Online supplemental material

Genetic variation in retinal vascular patterning predicts variation in pial collateral extent and stroke severity.

Pranay Prabhakar BS, Hua Zhang MD, De Chen PhD, James E. Faber PhD

Detailed materials and methods

Online Appendix 1. MATLAB code used to calculate fractal dimension and lacunarity.

Online Table 1. Collateral number, collateral diameter and retinal patterning metrics vary with genetic background.

Online Figure 1. Retinal tree segmentation.

Online Figure 2. Collateral number, collateral diameter and retinal patterning metrics vary with genetic background.

Online Figure 3. Among 4 strains of mice with large differences in collateral extent, the range of values is greater and

variance (SEMs) smaller for fractal dimension (panel C) determined for a randomly selected region of interest on arterial tree

(ROI) (inset in A) than for whole retina (B).

Online Figure 4. Fractal dimension of the distal-most region of the vasculature between adjacent artery and vein trees (ie, the

“capillary bed”) lacks strain-dependent differences shown in Online Figure 2 for whole retina or individual artery trees.

Online Figure 5. Complexity of genetic-dependent vascular patterning, as indicated by fractal dimension of randomly

selected artery trees, is not altered by removal of the distal-most region of the vasculature between adjacent artery and vein;

however, variance (SEMs) is reduced.

Online Figure 6. Comparison of fractal dimension (FD) and lacunarity (Lac) obtained from 3, 2 and 1 randomly chosen

arterial tree(s).

Online Figure 7. Retinal patterning predicts pial collateral number (COL-N) and diameter (COL-D).

Online Figure 8A. Differences in fractal dimension (FD) and lacunarity (L) of retinal artery trees are associated with

differences in retinal patterning metrics (RPMs). Online Figure 8B-I. Among RPMs characterizing retinal arterial tree

complexity, differences in FD and L are most strongly associated with differences in CRAE and average length of branch

segments, respectively.

Online supplemental material (continued)

Online Figure 9. Both retinal patterning metrics (RPMs) and middle-cerebral artery patterning metrics (MCAM) vary with

genetic background, but only half showed significant or suggestive correlations with each other).

Online Figure 10. Middle cerebral artery patterning metrics (MCAMs) predict pial collateral number (COL-N) and diameter

(COL-D).

Online Figure 11. Among the most predictive MCAMs, average number of MCA tree branch segments per unit MCA area (ie,

MCA branching density) contributes the most, statistically, to predicting collateral number and diameter (COL-N and COL-

D). MCA trees with larger branch angle, larger caliber of branching vessels (D1, D2), and larger cerebral hemisphere areas

tend to have greater collateral extent (COL-N and/or COL-D).

References for supplemental material.

Detailed materials and methods

Pial collateral number and diameter. Brains were obtained from a population of ~3 month-old male mice (n=81) composed of

10 strains that differ widely in collateral extent.1-3 The deficient strains were: VEGFAlo/+ A/J, AKR/J, CLIC4-/-, and BALB/cBy/J;

the abundant strains were: C57BLKS/J, DBA/2J, VEGFAhi/+, C57BL/6, and CD1/CR (this is the background strain for VEGFAlo/+,

VEGFAhi/+, and CLIC4-/-) (Figure 1). As described in detail elsewhere,1 mice were anesthetized with ketamine and xylazine (100

and 10 mg/kg ip), heparinized, and the cerebral vasculature perfused via the thoracic aorta at 100 mmHg with phosphate buffered

saline (PBS) containing 10-4M nitroprusside to produce maximal vasodilation and Evans blue to stain the endothelium. While this

proceeded, a craniotomy was performed and the dorsal surface of the neocortex was treated topically with 4% paraformaldehyde

(PFA) to fix the vasculature at maximal diameter. Under a stereomicroscope, the cerebral arterial vasculature was then filled with

yellow MicroFilR with a viscosity set to minimize capillary transit to allow filling of the entire pial arterial circulation. After the

microFil had set, the brain was fixed overnight in 4% PFA and imaged under a stereomicroscope to count the number of collaterals

(COL-N) interconnecting the middle and anterior cerebral arterial (MCA, ACA) trees. The brain was then immersed in Evans blue

in PBS to stain the brain parenchyma for contrast. Digital images were collected and collateral diameter (COL-D) was obtained as

the average of 3 points along the center-most length of each collateral using ImageJ software. The brain was oriented to present

the MCA tree in focus, and images were obtained for digital segmentation as describe below for the retina.

Mouse retina preparation. Before the above procedures, retinas were collected from one eye of each of the above mice (n=81).

Enucleation. Mice were anesthetized with ketamine and xylazine, and eyelids were reflected with a curved forceps. Using a

stereomicroscope, the optic-nerve was severed with irridectomy scissors and the eyeball was removed and immersed in 2% PFA for

2 hours or 4% PFA for 1 hour. Eyeballs were stored at 4C in PBS if necessary for 8 days. Removal of retina. The eyeball was

held in place with corneal side up in a Silastic-bottom glass petri dish using micropins (#26002-20, FST) passed through

connective tissue attached to the sclera, and kept moist with PBS throughout the procedure. Using a 27 gauge needle, a 1 mm slit

was cut at an oblique angle through the cornea at a point above the equator of the eye ball. The cornea was circumcised from the

sclera by placing one blade of a Vannas scissors into the slit and hinging it on the petri dish edge, positioning the scissors tangential

to the cornea and parallel to the surgical table surface, gradually cutting along the cornea’s circumference while rotating the dish

one whole turn in order to hemisect the eye just above the ora serrata. The lens and vitreous were gently suctioned using a

micropipette followed by rinsing the retinal cup with PBS without disrupting the retina. This process was repeated 2-3 times to

ensure maximum removal of the vitreous from the retinal surface. The sclera was further fastened to the silastic bottom using

additional pins. The retina was gradually separated from the sclera with the ora serrata intact, using fine forceps. The retinal cups

were transferred to 96 well-plates containing PBS. Staining. Following removal of PBS, retinal cups were incubated in ice cold

70% methanol for 10 minutes, rinsed with PBS 3 times for 5 minutes and incubated in PBS with 1% Triton X-100 for 30 minutes.

After an additional rinse with PBS, retinal cups were incubated overnight in Alexafluor 568 GS-IB4 (l21412, Invitrogen) at 10

μg/mL in PBS on a rotator at 4ºC in the dark. Retinas were then rinsed with PBS, incubated in 1% Triton X-100 in PBS for 20

minutes, and then re-rinsed 3 times for 5 minutes in PBS.

