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 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

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

Shape of the score sheet for the cost function at the endothelium (dashed line) and in the media (continuous line).

<p>Shape of the score sheet for the cost function at the endothelium (dashed line) and in the media (continuous line).</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

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

Release kinetics and resulting cost function scores and normalized concentration distributions for repesentative designs of <i>quasi-bolus</i>, <i>first-order</i>, and <i>zero-order</i> drug release.

<p><b>A</b>: Release profiles as quantified by the time evolution of the remaining mass percentage of drug in the polymer coating (RMC). <b>B</b> Time evolution of the endothelial toxicity score </p><p></p><p></p><p></p><p></p><p><mi>T</mi><mo>¯</mo></p>e<p></p><p></p><p></p><p></p> (left y-axis) and the inefficacy score <p></p><p></p><p></p><p></p><p><mi>I</mi><mo>¯</mo></p>m<p></p><p></p><p></p><p></p> (right y-axis). <b>C</b>: Contour plots of the concentration distribution normalized by the minimum efficacious concentration <i>c</i>_eff at 1 hour (<i>first row</i>), 1 day (<i>second row</i>) and 1 week (<i>third row</i>) post stent implantation. The highest concentration values encountered close to the stent strut surface are colored in black indicating toxic concentrations. A green contour line marks the threshold between efficacious and non-efficacious drug concentration in the media. If the contour is missing, the entire depicted domain is exposed to efficiacious concentrations. The red countour lines enclose toxic concentration regions in the media and mark concentration levels at the endothelial surface that are unacceptably elevated.<p></p