Fractal-assisted EUS image-analysis in the evaluation of variceal eradication after elastic band ligation

Demetrios KOUTSOMANIS MD PhD,

Unite Medico - Chirurgicale Digestive, Centre Hospitalier,76400 Fecamp, France

Professor Dr.Vasileios PAPAKWNSTANTINOU,

Eidgenossische Technische Hochschule(ETH),Zurich,Switzerland

ABSTRACT
EUS is a strongly operator-dependent method. Mathematical algorithms in image-analysis are likely to enhance diagnostic accuracy. Incomplete eradication of esophageal varices can be demonstrated with EUS. The presence of paraesophageal varices, visible only w ith EUS, has been recently identified as a predictor of recurrence. Object of this study was to evaluate the usefulness of fractal-geometry-algorithms for the interpretation of EUS images and their impact on treatment decisions.

Materials and Methods
EUS was performed in five consecutive patients in order to detect the presence of paraesophageal varices after complete eradication of esophageal varices with elastic bandi ng, .Static images were analyzed and the fractal dimension was calculated. Follow-up ranged between 8 & 12 months.Results:Fractal dimension was related to: 
a) the presence & size of paraesophageal varices b) Child score 
c ) re-bleeding rate. Patients with a fractal dimension>1.5 re-bled.
Conclusion
The use of mathematical algorithms derived from fractal geometry enhance interpretation in endosonographic imaging, increase the diagnostic yield and may prove helpful in making individual-tailored treatment decisions.

INTRODUCTION 
Endoscopic therapy aims to eradicate esophageal varices, a potential source of bleeding. 
Elastic band ligation is an established method in the treatment of esophageal varices. Its efficacy is comparable (1) or superior (2) to that of endoscopic scler otherapy and this was confirmed in a recent meta-analysis (3). The lack of a reduction in the rate of mortality observed in these studies, may be due to the fact that patients with end-stage liver disease were included. This is expected to change with the evolution of new imaging techniques, such as the EUS, which are expected to have an impact in the surveillance policy and treatment of these difficult patients. Combination therapy (elastic banding + low - volume sclerotherapy ) was shown to be superior to sclerothera py in terms of hastening variceal eradication (4). This benefit was related to elastic banding alone (5, 6) while combination therapy was linked to a higher rate of complications (7) without offering a particular advantage. This was only partly confirmed in our unp ublished series, since no differences were observed between combination therapy and banding alone in respect to both eradication and complications. 
The efficacy of endoscopic therapy has been correlated to the reduction of variceal bleeding episodes; this depends greatly on whether esophageal varices have been efficiently eradicated. Eradication of varices is usually evaluated with video-endoscopy. Endoscopic Ultrasonography has been evaluated in this indication ( 8, 9,10 ). Video-endoscopy fail to identify 17% of non-eradicated varices (8) and correlation between endoscopic ultrasonography and video-endoscopy seems to be poor(11,12). EUS appear to be more sensitive and reproducible (12) than endoscopy alone. 
By identifying non-eradicated and high-risk varices with E US, it is possible to predict variceal recurrence and subsequent bleeding (13).
It is postulated that EUS may be helpful in identifying high risk patients and in affecting surveillance policy. EUS is a strongly operator dependent technique. Currently available echoendoscopes enable measurement of euclidean dimensions while parameters such as density or texture are subjectively appreciated and cannot be measured objectively, leaving part of the im age\rquotes information unexploited. 
The use of mathematical algorithms derived from fractal geometry, may prove helpful in this respect, since they can provide objective measurements for, until now, subjectively appreciated parameters. Fractals arise naturally as attractors in classical dynamical systems which are "chaotic". Such systems have a close relationship to "stochastic" dynamical systems. Heraklitos, Greek philosopher of the pre-socratic period (5th century BC), noted the importance of LogoV, a sort of mathematical ratio, as a means to explain and describe dynamical processes in Nature or Life(14). 
In Greek geometry (codified in Euclidean geometry), geometrical figures such as circles, triangles, spheres, lines...were the natural objects of study and suitable for the description of  " idealized " events. 
Euclidean geometry was seen, after Riemann's influence, as a particular case of a more general and flexible "Riemannian" geometry. 
The necessity to investigate irregular geometric objects (e.g. Cantor sets) arose and it soon became obvious that these objects should be regarded as "typical" both in connection with dynamical systems and with probability theory (the typical path of Brownian motion being a fractal, irregular curve) 
In the 1970's, a whole area of studies on "Chaos" was started, under the influence of investigations by E.N.Lorenz(15)and S. Ulam. 
Powerful modern computers made complex mathematical operations and visualizations, possible. 
Benoit Mandelbrot, introduced fractals as "geometrical figures of chaos" (16,17). The studies on morphology by D'Arcy Thompson (18) had a particular influence in biology while the studies on dynamics, gave fractals a particular place. Nonlinear chaotic systems, and associated fractal geometry, are playing an increasingly \par important role in medicine. Medicine is distinguished among all sciences by the interaction of randomness (e.g. in evolutionary processes), non-linearity (e.g. for the creation of forms) and complexity (dissipative, fractal structures playing a determining role in generating and shaping life forms).