Detailed materials and methods (continued)

Mouse retina preparation. Mounting. Retinal cups were carefully lifted with fine forceps and placed onto Superfrost-Plus

charged slides in a PBS bubble within a Pap-Pen-marked hydrophobic boundary. Using the Vannas scissors, four deep cuts were

made along the circumference of the cup, extending from the ora serrata towards the optic nerve opening in order to sufficiently

flatten the retina. Flattened retina was mounted onto another Superfrost-Plus slide with Vectashield under a coverslip, which was

sealed with fingernail polish. Imaging. Slides were stored in paper folders in the dark at 4ºC and imaged and optically flattened

using a 10x objective lens on a Nikon Surveyor microscope within 5 days of cover-slipping.

Infarct volume. Permanent occlusion of the right MCA trunk by micro-cautery midway between the zygomatic arch and the pinna

of the ear, as detailed previously,2-3 was done on different mice from those used for the above procedures. Briefly, mice were

anesthetized with ketamine and xylazine and maintained at 37C rectal temperature. A 4mm skin incision was made, the midpoint

of the temporal muscle separated, and a 2mm burr-hole was made over the trunk of the MCA. The MCA was cauterized and

transected, the incision closed, cephazolin and buprenorphine administered, and mice were maintained at 37C rectal temperature

until awake. After an overdose of ketamine (100mg/kg ip) and xylazine (15 mg/kg ip) 24 hours later, brains were removed and

cooled on dry ice until the tissue became stiff, and 1 mm coronal slices were incubated in 1% 2,3,5-tripenyltetrazolium chloride in

PBS at 37C for 20 minutes, then fixed with 1% PFA overnight. Infarct volume was calculated as the sum of the unstained

volumes and expressed as a percent of total right cortical volume.

C57BLKS (8) DBA/2 (8) VEGFAhi/+

(10) C57BL/6 (8) CD-1 (8) VEGFAlo/+

(7) A/J (8) AKR (8) CLIC4-/-

(8) BALB/c (8) Adjusted R2 p-value

N Collateral number 24.75 (22.42, 27.08) 19.75 (17.42, 22.08) 20.60 (18.51, 22.69) 18.75 (16.42, 21.08) 18.13 (15.79, 20.46) 10.43 (7.93, 12.92) 6.13 (3.79, 8.46) 5.00 (2.51, 7.50) 2.75 (0.42, 5.08) 0.88 (-1.46, 3.21) 0.86 <.0001

DAverage collateral

diameter (µm)22.03 (20.97, 23.09) 20.73 (19.67, 21.79) 20.41 (19.47, 21.36) 20.71 (19.65, 21.77) 18.90 (17.85, 19.96) 17.23 (16.10, 18.36) 11.74 (10.69, 12.80) 11.94 (10.81, 13.07) 12.90 (11.84, 13.96) 13.92 (12.58, 15.26) 0.87 <.0001

1 Do (µm) 25.97 (24.27, 27.67) 22.51 (20.81, 24.22) 22.38 (20.85, 23.90) 18.93 (17.22, 20.63) 21.32 (19.62, 23.02) 17.70 (15.89, 19.52) 18.70 (17.00, 20.40) 18.17 (16.35, 19.99) 13.11 (11.41, 14.81) 16.05 (14.34, 17.75) 0.67 <.0001

2 D1 (µm) 12.04 (11.39, 12.69) 11.21 (10.56, 11.86) 10.44 (9.86, 11.02) 10.47 (9.82, 11.13) 9.95 (9.30, 10.60) 10.19 (9.50, 10.89) 11.02 (10.37, 11.67) 11.49 (10.80, 12.19) 8.58 (7.93, 9.23) 10.33 (9.68, 10.99) 0.46 <.0001

3 D2 (µm) 25.59 (23.97, 27.21) 22.29 (20.67, 23.91) 21.42 (19.98, 22.87) 18.51 (16.89, 20.13) 20.87 (19.25, 22.49) 17.37 (15.64, 19.10) 17.92 (16.30, 19.53) 17.60 (15.87, 19.33) 12.58 (10.96, 14.20) 15.53 (13.92, 17.15) 0.69 <.0001

4Tortuosity index (inner

zone)1.02 (1.01, 1.03) 1.01 (1.00, 1.02) 1.02 (1.02, 1.03) 1.01 (1.00, 1.02) 1.01 (1.01, 1.02) 1.02 (1.01, 1.03) 1.01 (1.00, 1.02) 1.02 (1.01, 1.03) 1.02 (1.01, 1.02) 1.02 (1.01, 1.03) 0.03 0.274

5 CRAE (µm) 46.03 (43.30, 48.77) 41.13 (38.40, 43.87) 42.61 (40.17, 45.06) 33.23 (30.50, 35.96) 41.18 (38.45, 43.92) 31.89 (28.97, 34.82) 33.14 (30.41, 35.88) 34.44 (31.52, 37.36) 25.45 (22.72, 28.18) 27.46 (24.72, 30.19) 0.73 <.0001

6 CRVE (µm) 77.63 (72.70, 82.57) 70.98 (66.05, 75.92) 63.49 (59.08, 67.91) 51.54 (46.61, 56.48) 59.61 (54.67, 64.54) 61.31 (56.03, 66.58) 51.01 (46.08, 55.94) 59.38 (54.11, 64.66) 38.18 (33.24, 43.11) 39.01 (34.08, 43.95) 0.74 <.0001

7 AVR 0.60 (0.55, 0.66) 0.58 (0.53, 0.64) 0.68 (0.63, 0.72) 0.65 (0.59, 0.70) 0.70 (0.65, 0.76) 0.53 (0.47, 0.59) 0.65 (0.60, 0.71) 0.58 (0.53, 0.64) 0.67 (0.61, 0.72) 0.71 (0.65, 0.76) 0.28 0.0001

8 Branch angle 83.74 (77.42, 90.07) 97.47 (91.15, 103.80) 75.85 (70.19, 81.51) 79.84 (73.52, 86.17) 80.45 (74.12, 86.77) 78.68 (71.91, 85.44) 68.39 (62.07, 74.72) 83.72 (76.95, 90.48) 66.25 (59.93, 72.58) 75.37 (69.04, 81.69) 0.43 <.0001

9 Optimality 0.83 (0.78, 0.88) 0.97 (0.92, 1.02) 0.81 (0.76, 0.85) 0.84 (0.79, 0.89) 0.85 (0.80, 0.90) 0.85 (0.80, 0.91) 0.84 (0.79, 0.89) 0.99 (0.94, 1.05) 0.86 (0.81, 0.91) 0.87 (0.82, 0.92) 0.35 <.0001

10 Retinal area (µm2)

1.66E+07 (1.53E+07,

1.79E+07)

1.61E+07 (1.49E+07,

1.74E+07)

1.72E+07 (1.61E+07,

1.84E+07)

1.62E+07 (1.50E+07,

1.75E+07)

1.64E+07 (1.51E+07,

1.77E+07)

1.60E+07 (1.46E+07,

1.74E+07)

1.56E+07 (1.43E+07,

1.69E+07)

1.57E+07 (1.43E+07,

1.70E+07)

1.48E+07 (1.35E+07,

1.61E+07)

