DANDI:000491

The distribution of the PVS-to-vessel area ratio in segmentations is matched most closely by the polynomial fit ( Figure 5E ), and the value of the area ratio in segmentations is matched most closely by the polynomial fit in 73% of cases ( Figure 5D ) ... the ellipse fit gives the closest match in only 8% of cases ... The spline fit gives the closest match in 19% of the cases

Results, Area ratio, paragraph 3; Figure 5D and 5E

Four of 96 combinations put the three shares within tolerance, all with P4 b and P5 a for the segmentation and the fitted circle for the fits: P1 a with erosion 5 (70.7, 20.6 and 8.8% with P9 a, the measured values; 70.4, 20.8 and 8.8% with P9 b) and P1 b with erosion 3 (71.4, 20.8, 7.9% and 71.0, 20.8, 8.3%). The polynomial share is the largest and above 50% in 92 of 96 (47.4 to 79.1% over all); under the other P5 readings the ellipse share is 0.1 to 4.7%. The outcome rests on those four combinations. Before the revision after round 1 none matched (closest 73.8, 24.8 and 1.4%) and the outcome was partially reproduced. Reference combination for measured values, P1 a (0.648 um), P2 a (cleaned longest path), P4 b (polynomial width), P5 a, P6 erosion 3, P7 b (outliers left out), unless stated.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• Assumed, within the vessel's horizontal extent, the polynomial fit's region runs from the line down to the vessel center height, minus the circle; the Methods and the claims file do not say how the region is closed across the vessel. The alternative was not run.
• The ellipse is fit to the region the PVS's outer boundary encloses, the PVS and vessel segmentations together with holes filled, as claims P9 has it since the answer of 2026-11-04. The crop window of each cross section now holds the whole ellipse; being larger, it also cuts less of the polynomial region at its edge, which moves the polynomial areas and resistances slightly; the values before the change are not in the notebook (with the reference combination and P9 a the polynomial area ratio now peaks at 1.684, median 1.710, table2).
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, 1 of the 96 combinations matches in place of 4, and the polynomial share is the largest and above 50% in 94.

The distribution of resistances for the optimal elliptical annulus is very similar to that of the ellipse fit ... Though both the ellipse fit and annulus tend to underestimate the resistance of the PVS

Results, Hydraulic Resistance, paragraph 3; Figure 6B

Both underestimate in all 48 combinations on linear bins (both readings). The annulus-over-ellipse ratios are within 10% of 1.87 and 1.61 in one: P1 b, P4 a, erosion 1, P5 b, outliers out, 1.82 and 1.702. The outcome rests on that one combination, under the P4 reading that leaves 4 segments without a cross section; over all 48 the median ratio is 1.409 to 2.264 and the peak ratio 0.038 to 2.259. Before the revision after round 1 the one matching combination was P1 b, P4 a, P5 b with erosion 3 (1.831 and 1.675); with the revised PVS and erosion 3 alone no combination matched, and solving the fits at erosions 1 and 5, as the verifier noted was missing, gives the one above. Reference combination for measured values, P1 a (0.648 um), P2 a (cleaned longest path), P4 b (polynomial width), P5 a, P6 erosion 3, P7 b (outliers left out), unless stated.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• Resistance is solved by finite differences on the pixel grid of the cross section, in place of finite elements (MATLAB solvepde). The domain is the region at least 1.5 pixels inside the mask's edge, which is the polygon through the boundary pixel centres after the Methods' one-pixel erosion. The Methods' check (a circle of the same area within 1% of the exact resistance) holds from 1000 um^2 at 0.648 um; at 300 um^2 and 1 um the error is 2.5%.
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• The bins follow fig5b-polynomial-closest-resistance, linear; logarithmic bins are shown as a variant and decide nothing.
• The ellipse is fit to the region the PVS's outer boundary encloses, the PVS and vessel segmentations together with holes filled, as claims P9 has it since the answer of 2026-11-04. The crop window of each cross section now holds the whole ellipse; being larger, it also cuts less of the polynomial region at its edge, which moves the polynomial areas and resistances slightly; the values before the change are not in the notebook (with the reference combination and P9 a the polynomial area ratio now peaks at 1.684, median 1.710, table2).
• Since the revision after round 1 the resistances and velocities of the fits are solved with the circle fit of every erosion of P6 (1, 3 and 5 pixels).
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, 1 of 48 combinations on linear bins matches, as with E.

