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2124 MORPHOMETRY OF PULMONARY VASCULATURE

Table 1. Specimen information

SpecimenNo. Age, y Sex

HoursPostmortem Preparation

PerfusionDirection

BodyWeight, kg

BodyHeight, cm

12

4424

MaleMale

186

Left lungRight lung

AntegradeRetrograde

95128

185180

the pulmonary artery to the pulmonary veins to establishvascular continuity across the lung. This step was followed byperfusion with silicone elastomer freshly catalyzed with 37ctin octoate (stannous 2-ethyl hexoate) and 5% ethyl silicate.Before perfusion the catalyzed solution was well stirred, andno air bubbles remained. The perfusion was carried out undera pressure drop of 34 cmH20 from inlet (34 cmH20) to outlet(0 cmHoO) for 20 min, while the alveolar gas pressure wasmaintained at 10 cmH20 and Ppl was zero (atmospheric).Then the perfusion pressure was lowered and maintained at 3cmH20, and the left atrial cannula was closed. The timecourse of hardening and the flow behavior of the catalyzedsilicone elastomer in the first 2 h are discussed in detail byFung et al. (Appendix in Ref. 4). The hardening was so slowwithin 1 h after the flow stopped that it was possible for thefluid to redistribute itself with the requirement of equilibrium(4). Because the fluid pressure in the capillary blood vessels waslower than the alveolar gas pressure under this condition, all thecapillary vessels were collapsed (4,29,30), separating the arterialand venous trees. After 3 h the cast lung was moved to arefrigerator and frozen for 2 wk to increase the strength of thesilicone rubber. Then the lung was carefully removed and suspended in a 10% KOH solution for 2 wk to dissolve the lungtissue. Next, the cast was washed several times with water toremove any remaining tissue. The pulmonary arterial andvenous trees were gently separated. Dimensional measurements were carried out on the pulmonary arterial cast of a leftlung and the pulmonary venous cast of a right lung.

Our method of preparation relies on two facts: 1) thepulmonary capillaries collapse when the pulmonary capillaryblood pressure is lower than the alveolar gas pressure by ^1cmH20 (27); and 2) the pulmonary arteries and veins do notcollapse when the pulmonary blood pressure falls below thealveolar gas pressure (4). In fact, according to Yen andFoppiano (27), for the cat, the slope ofthe vessel diameter-pressure difference AP = Pv - Pa (where Pv is the bloodpressure and Pa is the alveolar gas pressure) does not changein the range of -10 to +10 cmH20. The slope of thenormalized vessel diameter D/Dl0 (vessel diameter divided bydiameter at Pv - Ppl = 10 cmH20) depends somewhat on thePpl and vessel diameter. The relationship can be expressed as

DIDW = A(Pv - Pa) + Bfor -10 < Pv - Pa < 10 cmH90 (1)

where A and B are constants that vary with D10 and Pv - Ppl.According to fact 1, the capillaries are collapsed and dissolved. Lamm et al. (18) showed that the alveolar cornervessels (those at the junctions of interalveolar septa) will alsocollapse when Pv - Pa is less than -8 to -16 cmH20. At ourexperimental condition Pv - Pa = -7 cmH20, few cornervessels were seen. According to fact 2, the relative sizes(ratios of sizes) ofthe vessels of successive orders will remainapproximately the same whether the ratio is measured at -7cmH20 (as in our preparation) or at 10 cmH20 (at lower end ofin vivo values). Because the diameter-defined Strahler ordering method depends only on the ratio of the vessels ofsuccessive orders at points of bifurcation, our method ofpreparation will not affect the assignment of order numbersto vessels. The uncertainty is that the range -10 cmH20 <

Pv - Pa < 10 cmH20 is that of the cat (27), and the exactrange for humans is unknown. The possible species differencemust be checked in the future.