1.35E+07 (1.22E+07,

1.48E+07)0.16 0.009

11 Fractal dimension 1.503 (1.490, 1.517) 1.481 (1.467, 1.495) 1.488 (1.475, 1.500) 1.469 (1.455, 1.482) 1.484 (1.470, 1.497) 1.472 (1.458, 1.487) 1.472 (1.459, 1.486) 1.470 (1.456, 1.485) 1.446 (1.433, 1.460) 1.464 (1.450, 1.477) 0.32 <.0001

12 Lacunarity 15.82 (13.48, 18.17) 21.05 (18.71, 23.40) 18.05 (15.95, 20.15) 21.13 (18.79, 23.48) 18.32 (15.97, 20.66) 21.10 (18.59, 23.61) 21.62 (19.27, 23.96) 19.98 (17.47, 22.49) 23.64 (21.29, 25.98) 19.29 (16.94, 21.64) 0.23 0.001

13 Arterial tree area (µm2)2.04E+05 (1.80E+05,

2.27E+05)

1.61E+05 (1.37E+05,

1.85E+05)

1.82E+05 (1.61E+05,

2.04E+05)

1.71E+05 (1.47E+05,

1.94E+05)

2.12E+05 (1.88E+05,

2.36E+05)

1.90E+05 (1.64E+05,

2.15E+05)

1.64E+05 (1.40E+05,

1.88E+05)

1.51E+05 (1.26E+05,

1.77E+05)

1.09E+05 (8.47E+04,

1.33E+05)

1.43E+05 (1.20E+05,

1.67E+05)0.38 <.0001

14Skeltonized arterial tree

area (µm2)

1.46E+04 (1.27E+04,

1.65E+04)

1.08E+04 (8.86E+03,

1.27E+04)

1.41E+04 (1.24E+04,

1.58E+04)

1.35E+04 (1.16E+04,

1.54E+04)

1.60E+04 (1.41E+04,

1.79E+04)

1.50E+04 (1.29E+04,

1.70E+04)

1.28E+04 (1.09E+04,

1.47E+04)

1.11E+04 (9.10E+03,

1.32E+04)

9.49E+03 (7.59E+03,

1.14E+04)

1.23E+04 (1.04E+04,

1.42E+04)0.29 <.0001

15Average arterial tree

diameter (µm)14.02 (13.21, 14.84) 15.20 (14.38, 16.02) 13.06 (12.33, 13.79) 12.62 (11.80, 13.43) 13.25 (12.43, 14.06) 12.62 (11.75, 13.49) 12.87 (12.05, 13.68) 13.63 (12.76, 14.50) 11.53 (10.71, 12.34) 11.70 (10.88, 12.52) 0.40 <.0001

16

Number of arterial tree

branch segments/tree

area (µm2)

1.24E-03 (1.11E-03,

1.37E-03)

1.13E-03 (1.00E-03,

1.26E-03)

1.43E-03 (1.32E-03,

1.54E-03)

1.46E-03 (1.33E-03,

1.59E-03)

1.33E-03 (1.21E-03,

1.46E-03)

1.45E-03 (1.32E-03,

1.59E-03)

1.21E-03 (1.08E-03,

1.34E-03)

1.37E-03 (1.23E-03,

1.50E-03)

1.44E-03 (1.32E-03,

1.57E-03)

1.37E-03 (1.24E-03,

1.49E-03)0.20 0.0025

17Average tortuosity of

branch segments 1.07 (1.07, 1.07) 1.07 (1.06, 1.07) 1.07 (1.07, 1.07) 1.07 (1.06, 1.07) 1.07 (1.07, 1.07) 1.07 (1.06, 1.07) 1.07 (1.07, 1.07) 1.07 (1.07, 1.07) 1.07 (1.07, 1.07) 1.08 (1.07, 1.08) 0.33 <.0001

18

Skewness of distrubtion

of branch segment

tortuosity

3.64 (2.61, 4.66) 0.78 (-0.24, 1.81) 2.03 (1.11, 2.95) 0.99 (-0.04, 2.02) 3.02 (1.99, 4.05) 1.06 (-0.03, 2.16) 1.61 (0.59, 2.64) 2.00 (0.91, 3.10) 1.28 (0.26, 2.31) 3.51 (2.49, 4.54) 0.27 0.0002

19

Kurtosis of distribution

of branch segment

tortuosity

37.29 (23.53, 51.06) 2.92 (-10.84, 16.68) 15.10 (2.79, 27.41) 4.91 (-8.85, 18.68) 31.61 (17.85, 45.37) 4.92 (-9.79, 19.64) 9.61 (-4.15, 23.37) 10.84 (-3.87, 25.55) 5.84 (-7.92, 19.61) 28.47 (14.70, 42.23) 0.21 0.002

20Avg length of branch

segments (µm)66.26 (62.42, 70.10) 69.09 (65.25, 72.93) 62.29 (58.85, 65.72) 63.40 (59.56, 67.24) 66.21 (62.37, 70.05) 63.57 (59.46, 67.67) 76.04 (72.20, 79.88) 63.17 (59.07, 67.28) 71.37 (67.53, 75.21) 73.57 (69.73, 77.41) 0.38 <.0001

21

Skewness of distribution

of branch segment

lengths

3.19 (2.71, 3.67) 3.42 (2.95, 3.90) 3.11 (2.68, 3.53) 3.12 (2.64, 3.60) 3.04 (2.56, 3.51) 3.19 (2.68, 3.70) 2.66 (2.19, 3.14) 4.36 (3.85, 4.87) 2.47 (2.00, 2.95) 2.73 (2.25, 3.20) 0.28 0.0002

22

Kurtosis of distribution

of branch segment

lengths

17.68 (12.06, 23.30) 19.42 (13.80, 25.05) 17.40 (12.37, 22.43) 17.08 (11.45, 22.70) 16.31 (10.68, 21.93) 16.36 (10.35, 22.38) 11.56 (5.93, 17.18) 30.50 (24.49, 36.51) 9.84 (4.22, 15.47) 12.49 (6.87, 18.12) 0.24 0.0007

ANOVACOL-D, COL-N and

RPMs (Mean and

95% CI)

Mouse strain (n size)

Online Table 1. Collateral number, collateral diameter and retinal patterning metrics vary with genetic background. Table shows averages,

95% confidence intervals, and bivariate regression of COL-N, COL-D, and 22 RPMs versus 10 mouse strains (one-way ANOVA - adjusted R2 and

p-value). Strains arranged left-to-right according to strains with the largest and smallest number of pial collaterals (n = number of mice studied).

Shading in ANOVA column reflects relative strength of association (adjusted R2 value; shading same as black bars shown in Figure 5).