The resistance for the spline fit is considerably larger than that of the segmentation (distribution peak is 5 times larger)

Results, Hydraulic Resistance, paragraph 3; Figure 6B inset

On linear bins 4 of 24 combinations are within tolerance (4.85 and 5.25 within 0.5 of 5; 6.59, the measured value with P1 a, P4 b, erosion 3, and 6.57 within 0.62 of 6.2), and 11 more on logarithmic bins, which fig6b's criterion allows for both peaks. The median spline resistance exceeds the segmentation's in every combination (1.07e16 against 5.28e15). The spline area ratio exceeds the segmentation's in only 43.3% of cross sections, so the statement's "larger area ratio" does not hold. Before the revision after round 1 the result rested on P4 a (5.45); it now holds under P4 b on linear bins too. Reference combination for measured values, P1 a (0.648 um), P2 a (cleaned longest path), P4 b (polynomial width), P5 a, P6 erosion 3, P7 b (outliers left out), unless stated.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• Resistance is solved by finite differences on the pixel grid of the cross section, in place of finite elements (MATLAB solvepde). The domain is the region at least 1.5 pixels inside the mask's edge, which is the polygon through the boundary pixel centres after the Methods' one-pixel erosion. The Methods' check (a circle of the same area within 1% of the exact resistance) holds from 1000 um^2 at 0.648 um; at 300 um^2 and 1 um the error is 2.5%.
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• Both peaks are taken with the same bins, linear or logarithmic, the readings of fig6b-resistance-segmentation-peak.
• Since the revision after round 1 the resistances and velocities of the fits are solved with the circle fit of every erosion of P6 (1, 3 and 5 pixels).
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, 18 of 48 combinations (both bin scales) are within tolerance in place of 15.

In this example case, the velocity profile for the polynomial fit is similar to the velocity profile in the segmentation, whereas the ellipse fit results in much higher velocities, and the spline fit results in much lower velocities.

Results, Hydraulic Resistance, paragraph 4; Figure 7 legend

In all 24 combinations of P1, P4 and P6 and both readings the ellipse is faster than the segmentation in 99.9 to 100% of cross sections, the spline slower in 85.8 to 97.6% and the polynomial closest in 71.5 to 81.0%. Median maximum velocity (P1 a, P4 b, erosion 3) 79.88 um/s for the segmentation, 171.77 ellipse, 44.12 spline, 91.49 polynomial. Before the revision after round 1 the result was the same at erosion 3. Reference combination for measured values, P1 a (0.648 um), P2 a (cleaned longest path), P4 b (polynomial width), P5 a, P6 erosion 3, P7 b (outliers left out), unless stated.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• Resistance is solved by finite differences on the pixel grid of the cross section, in place of finite elements (MATLAB solvepde). The domain is the region at least 1.5 pixels inside the mask's edge, which is the polygon through the boundary pixel centres after the Methods' one-pixel erosion. The Methods' check (a circle of the same area within 1% of the exact resistance) holds from 1000 um^2 at 0.648 um; at 300 um^2 and 1 um the error is 2.5%.
• Assumed, within the vessel's horizontal extent, the polynomial fit's region runs from the line down to the vessel center height, minus the circle; the Methods and the claims file do not say how the region is closed across the vessel. The alternative was not run.
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• The ellipse is fit to the region the PVS's outer boundary encloses, the PVS and vessel segmentations together with holes filled, as claims P9 has it since the answer of 2026-11-04. The crop window of each cross section now holds the whole ellipse; being larger, it also cuts less of the polynomial region at its edge, which moves the polynomial areas and resistances slightly; the values before the change are not in the notebook (with the reference combination and P9 a the polynomial area ratio now peaks at 1.684, median 1.710, table2).
• Since the revision after round 1 the resistances and velocities of the fits are solved with the circle fit of every erosion of P6 (1, 3 and 5 pixels).
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, 24 of 24 combinations match, as with E.

We approximated the cross-sectional shape of the vessel as a circle and found that the peak of the vessel radius distribution is 28 μ m

Discussion, paragraph 2; Results, Characteristics of the typical PVS shape, paragraph 2; Figure 8A and 9C

The R1 peak is within 2.8 um of 28 in 13 of 24 combinations; the first the criterion lists, P1 a, P4 a, erosion 1, all values, gives 29.50 um (the measured value), and the reference combination 32.20. Peaks 28.75 to 33.03, medians 28.31 to 31.26 um. Per-location medians 17.8 (C, M) to 40.9 um (E). Before the revision after round 1 it held in 11 of 24. Reference combination for measured values, P1 a (0.648 um), P2 a (cleaned longest path), P4 b (polynomial width), P5 a, P6 erosion 3, P7 b (outliers left out), unless stated.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, 9 of 24 combinations are within tolerance in place of 13.

