Fractals and Iterated Function Systems in Medicine
11. Web sites involving fractals in medical research
Page contents: fractals in medicine
. . . Angiogenesis ___ Mammography ___ Melanoma
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My comments are in black. Plagiarized text is in maroon.
Web 90. Fractal Analysis of Trabecular Bone: University of Washington Department of Radiology. Trabecular bone has a branching pattern, as seen in this vertebral specimen. One can also see that it exhibits self-similarity. That is, the trabeculae and the marrow spaces between them look very similar no matter what their size. Estimating the Fractal Index of Bone. http://www.rad.washington.edu/exhibits/fractal.html An excellent site, referred to by many others. Clear intro to fractal geometry and its application to analysis of bone structure and osteoporosis.
Texture Analysis of Trabecular Bone in Radiographs: http://www.eur.nl/fgg/mi/annrep94/p_02.html Osteoporotic bone is not only characterized by a low bone density, but also by structural changes in the architecture. These changes in the three-dimensional structure are projected on the two-dimensional radiograph. The aim of this project is to describe, with the aid of computerized texture analysis methods, the structural changes occuring in bone due to osteoporosis. In the preceding year we focussed on statistical methods and techniques based on mathematical morphology. We found that the discriminative power of these techniques is as good as the bone mineral density.
At present we are investigating the suitability of fractal dimension for describing osteoporotic changes. The concept of fractals has been introduced by Mandelbrot. A true fractal structure is independent of scaling: at each different resolution the structure shows the same spatial properties. In the physical reality this usually is not an exact but a statistical similarity: the distributions of the spatial properties are similar. The main advantage of the fractal dimension is the independence of brightness and contrast in the image, so it is a true texture measure which also corresponds to a visually perceived notion of roughness.In the literature a variety of methods for estimating the fractal dimension of images has been described. It has been recognized that fractal dimensions computed by different methods do not necessarily correspond . . .
Quantitative diagnosis of osteoporosis optimised through computerised trabecular and cortical analysis: http://www.hoise.com/vmw/articles/LV-VM-05-98-2.html . . . Centre for Medical Diagnostic Systems and Visualisation (MeVis) at the University of Bremen has developed an automated procedure to calculate the fractal dimension of the trabecular bone in combination with the BMD values in the cortical shell. . . .
Thus, the Bremen team succeeds in a fairly precise diagnosis of the patient's level of osteoporosis combining fractal analysis of the trabecular structure with the structural analysis of the cortical shell. Please, check their web site for elucidating images and tables at the . . . See also:
. . . Osteoporosis Introduction: http://www.cevis.uni-bremen.de/MeVis/projects/osteoporosis/osteoporose.html . . . We propose an automated procedure based on the fractal analysis of the trabecular area by calculating the fractal dimension at various gray levels. It was found that this method allows an automated classification of the trabecular structure, which in combination with the measurement of the BMD may improve the quantitative diagnosis of osteoporosis. . . . A full presentation will be published in the British Journal of Radiology . . . Has images and diagrams.
OPTICS.ORG - Dental x-rays as screening tools for stroke, osteoporosis: http://optics.org/article/news/02/12/35
Two studies published in the December issue of the Journal of the American Dental Association (JADA) suggest that dental x-rays are effective screening tools for strokes and osteoporosis. One study, conducted by researchers at the Veterans Affairs Medical Center in Sepulvada, Calif., examined cepholometric x-rays of 1,063 healthy men between the ages 25 and 85 to determine if they revealed atherosclerotic lesions or blockage in the carotid artery that carries blood to the brain.
The V.A. researchers discovered that 2 percent of the subjects had blockages that were visible at the third and fourth cervical vertebrae, an area that is visible to dentists who use a cephalometric x-ray machine. This equipment is commonly used by orthodontists and oral and maxillofacial surgeons to evaluate the jaws and face for deformities.
"We found that using the pixel intensity and fractal dimension diagnosis of dental x-rays was just as effective as traditional diagnostic methods in measuring bone density," . . .
A fast method for calculation the fractal dimension of the brain: http://www.apnet.com/www/journal/hbm2000/6025.html
Cancer: Angiogenesis
Special Project Angiogenesis -- Cancer: http://www.med.unibs.it/~airc/cancer.html Accumulating evidences indicate that progressive tumor growth is dependent on angiogenesis. Most tumors in humans persist in situ for a long period of time (from months to years) in an avascular, quiescent status. In this phase the tumor may contain few million cells. When a subgroup of cells within the tumor switches to an angiogenic phenotype by changing the local equilibrium between positive and negative regulators of angiogenesis, tumor starts to grow rapidly and becomes clinically detectable. . . . Mathematical models have been developed to describe the tumor angiogenesis process. Fractal analysis of tumor vascular networks has indicated that the increase of the levels of diffusible angiogenesis growth factor(s) achieved by local release is a possible key determinant of the shape of the capillary networks. However, the same mathematical models have shown that also inhomogeneity of tumor extracellular microenvironment may play an important role. . . . Images.