Morphometric Measurement ofthe Polymer Castofthe Vasculature

The pulmonary vascular casts were dissected and viewedwith a zoom stereomicroscope (model SZH, Olympus). Animage-analysis system was set up to measure accurately thesize of the vessels. The system consists of a Zenith computerwith a DT2851 (Data Translation, Marlborough, MA), aninverted light microscope (model SZH-ILLB, Olympus), avideo monitor (Sony Trinitron color video monitor), and a.television camera (Cohu solid-state camera). The solid castswere viewed with the inverted light microscope and displayedon the video monitor through the television camera. Theimage was analyzed with the software package Optimas(BioScan). The Optimas computing program focuses on theimage of a blood vessel chosen by' the operator. By photodensity contrast, the computer draws the boundary contoursof the object. For diameter measurement, the program computes normal vectors to the contour, draws two neighboringnormals to define an area, measures the area, and computes awidth equal to the area divided by the length betweennormals. We use the word "diameter" to indicate the computed width of the vessel. Three diameter measurementswere made along each vessel to obtain a mean diameter. Asection normal to the vessel contour can be drawn on thescreen. The centers of the normal sections are joined by theoperator, and the line is considered to be the centerline ofthevessel. This centerline is that ofthe two-dimensional image.The intersection ofthe centerlines of two intersecting vessel?is the bifurcation point. The vessel segmental length wa.sobtained by measuring the length between two successivebifurcation points along the centerline of a vessel on thetwo-dimensional image. Tacitly, we assumed that the bloodvessels were round. Actually, the cross sections of the large-pulmonary veins were found to be noncircular, but in thepresent study this matter was not pursued. An analysis ofthe"errors" caused by these projections is made by Yen et al. (30).They found that if the diameter of a blood vessel with anelliptical cross section was measured by projection fromarbitrary directions, the mean diameter of a random sampling ofthe projected width is quite close to the diameter of acircular cylinder ofthe same circumference.

Because there are many branches in the human pulmonaryarterial and venous trees, it was impossible to examine,measure, count, and list every branch. Therefore, pruningand statistical methods were used to obtain representativemeasurements (5, 12-15, 29, 30). The backbone of the leftpulmonary artery was sketched, and its segments weremeasured. The subtrees arising from the backbone werelabeled, excised, and placed in separate dishes. To facilitatethe measurement, daughter trees with a diameter of 600-800pm were trimmed from each subtree. Daughter trees wererandomly selected as statistical samples from each subtreeand measured in detail. In the statistical samples of thedaughter trees, branches with a diameter <100 um werepruned. A small number of the branches with a diameter

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2126 MORPHOMETRY OF PULMONARY VASCULATURE

Table 2. Diameter and length of elements ofpulmonary arteries and veins of two human lungs

Order n Diameter, mm Length, mmArteries

+ 15 2 14.80 ±2.10 25.30 ±28.15+ 14 5 7.34±1.14 35.69 ± 10.28+ 13 16 4.16 = 0.60 25.97 r 14.19+ 12 36 2.71 ±0.35 18.07 ± 11.65- r l l 84 1.75 ±0.19 12.35 ±6.77+ 10 142 1.16±0.10 6.58 ±4.26

+9 182 0.77 ±0.07 3.73 ± 2.43+8 227 0.51 ±0.04 2.81 ±1.77+ 7 315 0.34 ± 0.06 1.92 ±1.22+6 315 0.22 r 0.02 1.08 ± 0.65+5 180 0.15 ±0.02 0.68 ± 0.36+4 50 0.097 ±0.012 0.45 ± 0.25+ 3 48 0.056 ±0.005 0.36 ±0.20+ 2 81 0.036 ±0.005 0.26 ±0.12+ 1 113 0.020 ± 0.003

Veins0.22 = 0.08

- 1 36 0.018 ±0.002 0.13 ±0.07- 2 31 0.031 ±0.005 0.21 ±0.15- 3 38 0.067 ±0.010 0.38 r 0.24- 4 195 0.13 ±0.02 1.06 ±0.54- 5 150 0.23 ± 0.03 1.50 = 0.85- 6 81 0.38 ± 0.04 2.92 ±1.91- 7 50 0.62 ± 0.06 4.79 ± 3.64- 8 33 0.90 ± 0.07 6.78 ±6.32- 9 64 1.42 ±0.15 11.24 ±6.91

- 1 0 79 1.99 ±0.21 14.78 ±7.71-11 42 2.88 ±0.21 17.90 ± 10.92- 1 2 25 4.00 ±0.33 26.49 ±13.11- 1 3 9 5.86 ±0.38 19.49 ±11.89- 1 4 4 8.65 ± 0.76 34.99 ± 16.97- 1 5 2 12.97 ±1.70 35.68 ± 7.36

Values are means ± SD; n, no. of elements.

and combined those vessels of the same order connected inseries as an element. Statistical data are obtained for elements and segments. Flow circuits are built of elements.