The distribution peaks at zero ( Figure 9C ), suggesting that the top of the vessel is most often very nearly aligned with the top of the PVS and that the PVS is often separated into two lobes. Even when the two sides are connected, the channel connecting them is quite narrow, usually less than 0.5 R 1 .

Results, Characteristics of the typical PVS shape, paragraph 2; Figure 9C; Table 3

The HC/R1 peak is within 0.1 of zero in 14 of 24 combinations (reference -0.061, median -0.005); among cross sections with HC above zero, 63.4 to 68.4% have HC below 0.5 R1. HC is above zero in 47.1 to 54.6%. Before the revision after round 1 the peak was within in 15 of 24. Reference combination for measured values, P1 a (0.648 um), P2 a (cleaned longest path), P4 b (polynomial width), P5 a, P6 erosion 3, P7 b (outliers left out), unless stated.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, 14 of 24 combinations match, as with E.

the distributions of heights of the PVS, H 1 , H 2 , and H 3 , peak at 1.34, 0.792, and 0.307, respectively, indicating that the PVS is larger closer to the vessel and smaller at the ends of the PVS. H 1 , the height of the PVS close to the vessel, is 4 times larger than H 3

Results, Characteristics of the typical PVS shape, paragraph 6; Figure 9A; Table 3

One of 48 combinations puts the three peaks within tolerance: P1 b, P4 b, erosion 3, both sides pooled, outliers out (1.228, 0.820, 0.305, the measured values). The outcome rests on that one combination; elsewhere the H1/R1 peak runs from 0.343 to 1.445. The order H1 > H2 > H3 holds for peaks and medians in 12 of 48. Medians H1/R1 1.037 to 1.199, H2/R1 1.108 to 1.205, H3/R1 0.458 to 0.536, so H1 is about 2.3 times H3 by median, not 4. Before the revision after round 1 no combination had all three and the outcome was partially reproduced. Reference combination for measured values, P1 a (0.648 um), P2 a (cleaned longest path), P4 b (polynomial width), P5 a, P6 erosion 3, P7 b (outliers left out), unless stated.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, no combination matches in place of 1, while the order H1 above H2 above H3 holds in 11 of 48, so the outcome would be partially reproduced.

The peak of the area ratio distribution for the polynomial fit is 1.21, similar to the peak of the segmentation distribution of 1.12 ... has a significantly higher peak of 2.08 because it does not narrow at the ends. The spline fit gives the closest match in 19% of the cases and has a peak of 1.48

Results, Area ratio, paragraph 3; Table 2; Figure 5E

No combination puts all seven values within tolerance; at most 3 of 7. The partial rule (ellipse peak above spline above polynomial, spline IQR the smallest) holds in 24 of 96 combinations, 19 with P4 a. Over all combinations the polynomial peak is 0.842 to 12.237, the ellipse peak 0.682 to 14.544, the spline peak 1.47 to 1.897, the medians 1.467 to 1.85, 1.848 to 2.455 and 1.504 to 1.71, and the spline IQR 0.019 to 0.26. Before the revision after round 1 at most 6 of 7 were within and the partial rule held in 12 of 96. Reference combination for measured values, P1 a (0.648 um), P2 a (cleaned longest path), P4 b (polynomial width), P5 a, P6 erosion 3, P7 b (outliers left out), unless stated.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• Assumed, within the vessel's horizontal extent, the polynomial fit's region runs from the line down to the vessel center height, minus the circle; the Methods and the claims file do not say how the region is closed across the vessel. The alternative was not run.
• The ellipse is fit to the region the PVS's outer boundary encloses, the PVS and vessel segmentations together with holes filled, as claims P9 has it since the answer of 2026-11-04. The crop window of each cross section now holds the whole ellipse; being larger, it also cuts less of the polynomial region at its edge, which moves the polynomial areas and resistances slightly; the values before the change are not in the notebook (with the reference combination and P9 a the polynomial area ratio now peaks at 1.684, median 1.710, table2).
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, no combination matches; the partial rule holds in 18 of 96 in place of 24.

