drug-eluting stents (DES), which release anti-proliferative drugs into the arterial wall in a controlled manner, have drastically reduced the rate of in-stent restenosis and revolutionized the treatment of atherosclerosis. However, late stent thrombosis remains a safety concern in DES, mainly due to delayed healing of the endothelial wound inflicted during DES implantation. We present a framework to optimize DES design such that restenosis is inhibited without affecting the endothelial healing process. To this end, we have developed a computational model of fluid flow and drug transport in stented arteries and have used this model to establish a metric for quantifying DES performance. The model takes into account the multi-layered structure of the arterial wall and incorporates a reversible binding model to describe drug interaction with the cells of the arterial wall. The model is coupled to a novel optimization algorithm that allows identification of optimal DES designs. We show that optimizing the period of drug release from DES and the initial drug concentration within the coating has a drastic effect on DES performance. Paclitaxel-eluting stents perform optimally by releasing their drug either very rapidly (within a few hours) or very slowly (over periods of several months up to one year) at concentrations considerably lower than current DES. In contrast, sirolimus-eluting stents perform optimally only when drug release is slow. The results offer explanations for recent trends in the development of DES and demonstrate the potential for large improvements in DES design relative to the current state of commercial devices.

Modeling the transport of drugs eluted from stents: physical phenomena driving drug distribution in the arterial wall.

Despite recent data that suggest that the overall performance of drug-eluting stents (DES) is superior to that of bare-metal stents, the long-term safety and efficacy of DES remain controversial. The risk of late stent thrombosis associated with the use of DES has also motivated the development of a new and promising treatment option in recent years, namely drug-coated balloons (DCB). Contrary to DES where the drug of choice is typically sirolimus and its derivatives, DCB use paclitaxel since the use of sirolimus does not appear to lead to satisfactory results. Since both sirolimus and paclitaxel are highly lipophilic drugs with similar transport properties, the reason for the success of paclitaxel but not sirolimus in DCB remains unclear. Computational models of the transport of drugs eluted from DES or DCB within the arterial wall promise to enhance our understanding of the performance of these devices. The present study develops a computational model of the transport of the two drugs paclitaxel and sirolimus eluted from DES in the arterial wall. The model takes into account the multilayered structure of the arterial wall and incorporates a reversible binding model to describe drug interactions with the constituents of the arterial wall. The present results demonstrate that the transport of paclitaxel in the arterial wall is dominated by convection while the transport of sirolimus is dominated by the binding process. These marked differences suggest that drug release kinetics of DES should be tailored to the type of drug used.