AIM 
Study of images in ultrasonography considers euclidean dimensions (e.g. measurement of the larger axis of a lesion ). In a recent study(13)the size of residual paraesophageal varices after endoscopic band ligation was found to be a predictor of recurrent varices & consequent bleeding. Images obtained in Endoscopic ultrasonography vehicle a large number of information which is inadequately exploited with the sole measurement of euclidean dimensions. The same may apply to ultrasonography or other imaging techniques. Fractal geometry offers the possibility to take in account virtually all of the information given by an image. This means that, in the case of paraesophageal varices, not only the largest varix is being taken in account but also the existence of smaller varices and their actual density. Large varices are likely to bleed but the role of the density of varices is unknown. This prospective study, evaluates the interest of fractal analysis of endosonographic images and its impact in the clinical course of cirrhotic patients after eradication of esophageal varices.

PATIENTS 
Between September 1997 & April 1998,five consecutive patients were considered in this study(4 male,1 female Age :42-65y)All patients presented with variceal bleeding and received endoscopic treatment within 6h after initial admission. Alcoholic cirrhosis was the underlying disease, while one patient ( LAUR ) was diagnosed to have hepatocellular carcinoma as well. Child Score on admission was as follows:

 LAUR=11

ROB=6

BOU=6

BAR=6

DES=6

MATERIALS & METHODS 
In our study, endoscopic variceal ligation was performed with the Speedband ligator. Four to six bands were positioned on the main variceal cords,starting as close as possible to the esophagogastic junction. No more than 4 (average=2.3) sessions were necessary to achieve eradication of varices. Endoscopic Ultrasonography using an Olympus EUM20 was performed two to four weeks (mean=2.5 weeks) after endoscopic confirmation of variceal eradication was obtained. It was searched for paraesophageal varices but also for specific changes caused by variceal ligation. Based on previous published data (7), patients with paraesophageal varices larger than 5mm were considered at high risk and were followed-up at 6 weeks intervalls; low-risk patients had endoscopy every 12 weeks.Endoscopic Ultrasonogr aphy photographs taken at the esophagogastric-junction,5cms above and at the azygos level were scanned with a Logitech, Pagescan Color handheld scanner. Image was then optimized and converted to a simple-pixel mode, keeping the number of pixels among different pictures, the same; information thus vehicled could be comparable. The KOLMOGOROV box-counting method was used to calculate the image's fractal dimension.

This is based on the formula:

Db=lim logN(e)/log(1/e)

where:

Db= the object's dimension using the box-counting method

e= the length of each box's side

N(e)=the smallest number of boxes required to fully cover the object's contour.

Nevertheless, zero limits are not applicable to biological objects and fractal dimension Db=d is empirically expressed as log N (e) / log (1/e) Fractal dimension was calculated, using the above given formula, with a Windows based program compiled with Borland's Pascal. The fractal dimension obtained at 126x126 boxes was considered.