The hydraulic resistance can be reasonably predicted with a power-law fit as a function of the PVS area alone (R 2 = 0.944). The exponent in the power law fit is −1.75 (95% confidence interval −1.763, −1.737)

Results, Hydraulic Resistance, paragraph 2; Figure 6A

What the paper reports

• power-law exponent of resistance on PVS area: power-law fit, 95% CI -1.763 to -1.737 (n = all segmented cross sections of the 14 segments)

The log-log fit (reading a) gives -1.926 to -2.039 with R2 0.911 to 0.944. The partial rule holds with P1 a, P4 a (-1.977, 95% CI -1.993 to -1.961, R2 0.944) and with P1 a, P4 b (-1.926, -1.939 to -1.912, R2 0.922). The nonlinear fit (reading b) gives -2.99 to -4.69; a few cross sections with resistance up to 1.88e21 dominate it, so it says little. Before the revision after round 1 only P1 a, P4 a met the partial rule (-1.965, R2 0.941); now a combination with all 14 segments does too. Reference combination for measured values, P1 a (0.648 um), P2 a (cleaned longest path), P4 b (polynomial width), P5 a, P6 erosion 3, P7 b (outliers left out), unless stated.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• Resistance is solved by finite differences on the pixel grid of the cross section, in place of finite elements (MATLAB solvepde). The domain is the region at least 1.5 pixels inside the mask's edge, which is the polygon through the boundary pixel centres after the Methods' one-pixel erosion. The Methods' check (a circle of the same area within 1% of the exact resistance) holds from 1000 um^2 at 0.648 um; at 300 um^2 and 1 um the error is 2.5%.
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, no combination matches; the partial rule holds in 3 of 8 in place of 2.

Figure 5B shows that the distribution of hydraulic resistances for the polynomial fit matches that of the segmentation most closely, followed by the ellipse fit

Results, Hydraulic Resistance, paragraph 2; Figure 6B and 6C; Table 2. The Results sentence cites Figure 5B, which is the resistance distribution of Figure 6B

The polynomial fit is the best match for the largest share in all 96 combinations, now with every erosion of P6: 81.4 to 85.7% against the fits and 52.8 to 76.5% with the annulus. On linear bins at most 2 of the 4 peaks are within tolerance (reference: spline and annulus). On logarithmic bins, a variant the claims file names for fig6b but not for this claim, two combinations (P1 a, P4 b, erosion 5, P5 b, all values) put all four within (1.37e15, 7.36e14, 1.08e16, 1.33e15); whether this claim should take fig6b's bins is asked in questions/000491.yaml. By the KS statistic the ellipse is the farthest of the four from the segmentation, not second. Before the revision after round 1 the fits were solved at erosion 3 only, and the outcome was the same. Reference combination for measured values, P1 a (0.648 um), P2 a (cleaned longest path), P4 b (polynomial width), P5 a, P6 erosion 3, P7 b (outliers left out), unless stated.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• Resistance is solved by finite differences on the pixel grid of the cross section, in place of finite elements (MATLAB solvepde). The domain is the region at least 1.5 pixels inside the mask's edge, which is the polygon through the boundary pixel centres after the Methods' one-pixel erosion. The Methods' check (a circle of the same area within 1% of the exact resistance) holds from 1000 um^2 at 0.648 um; at 300 um^2 and 1 um the error is 2.5%.
• Assumed, within the vessel's horizontal extent, the polynomial fit's region runs from the line down to the vessel center height, minus the circle; the Methods and the claims file do not say how the region is closed across the vessel. The alternative was not run.
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• The ellipse is fit to the region the PVS's outer boundary encloses, the PVS and vessel segmentations together with holes filled, as claims P9 has it since the answer of 2026-11-04. The crop window of each cross section now holds the whole ellipse; being larger, it also cuts less of the polynomial region at its edge, which moves the polynomial areas and resistances slightly; the values before the change are not in the notebook (with the reference combination and P9 a the polynomial area ratio now peaks at 1.684, median 1.710, table2).
• Since the revision after round 1 the resistances and velocities of the fits are solved with the circle fit of every erosion of P6 (1, 3 and 5 pixels).
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, no combination matches on linear bins and the polynomial is the closest for the largest share in all 96, as with E.

The peak of the curvature distribution is 0.108, showing that the PVS is most often concave

Results, Characteristics of the typical PVS shape, paragraph 7; Figure 9F

63.9 to 73.6% of values are below 1 in every combination (medians -0.627 to 0.465). The peak is within tolerance in none; with outliers out it is 0.164 to 1.162. Before the revision after round 1 the nearest peaks were 0.092 and 0.075. Reference combination for measured values, P1 a (0.648 um), P2 a (cleaned longest path), P4 b (polynomial width), P5 a, P6 erosion 3, P7 b (outliers left out), unless stated.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, no combination matches and the partial rule holds in 48 of 48, as with E.