Cancer: Mammography
Web 5060. Computer Aided Mammography. http://www.math.vt.edu/people/hoggard/FracGeomReport/node8.html#SECTION00021000000000000000 Since cancer growth is in some sense wild and unpredictable, we would expect cancerous masses to have a higher fractal dimension than benign masses.
Web 5064. Application of Fractal Dimension Analysis to Aspiration Cytologic Diagnosis of Breast Tumors: http://www.acta-cytol.com/Abs/IAC/IAC442.htm
APENN RESEARCH FRACTAL ANALYSIS OF BREAST CANCER: http://gwis2.circ.gwu.edu/~apenn/ I am Adjunct Professor of Mathematics and Engineering at The George Washington University. Breast Cancer diagnostic products using statistical fractal mathematics are being developed . . . Clinical application of MRI has been hampered by difficulty in determining which masses are benign and which are malignant. Our research has focused on developing robust fractal dimension estimates which will improve discrimination between benign and malignant breast masses. . . .
Cancer: Melanoma
Early Diagnosis of Malignant Melanoma Using Computer Assisted Image Analysis Techniques: http://www.bccrc.ca/ccr/tlee_melanoma.html (Which supercedes the previous URL address -- effective on or before 18 Sep 01 -- http://www.bccancer.bc.ca/research/ccr/people/tlee/melanoma.htm.) The goal of the project is to develop a diagnostically useful machine based on image processing and recognition algorithms for atypical melanocytic lesions. Since 1994, a weekly imaging collection session has been held in the Pigmented Lesion Clinic of the Division of Dermatology, the University of British Columbia and Vancouver Hospital to digitize moles under a controlled environment. Patients were first screened by a dermatologist. Any abnormal lesions were marked and the clinical symptoms were scored. Before the lesions were excised and biopsied, An RGB colour image was obtained by a hand-held video microscopy camera, . . .
Currently, we are working on feature extraction algorithms. The lesion border irregularity is modelled using fractal dimensions. Other features have also been studied. Once all the features are extracted, they are used to design a classifier for normal and atypical lesions. . . .
Skin Cancer Image Recognition System: http://www.dcs.lancs.ac.uk/dept/projects/sandrews.html . . . The heuristic seeks to quantify the basic characteristics delineated by the lesion, its geometric profile, coloration, its boundary interface condition, and whether the lesion had change shape. The heuristic is described by the mnemonic, 'ABCD'. The system developed as part of the research has two levels of application, the first to operate within the context of a General Practitioner Practice, and the other for a General Hospital Dermatology Department. We have applied both hard (production rules) and soft decision logic (fuzzy logic) in the context of a semi-automatic diagnosis system. In a further system which is fully automatic this uses a mix of neural network and soft decision process to perform analysis, recognition and diagnosis of the lesion presented. . . . The definition of the diagram is encoded using fractal encoding.
Web 5080. A Biological Application of Fractal Analysis on the World Wide Web: http://www.csu.edu.au/ci/vol03/complxb5/complxb5.html. Cat retinal ganglion cells were analysed using both the mass-radius (MR) and the cumulative intersection (CI) method incorporated in Fractop. There was no significant difference found between alpha and beta cells. However, using the criterion that a 0.06 difference in the fractal dimension between cell groups constitutes a different cell type, the alpha and beta cells can be separated into two groups.
FRACTAL PATTERNS INSIDE CELLS CAN REVEAL BREAST CANCER: http://www.aip.org/enews/physnews/1998/split/pnu353-1.htm The American Institute of Physics, January 5, 1998. Pathologists must traditionally detect breast cancer through subjective means by studying individual cells from suspicious tissue and checking for abnormal-looking cell shapes and features. Analyzing images of actual breast cells, the Mount Sinai researchers have looked within the cell nucleus to study the distribution of chromatin, DNA-protein compounds which contain the chromosomes in a cell. Like many other biological structures in nature, chromatin forms a fractal pattern; that is, the arrangement of chromatin looks similar over a range of size scales. . . . the researchers correctly diagnosed 39 out of 41 cases . . . by measuring differences in lacunarity (the largeness of gaps between chromatin regions in the nucleus) and by detecting differences in fractal dimension (which describes how fully a fractal object fills up the space that it occupies) between benign and malignant cells.