In this study we used the same terminology. The measurement of diameter and length were made in the two-dimensional grabbing images. We found that the diameter ofeach segment is constant, and we measured it at the midpointof each segment. The segment length is the distance betweenbifurcation points along the centerline of the segment. Thediameter of an element was computed as the average of thediameters of the segments that make up the element. Thelength of an element was obtained by adding the lengths ofthe segments within the element. The relationship betweenthe total number of segments of order n, Sin), and the totalnumber of elements ofthe same order, E(n), can be describedby

S(n) = E(n) X R(n) (4)where R(n) is the segment-to-element ratio in order n.

Connectivity matrix. We used the connectivity matrix toexpress how blood vessels of one order are connected tovessels of another order. Blood vessels of order n not onlyarise from vessels of order n + 1 but also originate fromvessels of order n, n + 2, n + 3,.... There was no quantitativeexpression for the connectivity feature of blood vessels of oneorder to another until the connectivity matrix was firstdeveloped and used by Kassab et al. (14,15). In the connectivity matrix, each component in the rath row and the nthcolumn, designated as C(ra,n), is expressed as mean ± SE.

The mean value is the ratio ofthe total number of elements oforder ra sprung from parent elements of order n divided bythe total number of elements of order n. The standard error ofC(ra,n), SEC(m „„ is obtained by

SESDf

Cm.n)\^*m(n)

(5)

where SDC(m „, is the standard deviation of C(m,n) andiVm(n) isthe number of observations of vessels of order ra connected tovessels of order n. For a tree with k orders, the connectivitymatrix is a k x k upper triangular matrix.

In addition to expressing the branching pattern for thewhole vascular tree, the connectivity matrix was used tocalculate the total number of elements in each order in thisstudy. The elements of order n, n - 1,...,1 spring directly fromthe elements of order n. Therefore, when the number ofelements of order n, N„, is known, the total numbers ofelements of order n, n -1,..., are C(n,n)N„, C(n - l,n)Nnrespectively. Considering all the vessels in a tree, we see thatthe total number of elements of order ra is given by

N„, = 2 C(ra, n)Nn (6)

where iVm and Nn are the total numbers of elements of ordersra and n, respectively. The summation is from n = ra to thehighest order ofthe tree', n = k.

Many branches are missing, because the tree was prunedfor practical counting or broken off, but the stubs wererecognizable. The number of missing branches must beconsidered while the total number of elements is counted. Theextrapolated number of the elements of each order in themissing subtrees is calculated from the number of cut-off andbroken-off subtrees and the connectivity matrix by the following equation

k

N ' m = 2 C ( m , n ) [ N ' n + N n t C J 1 7 )

where N'm and iV^ are the extrapolated number of elements oforders ra and n, respectively, in the missing subtrees, Nn cul isthe number of cut-off elements (pruned and broken-off elements) in order n, and n & ra with an upper limit of k. Thecalculation starts from n = k, which is the highest order, andthen proceeds down to n = 1, successively. Therefore, thisprocess includes all the missing subtrees.

The number of cut-off elements in order n, Nn cut, and thenumber of intact elements in order n, Nn in, are counted fromthe cast tree directly. The corrected total number of elementsof each order is the sum ofthe number of intact elements, thenumber of cut-off elements, and the extrapolated number ofelements.

RESULTS

This study shows that there are 15 orders of pulmonary arteries between the main pulmonary artery andthe capillaries in the left lung of one man and 15 ordersof veins between the capillaries and the left atrium inthe right lung of another man.