This resulted in between 54 and 451 different cross sections for each of the 14 PVS segments that were included in the subsequent analysis. The average distance between normal planes was approximately 0.8 μ m.

Methods, Creating normal cross sections

No combination of P1, P2 and P4 holds. With the cleaned path (P2 a) and P4 b the segments give 202 to 604 cross sections at 0.648 um (mean spacing 0.876 um, within tolerance, but the most above 496.1) and 124 to 394 at 1 um (within the widened range, but spacing 1.345 um). With P4 a, 4 segments keep none. P2 b gives up to 78712 points per segment. The spacing is the mean step between neighbouring kept points (0.83 to 0.93 um per segment at 0.648 um). Before the revision after round 1, with the uncleaned path, the counts were 390 to 669 and 248 to 415. The cleaned path still meanders, 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um at every location but E. Counted along the fitted centerline (a diagnostic in the notebook, with the share kept under P4 b), the segments would give 223 to 427 cross sections at each segment's own mean step (mean 0.876 um), 241 to 492 at the paper's 0.8 um, 219 to 447 at 0.88 um and 267 to 546 at 0.72 um; the first three are inside 48.6 to 496.1. The third verification did not accept these estimated counts as a test of the claim (no slices were taken along that path and its step was not measured), so the outcome stays not reproduced. Reference combination for measured values, P1 a (0.648 um), P2 a (cleaned longest path), P4 b (polynomial width), P5 a, P6 erosion 3, P7 b (outliers left out), unless stated.

Proposed after the last verification, not yet verified: reproduced. The criterion takes one slice per centerline point, so the count follows the length of the path. The cleaned path of this attempt, the stand-in for the paper's manual removal of erroneous points, is still 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (data check, as the verifier of round 2 found), and the voxel zigzag explains at most about 8% of that, so it holds more points than a centerline along the vessel. A centerline that follows the fitted curve is the better-supported reading of a hand-cleaned centerline. Counted along it with the share kept under P4 b (cell under cross-section-counts), P1 a gives 223 to 427 cross sections per segment at each segment's own mean step (mean spacing 0.876 um) and 241 to 492 at the paper's 0.8 um, both inside 48.6 to 496.1 with the spacing within tolerance, so the claim holds; P1 b still fails on its spacing (1.345 um). The margin is small: at a step of 0.72 um the most would be 546, and the counts are estimated from the kept share, not from slices taken along the fitted curve. The fewest, 223, is far above the paper's 54, which the criterion allows. The verifier of round 3 did not agree and would keep not reproduced: the counts come from scaling the kept share by the fitted arc over an assumed step, not from slices taken along a new path; a centerline that follows the fitted curve is a reading outside the claims file, which the Methods (points "manually removed" from the bwskel output) do not support; and the step of 0.876 um that passes is the mean step of the meandering path, not measured on a path along the vessel, while an average 26-connected step of about 0.73 um would give a most of about 539. The change could be considered if slices were taken along a path that follows the vessel, its own mean step met 0.72 to 0.88 um and the counts fell within 48.6 to 496.1; that analysis was not run and waits for a new attempt.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• For P2 b the median widths of P4 are taken from 150 evenly spaced points per segment (a standard choice), and the spacing is between consecutive points sorted along the main axis.
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, the fewest cross sections at 0.648 um (P4 b) become 409 and the most stays 604; no combination holds.

The area of the PVS generally increases with the area of the vessel, but the trend is only approximate, as evidenced by the low R 2 value of the fit line (0.158). The slope of the fit line is 1.05, (95% confidence interval 0.973, 1.12).

Results, Area ratio, paragraph 1; Figure 5A

What the paper reports

• slope of PVS area on vessel area: least-squares fit, 95% CI 0.973 to 1.12 (n = all cross sections of the 14 segments)

Slope 0.912 to 1.543 and R2 0.072 to 0.527 over the eight combinations of P1, P4 and intercept. Nearest, P1 a, P4 b with intercept, slope 0.912 (95% CI 0.865 to 0.959) and R2 0.176, and P1 b, P4 b, slope 0.951 (0.894 to 1.007) and R2 0.199; the slope tolerance is 0.973 to 1.127 and the R2 tolerance 0.142 to 0.174. Within segments the slope runs from -6.911 (G) to 2.462 (D). Before the revision after round 1, with all PVS pixels of the plane, the slope was 1.504 to 2.718. Reference combination for measured values, P1 a (0.648 um), P2 a (cleaned longest path), P4 b (polynomial width), P5 a, P6 erosion 3, P7 b (outliers left out), unless stated.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, no combination matches; with the reference combination and an intercept the slope is 1.025 and R2 0.199 (0.912 and 0.176 with E).