Fractals In the Biological Sciences: http://www.poignance.com/math/fractals/Fractbio/Fractbio.html Fractals in Biological Systems.
http--www.cs.rug.nl-~michael-nonlin96.pdf: http://www.cs.rug.nl/~michael/nonlin96.pdf Nonlinear Dynamics, Chaos-theory, and the "Sciences of Complexity": Their Relevance to the Study of the Interaction between Host and Microflora
G. Landini - WWW Homepage: http://web.bham.ac.uk/G.Landini/home.htm I work at the Oral Pathology Unit, School of Dentistry, The University of Birmingham, England, U.K. My research interests are Digital Image Analysis and Fractal Geometry applied to Biomedical problems. Some areas in which I have applied Fractal principles to gather information regarding morphological complexity include: Quantification of tumour shape, Nuclear pleomorphism in squamous cell carcinomas, Computer modelling of periodontal breakdown in periodontal disease, Analysis of retinal angiography, Analysis and modelling of Herpes Simplex virus spread in epithelium, Analysis and modelling of parenchyma organisation (mosaic patterns) in chimaeric animals, Three dimensional structure of trabecular bone, Cell morphology in culture with Biomaterials. Research papers and many links.
Web 89. Universal template of life modeled. LOS ALAMOS, N.M. - In a fundamental way, whales are just . . . http://www.lanl.gov/external/news/releases/archive/97-029.html.
Fractals in Cardiology: http://www.sewanee.edu/Phy_Students/smithjs0/Fractals_in_Cardiology.html Excellent brief overview of fractals and the heart. "Yes, for all these years, we have been living with fractal arteries, not far from fractal river systems, draining fractal mountainscapes under fractal clouds, toward fractal coastlines." . . .
A snowflake in Vermont, the coastline of Italy, the Nile River: all of these share a characteristic that is very common in nature (Iannaccone 5). They all have geometric complexity (Iannaccone 5). In each of these fractal objects self-similarity exist (Iannaccone 5). "Self-similarity implies that looking at one part of the object offers the same information as looking at another part of the object" (Iannaccone 5). In biological systems fractal geometry abounds in many was comparable to that seen in physical systems. Self-similarity appears to be a property of the healthy function of the human cardiovascular system (Innaccone 250). This self-similarity appears at both the microscopic and macroscopic levels of observation (Iannaccone 250).
Fractal Geometry of the Heart
A number of cardiopulmonary structures have a fractal-like appearance (Iannaccone 251).
Examples of Fractals in Cardiovascular Physiology (Iannaccone 251).
I. Structural
A. Vascular: arterial and venous tress
B. Muscular:
1. Hierarchical organization of muscle bundles
2. Branching of certain intracardiac muscles
C. Electrical: His-Purkinje network
D. Connective tissue: chordae tendineae; aortic valve leaflets
II. Dynamical (1/f spectra)
A. Regulation of healthy heartbeat fluctuations
B. Regulation of healthy beat-to-beat blood pressure fluctuations
Excellent diagrams.
Conclusion: The consecpt of fractals may be useful in understanding spatial and temporal "structure" of the human heart. Fractal analysis can be used to examine time serices of the heart. Studying the different fractal structure of time series it may be possible to identify at-rick patients.
Fractal Mechanisms in Neural Control: http://reylab.bidmc.harvard.edu/tutorial/DFA/master.html Fractal Mechanisms in Neural Control: Human Heartbeat and Gait Dynamics in Health and Disease. By: Peng C-K, Hausdorff JM, Goldberger AL. Fractal mechanisms in neural control: Human heartbeat and gait dynamics in health and disease. In: Walleczek J, ed. Nonlinear Dynamics, Self-Organization, and Biomedicine. Cambridge: Cambridge University Press, 1999.
The following are some extracts from this detailed and well-written paper.
Clinical diagnosis and basic investigations are critically dependent on the ability to record and analyze physiologic signals. Examples include heart rate recordings of patients at high risk of sudden death (Fig. 1), electroencephalographic (EEG) recordings in epilepsy and other disorders, and fluctuations of hormone and other molecular signal messengers in neuroendocrine dynamics. However, the traditional bedside and laboratory analyses of these signals have not kept pace with major advances in technology that allow for recording and storage of massive datasets of continuously fluctuating signals. Surprisingly, although these typically complex signals have recently been shown to represent processes that are nonlinear, nonstationary, and nonequilibrium in nature, the tools to analyze such data often still assume linearity, stationarity, and equilibrium-like conditions. Such conventional techniques include analysis of means, standard deviations and other features of histograms, along with classical power spectrum analysis.
