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.
References
1)Stiegmann GV,Goff JS,Michaletz-Onody PA,et al.
Endoscopic Sclerotherapy as compared with endoscopic ligation for bleeding
esophageal varices N Engl J Med 1992;326:1527-32
2)Gimson AES,Ramage JK,Panos MA
Randomized trial of variceal banding ligation versus injection sclerotherapy
for bleeding esophageal varices Lancet 1993;342:391-4
3)Laine L,Cook D
Endoscopic variceal ligation compared with sclerotherapy for the treatment of
esophageal variceal bleeding:A meta-analysis Ann Intern Med 1995;123:280-7
4)Koutsomanis D
Endoscopic variceal ligation combined with low volume sclerotherapy: A
controlled study Gastroenterology 1992;102:A835
5)Reveille RM,Goff JS,Stiegmann GV et al.
Combination endoscopic variceal ligation (EVL)and low volume sclerotherapy
(ES) for bleeding esophageal varices:A faster route to variceal eradication?
Gastrointest Endosc 1991;37:243
6) Saeed ZA ; Stiegmann GV ; Ramirez FC ; Reveille RM ; Goff JS ; Hepps KS
Cole RA
Endoscopic variceal ligation is superior to combined ligation and
sclerotherapy for esophageal varices : a multicenter prospective randomized
trial Hepatology, 1997 Jan, 25:1, 71-4
7) Laine L ; Stein C ; Sharma V
Randomized comparison of ligation versus ligation plus sclerotherapy in
patients with bleeding esophageal varices Gastroenterology, 1996 Feb, 110:2,
529-33
8) Dhiman RK ; Choudhuri G ; Saraswat VA ; Agarwal DK ; Naik SR
Role of paraoesophageal collaterals and perforating veins on outcome of
endoscopic sclerotherapy for esophageal varices : an endosonographic study Gut,
1996 May, 38:5, 759-64
9) Wojtowycz AR ; Spirt BA ; Kaplan DS ; Roy AK
Endoscopic US of the gastrointestinal tract with endoscopic, radiographic,
and pathologic correlation Radiographics, 1995 Jul, 15:4, 735-53
10) Nagamine N ; Ido K ; Ueno N ; Kimura K ; Kawamata T ; Kawada H ; Hirasawa
T ; Suzuki T ; Kubo H ; Tokumaru K ; Seki M
The usefulness of ultrasonic microprobe imaging for endoscopic variceal
ligation. Am J Gastroenterol, 1996 Mar, 91:3, 523-9
11) Pontes JM ; Leitao MC ; Portela FA ; Rosa AM ; Ministro P ; Freitas DS
Endoscopic ultrasonography in the treatment of esophageal varices by
endoscopic sclerothrapy and band ligation : do we need it? Eur J Gastroenterol
Hepatol, 1995 Jan, 7:1, 41-6
12) Miller LS ; Schiano TD ; Adrain A ; Cassidy M ; Liu JB ; Ter H ; Vellary
SM Dabezies MA ; Black M
Comparison of high-resolution endoluminal sonography to video endoscopy in
the detection and evaluation of esophageal varices Hepatology, 1996 Sep, 24:3,
552-5 \
13) Leung VK ; Sung JJ ; Ahuja AT ; Tumula IE ; Lee YT ; Lau JY ; Chung SC
Large paraesophageal varices on endosonography predict reccurrence of
esophageal varices and rebleeding Gastroenterology, 1997 Jun, 112:6, 1811-6
14)C.A.Lampridh: HrakleitoV , EkdoseiV Kleiw,Patrai,1996
15)E.Lorenz
J.Atmosph.Sci :20,130(1963)
16) B.B. Mandelbrot,
The fractal geometry of nature, WH Freeman 1982
17) B.B. Mandelbrot,
Les Objets fractales: forme, hasard et dimension, coll. Champs, Flammarion,
Paris, 1995
18)D'Arcy W.Thompson
On growth and form,2 nd ed., Cambridge UP,1963
19)T.Mattfeld
Spatial Pattern Analysis using Chaos Theory: A Nonlinear Deterministic
Approach to the Histological Texture of Tumours In: Fractals in Biology and
Medicine (Basel, Birkhaeuser) Vol II (1997)\~:50-72
20)Vehel J.L.
Using fractal and morphological criteria for automatic classification of lung
diseases In: Visual Communication and Image Processing IV, Philadelphia, Pennsylvania.
Proc SPIE.1989;1989:1-10
21)C.K.Peng et al.
Fractal Landscapes in Physiology & medicine:Long Range Correlations in
DNA sequences and heart Rate intervals In\~:Fractals in Biology and Medicine (Basel,Birkhaeuser
Vrlg Vol I (1994):55-65
This work is currently in press in the journal "Hepatogastroenterology"