There is considerable variation in the area ratio, and the interquartile range of the segmented area ratio is 1.79 ( Table 2 ), a value on the same order as the median value of 1.88, meaning that the area ratio varies by more than 100%. The peak value of 1.12

Results, Area ratio, paragraph 1; Figure 5E; Table 2

No combination puts the median and IQR within tolerance, which the partial rule needs. The median is 1.226 to 1.565 (expected 1.88 within 0.188), the IQR 0.874 to 1.287 (1.79 within 0.179), the 25th percentile 0.875 to 1.016 and the 75th 1.749 to 2.282. The peak is within tolerance in eight combinations, all with P5 b, at 1.133 to 1.230. Before the revision after round 1, with all PVS pixels of the plane, the median (1.718) and IQR (1.831) were within tolerance and the outcome was partially reproduced; keeping the lobes beside the vessel lowers the large ratios. Reference combination for measured values, P1 a (0.648 um), P2 a (cleaned longest path), P4 b (polynomial width), P5 a, P6 erosion 3, P7 b (outliers left out), unless stated.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, no combination has the median and IQR within; with the reference combination the peak is 1.508, the median 1.566 and the IQR 1.23.

The peak of the area ratio distribution ranges from 0.6 to 11.43 across the different locations. Although their area ratio varies along the length of each vessel, in all but one case, this variation occurs within 30% of the peak

Results, Area ratio, paragraph 2; Additional File 3 (Additional File 4 in the list)

None of 128 combinations matches. The smallest per-location peak is 0.052 to 0.74 and the largest 1.7 to 9.04; with the reference combination 0.053 (C) and 9.045 (G). At most 9 locations meet a reading of "within 30% of the peak" (reading c), against 11.7 to 14.3, and none meets reading (d). Count for reading (a). Before the revision after round 1 the largest peak reached 257.17 and at most 10 locations met a reading. Reference combination for measured values, P1 a (0.648 um), P2 a (cleaned longest path), P4 b (polynomial width), P5 a, P6 erosion 3, P7 b (outliers left out), unless stated.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, no combination of 128 matches, as with E.

Here, we report the distribution of hydraulic resistances for thousands of PVS cross sections, with its peak at 1.73×10 15 Pa· s/m 4

Discussion, paragraph 4; Conclusion; Table 2; Figure 6B

The peak is within tolerance in three combinations, 1.86e15 (P1 a, P4 a, all values, log bins), 1.68e15 (P1 a, P4 b, outliers out, linear bins) and 1.83e15 (P1 b, P4 b, outliers out, linear bins). The median is 5.28e15 to 6.87e15 in every combination, against 3.84e15 within 3.84e14. The partial rule needs the median within tolerance and the peak not; here it is the other way round, so the outcome is not reproduced. Before the revision after round 1 the median (4.16e15) was within and the peak (1.25e15) was not, and the outcome was partially reproduced; dropping PVS far from the vessel lowers the PVS area and raises the resistance. Reference combination for measured values, P1 a (0.648 um), P2 a (cleaned longest path), P4 b (polynomial width), P5 a, P6 erosion 3, P7 b (outliers left out), unless stated.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• Resistance is solved by finite differences on the pixel grid of the cross section, in place of finite elements (MATLAB solvepde). The domain is the region at least 1.5 pixels inside the mask's edge, which is the polygon through the boundary pixel centres after the Methods' one-pixel erosion. The Methods' check (a circle of the same area within 1% of the exact resistance) holds from 1000 um^2 at 0.648 um; at 300 um^2 and 1 um the error is 2.5%.
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, the median is within tolerance in no combination; with the reference combination the peak is 1.63e15 and the median 5.19e15.

it is evident that the variation between locations is much larger than that along the PVS at each location. The peak of hydraulic resistance distributions ranges from 3.23×10 14 to 1.98×10 16 across different locations, whereas, in 65% of the vessels, all the variation occurs within 37% of the peak of the distribution