Online Figure 1. Retinal tree segmentation. Image of flat-mounted stained retina (A) is segmented using Photoshop CS4, 3

retinal trees are randomly selected and capillaries are manually pruned away using specified segmentation rules so that only 1st,

2nd, 3rd, and the half-length of 4th order arterioles are retained (B). Using a combination of the Leveling tool and optimization of

brightness and contrast, background is eliminated, dark or missing segments of trees are filled in and the image is thresholded (C).

A B

C

*0.86 (<.0001)

0.87 (<.0001) 0.67 (<.0001) 0.46 (<.0001)

0.69 (<.0001) 0.03 (0.274) 0.73 (<.0001) 0.74 (<.0001)

0.28 (0.0001) 0.43 (<.0001) 0.16 (0.009)

0.32 (<.0001) 0.23 (0.001) 0.38 (<.0001)

0.4 (<.0001) 0.2 (0.0025) 0.33 (<.0001) 0.27 (0.0002)

0.21 (0.002) 0.38 (<.0001) 0.28 (0.0002) 0.24 (0.0007)

0.35 (<.0001)

0.29 (<.0001)

Strain: (A) A/J; (B) AKR; (C) BALB/c; (D) C57BLKS; (E) C57BL/6; (F) CLIC4-/-; (G) DBA/2; (H) VEGFAhi/+; (I) VEGFAlo/+; (J) CD-1

Online Figure 2. Collateral number, collateral diameter and retinal patterning metrics vary with genetic

background. Graphs show averages, 95% confidence intervals, and bivariate regression of COL-N, COL-D, and 22 RPMs

versus 10 mouse strains (one-way ANOVA - adjusted R2 and p-value are given on the graphs). Horizontal line across each

graph represents mean of the metric across all strains. Top and bottom points of diamond represent the 95% confidence

interval of the mean for each strain. Diamond width is proportional to the n-size of the strain. Relative variation in vertical

position of diamonds reveals degree to which COL-N, COL-D, and RPMs vary across all strains.

Note, Figure 3D in the manuscript proper shows 1 of 3-4 selected arterial trees chosen randomly from a retina. The

distribution displayed for this arterial tree happens to lack branch segments measuring 175-200 microns length, which makes

the distribution appear to have two peaks, ie, one large population of small branches and another smaller population with

really large branches. This is an incidental finding secondary to biological variation and experimental error. The consistently

positive skewness of distribution of branch segment lengths for all arterial trees reflects continued branching of the central

retinal artery into a few large parent trunks which, in turn, further divide into smaller daughters as terminal branching

approaches capillaries.

0 1 2 3 4 5 6 7 80

2

4

6

8 BC

BLKS

DBA/2

AKR

Log2 (r)

La

cu

na

rity

of

RO

I

A B

D

1.72

1.74

1.76

1.78

1.80

1.82

1.84

1.86

BC AKR BLKS DBA/2

Fra

cta

l d

ime

ns

ion

of

wh

ole

re

tin

a1.56

1.60

1.64

1.68

1.72

1.76

1.80

1.84

BC AKR BLKS DBA/2

Fra

cta

l d

imen

sio

n o

f R

OI

C

Online Figure 3. Among 4 strains of mice with large differences in collateral extent, the range of values is greater and

variance (SEMs) smaller for fractal dimension (panel C) determined for a randomly selected region of interest on arterial

tree (ROI) (inset in A) than for whole retina (B). Thus, the complexity of the branching pattern of arterial trees likely contain

more genetic background-specific features than the capillary bed and venous trees. Removal of the capillaries and venules/veins

will therefore increase the statistical power to test for association of retinal vascular patterning metrics with pial collateral number

and diameter among genetically distinct strains. A, representative image stained with IB4 lectin and converted to gray-scale. Distal

arterial trees were randomly selected and analyzed for an ROI of constant dimension. See Figure 3 for determination of fractal

dimension and lacunarity. Values here and in other on-line figures are means ± SEM unless indicated otherwise. Fractal dimension

and lacunarity varied with strain (ANOVA, p < 0.05). BC, BALB/c strain; BLKS, C57BLKS strain. N = 5 mice per strain.

Online Figure 4. Fractal dimension of the distal-most region of the vasculature between adjacent artery and vein trees (ie,

the “capillary bed”) lacks strain-dependent differences shown in Online Figure 2 for whole retina or individual artery trees.

The lower values than in Online Figure 3 indicate that patterning of the capillary bed has less complexity than individual arterial

trees or whole retina. Fractal dimension was determined for randomly selected ROIs of constant dimension that encompassed the

capillary bed between an artery and vein tree (See Online Figure 1 for methods). These findings indicate that removal of capillaries

from each artery tree during image processing (“pruning”) is required to obtain arterial patterning metrics to test for association with

genetic background-dependent differences in collateral number and diameter. A representative ROI showing Alexa-568 isolectin B4

staining is shown above left. N = 5 mice per strain. The absence of strain dependent differences in fractal dimension for the

capillary bed is consistent with evidence that angiogenesis (capillary formation) is dominated by stochastic processes. 4 The

findings in Online Figures 2-4 that the more mesh-like capillary network must be removed to accurately measure fractal dimension

of a dichotomously branching artery tree is intuitive and also supported elsewhere.5

1.20

1.24

1.28

1.32

1.36

1.40

1.44

1.48

1.52

1.56

1.60

BALB/c AKR C57BLKS DBA/2

Fra

cta

l d

imen

sio

n

connect to vein

connect to artery

Data at right, taken from Online

Figure 2, shows FD and Lac for fully

processed arterial trees used in the

main analysis in this study (Figure 5)

– for comparison to the above data.

Strains: B – AKR, C – BALB/c, D –

C57BLKS, G – DBA/2 (red boxes).

Type I Type II BC B6

Type I Type II BC B6

1.40

1.42

1.44

1.46

1.48

1.50

1.52

1.54

1.56

BC B6

*

5 5

Fra

cta

l d

ime

ns

ion

1.40

1.42

1.44

1.46

1.48

1.50

1.52

1.54

1.56

BC B6

**

5 5

Fra

cta

l d

ime

ns

ion

A

C

B

D

Online Figure 5. Complexity of genetic-dependent vascular patterning, as indicated by fractal dimension of randomly

selected artery trees, is not altered by removal of the distal-most region of the vasculature between adjacent artery and

vein; however, variance (SEMs) is reduced. A,B, representative binarized images and summary data after pruning away the

venous side of the “capillary” bed back to the capillary midpoints. C,D, images and data of artery trees after pruning away

capillaries and distal-most arterioles to just before joining the parent arteriole. Thus, pruning away of capillaries and distal-

most arterioles of each retinal artery tree during image processing yields genetic-dependent arterial patterning metrics with the

least variance. N = 5 mice per strain. , p <0.05, 0.01. BC, BALB/c strain; B6, C57Bl/6 strain. Fractal dimension,

lacunarity and the Image J “plug-in” metrics reported in figures and tables in the paper and in the on-line section were obtained

from artery tree images processed as shown in Figure 2 and On-line Figures 1 and 5A,C.

