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

Vico, Pierre; Kyriacos, S.; Heymans, Olivier; Louryan, Stéphane; Cartilier, L.

doi:10.1006/jtbi.1998.0810

Cited by 42 publications

(38 citation statements)

References 25 publications

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“…(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) systematically demonstrated to be quasi-fractals by others when studied separately from the capillary component (Gazit et al, 1995;Sandau and Kurz, 1997;Kirchner et al, 1996;Wilting et al, 1996;Vico et al, 1998;Parsons-Wingerter et al, 1998;Bergman and Ullberg, 1998;Herman et al, 2001;Masters, 2004;Cassot et al, 2006;Kassab, 2000;Gan et al, 1993;Jiang et al, 1994;Hahn et al, 2003). Because of the variety of vascular structures considered in these studies (subcutaneous, extraembryonic, pial, retinal, coronary, pulmonary, hepatic, intracortical) and because the homogeneous nature of capillaries has also been demonstrated in various systems (subcutaneous (Gazit et al, 1995;Baish and Jain, 2001), epifoveal (Panico and Sterling, 1995), hepatic (Gaudio et al, 2005)); this conclusion appears to be very general.…”

Section: Discussionmentioning

confidence: 86%

“…In addition, beside these intrinsic scales limitations, it is technically very challenging to collect morphometric data on sufficiently large volumes of tissue at high resolution (Cassot et al, 2006;Heinzer et al, 2006;Risser et al, 2007). Therefore, almost every previous study of the scaleinvariant properties of healthy vascular networks is either limited to the micro-vascular end of the vascular network (Gazit et al, 1995;Panico and Sterling, 1995;Arlt et al, 2003;Gaudio et al, 2005) or to its arterial and/or venous arborescences (Gazit et al, 1995;Sandau and Kurz, 1997;Kirchner et al, 1996;Wilting et al, 1996;Vico et al, 1998;Parsons-Wingerter et al, 1998;Bergman and Ullberg, 1998;Herman et al, 2001;Masters, 2004). In the latter studies, the spatial resolution is not sufficient to resolve the capillary vessels, which is evident while looking at typical images of the vascular networks used for such fractal analysis.…”

Section: Fractal Analysis Of Healthy Vascular Network: a Reviewmentioning

confidence: 99%

“…be based on the real biological situation and try to isolate the key steps of the growth process. Indeed, although one of the recurrent ideas behind the study of the multi-scale behavior of vascular networks is that it is potentially useful in revealing the physical mechanisms underlying their morphogenesis (Gazit et al, 1995;Bergman and Ullberg, 1998;Baish and Jain, 2000;Masters, 2004;Cassot et al, 2006), several authors warn that two branching patterns with the same fractal dimension have not necessarily been formed by the same class of fundamental processes (Vico et al, 1998;Murray, 1995;Meakin et al, 2001;Fleury and Schwartz, 2001). In case of vascular morphogenesis, models must thus be consistent with the morphogenetic events and dynamics known to be involved in the formation of new vascular structures.…”

Section: Vascular Branching Morphogenesis: Predictions Regarding the mentioning

confidence: 99%

“…To address these issues, fractal analysis has been applied to a large variety of healthy or pathologic vascular networks whose fractal dimensions (d f ) have been sought (Gazit et al, 1995;Panico and Sterling, 1995;Sandau and Kurz, 1997;Kirchner et al, 1996;Wilting et al, 1996;Vico et al, 1998;Parsons-Wingerter et al, 1998;Bergman and Ullberg, 1998;Baish and Jain, 2000;Herman et al, 2001;Arlt et al, 2003;Masters, 2004;Gaudio et al, 2005;Cassot et al, 2006;Risser et al, 2007). However, from these previous studies, no consensus has emerged about whether normal vascular networks must be considered as fractals (at least within a limited range of scales, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Fractal analysis of vascular networks: Insights from morphogenesis

