Enteromorphognosia Project

THE ENTEROMORPHOGNOSIA PROJECT

A. THEORETICAL BACKGROUND

1.Historical Introduction

Fractals arise naturally as attractors in classical dynamical systems which are "chaotic". Such systems have a close relation with "stochastic" dynamical systems.

Greek pre-socratic philosophers (Thales, Anaxagoras..ca 450BC) developed concepts of this sort,early in history: Chaos as opposite to Nous. Democritos was one of different Greek philosophers who elaborated concepts of "chance".

For Hrakleitos, Greek philosopher of the Vth century BC, the "Logos" (mathematical ratio, but also reason, cause..) is the existing link of the Universe:ouk emou,alla tou logou akousantaV omologein sofon estin en panta einai(1)

In Plato's "Timaios", "QeoV" (god) in relation with "Anagkh" (necessity), creates the "KosmoV" (universe, literally: jewel);the description of the creation of the Kosmos resembles a "chaotic deterministic system"

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 "idealised" 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(1963)and S.Ulam(1950).Powerful modern computers made complex mathematical operations and visualizations, possible. Benoit Mandelbrot, introduced fractals as "geometrical figures of chaos"(2).

The studies on morphology by D'Arcy Thompson (1917) had a particular influence in biology and the studies on dynamics, gave fractals a particular place.

2.Why Chaos in Medicine?

Nonlinear chaotic systems, and associated fractal geometry, are playing an increasingly important role in medicine.

Medicine is distinguished among all sciences by the interaction of randomness (e.g. in evolutionary processes), nonlinearity (e.g. for the creation of forms) and complexity (dissipative, fractal structures playing a determining role in generating and shaping life forms).

As expected, truly interdisciplinary research on this field is already influencing both mathematics and medicine; an example is the study of neural networks and image processing (see other related research in this web page), with geometric, probabilistic and algorithmic methods.

3.Fractals & Texture

An empirical connection between fractal dimension and roughness perception from the human visual system, was studied by Pentland(4).He showed ten naive subjects 15 surfaces of varying fractal dimension and asked them to estimate roughness on a scale of one to ten. The correlation coefficient between roughness estimates and fractal dimensions was 0.98,indicating an extremely close relationship between textural perception and fractal dimension. Richards and Polit (5) have shown evidence that texture perception is based on physiological spatial frequency filters. One way of computing an image's fractal dimension is to consider its frequency spectrum. Pentland has suggested that the human visual system determines fractal dimension by responding to linear trends in the spatial frequency spectrum(6).

Serra (7)and Rigaut(8)suggest that the brain evaluates self-similarity (fractals) using mathematical morphology-like operations based on signals produced by interacting retinal cells while Rigaut wonders by what mechanism the brain could examine a frequency spectrum.

The mechanism for a fractal evaluation of texture by the human visual system is largely speculative, but the connection between fractal dimension and roughness perception has been demonstrated.

The gastrointestinal system has a capacity to recognize volume variations,thermic or electrical impulses that are directly applied on the mucosa.It has been shown that in certain diseases (e.g. IBS) the threshold of pain in the variation of intraluminal volume may be lowered.

No study has been done to establish whether the gut has the ability (termed here: Enteromorphognosia, from Greek : enteron=gut,morphe=form,gnosis=knowledge) to recognize intraluminal forms or textures and whether this ability is impaired in certain pathological conditions (e.g. Intractable Constipation, BS etc..). Lastly, whether operant conditioning methods, now widely used in the reeducation of the pelvic floor and in the treatment of Intractable Constipation (e.g. Biofeedback), or, certain pharmacological agents are likely to modify Enteromorphognosia.

It is speculated that Enteromorphognosia may be the cause or the effect of certain pathological conditions that involve the gut. Therefore research on this subject may prove useful in the understanding of the pathophysiology of these conditions and lead to alternatives in their treatment.

B. AIM

Aim of this project is to explore whether:

1)forms & texture can be perceived by the anorectum

2)there is a correlation between the subjective visceral perception and the objective degree of irregularity as this can be measured using fractal geometry

3)texture perception is impaired in idiopathic constipation and/or incontinence

4)texture perception of the gut can be modified using behavioural treatment approaches such as Biofeedback

5)texture perception can be modified using prokinetik drugs

We decided to present this work in the form of Case Reports, that will be periodically updated and enriched with new data.

C. METHODS

In all of the following examples the box-counting method was used to determine the fractal dimension. At this point it must be stressed that there is not one single mathematical definition of fractal dimension but rather several related ones, such as Hausdorf-Besicovitch dimension, Minkowski-Bouligand dimension, Kolmogorov box-counting dimension, Korcak dimension and spectral dimension. Mandelbrot commented recently that fractal dimension is a multifaceted concept. Therefore, different computational methods need not even theoretically yield the same value for fractal dimension; a surface may have several distinct fractal dimensions as well as various measures of lacunarity.

All measurements were performed on equal-pixel-size Bitmap files using the box-counting method. For this purpose a Windows based program was used, compiled with Borland-Pascal. The value referred to as "fractal dimension" is the value estimated at 128x128 boxes.

D. CASE REPORTS

Case 1

L.L., a 17-y-old patient, complains of Intractable Constipation over the past 8 months. She opens her bowels only once weekly with great efforts of straining. She has been constipated throughout her entire life and has had infrequent motions usually every two to three days. Abdominal pain in the right iliac fossa was a prominent complaint as well as vomiting.

Physical examination revealed a painful left and right iliac fossa. Per rectum examination revealed some degree of anismus and no stool in the rectal ampulla.

Full blood count, CRP and TSH were all normal.

Rectosigmoidoscopy was normal.

Physiology showed a threshold of perception of the intrarectally inflated balloon at 60cc while the urge to defecate was present at 80cc and the maximum tolerable volume was 100cc.The balloon was then filled with a watersoluble radio-opaque medium and an en-face and profil radiograph of the pelvis were taken.

Transit time showed

The patient was asked to describe verbally the shape of the intrarectal balloon that was filled with 60cc of air and then of Gastrografin. She described this as being a "round object" but when she was asked to draw the shape of what she had felt, she draw a clearly oval object, very similar to the radiological image.

As neither the drawing nor the radiological images were euclidean objects, it was decided to compare their fractal dimensions. These were 1,80 and 1,83 respectively.

References

1) H.A.Lampridis, Hrakleitos,Clio Editions,Patras,1996(greek)

2)B.B.Mandelbrot,The fractal geometry of nature,W.H.Freeman,1982

3)D'Arcy W.Thompson, On growth and form,2nd Ed., Cambridge UP,1963

4)A.P.Pentland,Fractal based description on natural scenes. IEEE Trans Pattern Anal Machine Intell 1984;PAMI-6:661-674

5)W Richards, A Polit. Texture Matching. Kybernetik 1974;16:155-162

6)JP Serra, Morphological Optics. J Microsc 1987;145:1-22

7)JP Rigaut. Fractal models in biological image analysis and vision.Acta Stereol 1990;9:37-52

Last edition of this page:11/10/05