J. theor. Biol. (1998) 195, 525-532Article No. jt980810

Dynamic Study of the Extraembryonic Vascular Network of theChick Embryo by Fractal Analysis

PIERRE G VlCO*t, SOULA KYRIACOSi, OLIVIER HEYMANS*, STEPHANELOURYAN§ AND LOUIS CaRTILIERJ

9 L i b r e d e B r u x e l l e s , B r u s s e l s , B e l g i u m

(Received on 2 October 1997, Accepted in revised form on 12 August 1998)

F r a c u l a n a j y s i s i s ^ l y u ^ i n ^I, is a convenient method that defines theaW^0^mentalmodel for the studychorioallantoic membrane of lhe ch.ck embryo i a.J**"^^ demonstrate th,of vasculogenesis and angiogenesis. The a,m of th* nvesug ^ ,.fractal geometry is more appropriate ^^^bryonarvascular network of the chickevolution of a vascular network i.e. the «l^™r5'°™complexity of this network in theembryo. We used an original methodoto© » ^^J^^tei an increase of fractal

t r e e . © 1 9 9 8 A c a d e m i c P r e s s

Introduction

Fractal geometry has been widely used tocharacterize irregular structures (Mandelbrot,1982), e.g. vascular networks (Vico & Cartilier,1993; Vico et al., 1994). The deis estimated by fractal dimension vhave a non-integer value, anddetermined, for instance, by thmethod (Feder, 1988). Fractal analysis allthe complexity of a bidimensional vascular

tAuthor to whom correspondence should be addressed.

0022-5193/98/024525 + 08 S30.00/0

network to be easily quantified objectively andreproducibly. Current methods used to evaluatethis complexity and its eventual variations inphysiological or pathological circumstances lackprecision or remain semi-quantitative. The aim- ., ♦ «,»i,^« wac tn demonstrate tnat

of a vasculature in the process of formation, i.the extraembryonar vascular network of thechick embryo. Several parameters (Z>, fractal

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dimension; total length of vessels, Sr, total areaof the area vasculosa, 5,; and vascular density.D,) were evaluated. The superiority ofthe fractalapproach was demonstrated, and the physiological information it generated is discussed.

Materials and MethodsThe chorioallantoic membrane (CAM) of

chick embryo has been chosen for methodological and practical reasons. This model is easy tomanipulate, inexpensive, well established andwidely accepted. It is the largest extraembryonarorgan, easily accessible because of its superficiality. It is a bidimensional, vascularized structure,growing in a topologically two-dimensionaltissue sheet. Therefore, its D will lie between 1.0and 2.0 and can be treated easily with standardimage analysis. Moreover, the CAM is astandard experimental model for the study of

angiogenesis (Folkman, 1974). and tumor graftculture (Ausprunk el at.. 1974).

ANIMAL EXPERIMENTSChick embryos were grown by the windowed

method (Auerbach el al.. 1974). Twenty fertilized eggs {Gallus domesticus) were incubated ina standard egg incubator al 38 C for 6 daysunder atmospheric conditions (21% oxygenlevel). The atmosphere was constantly humidified (100% relative humidity). The eggs werewindowed on the second day of incubation, afterthe shell had been wiped with chlorhexidine andallowed to dry. and after removal of 6 mlalbumen. An oval window (approximately5.0 x 3.5 cm) was created with sterile scissors,and sealed with paralilm to avoid desiccation ofthe embryos. Under our experimental conditions, the first blood vessels in the CAM werevisualized by the 60th hour. The vascularnetworks were controlled every 8 hours for the

Fig. I. Chick embrvo at 96 hours.

FRACTAL ANALYSIS OF THF CHICK EMBRYO

3-following days, and every 12 hours on the lastday. Pictures were taken with a Macrolens60 mm Nikon F801 (Kodak T-Max 100) (Fig. 1).Only nine embryos reached the 142th hour; theothers died before this time period and/or werenot considered because of incomplete visualization of the vascular network. Vascular networks were hand traced on overheadtransparencies for image analysis. No distinctionwas made between arterial and venous trees.

IMAGE ANALYSIS

Images were grabbed using Neotech ImageGrabber software 2.1 (NeotechTM. Eastleigh,U.K.). Gray level images were obtained on agraphic window of 640 x 480 pixels andprocessed with Ultimage/X 1.41 software(Graftek, Meudon-LaForet, France) on aQuadra 900 Apple MacintoshII. To extract blood vessels, the images were

thresholded for the production of binary images.Thresholding consisted of segmenting imagesinto two regions where the structure and background were characterized by two differentintensities: pixels belonging to a given gray levelinterval were highlighted while others becameblack. An approximately same gray level intervalwas considered for all images. Then, the imageswere subjected to an L-skeleton command (Russ,1990). Skeletons allow representation of thestructural shape of an object by reducing itsthickness to 1 pixel. L-skeleton uses masksknown as structuring elements with an L-shape.As this study was concerned with the spatialdistribution of vessels, vessel width was ignored.