Lorthois

Cassot

2010

Journal of Theoretical Biology

135

119

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao. a b s t r a c t Considering their extremely complicated and hierarchical structure, a long standing question in vascular physio-pathology is how to characterize blood vessels patterns, including which parameters to use. Another question is how to define a pertinent taxonomy, with applications to normal development and to diagnosis and/or staging of diseases.To address these issues, fractal analysis has been applied by previous investigators to a large variety of healthy or pathologic vascular networks whose fractal dimensions have been sought. A review of the results obtained on healthy vascular networks first shows that no consensus has emerged about whether normal networks must be considered as fractals or not.Based on a review of previous theoretical work on vascular morphogenesis, we argue that these divergences are the signature of a two-step morphogenesis process, where vascular networks form via progressive penetration of arterial and venous quasi-fractal arborescences into a pre-existing homogeneous capillary mesh. Adopting this perspective, we study the multi-scale behavior of generic patterns (model structures constructed as the superposition of homogeneous meshes and quasi-fractal trees) and of healthy intracortical networks in order to determine the artifactual and true components of their multi-scale behavior. We demonstrate that, at least in the brain, healthy vascular structures are a superposition of two components: at low scale, a mesh-like capillary component which becomes homogeneous and space-filling over a cut-off length of order of its characteristic length; at larger scale, quasi-fractal branched (tree-like) structures. Such complex structures are consistent with all previous studies on the multi-scale behavior of vascular structures at different scales, resolving the apparent contradiction about their fractal nature.Consequences regarding the way fractal analysis of vascular networks should be conducted to provide meaningful results are presented. Finally, consequences for vascular morphogenesis or hemodynamics are discussed, as well as implications in case of pathological conditions, such as cancer.

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Section: Discussionmentioning

confidence: 86%

Section: Fractal Analysis Of Healthy Vascular Network: a Reviewmentioning

confidence: 99%

Section: Vascular Branching Morphogenesis: Predictions Regarding the mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fractal analysis of vascular networks: Insights from morphogenesis

Lorthois

Cassot

2010

Journal of Theoretical Biology

135

119

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“…16,25 However, the vascular bed should be addressed as a highly complex structure, and fractal dimension alone may not fully characterize all the aspects of its complexity. As pointed out by Smith et al, a given value of D does not uniquely specify a structure morphology and very differently looking structures can have the same or very similar fractal dimension.…”

Section: Guidolin Et Almentioning

confidence: 99%

Order and disorder in the vascular network

et al. 2004

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A structural feature of particular interest in order to get a better understanding of tissue perfusion is the way a pattern of growing vessels fills the available space. To address this point, we have developed automatic image analysis methods allowing a quantitative evaluation of several parameters (fractal dimension, lacunarity and nonfractal order–disorder parameters, such as positional, topological and orientational order) characterizing the level of spatial order/disorder exhibited by the vascular network of the CAM in basal conditions and after treatment for 96 h with an angiogenic cytokine, such as fibroblast growth factor-2 (FGF-2), or with an angiostatic molecule, such as vinblastine

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Fractal analysis of extra‐embryonic vascularization in Japanese quail embryos exposed to extremely low frequency magnetic fields

Costa

Jimenez

Barbosa

et al. 2012

Bioelectromagnetics

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Magnetic fields (MF) can alter the dynamic behavior of vascular tissue and may have a stimulatory or inhibitory effect on blood vessel growth. Fractal geometry has been used in several studies as a tool to describe the development of blood vascular networks. Due to its self-similarity, irregularity, fractional dimension, and dependence on the scale of vessel dimensions, vascular networks can be taken as fractal objects. In this work, we calculated the fractal dimension by the methods of box counting (D(bc)) and information dimension (D(inf)) to evaluate the development of blood vessels of the yolk sac membrane (YSM) from quail embryos exposed to MF with a magnetic flux density of 1 mT and a frequency of 60 Hz. The obtained results showed that when the MF was applied to embryos aged between 48 and 72 h, in sessions of 2 h (6 h/day) and 3 h (9 h/day) with exposure intervals between 6 and 5 h, respectively, blood vascular formation was inhibited. Exposure sessions shorter than 2 h or longer than 3 h had no observable change on the vascular process. In contrast, the magnetic field had no observable change on the YSM vascular network for embryos aged between 72 and 96 h, irrespective of the exposure time. In conclusion, these results show a "window effect" regarding exposure time.

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

Cited by 42 publications

References 25 publications

Fractal analysis of vascular networks: Insights from morphogenesis

Fractal analysis of vascular networks: Insights from morphogenesis

Order and disorder in the vascular network

Fractal analysis of extra‐embryonic vascularization in Japanese quail embryos exposed to extremely low frequency magnetic fields

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