Online Figure 6. Comparison of fractal dimension (FD) and lacunarity (Lac) obtained from 3, 2 and 1 randomly chosen

arterial tree(s). Tree segmentation for obtaining semi-automated retinal patterning metrics (Online Figure 1) is a labor-intensive

process. Average FD and Lac, two dimensionless measures of image complexity (Figure 3), were measured from 3 randomly

chosen tree(s) from 5 mouse retinas each for 4 strains (AKR, BALB/c, C57BLKS, and DBA/2) that vary widely in collateral

number (n=20) (Online Table 1). The above data show a strong correlation between average FD and lacunarity obtained from 3

versus 2 trees (A, C) (adjusted R2 of 0.86 and 0.83, respectively), which drops significantly when comparing 3 versus 1 tree (B,

D) (adjusted R2 of 0.64 and 0.55, respectively). Thus, for the remaining 60 mice in the study, only 2 randomly chosen arterial

trees were segmented in order to achieve an optimal trade-off between accuracy and time required for image segmentation.

Adjusted R2 = 0.86

P value = <0.0001

Adjusted R2 = 0.64

P value = <0.0001

Adjusted R2 = 0.83

P value = <0.0001

Adjusted R2 = 0.55

P value = <0.0001

A Strain

B. AKR

C. BALB/c

D. C57BLKS

G. DBA/2

B

C D

Fra

cta

l d

ime

ns

ion

L

ac

un

ari

ty

Online Figure 7. Retinal patterning predicts pial collateral number (COL-N) and diameter (COL-D). Figure shows results of forward, backward, and mixed

direction stepwise multivariate regression of COL-N and COL-D versus retinal patterning metrics (RPMs) using different stopping rules—minimum AIC, minimum

BIC, and p-value cutoffs (p<0.25 for RPM to enter and >0.10 to leave model) before (RM1) and after (RM2 and 3) removal of influential outliers (Figure 4). Predictive

performance across all models (RM1, RM2, and RM3) as determined by K-fold R2 calculated from leave-one-out cross validation was strong (0.73-0.83 for COL-N

and 0.59-0.73 for COL-D) and confirmed our hypothesis that RPMs can be used to predict COL-N and COL-D. Removal of outliers improved K-fold R2 but did not

change our conclusion. Directionality, strength, and significance of correlation of RPMs with COL-N and COL-D across all models is displayed and highlights the

RPMs that remained predictive throughout all models. 11 of the 16 RPMs found to predict COL-N also predicted and correlated with COL-D in a similar direction,

consistent with the covariance of COL-N and COL-D in the mouse population (Figure 1) suggesting that genetic determinants of variation in collateral extent also

influence variation in key features of retinal vascular patterning. The most predictive models based on highest K-fold R2 was used to calculate a Retinal Predictor Index

for COL-N and COL-D (RPIn and RPId, respectively) and further examined to determine comparative predictive ability of individual RPMs (Figure 6).

a b c d e f g a b c d e f g a b c d e f g a b c d e f g a b c d e f g a b c d e f g

1 Do (µm) ↓ ↓

2 D1 (µm)

3 D2 (µm) ↑ ↑

4 Tortuosity index (inner zone)

5 CRAE (µm) ↑

6 CRVE (µm) ↑ ↑

7 AVR ↑

8 Branch angle ↑ ↑

9 Optimality ↓ ↓

10 Retinal area (µm2) ↑ ↑

11 Fractal dimension ↑

12 Lacunarity ↑

13 Arterial tree area (µm2) ↓ ↓

14 Skeltonized arterial tree area (µm2)

15 Average arterial tree diameter (µm)

16 Number of arterial tree branch segments/tree area (µm2)

17 Average tortuosity of branch segments ↓ ↓

18 Skewness of distrubtion of branch segment tortuosity

19 Kurtosis of distribution of branch segment tortuosity ↑

20 Avg length of branch segments (µm) ↓ ↓

21 Skewness of distribution of branch segment lengths ↓ ↓22 Kurtosis of distribution of branch segment lengths ↓ ↓

RM2 RM3R elat io nship

with C OL-N

RM1 RM2 RM3R elat io nship

with C OL-D

RM1Retinal Patterning Metric (RPM)

Collateral number (COL-N) Collateral diameter (COL-D)

p<0.001

p<0.01

p<0.05

p>0.05

P-valueDirection Criteria

a Forward

b Backward

c Forward

d Backward

e Forward

f Backward

g Mixed

ModelStewise Regression

Minimum AIC

Minimum BIC

P-value (<0.25 to enter

and <0.10 to leave

model)

0.55

0.65

0.75

0.85

0.55

0.65

0.75

0.85

RPIn

RPId

K-f

old

R2

= Most predictive models

0.4

0.5

0.6

0.7

p<0.001

p<0.01

p<0.05

p>0.05

P-valueDirection Criteria

a Forward

b Backward

c Forward

d Backward

e Forward

f Backward

g Mixed

ModelStewise Regression

Minimum AIC

Minimum BIC

P-value (<0.25 to enter

and <0.10 to leave

model)

RPMFD

K-f

old

R2

= Most predictive models

0.4

0.5

0.6

0.7

RPMLac

Online Figure 8A (below) and 8B-I (next page). See subsequent pages for legend.

A

a b c d e f g a b c d e f g

1 Do (µm)

2 D1 (µm)

3 D2 (µm) ↑ ↓

4 Tortuosity Index (Inner zone) ↓

5 CRAE (µm) ↑ ↓

8 BranchAngle ↓

9 Optimality

13 Arterial tree area (µm^2) ↑

14 Skeltonized arterial tree area (µm) ↑

15 Average arterial tree diameter (µm) ↑ ↑

16 Number of arterial tree branch segments/tree area (µm^2) ↑

17 Average tortuosity of branch segments ↑ ↓

18 Skewness of distrubtion of branch segment tortuosity ↑

19 Kurtosis of distribution of branch segment tortuosity ↓

20 Average length of branch segments (µm) ↓ ↑

21 Skewness of distribution of branch segment lengths ↓ ↑22 Kurtosis of distribution of branch segment lengths ↓

RMR elat io nship

with L

RMRetinal Patterning Metric (RPM)

Fractal dimension (FD) Lacunarity (Lac)

R elat io nship

with F D

B

D

C

E

Predicted Lacunarity (RPMLac)

Predicted Fractal dimension (RPMFD)

K-fold R2=0.64****

K-fold R2=0.49****

F

G

Strain

A. A/J

B. AKR

C. BALB/c

D. C57BLKS

E. C57BL/6

F. CLIC4-/-

G. DBA/2

H. VEGFAhi/+

I. VEGFAlo/+

J. CD-1

Lacu

nar

ity

(Lac

) Fr

acta

l dim

en

sio

n (

FD)