FRACTAL ANALYSIS

Classically, the D of a vascular tree isdetermined by the box-counting method. It relieson the fact that boxes of different sizes used tocover a vessel structure yield different estimatesof its length. The equation is N(c) = k. c~D wheree is the box size, N(c) is the number of boxes ofsize e needed to cover the structure studied, andD is the fractal dimension. A detailed explanation of the experimental procedure has beenpublished elsewhere (Vico & Cartilier, 1993).

A more efficient box-counting method hasbeen developed recently in our laboratory(Kyriacos et al.. 1994). It is based on a

modification of the classical computerizedbox-counting method (Feder, 1988) in which thecounting method, the type of step sequence andrange of length scales have been defined preciselyin order to provide an accurate estimation of D.Briefly, the method consists of dividing theembedding space into a sequence of boxes ofdecreasing size («:), and counting the number ofboxes N(e) of size c that contain at least 1 pixelof the structure. Thus, using boxes of differentsizes to cover an object yields different estimatesof N(c) because the smaller the boxes, the moredetails of the structure are taken into account.For c->0, the relationship, if any, is N(e) = k.e*° where D is the fractal dimension. D iscalculated from the slope ofthe points (log (1/e),log N{c)) which normally lie on a straight line,because of the power-law relationship. Countingis performed in a range defined by eml„ to emaxHence, emi„ corresponds to a box size larger thanthe thickness of the structure (in our case,£,„,,, = 2) and emax is what gives a box numberequal to 2. One important and specific feature ofthis method is that the step sequence isdetermined by an arithmetic subset, whererepetitions of the same values of N(e) as well asplateaus are ignored (Kyriacos et al., 1994). Itwas applied to estimate the D of the humanretinovasculature to obtain one of the components used to support existing growth modelsthat have been proposed so far (Kyriacos et al.,1997). Digitization, image processing and fractalanalysis required a few minutes for a singlevascular network.

Other usual parameters were also evaluated: -S,and D, which is defined as the ratio between S,-and the total area (S,) of the area vasculosaconsidered (pixel/pixel).

ResultsThe first vessels appeared by about the 60th

hour. D increased from about 1.30 by the 64thhour to 1.68 by the 112th hour. By the 112thhour, a plateau was reached for Z)=1.70asymptotically. The measurement of D is shownin Figs 2 and 3, D being the slope of the log-logplot of N(e) vs. 1/e, for the ascending and plateauphases, respectively. These figures show theexcellent linearity of the plots with R2 > 0.99.

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log (1/E)Fig. 2. Estimation of fractal dimension on a CAM at 88

hours. D= 1.64; R2 = 0.992.

The measures were widely distributed in the earlystages of vasculogenesis, but the distributionbecame narrower as vasculogenesis developed(Fig. 4). Si as well as D„ increased linearly withtime (Fig. 5). The distribution of Si and D,

Time (hours)Fig. 4. D vs. time. D increases continuously from about

1.30 by the 60th hour, until about 1.68 by the 112th hour.Then, a plateau is reached and D remains stable with timeat approximately 1.70. Note that, although the measures arewidely distibuted in the early stages of vasculogenisis, thedistribution becomes narrower for later and ultimate stages,when studies concerning angiogenesis are usually performed.

measures remained wide, whatever the stage ofdevelopment of the vascular tree. When D wasexpressed as a function of Si, asymptoticalbehavior was demonstrated (Fig. 6). Also, Dshowed a similar asymptotic behavior whenrelated to D, (Fig. 7). Finally, the coefficient ofvariation (CV) of each parameter revealed anobvious superiority for D, with a very low valueof 2 to 3%, specially when considering this isbiological material, in contrast to 15 to 35% forSi and A (Fig. 8).

log (1/8)Fig. 3. Estimation of fractal dimension on a CAM at 112

hours. D,= 1.70; R2 = 0.995.

Time (hours)Fig. 5. 5, vs. time. The total vessel length. S,. increases

linearly with time, with wide distribution of results whateverthe stage of development.

