Optimization of Drug Delivery by Drug-Eluting Stents

International audienceDrug-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

Orbital-selective Mott transitions: Heavy fermions and beyond

Quantum phase transitions in metals are often accompanied by violations of Fermi liquid behavior in the quantum critical regime. Particularly fascinating are transitions beyond the Landau-Ginzburg-Wilson concept of a local order parameter. The breakdown of the Kondo effect in heavy-fermion metals constitutes a prime example of such a transition. Here, the strongly correlated f electrons become localized and disappear from the Fermi surface, implying that the transition is equivalent to an orbital-selective Mott transition, as has been discussed for multi-band transition-metal oxides. In this article, available theoretical descriptions for orbital-selective Mott transitions will be reviewed, with an emphasis on conceptual aspects like the distinction between different low-temperature phases and the structure of the global phase diagram. Selected results for quantum critical properties will be listed as well. Finally, a brief overview is given on experiments which have been interpreted in terms of orbital-selective Mott physics.Comment: 29 pages, 4 figs, mini-review prepared for a special issue of JLT

Quantum Criticality in Heavy Fermion Metals

Quantum criticality describes the collective fluctuations of matter undergoing a second-order phase transition at zero temperature. Heavy fermion metals have in recent years emerged as prototypical systems to study quantum critical points. There have been considerable efforts, both experimental and theoretical, which use these magnetic systems to address problems that are central to the broad understanding of strongly correlated quantum matter. Here, we summarize some of the basic issues, including i) the extent to which the quantum criticality in heavy fermion metals goes beyond the standard theory of order-parameter fluctuations, ii) the nature of the Kondo effect in the quantum critical regime, iii) the non-Fermi liquid phenomena that accompany quantum criticality, and iv) the interplay between quantum criticality and unconventional superconductivity.Comment: (v2) 39 pages, 8 figures; shortened per the editorial mandate; to appear in Nature Physics. (v1) 43 pages, 8 figures; Non-technical review article, intended for general readers; the discussion part contains more specialized topic

Applications on Multi-Dimensional Sphere Packings: Derivative-Free Optimization

The field of n-dimensional sphere packings is elegant and mature in its mathematic development and characterization. However, practical application of this powerful body of work is lacking. The line of research presented in this work explores the application of sphere packings to the field of derivative-free optimization. Chapter 2 reviews the essential results available in this field, then extends these results by: (a) assembling a catalog of key properties of the principle dense and rare sphere packings and nets available, including hundreds of values not previously known; (b) introducing and characterizing several new families of regular rare sphere packings and nets; and (c) developing a new algorithm for efficient solution of discrete Thompson problems, restricted to nearest-neighbor points. These results are leveraged heavily in the applications addressed in Chapters 3 and 4. In particular, Chapter 3 builds from this presentation to develop a new algorithm for Lattice-Based Derivative-free Optimization via Global Surrogates (LABDOGS), leveraging dense sphere packings as an alternative to Cartesian grids to coordinate derivative-free searches. The LABDOGS algorithm provides a highly efficient, globally convergent optimization algorithm that requires nothing more than a definition of a feasible domain and a cost function handle. The LABDOGS algorithm demonstrates superior performance and convergence rates to its Cartesian-based competitors. Chapter 4 builds from the material of Chapter 2 and 3 to develop a highly efficient locally convergent derivative-free optimization algorithm called Lambda-MADS, which builds from and improves upon the Mesh Adaptive Direct Search (MADS) class of optimization algorithms. The Lambda-MADS algorithm offers an alternative to the Successive Polling substep of LABDOGS, providing a locally convergent pattern search algorithm that, unlike SP, offers good convergence behavior when challenging constraints on the feasible region are encountered. Lambda-MADS inherits all the convergence characteristics of the best available MADS algorithms, while significantly improving convergence rates. This work demonstrates effectively how modern grid-based derivative-free optimization algorithms benefit significantly from the incorporation of n-dimension sphere packings for the purpose of discretizing parameter space, replacing the ubiquitous Cartesian grid

Contour plots of the cost function for paclitaxel (left column) and sirolimus (right column) over the design space consisting of <i>initial concentration in the stent polymer</i><i>c</i>₀ and <i>release time</i><i>t</i>_E.

