**4. Discussion**

The objective of this study was to analyze the influence of the microsphere concentration in the vial on the microsphere distribution in the blood using CFD techniques. The concentration of microspheres in the blood depends on the injection conditions (e.g., the microsphere concentration in the vial and injection velocity) and the hemodynamic characteristics of patients. This concentration could play a role in the final distribution of microspheres within tumors because of potential microsphere aggregation, distal vessel clogging, and hemodynamic redistributions in the microvasculature. Indeed, the study of the microsphere density in tumors is an active area of ongoing research. Recent studies have shown that the resin microsphere distribution in tumors determines the treatment outcome [12,13], and that the number of microspheres injected and the method of administration play a role in the microsphere distribution [14,15].

Regarding segment-to-segment microsphere distributions, our results showed that the microsphere dynamics' and hemodynamics' interaction could play a role in microsphere transport and therefore should be considered. Indeed, a difference of 16 percent was obtained between simulations #1 and #3 in segmen<sup>t</sup> S7, and no microspheres targeted the left lobe in simulation #1, with microspheres targeting the left lobe only in simulations #2 and #3; the only difference between simulations was the concentration of microspheres in the vial, and therefore the rate at which microspheres were injected.

With regard to the microsphere concentration in the blood, periodic patterns were observed. As for the specific patterns, no relationship was observed between the concentration of microspheres in the blood in the PHA and the microsphere concentration in the blood at the outlets, nor between the shape of the microsphere distribution in the blood and the shape of the blood flow. The microsphere concentration decreased as the flow reached distal vessels of the hepatic artery tree studied, from 10<sup>5</sup> MS/mL in the PHA to 10<sup>4</sup> MS/mL or lower values. However, these results showed a relationship between the microsphere concentration in the vial and the peak value of the microsphere concentration in the blood. In fact, the concentration of microspheres in the vial was reduced by 50%

between simulations #1 and #2, and on average the peak of microsphere concentrations in the blood was reduced by 52%. Between simulations #1 and #3, the concentration of microspheres in the vial was reduced by 67%, and on average the peak of microsphere concentrations in the blood was reduced by 69%. This relationship could be of interest for future research. Additionally, the influence of the microsphere concentration in the blood in distal arterioles and capillaries needs to be assessed. As the ratio of the vessel diameter to the microsphere diameter approaches a value of 3, the probability of clogging depends on the microsphere volume fraction [16], which is similar to the microsphere concentration in the blood. Microspheres could become clogged before reaching the distal arterioles and capillaries with diameters similar to that of the microsphere, influencing the final microsphere distribution in tissues.
