The Impact of Blood Rheology on Drug Transport in Stented Arteries: Steady Simulations

Background and Methods It is important to ensure that blood flow is modelled accurately in numerical studies of arteries featuring drug-eluting stents due to the significant proportion of drug transport from the stent into the arterial wall which is flow-mediated. Modelling blood is complicated, however, by variations in blood rheological behaviour between individuals, blood’s complex near-wall behaviour, and the large number of rheological models which have been proposed. In this study, a series of steady-state computational fluid dynamics analyses were performed in which the traditional Newtonian model was compared against a range of non-Newtonian models. The impact of these rheological models was elucidated through comparisons of haemodynamic flow details and drug transport behaviour at various blood flow rates. Results: Recirculation lengths were found to reduce by as much as 24% with the inclusion of a non-Newtonian rheological model. Another model possessing the viscosity and density of blood plasma was also implemented to account for near-wall red blood cell losses and yielded recirculation length increases of up to 59%. However, the deviation from the average drug concentration in the tissue obtained with the Newtonian model was observed to be less than 5% in all cases except one. Despite the small sensitivity to the effects of viscosity variations, the spatial distribution of drug matter in the tissue was found to be significantly affected by rheological model selection. Conclusions/Significance: These results may be used to guide blood rheological model selection in future numerical studies. The clinical significance of these results is that they convey that the magnitude of drug uptake in stent-based drug delivery is relatively insensitive to individual variations in blood rheology. Furthermore, the finding that flow separation regions formed downstream of the stent struts diminish drug uptake may be of interest to device designers

Local non-Newtonian importance factors, <i>I</i>_<i>L</i>.

<p>This non-dimensional parameter is used to illustrate the spatial variation in non-Newtonian behaviour for each blood rheological model. Although the plasma case (a) yielded a constant value of <i>I</i>_<i>L</i>, the remaining cases (b-h) showed that the most significant non-Newtonian behaviour occurs in the recirculation zones.</p

Mesh Independence of the Flow.

<p>Mesh Independence of the Flow.</p

The effect of blood rheological model and flow rate on diffusive mass transport behaviour.

<p>a) The plot of the normalised drug concentration gradient for the case in which blood is modelled as a Newtonian fluid revealed five peaks and troughs, labelled A, B, C, D and E. Local minima (A and E) show where drug is removed from the tissue while local maxima (B-D) show where it diffuses into the tissue. b) The dashed blue line shows the distribution of the normal component of the blood velocity along a line 0.1 strut widths above the lumen-tissue interface. Comparison with the red <i>dc/dn</i> line confirmed that the upward flow at points A and E resulted in loss of drug from the tissue due to convection. The purple <i>∂c/∂x</i>’ line revealed that drug transport in the horizontal direction was significant between points A and B, and at points C and E. c) the distal recirculation zone was found to remove drug from the tissue for non-Paclitaxel drugs, although this behavior diminished as </p><p></p><p></p><p></p><p><mi>D</mi></p><p><mi>l</mi></p><p><mi>'</mi></p><p></p><p></p><p><mo>/</mo><mi>D</mi></p><p><mi>t</mi></p><p><mi>'</mi></p><p></p><mo>≥</mo><mn>100</mn><p></p><p></p>. d) The non-Newtonian blood rheological models produced similar <i>dc/dn</i> patterns to the Newtonian model; however, their local maxima and minima were up to 59% smaller in magnitude. The size of these peaks and troughs was found to be directly related to the recirculation lengths predicted by each model. Hence, the choice of rheological model not only influenced the fluid dynamics, but also the drug transport behaviour.<p></p

The effect of blood rheological model and flow rate on the average tissue drug concentration.

<p>Increases in bulk flow rate were found to correspond with reduced area-weighted average drug concentrations (AWAC) in the tissue. Rheological models which produced larger recirculation lengths were also found to produce lower AWAC values; however, the deviation from the AWAC obtained with the Newtonian model was observed to be less than 5% for each non-Newtonian case. It was only when modelling plasma instead of blood that any considerable deviations from the Newtonian model’s AWAC were observed and even these were only observed at </p><p></p><p></p><p></p><p></p><p><mi>Q</mi><mo>′</mo></p><p><mi>h</mi><mi>i</mi><mi>g</mi><mi>h</mi></p><p></p><p></p><p></p><p></p>.<p></p

Contour plots of the non-Newtonian drug concentration difference factor, <i>I</i>_<i>D</i>.

<p>These contours display the degree to which a rheological model’s predicted drug concentration departs from that associated with the traditional Newtonian model. The regions highlighted in red (<i>I</i>_<i>D</i>>0) depict where the non-Newtonian blood model predicts a greater drug concentration, whilst the blue regions (<i>I</i>_<i>D</i><0) show where the Newtonian model predicts a higher drug concentration. The plasma case (a) is different from the other cases examined in that its larger distal recirculation zone resulted in a less concentrated distal drug pool than that of the Newtonian model. This larger pool allowed a greater region of the lumen-tissue interface to be exposed to recirculating drug; however, no significant positive <i>I</i>_<i>D</i> values were observed in the tissue. In contrast, the larger proximal drug pool of the Newtonian model did facilitate significant negative <i>I</i>_<i>D</i> values in the proximal sections of the tissue. In contrast, cases b-h show that the smaller recirculation lengths of the non-Newtonian models enable the formation of higher concentration drug pools than the Newtonian model. Although significant negative <i>I</i>_<i>D</i> values were again observed in the proximal aspects of the tissue, significant positive <i>I</i>_<i>D</i> values were also observed in the distal tissue aspects in some models. The non-Newtonian blood rheological models therefore typically produced much higher tissue drug concentrations than the Newtonian model in the distal regions and significantly lower concentrations in the proximal regions.</p

Drug concentration distribution and flow pathlines in the stented artery.

<p>Drug concentration distribution and flow pathlines in the stented artery.</p

Blood rheological model equations.

<p>Blood rheological model equations.</p

The effects of flow rate and blood rheology on the proximal and distal recirculation lengths.

<p>a) Increases in bulk flow rate were found to cause reductions in the proximal recirculation length and increases in the distal recirculation length produced by each rheological model. b) The relationship between recirculation length and normalised mean viscosity, which measures the ratio of the average apparent viscosity in a recirculation zone and the Newtonian model’s dynamic viscosity (</p><p></p><p></p><p></p><p></p><p><mi>μ</mi><mo>′</mo></p><mi>N</mi><p></p><p></p><p></p><p></p> = 0.00345Pa·s), was found to closely approximate linearity at each inlet flow rate. Furthermore, increases in normalised mean viscosity were found to cause reductions in recirculation length at each flow rate.<p></p

Schematic Diagram of Geometry: Dimensions and Boundary Conditions.

<p>Schematic Diagram of Geometry: Dimensions and Boundary Conditions.</p