Par

eto

plo

t Sc

ale

d p

aram

ete

r e

stim

ates

Lacu

nar

ity

(Lac

)

Par

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plo

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d p

aram

ete

r e

stim

ates

Frac

tal d

ime

nsi

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(FD

)

Term Scaled Estimate Std Error P-value

Intercept 1.475 0.001 <.0001

Average tortuosity of branch segments 0.030 0.005 <.0001

CRAE (µm) 0.025 0.005 <.0001

Average arterial tree diameter (µm) 0.022 0.005 <.0001

Kurtosis of distribution of branch segment tortuosity -0.021 0.006 0.0007

Skewness of distribution of branch segment lengths -0.014 0.005 0.004

Skeltonized arterial tree area (µm) 0.013 0.003 0.0002

Average length of branch segments (µm) -0.011 0.004 0.011

TermOrthogonalized

Estimate

CRAE (µm) 0.0163

Skeltonized arterial tree area (µm) 0.0058

Kurtosis of distribution of branch segment tortuosity -0.0050

Average tortuosity of branch segments 0.0045

Average length of branch segments (µm) -0.0038

Average arterial tree diameter (µm) 0.0038

Skewness of distribution of branch segment lengths -0.0034

H FD = 1.41; L = 27.0 FD = 1.54; L ac= 13.7 I

1 mm 1 mm 0.5 mm 0.5 mm

Term Scaled Estimate Std Error P-value

Intercept 19.937 0.287 <.0001

Skewness of distribution of branch segment lengths 11.609 4.175 0.0069

Number of arterial tree branch segments/tree area (µm2) 10.455 4.303 0.0176

Kurtosis of distribution of branch segment lengths -8.870 3.816 0.023

Average length of branch segments (µm) 8.116 2.426 0.0013

Average tortuosity of branch segments -5.663 1.094 <.0001

Average arterial tree diameter (µm) 4.659 2.737 0.0931

CRAE (µm) -3.313 1.064 0.0027

Kurtosis of distribution of branch segment tortuosity 1.938 1.157 0.0984

TermOrthogonalized

Estimate

Average length of branch segments (µm) 1.775

Average tortuosity of branch segments -1.569

Kurtosis of distribution of branch segment lengths -1.068

CRAE (µm) -0.776

Number of arterial tree branch segments/tree area (µm2) 0.579

Kurtosis of distribution of branch segment tortuosity 0.480

Average arterial tree diameter (µm) 0.475

Skewness of distribution of branch segment lengths 0.433

Online Figure 8A. Differences in fractal dimension (FD) and lacunarity (Lac) of retinal artery trees are associated with

differences in retinal patterning metrics (RPMs). Online Figure 8B-I. Among RPMs characterizing retinal arterial tree

complexity, differences in FD and Lac are most strongly associated with differences in CRAE and average length of branch

segments, respectively.

Fractal dimension and lacunarity are global, non-Euclidean dimensionless metrics that have been used to define complexity of the

retinal vasculature in association studies. In the present study we found that differences in fractal dimension and lacunarity were

associated with differences in retinal patterning metrics (RPMs) (Figure 5B,C; orange boxes). Thus, our data set offers a unique

opportunity to identify the relationship between these global metrics and Euclidean metrics in a complex branching network, ie the

retinal vasculature. Fractal dimension was not found to be a significant predictor of COL-N and COL-D across most models (Online

Figure 7), and lacunarity was only moderately predictive of COL-N (Figure 8B). These findings were likely due to the narrow range

of fractal dimension (1.41-1.54) and high covariance of it and lacunarity with other RPMs (Figure 5B), many of which were more

specific features of arterial tree complexity and thus emerged as stronger predictors of COL-N and COL-D. To better characterize

global differences in complexity of the retinal artery trees, as measured by FD and Lac, in terms of Euclidean metrics that are more

intuitive and visualizable, we examined the association between RPMs and fractal dimension and lacunarity (Online Figure 8). We

performed forward, backward, and mixed stepwise multivariate regression modeling of fractal dimension and lacunarity versus RPMs

using a variety of criteria as detailed in Online Figure 7. Average fractal dimension and lacunarity of retinal artery trees (dependent

variables) from 80 mice were modeled versus other RPMs (independent variables) that strictly characterize only arterial tree

patterning (ie, we excluded CRVE, AVR, and retinal area) (Online Figure 8A). Significance of RPMs for a given model and their

strength of association with fractal dimension and lacunarity, as measured by K-fold R2, were identified.

Differences in many RPMs defining retinal arterial tree patterning (vessel caliber, branch angle, tortuosity, etc.) were associated

with differences in fractal dimension and lacunarity (ie, K-fold R2 was 0.60-0.64 and 0.47-0.49, respectively) (Online Figure 8A).

When a given RPM was associated with both fractal dimension and lacunarity, it correlated with both metrics in an opposite

direction, consistent with the inverse relationship between fractal dimension and lacunarity (Figure 8A). The only exception to this

observation was average arterial tree diameter, which was directly associated with both fractal dimension and lacunarity. To compare

relative strength of association of specific RPMs with fractal dimension and lacunarity, parameter estimates from the 2 most

predictive models (Online Figure 8A, RPMFD and RPMLac) were obtained and plotted as scaled estimates (ie, centered by mean and

normalized to have identical range) (Online Figure 8B,D). In addition, parameter estimates were standardized to have equal

variances, orthogonalized to be uncorrelated, and plotted—in descending order of scaled estimates—as a pareto plot (Online Figure

8C,E). The scaled estimates show the relative extent of change in fractal dimension and lacunarity as a specific RPM is varied from

the lowest to highest value in the population of mice.

Online Figure 8 legend (continued)

The pareto plot accounts for covariance and extent of variability of an RPM in the mouse population to estimate and arrange the

RPMs in descending order of “explanatory power” for fractal dimension and lacunarity. Plots of predicted (ie expected) fractal

dimension and lacunarity based on models from strongly correlated and explanatory RPMs, along with K-fold R2, reveals the spread

of data and the strength of correlation (Online Figure 8F,G; ****P<0.0001). In addition, segmented arterial trees from two retinas in

our study with the widest difference in fractal dimension (1.41 vs 1.54) and lacunarity (27.0 vs 13.7) were also compared to better

visualize differences in arterial tree patterning in the context of respective differences in RPMs (Online Figure 8H,I).