Results, Hydraulic Resistance, paragraph 2; Figure 6B; Additional File 5

No combination matches. The smallest per-location peak is 8.93e14 to 2.35e15 (against 3.23e14), the largest 3.78e16 to 4.69e19 (1.98e16), and the share within 37% of the peak 0 to 35.7% (65%). Share for reading (a). Per-location medians run from 1.72e15 (G) to 1.11e17 (C). Before the revision after round 1 the smallest peak was about 5e13 at E. Reference combination for measured values, P1 a (0.648 um), P2 a (cleaned longest path), P4 b (polynomial width), P5 a, P6 erosion 3, P7 b (outliers left out), unless stated.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• Resistance is solved by finite differences on the pixel grid of the cross section, in place of finite elements (MATLAB solvepde). The domain is the region at least 1.5 pixels inside the mask's edge, which is the polygon through the boundary pixel centres after the Methods' one-pixel erosion. The Methods' check (a circle of the same area within 1% of the exact resistance) holds from 1000 um^2 at 0.648 um; at 300 um^2 and 1 um the error is 2.5%.
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, no combination matches, as with E.

the distribution of R 1 , the vessel radius, is similar to that of R 3 , the minor axis length (distribution peaks at 28 μ m and 35 μ m, respectively, see Figure 8A ), and the ratio between them ( R 3 / R 1 ) is generally close to 1 (distribution peaks at 0.80, Figure 8E )

Results, Characteristics of the typical PVS shape, paragraphs 2 to 5; Figure 8A, 8C, 8D, 8E and 8F

No combination matches and none has the three ratios within tolerance. R3 peaks at 27.35 to 30.10 um and R3/R1 at 0.965 to 1.107, within tolerance in none; R2/R1 is within in 69 of 72 and R3/R2 in 54 of 72; Ov in 5. Oh's IQR is at least twice Ov's in all 72 and its median within one Ov peak of zero in 11. Before the revision after round 1 R3/R1 was within in 3 combinations. Reference combination for measured values, P1 a (0.648 um), P2 a (cleaned longest path), P4 b (polynomial width), P5 a, P6 erosion 3, P7 b (outliers left out), unless stated.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• The ellipse is fit to the region the PVS's outer boundary encloses, the PVS and vessel segmentations together with holes filled, as claims P9 has it since the answer of 2026-11-04. The crop window of each cross section now holds the whole ellipse; being larger, it also cuts less of the polynomial region at its edge, which moves the polynomial areas and resistances slightly; the values before the change are not in the notebook (with the reference combination and P9 a the polynomial area ratio now peaks at 1.684, median 1.710, table2).
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, no combination matches, but the three ratios are within tolerance in 12 of 72 in place of none, so the partial rule would hold and the outcome would be partially reproduced.

The short side is significantly shorter than the long side (distribution peaks of 1.1 and 1.9, respectively, Figure 9E ) and for the ratio between them, W S / W L , the distribution peaks at approximately 0.5, indicating that the two PVS sides are typically asymmetric

Results, Characteristics of the typical PVS shape, paragraphs 3 and 5; Figure 9E; Table 3

No combination has the three peaks within tolerance. WS/R1 peaks at 1.000 to 1.630, WL/R1 at 1.146 to 3.905 and WS/WL at 0.629 to 0.729; with P1 b, P4 a, erosion 1 and all values the first two are within (1.186, 1.887) but WS/WL is 0.729. Medians WS/R1 1.197 to 1.484, WL/R1 2.230 to 3.136, WS/WL 0.564 to 0.595. Before the revision after round 1 the WS/WL peak was 0.38 to 0.63. Reference combination for measured values, P1 a (0.648 um), P2 a (cleaned longest path), P4 b (polynomial width), P5 a, P6 erosion 3, P7 b (outliers left out), unless stated.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, no combination matches, as with E.

From Figure 5 , it is clear that the variation in PVS area is much larger between segments of PVS than along the length of a single PVS segment. We quantified this difference by plotting the median PVS area from each segment and the interquartile range of each segment

Results, Area ratio, paragraph 2; Figure 5B and 5C

Reading (a) holds in all four combinations of P1 and P4 (P1 a, P4 b, IQR of the 14 segment medians 3260.3 um^2 against a median within-segment IQR of 1621.5). Reading (b) holds only with P1 a, P4 a, which keeps 10 segments (range of medians 8887.3 against 7661.6 at H); with all 14 (P4 b) the range of the medians, 8461.9 and 8603.5, is below the largest within-segment IQR, 9476.5 (H) and 10464.5. The criterion sends a split to methods_underspecified. What is open is the measure of "much larger" (Figures 5B and 5C are compared by eye); a question for the authors is under findings. Before the revision after round 1 both readings held under P4 b (range 30496.8 against 13614.7), because the PVS of E and F included most of the plane; the outcome was reproduced, resting on P4 b.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• P4 reading (b) is no longer adopted as an assumption here: the readings of the criterion split under it, so the outcome follows the criterion.
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, reading (a) holds in 4 of 4 combinations and reading (b) in 1, as with E.