The mean and standard deviation of the diametersand lengths of the elements in each order are listed inTable 2. Two significant digits after the decimal pointfor diameters and lengths are justifiable in Table 2. The

MORPHOMETRY OF PULMONARY VASCULATURE

liameters ofthe elements for arterial and venous treesire plotted in logarithmic scale against the orderlumber in Fig. 2. Straight regression lines .were deter-nined by the least squares method. If y represents theogarithm of the diameter and x represents the orderlumber, the regression lines for pulmonary arterialind venous trees are y = -1.84 + 0.19* and y =

1.74 + 0.20a:, respectively. The antilog of the slopefives an average diameter ratio of 1.56 for all pulmo-lary arteries and 1.58 for all veins. The ratio of theliameter ofthe elements of order n to that of order n +is called the diameter ratio. The relationship between

he logarithm of element length and the order numbers depicted in Fig. 3. Similarly, the least squares fitegression line for pulmonary arteries isy = -0.95 +

0.17.x- and that for veins is y = -0.79 + 0.18.v. Thentilog of the slope yields an average length ratio of

1,49 for all pulmonary arteries and 1.50 for all veins,lie length ratio is defined as a ratio ofthe length ofthelements of order n to that of n + 1.The connectivity matrices of pulmonary arteries and

eins are presented in Tables 3 and 4, respectively. Theorrected total number of elements of each order in theulmonary arterial tree ofthe left lung of one man and■\ the pulmonary venous tree of the right lung ofnother man is computed from the connectivity matri-es given in Tables 3 and 4 starting from order 15 forrteries and veins and extrapolating downward. Theesults are shown in Table 5. The total number of intactlements and the total number of cut-off subtrees inach order are listed in columns 2 and 3, respectively, ofable 5. The values in column 4 were computed by Eq.. The last column shows the corrected total number oflements in each order, which is the sum of numbers intie previous three columns of the given order. If the)garithm ofthe corrected total number of elements (y)l each order is plotted against the order number (x) asisplayed in Fig. 4, the relationship between the corseted total number of elements and the order number; given by a regression line y = 8.41 - 0.53a for

D Arteries (mean i SD)6 Veins (mean ± SD) \ ^ ,

10,

$ Arteries (mean ± SD)§ Veins (mean ± SD)

V e i n s ^ \

l1;

0.1-^ s ^ J ^ A r t e r i e s

10.01. H 1 1 1 1 ! ! 1 ! 1 i i i i

-7 ±S ±9 +10 ±11 ±12 ±13 =14 ±15

Order ("+", arteries; "-", veins)p.<jFUr.)!«rn« er number and mean and standard

iviation of diameters of arterial and venous elements of each order,v represents logarithm of diameter and .r represents order number,gression line is y = -1.84 + 0.19.x for pulmonary arteries andy =1.74 + 0.20.x for pulmonary veins.

±1 ±2 ±3 ±4 ±5 ±6 ±7 ±8 ± 9 ± 1 0 ± 1 1 ± 1 2 ±1 3 ±1 4 ± 1 5

Order ("+", arteries; "-", veins)Fig. 3. Relation between order number and mean and standarddeviation of length of arterial and venous elements of each order. If vrepresents logarithm of length and x represents order number,regression line isy = -0.95 + 0.17.x for arterial tree and y = -0.79 +'0.18.v for venous tree.

pulmonary arteries andy = 7.66 - 0.52* for pulmonaryveins. The antilog of the absolute value of slope yieldsan average branching ratio of 3.36 for all orders ofpulmonary arteries and 3.33 for veins. The branchingratio is a ratio ofthe corrected total number of elementsof order n to that of order n + 1.

Data on the segmental diameter, length, and segment-to-element ratio of each order in the pulmonaryarterial and venous trees are listed in Table 6. Twodigits after the decimal point in Table 6 are significant.

The average cross-sectional area of vessel elementsof order n, an, is calculated as

O n = 4 ^ « ( 8 )

where D„ is the average diameter of elements in ordern. The total cross-sectional area of vessel elements oforder nt An, is calculated from the formula

A n = a n N „ = ^ D ' i N n ( 9 )

where Nn is the number of elements of order n. Figure5A illustrates the distribution of the total cross-sectional area of elements with the order number in theleft pulmonary arterial tree of a 44-yr-old man and theright pulmonary venous tree of a 24-yr-old man. Forcomparison, the total cross-sectional area distributionof arteries and veins in the whole lung from data ofHorsfield (7) and Horsfield and Gorden (11) is shown inFig. 55. Our data on total cross-sectional areas ofarteries and veins are larger than the respective areasgiven by Horsfield and Gorden. The total cross-sectional areas are related to the total number ofbranches. According to our data the total number ofbranches in small vessels is greater than that reportedby Horsfield and Gorden. Additionally, the total cross-