<p>The scale for the cost function representation is truncated at a maximum of 1; all values larger than 1 are colored black. The dashed magenta lines in panels A and B mark the time scales for drug unbinding. The green contour line traces </p><p></p><p></p><p></p><p></p><p><mi>I</mi><mo>¯</mo></p>m<p></p><mo>=</mo><mn>1</mn><p></p><p></p><p></p>, the yellow contour line <p></p><p></p><p></p><p></p><p><mi>T</mi><mo>¯</mo></p>m<p></p><mo>=</mo><mn>1</mn><p></p><p></p><p></p>, and the red contour line <p></p><p></p><p></p><p></p><p><mi>T</mi><mo>¯</mo></p>e<p></p><mo>=</mo><mn>1</mn><p></p><p></p><p></p>. The horizontal axis at the top of the plot marks the time points of 1 (h)our, 1 (d)ay, 1 (w)eek, 1 (m)onth and 1 (y)ear. Gray dots indicate evaluated designs. Optimization cases <b>A</b>: paclitaxel release and <b>B</b>: sirolimus release with baseline cocnentration thresholds. <b>C</b>: Paclitaxel release and <b>D</b>: sirolimus release with concentration thresholds reduced by a factor of 10. <b>E</b>: Paclitaxel release and <b>F</b>: sirolimus release with concentration thresholds increased by a factor of 10.<p></p

Approximate initial concentration (in mol m⁻³) at distinct time points on the endothelial toxicity contour line for paclitaxel and sirolimus release strategy optimization.

<p>Approximate initial concentration (in mol m⁻³) at distinct time points on the endothelial toxicity contour line for paclitaxel and sirolimus release strategy optimization.</p

Contour plots of the effect of the presence of SMCs in the SES on the cost function for paclitaxel (left column) and sirolimus (right column) over the design space consisting of <i>initial concentration in the stent polymer</i><i>c</i>₀ and <i>release time</i><i>t</i>_E.

<p>The scale for the cost function representation is truncated at a maximum of 1; all values larger than 1 are colored black. The green contour line traces </p><p></p><p></p><p></p><p></p><p><mi>I</mi><mo>¯</mo></p>m<p></p><mo>=</mo><mn>1</mn><p></p><p></p><p></p>, the yellow contour line <p></p><p></p><p></p><p></p><p><mi>T</mi><mo>¯</mo></p>m<p></p><mo>=</mo><mn>1</mn><p></p><p></p><p></p>, and the red contour line <p></p><p></p><p></p><p></p><p><mi>T</mi><mo>¯</mo></p>e<p></p><mo>=</mo><mn>1</mn><p></p><p></p><p></p>. The horizontal axis at the top of the plot marks the time points of 1 (h)our, 1 (d)ay, 1 (w)eek, 1 (m)onth and 1 (y)ear. Gray dots indicate evaluated designs. Optimization cases <b>A</b>: paclitaxel release and <b>B</b>: sirolimus release with SES SMC density corresponding to 1% of the medial SMC density. <b>C</b>: Paclitaxel release and <b>D</b>: sirolimus release with SES SMC density corresponding to 5% of the medial SMC density. <b>E</b>: Paclitaxel release and <b>F</b>: sirolimus release with SES SMC density corresponding to 25% of the medial SMC density.<p></p

Polling the design space.

<p><b>A</b>: Two consecutive factor of 4 grid refinements and factor of 2 shell of prospective polling points refinements of the LT-MADS algorithm on a 2-dimensional Cartesian lattice; <b>B</b>: Two consecutive factor of 2 mesh refinements of the <i>λ</i>-MADS algorithm on a hexagonal lattice <i>A</i>₂ with a shell of prospective polling points at a distance of 1, 2 and 3 grid points for the initial grid (<i>k</i> = 0) and after <i>k</i> = 1 and <i>k</i> = 2 consecutive grid refinements, respectively. Search directions (in blue) of a minimal positive basis connect the current optimum point (in green) with the selected poll designs (red). Current shell of prospective polling points is marked in red, previous shell of prospective polling points is marked in orange.</p

Drug unbinding time scale and dimensionless quantities for the stented part of the media for paclitaxel and sirolimus.

<p>Drug unbinding time scale and dimensionless quantities for the stented part of the media for paclitaxel and sirolimus.</p