The pareto plot (Online Figure 8D) and comparison of retinas (Online Figure 8H,I) shows that fractal dimension is

disproportionately sensitive to changes in caliber of the central artery (CRAE) in comparison to other RPMs. In general, mice with

retinal arterial trees with a larger CRAE, shorter and greater proportion of shorter branch segment lengths (as measured by average

length of branch segments and skewness of distribution of branch segment lengths), more tortuous branch segments and a wider

distribution of branch segment tortuosity (as measured by average tortuosity of branch segments and kurtosis of distribution of branch

segment tortuosity) tend to have a higher FD and lower lacunarity. Higher FD (Online Figure 8A,B,I) is also associated with greater

extent of coverage of arterial tree (as measured by skeletonized arterial tree area). Other associated differences in RPMs are less

visually appreciable, consistent with their relatively lower rank on the pareto plots (Online Figure 8B,C,E); for example, low

lacunarity is also associated with a lower branch density (as measured by number of arterial tree branch segments/tree area) and a

greater proportion of branch segments with a similar length (as measured by kurtosis of distribution of branch segment lengths). As

found across all significant models (Online Figure 8A), a high fractal dimension and lacunarity were both associated with larger

vessel caliber (as measured by average arterial tree diameter). RPMs had a lower strength of association with lacunarity in

comparison to fractal dimension (Online Figure 8F,G) (K-fold R2 0.49 vs 0.64), suggesting that, in the context of our study, lacunarity

captures additional information on arterial tree patterning beyond the most descriptive RPMs.

Adjusted R2 p-value Adjusted R2 p-value Adjusted R2 p-value Adjusted R2 p-value

N Collateral number 0.86 <.0001 0.93 <.0001 0.93 <.0001

D Average collateral diameter (µm) 0.87 <.0001 0.95 <.0001 0.95 <.0001

1 Do (µm) 0.67 <.0001 0.80 <.0001 0.54 0.001 0.02 0.5

2 D1 (µm) 0.46 <.0001 0.51 0.0015 0.30 0.03 0.17 0.04

3 D2 (µm) 0.69 <.0001 0.79 <.0001 0.38 0.011 0.04 0.7

8 Branch angle 0.43 <.0001 0.06 0.3 0.66 <.0001 0.01 0.8

9 Optimality 0.35 <.0001 0.72 <.0001 0.09 0.21 0.05 0.8

10Retinal area or cerebral hemisphere

area (µm2)0.16 0.009 0.24 0.052 0.73 <0.0001 0.03 0.2

11 Fractal dimension 0.32 <.0001 0.48 0.003 0.36 0.013 0.21 0.02

12 Lacunarity 0.23 0.001 0.44 0.005 0.10 0.19 0.11 0.08

13 Arterial tree area (µm2) 0.38 <.0001 0.17 0.11 0.59 0.0004 0.06 0.3

14 Skeltonized arterial tree area (µm) 0.29 <.0001 0.05 0.3 0.41 0.008 0.05 0.8

15 Average arterial tree diameter (µm) 0.40 <.0001 0.50 0.002 0.38 0.01 0.17 0.04

16Number of arterial tree branch

segments/tree area (µm2)0.20 0.0025 0.21 0.074 0.40 0.008 0.04 0.2

17 Average tortuosity of branch segments 0.33 <.0001 0.24 0.054 0.14 0.14 0.05 0.8

18Skewness of distrubtion of branch

segment tortuosity0.27 0.0002 0.31 0.02 0.17 0.11 0.05 0.9

19Kurtosis of distribution of branch

segment tortuosity0.21 0.002 0.27 0.04 0.14 0.14 0.04 0.6

20 Avg length of branch segments (µm) 0.38 <.0001 0.59 0.0004 0.22 0.066 0.05 0.9

21Skewness of distribution of branch

segment lengths0.28 0.0002 0.36 0.014 0.01 0.4 0.18 0.03

22Kurtosis of distribution of branch

segment lengths0.24 0.0007 0.31 0.025 0.02 0.37 0.13 0.06

Bivariate ANOVAOneway ANOVA

N/A

4 strains, n=2110 strains, n=80

RPM vs strain RPM vs strain MCAM vs strain RPM vs MCAMCOL-N, COL-D, Retinal patterning metrics

(RPM) or Middle cerebral artery metrics

(MCAM)

Online Figure 9. Both retinal patterning metrics (RPMs) and middle-cerebral artery patterning metrics (MCAM) vary with genetic background, but only half

showed significant or suggestive correlations with each other. A subset of 18 MCAMs analogous to patterning metrics derived from the retina (RPMs) were measured in a

subset of 21 mice belonging to 4 strains (BALB/c, C57BLKS, AKR, and C57BL/6). Using definitions and methods previously detailed for the derivation of RPMs (Figure 2,

4), inner-zone metrics (RPMs/MCAMs 1-3, 8, 9) were measured on the 1st order of the MCA trunk and extended zone metrics (RPMs/MCAMs 11-22) were derived from

segmented MCA trees (Online Figure 11). Cerebral hemisphere area, the area of the hemisphere supplied by the MCA, is analogous to retinal area (RPM/MCAM 10)

supplied by the retinal arterial tree and was measured as described previously3 (Online Figure 11). Bivariate regression (one-way ANOVA adjusted R2 and p-value) of COL-

N, COL-D, and MCAMs versus mouse strain shows that COL-N, COL-D and at least 9 out of 18 MCAMs vary with genetic background (red dashed line, cutoff for adjusted

R2 of >0.35, p = 0.0001-0.13), comparable to the 10 out of 22 metrics found to strongly vary with genetic background in the retina (Figure 5). Black boxes reflect relative

strength of correlation. These data suggest that similar to its contribution to the variation in COL-N, COL-D and RPMs, genetic background also plays a significant role in

specifying variation in features of the MCA tree, such as vessel caliber, branch angle, fractal dimension, and MCA tree area. Optimality of the MCA tree did not vary with

genetic background as it did in the retina, and unlike in the retina, area of the skeletonized MCA tree and cerebral hemisphere and number of arterial tree branch segments per

unit tree area showed strong variation with genetic background. Bivariate regression of MCAMs versus analogous RPMs (Bivariate ANOVA adjusted adjusted R2 and p-

value) shows little to no correlation (adjusted R2 of 0.02- 0.21), with only fractal dimension showing some degree of correlation (adjusted R2 of 0.21, p = 0.02). The low

MCAM-RPM correlation may be attributable to low overall n-size (22), measurement of only 1 MCA tree versus 2-3 trees in the retina, truly flat-mounted 2D measurement in

retina versus 3D angular view of the MCA, possible lack of true analogy between MCAMs and RPMs, and reasons related to different times of formation (see Discussion).