RESULTS
During the eight months follow-up period, one patient (LA) died of a peptic ulcer bleeding followed by a disseminated intravascular coagulation. Another patient (BO) presented with recurrent variceal bleeding and band ligation was necessary until eradication of the varices was achieved (2 sessions). Two other patients (BA, RO) had a further session of band ligation,to prevent bleeding from recurrent Grade II high risk-varices on endoscopy. It is worth noting that all patients but two (BA, DE) continued alcohol intoxication. Patient (DE) did not require any further endoscopic treatment and had no recurrent varices. 

Endoscopic & Endosonographic evaluation: 
All patients were endoscopically assessed from two independent endoscopists and there has been full agreement in the endoscopic grading of varices: eradication was achieved in all cases. This was confirmed at EUS examination because no variceal cord was seen at submucosal level. Thickening of the wall was observed at the sites of previous ligations and this was more prominent at the gastroesophageal junction. In two patients (LA, BO), paraesophageal varices larger than 5mms were observed. As mentioned above, the higher the degree of complexity in a studied image,the higher its fractal dimension is expected to be. Three different EUS pictures per patient were studied. These were taken at the gastroesophageal junction level, 5cms above and at t he azygos vein level. The fractal dimension obtained at the higher number of boxes(126x126)was considered after image analysis as described above. Results of this image analysis and follow-up are summarized below.

DISCUSSION Image analysis using fractals has been reported in various fields of medicine,: pathology(19),radiology(20),physiology(21) etc. Common aim of these studies was to examine whether offering a mathematical tool,one can increase the diagnostic yield. Mathematical algorithms challenge to enhance information in medical imaging, providing an objective measurement where otherwise subjective appreciation is the rule (appreciation of texture for example). Both perception and interpretation have a component o f subjectivity, despite the attenuative effect of learning. Less clear-cut cases may prove difficult to interpret and objective measurements are welcome. As discussed above,most objects encountered in nature are non-euclidean objects. Their geometrical description requires a non-euclidean approach. In that respect, fractals have a particular interest. This is the first report applying fractals in the analysis of EUS images. Euclidean measurements help appreciate the size of an object in EUS. The size of paraesophageal varices has been correlated with an increased risk of recurrent varices and bleeding .In our study, we postulated that a further factor for recurrence may be the increased number (density) of paraesophageal varices. The density of paraesophageal varices is being (subjectively) assessed by the operator during EUS examination. Patients with a large number of paraesophageal collaterals are expected to have larger varices; this is confirmed in this study: patients with high fractal dimensions, i.e. a high image complexity resulting from a higher number (density) of paraesophageal varices, were those having larger varices. Using fractal analysis it was possible to identify two more patients who had recurrent varices during the six months follow-up period. Endoscopic surveillance of these patients is a common clinical problem and fractals appear to offer an objective tool in the appreciation of further management. This study confirms previously published data (13) who suggested that recurrence and subsequent variceal bleeding was related to large paraesophageal varices. Based on previously published data(13) two grous of patients were considered:: high ( paraesophageal varices greater than 5mms ) and low risk(<5mms)patients.

Fractals clearly offered the possibility of an accurate estimation of the individual patient's disease severity in respect to esophageal varices, when the result was retrospectively compared to the sole measurement of euclidean dimansions: in all cases a fractal dimension above 1,5 was predictive of recurrence whereas only two patients had paraesophageal varices greater than 5mms. It may be that more factors are implicated in the recurrence of varices (e.g.  their density) than just the size of paraesophageal varices and/or that more information is exploited with fractal analysis. The individual patient' s fractal dimension corresponded to the clinical course, when studied retrospectively. A correlation may exist between variceal recurrence, clinical course and the individual patient's fractal dimension; this may lead to a more individualized approach of risk evaluation but further studies are needed on this field.

To the authors' best knowledge, this is the first study applying fractals in Endosonographic imaging and looking at the clinical impact. It is postulated that true interdisciplinary research like the present study is likely to benefit both sciences :mathematics & medicine.

ACNOWLEDGEMENTS
The authors wish to thank Artemis Mertani-Liza & Haralambos Lamprides for unravelling Heraclitian LogoV that inspired this work.We are indebted to Dr.L.Palazzo for providing static EUS pictures for each patient.

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This work is currently in press in the journal "Hepatogastroenterology"