MORPHOMETRY OF PULMONARY VASCULATURE

Table 3. Connectivity matrix of elements of pulmonary arteries of a human left lung

1 0 . 1 7 2 . 5 4 1 . 1 1 0 . 3 8 0 . 0 2 0 . 0 1 0 . 0 2 0 0 0 2= 0 .05 ±0.16 ±0.18 ±0.20

2 0 . 2 3 1 . 6 7 0 . 9 7 0 . 1 7 0 . 0 9 0 . 0 6 0 . 0 4 0 0 2r 0 . 0 6 £ 0 . 1 6 = 0 . 1 4 = 0 . 0 7 = 0 . 0 3 = 0 . 0 3

- I 0 . 2 6 1 . 4 4 0 . 6 3 0 . 2 8 0 . 2 0 0 . 1 9 0 . 1 1= 0 .08 =0 .12 =0 .08 =0 .06 =0 .05 =0 .04 =0 .06

0 . 0 2 0

0 . 0 3 0

= 0 . 0 8 = 0 . 0 8 = 0 . 0 9 = 0 . 11 = 0 . 1 4 = 0 . 1 4 = 0 . 0 40 . 6 5 0 . 1 6 0 . 0 3 0

0 . 8 1 0 . 8 3 0 . 4 5 0 . 1 2 0 . 0 2 0= 0 . 0 4 = 0 . 0 8 = 0 . 0 6 = 0 . 0 9 = 0 . 11 = 0 . 0 9 = 0 . 0 8

0 . 1 2 2 . 5 4 1 . 1 6 0 . 8 3 0 . 9 3 0 7 10 . 1 2 2 . o 4 1 . 1 6 0 . 8 3 0 . 9 3 0 . 7 1 0 . 2 0 0 0 5= 0 . 0 2 ± 0 . 0 9 ± 0 . 1 0 ± 0 . 1 0 ± 0 . 11 ± 0 . 1 3 ± 0 . 0 2

0 . 2 5 2 . 5 2 1 . 0 8 1 . 0 8 1 . 4 9 0 . 9 4 0 4 3= 0 .03 =0 .10 =0 .11 =0 .13 =0 .15 =0 .13 =0 .18

0 . 2 8 2 . 0 6 1 . 4 5 0 . 4 3= 0 .04 =0 .08 =0 .08 =0 .16 =0 .20 =0 .18

0 . 2 1 2 . 3 8 1 . 4 7 0 . 8 8 0 . 8 1= 0 .03 =0 .08 =0 .12 =0 .13 =0 .25

0 . 2 1 2 . 5 2 1 . 3 5 1 . 4 8

0 . 3 3 0

0 . 2 1 2 . 5 2 1 . 3 5 1 . 4 8 0 0= 0.02 ±0.19 ±0.23 ±0.29

0 . 2 5 2 . 4 3 0 . 9 5 0 . 3 3 0= 0.03 =0.15 ±0.07

0 . 1 4 2 . 5 7 1 . 0 0 0 . 5 0±0.19 ±0.24

0 . 1 9 2 . 8 3 1 . 5 0±0.40

0 3 . 5 0

Values are means ± SE. Each entry is ratio of total no. of elements of order m produced from a parent element of order n divided bv totalI ' c n i o n t s n i n r r l n r u Jof elements of order;;

Table 4. Connectivity matrix of elements of pulmonary veins of a human right lung

0

0

0

0

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2130 MORPHOMETRY OF PULMONARY VASCULATURE

Arteries (left lung, 44-ycar-old man, 95 kg)

Veins (right lung, 24-year-old man, 128 kg)

D Arterieso Ve i n s

±1 ±2 ±3 ±4 iS ±6 ±7 ±S ± 9 ±10 ill ±12 ±13 ±14 ±15Order ("+". arteries; "-", veins)