FRACTAL ANALYSIS OF THE CHICK EMBRYO

Fig. 6. D vs. S,. D is asymptotically linked with Si.

DiscussionSeveral studies have been performed to

understand the logic of vascular networkgrowth. Experimental models have been developed: the newborn rat lung (Caduffet al., 1986),the CAM of quail embryos (Pardanaud et al.,1987; Poole & Coffin, 1988), the CAM of chickembryos (Folkman, 1974), and the cornea ofrabbits and rats (Gimbrone et al., 1974). TheCAM has been used as a standard andexperimental model for angiogenesis (Folkman,1974), and for tumor graft culture (Ausprunk etal., 1974). Fractal organization ofthe vasculartree was suggested by Mandelbrot a long timeago (Mandelbrot. 1982). It was later demonstrated not only in the retina by several authors(Masters et al., 1992), but also in the skin (Vico& Cartilier, 1993; Vico et al., 1994), kidney

0.02 0.04 0.06 0 .08 0 .10 0 .12 0 .14

Fig. 7. D vs. D,. The vascular density, Dr, has a similarevolution as the total vessel length, S,, when related to D.

Time (hours)Fig. 8. The CV of D, Dr and 5, vs. time. (A) 5„ (•) Dr

(D) Df.

(Cross et al., 1993), and lungs (Gan et al., 1993;Jiang et al., 1994). Until recently, quantitativeand objective measures of vascular growth werelacking. Grading or scoring methods comprisingvisual assessment ofthe vascular network are tooapproximative, subjective and unreproducible.The use of 3H amino acids has been suggested toevaluate angiogenesis in the CAM (Splawinski etal., 1988; Thompson et al., 1985). Somegeometrical approaches have been proposed, butare difficult to apply in practice (Barnhill &Ryan, 1983). Among all these methods, Dv andrelated measurements are more objective inquantifying vascular structures (Hayek et al.,1991).

Some studies based on fractal analysis wereperformed on the CAM of the chick embryo toevaluate vasculogenesis and angiogenesis. Tsonis& Tsonis (1987) described a D close to 5/3 for the4-day-old embryo. They suggested diffusion-limited aggregation (DLA), largely used in physics'Witten & Sander, 1981, 1983), as a possiblemodel for vascular growth. However, themethod used for D determination was notdescribed. Moreover, DLA was proposed bythese authors and others only on the basis of aroughly similar macroscopic pattern aspect, andsimilar D of about 1.70. Based on mathematicaland physical arguments, it was shown recentlythat DLA cannot be accepted as a valid modelfor vessel growth (Kyriacos et al., 1997). Briefly,it was demonstrated that there exists a preferential angle of bifurcation of 36° (n/5) forstructures generated by the DLA process

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(Ameodo et al., 1992); in the case of the retina,the angles observed for vessels are higher, above60° for arteries and about 90° for veins.Moreover, DLA is an irreversible growthprocess, while vasculogenesis and angiogenesisare reversible with regression and remodeling. Itmust be remembered that there is an infinity ofstructures with a given D for a geometric patternor growth process that can be completelydifferent. Therefore, at steady state, a different Dfor two structures implies a different growthmechanism, while an identical D does not implyan identical growth process. Hence Laplacianprocess governing growth mechanisms such asDLA are not responsible—at least alone—forthe formation ofthe retinal vasculature, as staticand dynamic analyses do not display characteristics similar to the existing retinal vasculature.More complex phenomena seem to account forthe formation of retinal vessels that involvemechanical and physico-chemical factors (Kyriacos et al., 1997). Thus, one should be cautiousbefore considering DLA as the only growthmechanism involved on the sole basis of a Dclose to 1.70.

Kurz et al. (1994) investigated the development of blood vessels in the CAM of chickembryos between days 6 and 19 under otherexperimental conditions They examined fragments of the vascular tree (the CAM surfacestudied was 1 cm2), while our experimentinvolved its entirety. They showed a triple scatterplot establishing relations between D, total vessellength density, and the density of proliferatingcells, suggesting a higher proliferation rate in thecapillary layer in the first part of vasculogenesis(Kurz et al., 1994). They reported a stable D ofabout 1.1 for capillaries (smaller boxes), a Dranging from 1.3 to 1.5 with no further increasefor intermediate vessels, and a D approaching 2.0for greater vessels. This could be related to themultifractal concept, corresponding to thepossibility of a given natural structure exhibitingdifferent fractal behaviours in function of thescale of observation (Stanley & Meakin, 1988).Our method permits us to study vessels as asingle entity: our D presents a differentbehaviour with time than that described by theseauthors, as we observed an asymptotic increaseof D until values of about 1.70.