Since there was no statistically significant difference between the left and right sides, we report the distribution of the short ( W S ) and long ( W L ) sides of each cross section.

Results, Characteristics of the typical PVS shape, paragraph 5

Readings (a) and (b) find a difference in every combination (p 2e-30 to 8e-190 and 1e-31 to 2e-142; median left minus right -9.6 to -18.0 um); reading (c), on the per-segment medians, does not (p 0.055 to 0.715). Readings (a) and (b) treat thousands of neighbouring, autocorrelated cross sections as independent, so their p-values overstate the evidence; only (c) has independent units, but the criterion sends the split to methods_underspecified. The question for the authors is under findings.

How the test differed from the paper’s method

• Starts from the deposited final segmentations, as the claims file says; the vessel centerline is skimage's 3D thinning in place of MATLAB bwskel. Assumed, for the manual removal of erroneous points (Methods, Creating normal cross sections, "then manually removed erroneous points"), which the paper does not describe: the longest path through the skeleton (P2 a), less the points farther from the second-order polynomial fit of the centerline than the vessel radius (95th percentile of the vessel's inscribed radius along the path) and the points that revisit a stretch of the fitted centerline already passed (pvs.clean_path). Added after the first verification, which found the uncleaned path 1.28 to 2.24 times the distance between its ends; 7534 of 9564 path points are kept at 0.648 um and 4974 of 6010 at 1 um. The cleaned path is still 1.13 to 1.78 times the distance between its kept ends and 1.08 to 1.44 times the arc of the fitted centerline at 0.648 um (E excepted), more than the zigzag of a 26-connected voxel path (at most about 8% on a straight line) explains, so it still meanders inside the vessel; the slices are oriented by the fitted centerline, so the meander changes how many there are more than where they lie.
• Cross sections are sampled by linear interpolation of the masks, thresholded at 0.5, on planes normal to the fitted centerline, one per path point, with pixels of the P1 voxel size, in place of MATLAB obliqueslice (a standard choice).
• Pixels in both the vessel and the PVS mask are counted as vessel. The Methods say overlaps were resolved by hand, case by case, but the deposited masks still overlap; the overlap exceeds 5% of the PVS in 381 of 6683 cross sections (P1 a, P4 b), 247 of them at J and 131 at E, so the choice is unlikely to change an outcome. The other assignment was not run.
• Assumed, the PVS of a cross section is the two largest PVS regions (8-connected) that come within one vessel radius, sqrt(area / pi), of the vessel region, the vessel being the connected region at or nearest the slice center. The segmentation "removed ... all but the two largest regions in the PVS segmentation" (Methods, Segmentation) and the fits are of the lobes beside the vessel (Figure 4), while the deposited masks hold PVS around other vessels and far from the artery. Added after the first verification; before it all PVS pixels of the 332 um plane were used. By median area the lobes are 91 to 99% of a slice's PVS at every location but E (29 to 52%) and, at 1 um, H (70%). Cross sections with fewer than 20 vessel or PVS pixels have no fits (shown per location in the data check).
• Assumed, planes where the deposited PVS mask covers more than 90% of the field are cleared before the cross sections are taken: at E and F the mask fills every plane below a depth (87 and 58 planes), and no plane of any other file is more than 50% PVS. Added after the first verification.
• The edge distance of P4 is measured from the vessel center in the slice (circle fit, erosion 3), to which the Methods shift the slice ("The slices were then shifted so the center point of the vessel was located in the center of the image", Methods, Creating normal cross sections). Before the first verification it was measured from the skeleton point; the change is 0.75 to 3.85 um by median per location and keeps 6683 cross sections in place of 6665 (P1 a, P4 b).
• P4 reading (a), the horizontal extent of the PVS, keeps no cross section in 4 of the 14 segments (A, B, F, G), while the paper analysed all 14; its results are shown but it is the less supported reading.
• Location E is kept, as one of the paper's 14 segments, though its cleaned path follows a side branch of the vessel network in its mask, not the vessel with PVS beside it, and its lobes are 29 to 52% of the slice's PVS; it gives 202 of the 6683 cross sections (P1 a, P4 b). Neither keeping nor dropping it gives the paper's E. Added after the second verification, the notebook computes every claim's table again without E (the cell before the summary). Without E, the readings still split in all 12 combinations (reading c p 0.055 to 0.414).