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Fractal dimension and vessel complexity in patients with cerebral arteriovenous malformations.

Reishofer G, Koschutnig K, Enzinger C, Ebner F, Ahammer H - PLoS ONE (2012)

Bottom Line: We found that for all methods, the Box-counting dimension, the Minkowski dimension and the generalized dimensions FD was significantly higher in the hemisphere with AVM compared to the hemisphere without AVM indicating that FD is a sensitive parameter to capture vascular complexity.Furthermore we found a high correlation between FD and the maximum slope of contrast media transit and between FD and the size of the central nidus pointing out the physiological relevance of FD.The proposed method may therefore serve as an additional objective parameter, which can be assessed automatically and might assist in the complex workup of AVMs.

View Article: PubMed Central - PubMed

Affiliation: Department of Radiology, MR-Physics, Medical University of Graz, Graz, Austria. gernot.reishofer@medunigraz.at

ABSTRACT
The fractal dimension (FD) can be used as a measure for morphological complexity in biological systems. The aim of this study was to test the usefulness of this quantitative parameter in the context of cerebral vascular complexity. Fractal analysis was applied on ten patients with cerebral arteriovenous malformations (AVM) and ten healthy controls. Maximum intensity projections from Time-of-Flight MRI scans were analyzed using different measurements of FD, the Box-counting dimension, the Minkowski dimension and generalized dimensions evaluated by means of multifractal analysis. The physiological significance of this parameter was investigated by comparing values of FD first, with the maximum slope of contrast media transit obtained from dynamic contrast-enhanced MRI data and second, with the nidus size obtained from X-ray angiography data. We found that for all methods, the Box-counting dimension, the Minkowski dimension and the generalized dimensions FD was significantly higher in the hemisphere with AVM compared to the hemisphere without AVM indicating that FD is a sensitive parameter to capture vascular complexity. Furthermore we found a high correlation between FD and the maximum slope of contrast media transit and between FD and the size of the central nidus pointing out the physiological relevance of FD. The proposed method may therefore serve as an additional objective parameter, which can be assessed automatically and might assist in the complex workup of AVMs.

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Related in: MedlinePlus

The curves in the double logarithmic plots show the relationship between the scales of measurement and object size in one representative patient.Values of FD assessed by means of Db (left side of the figure) and Dm (right side of the figure) were evaluated from the different slopes using Eq. (3) and (4). The red lines were obtained from the hemisphere with AVM and the black lines were obtained from the hemisphere without AVM demonstrating that FD is sensitive to the vascular complexity due to AVMs.
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pone-0041148-g003: The curves in the double logarithmic plots show the relationship between the scales of measurement and object size in one representative patient.Values of FD assessed by means of Db (left side of the figure) and Dm (right side of the figure) were evaluated from the different slopes using Eq. (3) and (4). The red lines were obtained from the hemisphere with AVM and the black lines were obtained from the hemisphere without AVM demonstrating that FD is sensitive to the vascular complexity due to AVMs.

Mentions: To illustrate the proposed methods, the log-log plots for Db and Dm are shown in Figure 3 for a single patient. The different slopes reveal the higher FD in the left hemisphere suffering from a large AVM (nidus size = 2.9 cm) (Db = 1.28, Dm = 1.61) compared to the unaffected hemisphere (Db = 1.11, Dm = 1.24).


Fractal dimension and vessel complexity in patients with cerebral arteriovenous malformations.

Reishofer G, Koschutnig K, Enzinger C, Ebner F, Ahammer H - PLoS ONE (2012)

The curves in the double logarithmic plots show the relationship between the scales of measurement and object size in one representative patient.Values of FD assessed by means of Db (left side of the figure) and Dm (right side of the figure) were evaluated from the different slopes using Eq. (3) and (4). The red lines were obtained from the hemisphere with AVM and the black lines were obtained from the hemisphere without AVM demonstrating that FD is sensitive to the vascular complexity due to AVMs.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3399805&req=5

pone-0041148-g003: The curves in the double logarithmic plots show the relationship between the scales of measurement and object size in one representative patient.Values of FD assessed by means of Db (left side of the figure) and Dm (right side of the figure) were evaluated from the different slopes using Eq. (3) and (4). The red lines were obtained from the hemisphere with AVM and the black lines were obtained from the hemisphere without AVM demonstrating that FD is sensitive to the vascular complexity due to AVMs.
Mentions: To illustrate the proposed methods, the log-log plots for Db and Dm are shown in Figure 3 for a single patient. The different slopes reveal the higher FD in the left hemisphere suffering from a large AVM (nidus size = 2.9 cm) (Db = 1.28, Dm = 1.61) compared to the unaffected hemisphere (Db = 1.11, Dm = 1.24).

Bottom Line: We found that for all methods, the Box-counting dimension, the Minkowski dimension and the generalized dimensions FD was significantly higher in the hemisphere with AVM compared to the hemisphere without AVM indicating that FD is a sensitive parameter to capture vascular complexity.Furthermore we found a high correlation between FD and the maximum slope of contrast media transit and between FD and the size of the central nidus pointing out the physiological relevance of FD.The proposed method may therefore serve as an additional objective parameter, which can be assessed automatically and might assist in the complex workup of AVMs.

View Article: PubMed Central - PubMed

Affiliation: Department of Radiology, MR-Physics, Medical University of Graz, Graz, Austria. gernot.reishofer@medunigraz.at

ABSTRACT
The fractal dimension (FD) can be used as a measure for morphological complexity in biological systems. The aim of this study was to test the usefulness of this quantitative parameter in the context of cerebral vascular complexity. Fractal analysis was applied on ten patients with cerebral arteriovenous malformations (AVM) and ten healthy controls. Maximum intensity projections from Time-of-Flight MRI scans were analyzed using different measurements of FD, the Box-counting dimension, the Minkowski dimension and generalized dimensions evaluated by means of multifractal analysis. The physiological significance of this parameter was investigated by comparing values of FD first, with the maximum slope of contrast media transit obtained from dynamic contrast-enhanced MRI data and second, with the nidus size obtained from X-ray angiography data. We found that for all methods, the Box-counting dimension, the Minkowski dimension and the generalized dimensions FD was significantly higher in the hemisphere with AVM compared to the hemisphere without AVM indicating that FD is a sensitive parameter to capture vascular complexity. Furthermore we found a high correlation between FD and the maximum slope of contrast media transit and between FD and the size of the central nidus pointing out the physiological relevance of FD. The proposed method may therefore serve as an additional objective parameter, which can be assessed automatically and might assist in the complex workup of AVMs.

Show MeSH
Related in: MedlinePlus