**3. Results**

First, the segment-to-segment microsphere distribution was analyzed. The total number of microspheres injected was the same in all simulations (4.45 × 10<sup>5</sup> MS), so the results were normalized with respect to the total number of microspheres injected. For example, a value of 50% for a given segmen<sup>t</sup> means that half of the injected microspheres reached that segment. When analyzing the differences between simulations, the absolute differences were computed, i.e., the differences in percent (%). These results are shown in Figure 2a, where the blood flow distribution and segment-to-segment microsphere distribution are shown. Despite the disease being bilobar (present in segments S2, S3, S6, S7, and S8), almost no microspheres reached the left lobe, and those which did reach the left lobe reached segments S1 and S4. Therefore, the injection point used in this study did not produce an effective microsphere distribution. In fact, three injections were given to this patient. It can be noted that for the segments of the right lobe (S5, S6, S7, and S8), the microsphere distribution followed a trend where the greater the blood flow rate to a given segment, the greater the number of microspheres exiting toward that segment. Moreover, differences can be seen between simulations. For example, microspheres flowed toward segments S1 and S4 in simulations #2 and #3, while no microsphere flowed toward the left lobe in simulation #1. In all simulations, the segmen<sup>t</sup> receiving the most microspheres was segmen<sup>t</sup> S7, which is the segmen<sup>t</sup> with the biggest nodule (a 23 mL nodule). It can also be noted that even though segmen<sup>t</sup> S3 received 17% of the total blood flow, no microspheres reached that segment. Additionally, the microsphere distributions were different in the simulations, with an absolute difference of 16 percent between simulations #1 and #3 for segmen<sup>t</sup> S7. The average absolute difference between simulations in all segments was 5 percent.

Second, the concentration of microspheres in the blood over time in the PHA and at each outlet was studied. In this study, the concentration of microspheres in the vial was of the order of 10<sup>6</sup> MS/mL, which was reduced to a concentration of microspheres in the blood of the order of 10<sup>5</sup> MS/mL in the PHA, and was further reduced to a concentration of microspheres in the blood of the order of 10<sup>4</sup> MS/mL (and below that value) in segmental arteries, meaning that the concentration decreased as microspheres flowed toward distal vessels. Figure 2b shows the microsphere concentration in blood at the PHA level over time. A constant injection flow and microsphere injection rate resulted in a microsphere concentration in the blood with a minimum value during systole and a maximum value during diastole. The geometry had 43 outlets, but only the outlets with a flow fraction greater than 1% and a concentration of microspheres in the blood greater than 40,000 MS/mL are reported, resulting in an analysis of eight outlets: outlet 21 feeding segmen<sup>t</sup> S6, outlets 26, 27, 29, 32, and 33 feeding segmen<sup>t</sup> S7, and outlets 34 and 38 feeding segmen<sup>t</sup> S8. These results are shown in Figure 2c–j. In each panel, the time-dependent microsphere concentration in the blood is plotted for simulations #1, #2, and #3. Additionally, the shape of the blood flow rate is plotted in dotted lines, and the percentage of blood flow feeding that outlet and the percentage of microspheres exiting that outlet are indicated. Figure A1 in Appendix A shows the same information as in Figure 2 for the outlets that had a flow of microspheres but did not meet the criteria of having a flow fraction greater than 1% and a concentration of microspheres in the blood greater than 40,000 MS/mL.

Regarding the percentage of microspheres exiting the eight outlets of Figure 2, this value was, in general, different from the blood flow percentage, but it also differed slightly among simulations. The mean value of the difference in microsphere distributions in these outlets was 3 percent, with the greatest difference being 8 percent for outlet 29 between simulations #1 and #3 (see Figure 2f).

**Figure 2.** (**a**) Segment-to-segment blood flow and microsphere distributions. (**b**) Concentration of microspheres in the blood at the PHA level. (**<sup>c</sup>**–**j**) Concentration of microspheres in the blood reaching outlets 21, 26, 27, 29, 32, 33, 34, and 38 over time. These outlets feed tumor-bearing segments S6, S7, and S8. In each panel (**b**–**j**), the shape of the blood flow is in a dotted red line and the percentages indicate the percentage of blood, and percentage of microspheres exiting through those outlets.

As for the microsphere concentration in the blood over time, the following trend was seen for the outlets in Figure 2c–j for a periodic flow and a constant microsphere infusion: (i) the greater the concentration of microspheres in the vial, the greater the microsphere concentration in the blood at the outlets, and (ii) the concentration of microspheres in the blood was periodic-like, meaning that the same shape was repeated over the cardiac cycles with a period similar to that of the cardiac cycle. In this case, for simulations #1, #2, and #3 (with microspheres injected during one, two, and three cardiac cycles, respectively), one-cycle, two-cycle, and three-cycle outlet-specific patterns were observed. This trend was not seen at the outlets shown in Figure A1.

It is also important to note that the peaks of the periodic-like patterns did not coincide with any specific moment of the cardiac cycle (e.g., the systole or diastole) (see Figure 2c–j). Microspheres were injected at a constant rate, and their velocity matched the blood flow velocity shortly after they were incorporated into the bloodstream. If the microspheres had traveled through straight streamlines, the concentration of microspheres in the blood at the outlet should have had the same pattern as that in the PHA (Figure 2b). However, the tortuosity of arteries made the blood flow and microsphere trajectories intricate, and this fact made the concentration of microspheres inconstant. Likewise, there were some non-periodic peaks for outlets 34 and 38 at the beginning of microsphere crossing (see Figure 2i,j), which could be due to transient effects. When analyzing the peak values, if the outlets of Figure 2 were considered, on average, the concentration values were reduced by 52% from simulation #1 to simulation #2, and by 69% from simulation #1 to simulation #3. These values were similar to the decrease in the concentration of microspheres in the vial between simulations #1 and #2 and simulations #1 and #3 (50% and 67%, respectively). If all the outlets were considered, these average peak values decreased to 27% for simulation #2 and 45% for simulation #3.