B100

~Cv 80 - \\— wfa<<caB

6 0 - V0~ VS: OslM © v

E A r t e r i e sc \ \ . O V e i n su • s ^ ^ r

20 - \ ^ ^■2

0 -

e- -cx. •e - ^S-T t~=§>-dL—-S "**3

Table 7. Blood volumes of arteries in left lung andveins in right lung

Artery Vein

v.. Cumulative v„, CumulativeOrder ml volume, ml ml volume, ml

= 15 8.71 8.71 9.43 9.43±14 10.56 19.27 8.22 17.65±13 15.20 34.47 5.78 23.43±12 13.19 47.66 10.31 33.74±11 13.35 61.01 7.33 41.07= 10 11.92 72.93 6.58 47.65= 9 10.83 83.76 7.73 55.38± 8 12.70 96.46 4.63 60.01± 7 15.00 111.46 5.38 65.39± 6 11.55 123.01 5.20 70.59=5 7.84 130.85 4.39 74.98±4 7.56 138.41 6.07 81.05=3 4.50 142.91 2.89 83.94* 2 3.68 146.59 1.36 85.30±1 3.47 150.06 1.29 86.59

±1 ±2 +3 +4 ±5 ±6 ±7 ±8 ±9±10±11±12±13±14+15 16 17

Order ("+", arteries; "-", veins)

Fig. 5. Distribution of total cross-sectional area of all elements ofeach order with order number. A: left pulmonary arterial tree of a44-yr-old man and right pulmonary venous tree of a 24-yr-old manlour data). B: pulmonary arterial and venous trees in whole humanlung; values for arteries are from Horsfield (7); values for veins arefrom Horsfield and Gorden (11).

DISCUSSION

The morphometric data of pulmonary vascular treesof the cat, dog, rat, and human are now available invarious degrees of completeness. Table 8 summarizesthe total order number, the mean diameter of order 1vessels, the diameter ratio, the length ratio, and thebranching ratio of the pulmonary vascular trees ofthese animals. Fung (2) and Zhuang et al. (31) demonstrated the application of morphometric data in pulmonary hemodynamics. The data ofthe cat (29, 30) andhuman (7, 11, 22) by Horsfield, Singhal, and theircolleagues were obtained by Strahler's ordering system, whereas the other data were obtained by thediameter-defined Strahler system. The connectivitymatrix is defined only in the latter system, for reasonsto be explained.

Cumming and Horsfield (1) pioneered the use ofStrahler's ordering system in the morphometry of thelung. The first set of data on the human pulmonary

V„, total blood volume of order n computed by Eq. 10. Left lung wasfrom 44-yr-old man; right lung was from 24-yr-old man.

arterial tree was published by Singhal et al. (22).Horsfield (7) and Horsfield and Gorden (11) amplifiedthe data and used them to analyze pulmonary circulation.

The diameter-defined Strahler system used herc-modifies Horsfield's Strahler system by adding a diameter judgment at the junction where two vessels meet tobecome one confluent vessel. Horsfield's rule is toincrease the order number of the confluent vessel by 1indiscriminately. Our rule is to increase the ordernumber of the confluent vessel by 1 if and only if the

Table 8. Total order number, mean diameterof order 1 vessels, and diameter, length, andbranching ratios in pulmonary vascular treesof cats, dogs, rats, and humans

Oats D0gy Rats / Humans* Hunjtfn.s'1'V

Ar/eries,Total order no. 12 12 11 1 17

Order 1 diame-ter, pm 21 28 13 13 20

Diameter ratio 1.72 1.67 1.58 1.60 1.56Length ratio 1.81 1.52 1.60 1.49 1.49

^Branch ratio 3.58 3.69

Veins

2.76 3.03 (6-3.37 (1-

-17)-5)

3.36

Total order no. 11 11 X 15 15Order 1 diame

ter, pm 22 29 X 13 18Diameter ratio 1.73, 1.70 X 1.68(7-

1.49(1--14)-6)

1.58

Length ratio 1.53 (4--10) 1.56 X 1.68(7--14) 1.502.40(1--3) 1.48(1- -6)

__ Branch ratio 3.52 3.76 X 3.30 3.33

Data for cats are from right pulmonary arterial and venous trees(29, 30), data for dogs from right pulmonary arterial and venous trees(Y. Tien, R. Z. Gan, and R. T. Yen, unpublished observations; 5), datafor rats from left pulmonary arterial tree (12). * Data from whole lung(7, 11. 22); tdata from left pulmonary arterial tree of a 44-yr-old manand right pulmonary venous tree of a 24-yr-old man (our data).

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