MCA

a b c d e f g a b c d e f g

1 Do (µm) ↓ ↓

2 D1 (µm) ↑ ↑

3 D2 (µm) ↑ ↑

8 Branch angle ↑ ↑

9 Optimality ↓

10 Cerebral hemisphere area (µm2) ↑ ↑

11 Fractal dimension ↑

12 Lacunarity ↑ ↑

13 Arterial tree area (µm2) ↑ ↓

14 Skeltonized arterial tree area (µm2) ↓

15 Average arterial tree diameter (µm) ↑

16 Number of arterial tree branch segments/tree area (µm2) ↑ ↑

17 Average tortuosity of branch segments ↑

18 Skewness of distrubtion of branch segment tortuosity ↓ ↓

19 Kurtosis of distribution of branch segment tortuosity ↓

20 Avg length of branch segments (µm) ↑ ↑

21 Skewness of distribution of branch segment lengths ↑22 Kurtosis of distribution of branch segment lengths ↓

R elat io nship

with C OL-N

RMR elat io nship

with C OL-D

RMMiddle cerebral artery metrics (MCAM)

Collateral number (COL-N) Collateral diameter (COL-D)

0.55

0.65

0.75

0.85

0.95

0.55

0.65

0.75

0.85

0.95

Direction Criteria

a Forward

b Backward

c Forward

d Backward

e Forward

f Backward

g Mixed

ModelStewise Regression

Minimum AIC

Minimum BIC

P-value (<0.25 to enter

and <0.10 to leave

model)

K-f

old

R2

p<0.001

p<0.01

p<0.05

p>0.05

P-value

Co

rre

lati

on

S

ign

ific

an

ce

+/- R2

P-value

A

B

C

Online Figure 10. Middle cerebral artery patterning metrics (MCAMs) predict pial collateral number (COL-N) and diameter (COL-D). Multivariate correlation

matrices (A and B) of COL-N (N), COL-D (D) and MCA patterning metrics (MCAMs 1-3, 8-22) show significant covariance, similar to RPMs (Figure 5); matrices show

direction and strength (+/- adjusted R2 (A)), and significance (p-value, (B)) of covariance. Highlighted regions of matrices (A,B; yellow boxes) show that a number of

MCAMs (2, 8, 10, 15, 16, 20) also vary strongly with COL-N and COL-D, suggesting that they may also predict collateral extent. Thus, similar to methods detailed for

RPMs (Online Figure 7), forward, backward, and mixed direction stepwise multivariate regression of COL-N and COL-D versus MCAMs was performed using different

stopping rules—minimum AIC, minimum BIC, and p-value cutoffs (p<0.25 for RPM to enter and >0.10 to leave model). Predictive performance across all models as

determined by K-fold R2 calculated from leave-one-out cross validation was strong (0.61-0.78 for COL-N and 0.60-0.86 for COL-D) and confirmed our hypothesis that

similar to features of retinal patterning, features of MCA tree patterning strongly associate with and can predict COL-N and COL-D. Directionality, strength, and

significance of correlation of MCAMs with COL-N and COL-D across all models is displayed and highlights a select few MCAMs that remained significantly predictive for

either COL-N or –D throughout all models; thus, MCA trees with greater branching density (MCAM 16), at wider branch angles (MCAM 8), with smaller parent

(D0) but larger daughter vessel calibers (D1, D2) (MCAMs 1-3), supplying larger cerebral hemispheres (MCAM 10) were associated with a greater number of

collaterals. The most predictive models based on highest K-fold R2 was used to calculate an “MCA predictor index” for COL-N and COL-D similar to the retinal predictor

index (MCAPIn and MCAPId, respectively) to further examine and determine comparative predictive ability of individual features of MCA patterning (Online Figure 11).

MCAPIn MCAPId

Intercept 13.10 0.72 <.0001

D0 (µm) -53.91 11.41 0.0011

Number of MCA tree branch segments/MCA area (µm2) 28.70 6.94 0.0025

D2 (µm) 25.36 7.48 0.0080

Average length of MCA branch segments (µm) 18.94 6.51 0.0173

D1 (µm) 18.40 3.47 0.0005

Average tortuosity MCA branch segments 17.27 3.60 0.0010

Cerebral hemisphere area (µm2) 17.15 2.96 0.0003

Branch angle 11.17 3.99 0.0208

Skewness of distribution of MCA branch segment tortuosity -11.16 3.28 0.0079

MCA tree area (µm2) 10.62 3.46 0.0134

Optimality -9.26 2.92 0.0114

Number of MCA tree branch segments/MCA area (µm2) 6.36

Cerebral hemisphere area (µm2) 5.94

D1 (µm) 3.71

Optimality -2.28

Average tortuosity MCA branch segments 1.99

Branch angle 1.35

Skewness of distribution of MCA branch segment tortuosity -1.22

MCA tree area (µm2) 1.19

D2 (µm) -0.39

Average length of MCA branch segments (µm) -0.2

D0 (µm) 0.03

TermOrthogonalized

Estimate

Term Scaled Estimate Std Error P-value

Intercept 17.59 0.36 <.0001

Branch angle 6.39 0.98 <.0001

Number of MCA tree branch segments/MCA area (µm2) 5.92 0.76 <.0001

Lacunarity 3.29 0.84 0.0016

D1 1.96 1.03 0.0763

Branch angle 2.99

Number of MCA tree branch segments/MCA area (µm2) 2.60

Lacunarity 1.39

D1 0.69

Term Scaled Estimate Std Error P-value

TermOrthogonalized

Estimate

Predicted collateral diameter (MCAPId)

Par

eto

plo

t

Scal

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par

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ter

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imat

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Par

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Scal

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par

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A

C

Predicted collateral number (MCAPIn)

K-fold R2=0.78****

K-fold R2=0.86****

B

D

E

F

Co

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nu

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Co

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Ave

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co

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(µm

) A

vera

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olla

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l n

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Strain

B. AKR

C. BALB/c

D. C57BLKS

E. C57BL/6

Figure 11. Among the most predictive MCAMs, average number of MCA tree branch segments per unit MCA area (ie, MCA branching density)

contributes the most, statistically, to predicting collateral number and diameter (COL-N and COL-D). MCA trees with larger branch angle, larger

caliber of branching vessels (D1, D2), and larger cerebral hemisphere areas tend to have greater collateral extent (COL-N and/or COL-D). To

compare the relative predictive power of the MCAMs, parameter estimates from the 2 most predictive models for MCAPIn and MCAPId (Online Figure 10)

were obtained and plotted as scaled estimates (ie centered by mean and normalized to have identical range) (A,C); in addition, the parameter estimates were

standardized to have equal variances, orthogonalized to be uncorrelated, and plotted—in descending order of scaled estimates—as a pareto plot (B,D). The

scaled estimates show the relative extent of change in COL-N or COL-D as a specific MCAM is varied from the lowest to highest value in the population of

mice. The pareto plot accounts for covariance and extent of variability of an RPM in the mouse population to estimate and arrange the MCAMs in descending

order of relative “explanatory power.” Plots of predicted COL-N and COL-D versus MCAPIn and MCAPId, along with K-fold R2 reveals the spread of data

and the strength of correlation (E,F). ****P<0.0001. Therefore, mice with greater MCA tree branching density, larger branch diameter at bifurcations (D1),

and larger branch angles tend to have greater collateral extent (COL-N and COL-D). Mice with relatively larger cerebral hemisphere areas also tend to have

greater COL-N.

References for Supplemental Section

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