More recently, fractal analysis was used toquantify angiogenesis in the CAM (Kirchner etal., 1996). This study was also performed on alimited area of the vascular tree, at a highermagnification. The D determined by the classicbox-counting method showed a nearly linearincrease from day 6 until days 11-12. The rate ofincrease peaked at approximately 1.80 aroundday 13, and by day 16, D began to decreaseslightly. These results are in better accordancewith our own. as the methodology for imageanalysis is closer to ours: the vascular networkbecomes progressively more complex up to amaximum value. However, these authors showeda decrease of D after a peak of similar value asthe plateau we observed. This may be due to thefact that they tried to establish a polynomialrelationship in base 2. It seems inappropriate touse polynomial regression (y = ax2 + bx + c) inthis case, since that kind of function will alwayslead to a maximum followed by a decrease whichcould continue till value y = 0; this means thatvessels would spontaneously regress completely,which is a false assumption.

In our study, an asymptotic value of D = 1.70reveals a stable vascular architecture in terms offractal organization: even if S, and D, increase,the structure remains the same in fractallanguage. S, and D, appeared to be linearlyrelated to the time of incubation; therefore D wasalso asymptotically related to S, and D,. Onereason why S; and D,. continued to increaselinearly with time while D remained stable is thatthe entire vascular network grows proportionallywithin the growing embedding tissue (the totalarea of the area vasculosa increases with time).Another reason is that new iterations appearfollowing the rule of division of vessels. Morelikely, we should have a combination of bothreasons. Our results suggest progressive vascularnetwork formation until a stable vasculararchitecture is reached after about 100 hours ofincubation under our experimental conditions. Itis hypothesized that a network of such acomplexity should correspond to a more efficientvascular supply in terms of metabolism regarding spatial occupation; in this hypothesis,efficient should be understood as being thecapacity for a vascular network to maximallycover (perfuse) the surface while minimally

FRACTAL ANALYSIS OF THE CHICK EMBRYO

occupying the tissue itself. Variations of D areconsiderable at the beginning of vasculogenesis,but become narrower along the time course(Fig. 4). This could signify that some embryosshow faster and/or larger growth than others,but all will develop until that final stagecharacterized by D = 1.70. This point is alsosuggested by the asymptotic behavior of D vs. S,and D,: a stable vascular architecture is achievedwhatever the 5, and D,. However, one mustremain cautious before assigning the value ofZ)=1.70 to any physica l growth model ,particularly the DLA model often mentioned inthe literature, as discussed previously. On theother hand, D appears as a sensitive parameterto evaluate a vascular network and its evolutionor modification. The disparity of the resultsdecreases with time and becomes narrower atperiods of incubation where the CAM is used tostudy angiogenic factors.

Furthermore, Si and D, appear to be less thanideal parameters, showing a linear relationshipw i t h t i m e a n d a h i g h e r C V. W i t h o u rmethodology (windowed eggs), it is not possibleto follow these parameters for periods of timelonger than 100 hours, because the CAM is notcompletely visualized at these stages. Because ofthe asymptotic evolution of D in function of S.and D,, these cannot be accurate to evaluate thequality of a vascular network in terms of tissueperfusion. Indeed, it is clear that greater S,(above 13000) and greater D, (above 0.11) do notsignify better tissue perfusion, as D remainsconstant. This shows that S, and D, areparameters which are not accurate enough toestimate the quality of a vascular tree, while Daccurately estimates its complexity and perfusingcapacity.

Finally, the CV for the parameters studied alsofavors the superiority of D. The CV of D is small,and is practically constant after 90 hours ofincubation (2-3%). One could take advantage ofthese minimal variations of D in further studiesevaluating the effects of angiogenic factors on thevascular network.

Conclusion

Based on the general concept of fractalanalysis and on a modified box-counting

method, we are able to evidence a stable vasculararchitecture when studying the evolution of thebranching patterns of extraembryonar vascularstructures of the chick embryos CAM. Duringgrowth of the embryo, D increases up to anasymptotic value of about 1.70. D, as comparedwith Si or D,, appears to be the most sensitiveparameter to evaluate the evolution of anembryonic vascular network, and could be used.to study the influence of angiogenic factors onthe geometry and branching patterns of vascularstructures. The advantages of this parameterover other more usual methods are: it is an easy,precise and reproducible automated method forevaluation of the complexity ofthe vascular tree;the CV for the biological pattern is very smalland there is an asymptotical relationship withtime with a stable plateau.

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