An exciting recent finding is that such complex datasets may contain hidden information, defined here as information not extractable with conventional methods of analysis. Such information promises to be of clinical value (forecasting sudden cardiac death in ambulatory patients, or cardiopulmonary catastrophes during surgical procedures), as well as to relate to basic mechanisms of healthy and pathologic function. Fractal analysis is one of the most promising new approaches for extracting such hidden information from physiologic time series. This is partly due to the fact that the absence of characteristic temporal (or spatial) scales -- the hallmark of fractal behavior -- may confer important biological advantages, related to the adaptability of response . . .
In this chapter, we present some recent progress in applying fractal analysis to human physiology. We begin with a definition of fractal dynamics, followed by an introduction to some special problems posed by physiological time series. We then discuss the analysis of the output from two model systems: (1) human heartbeat regulation, which is under involuntary (neuroautonomic) control; and (2) human gait regulation (in walking), which is under the voluntary control of the central nervous system. We focus on the analysis of the output of these two systems in health and disease. . . .
Important diagrams: beat-to-beat analysis of heart rate in health and disease.
Conclusion: Note the highly nonstationary and ``noisy'' appearance of the healthy variability which is related in part to fractal (scale-free) dynamics. In contrast, pathologic states may be associated with the emergence of periodic oscillations, indicating the emergence of a characteristic time scale.
In other words, the beats of a healthy heart are not regular, but are irregular and fractal, contrary to much "accepted wisdom".
Nonlinear Dynamics for Clinicians: http://www.physionet.org/tutorials/ndc/ Nonlinear Dynamics, Fractals, and Chaos Theory: Implications for Neuroautonomic Heart Rate Control in Health and Disease
Figure 1. Two heart rate time series, one from a healthy subject (top) and the other from a patient with severe congestive heart failure (CHF) (middle) have nearly identical means and variances (bottom), yet very different dynamics. Note that according to classical physiological paradigms based on homeostasis, neuroautonomic control systems should be designed to damp out noise and settle down to a constant equilibrium-like state. However, the healthy heartbeat displays highly complex, apparently unpredictable fluctuations even under steady-state conditions. In contrast, the heart rate pattern from the subject with heart failure shows slow, periodic oscillations that correlate with Cheyne-Stokes breathing.
Excellent article, with detailed diagrams and theory.
http--polymer.bu.edu-~amaral-Papers-physa99c.pdf: http://polymer.bu.edu/~amaral/Papers/physa99c.pdf Application of statistical physics to heartbeat diagnosis. Long-range correlations in heartbeat time series, and multifractal features in heartbeat rythm. . . . Very technical paper, but with practical applicability to diagnosis and understanding. It also correlates increasing regularity with declining health.
Circadian Rhythmic Fractal Scaling of Heart Rate Variability in Health and Coronary Artery Disease: http://www.clinicalcardiology.org/briefs/9707briefs/cc20-631.html Clin Cardiol. 1997 Jul; 20(7): 631-638. Using 24-h Holter records, phase space plots and correlation dimensions were obtained for the RR intervals in 11 healthy controls and 10 patients with coronary artery disease. A circadian rhythm peaking during the night is demonstrated for the correlation dimension in clinical health. In patients with coronary artery disease, the correlation dimension is reduced and an approximately 12-h (circasemidian) component is needed to describe the pattern.
Music of the Heart: http://polymer.bu.edu/music/ The Music of the Heart is derived from electrocardiogram (ECG) data, actual digital recordings of the electrical signals of the human heart. These HeartSongs began as musical notes mapped from the heartbeat data. The composer then added harmonies and rhythm to make pleasant sounding music. A complete set of over 20 recordings can be found . . .
There is also a hands-on exhibit at the Boston Museum of Science which allows museum-goers to record their own electrocardiogram and, in real time, listen to the music it produces. This 'heart music' created by museum-goers is different from the HeartSongs above which were 'interpreted' by a composer (i.e., chords and rhythm was added by the composer on top of the melody created from the data). Heart music you would hear at the museum exhibit which is based solely on the raw data . . .
While your pulse may feel perfectly regular, you actually have a great deal of subtle variability from one beat to the next. These fluctuations are produced by the normal functioning of the involuntary nervous system, which can cause your heart to slow down or speed up. The normal heartbeat, therefore, does not follow a metronomic or march-like beat---suprisingly, it has a dance-like plasticity and variability.
KurzweilAI.net: http://www.kurzweilai.net/news/frame.html?main=news_single.html?id%3D933
Artificial liver uses 3-D modeling KurzweilAI.net, April 25, 2002
Researchers believe they have solved the problem of growing the complex networks of blood vessels that artificial organs would need to sustain themselves within the body.
The idea, so far tested in
rats, involves copying the blood vessel network of a real liver and using 3D fractal computer modelling and
machining to mimic its construction.
The scientists use the model to construct a silicon-mould scaffold. They then pump a solution of
endothelial cells into empty channels in the scaffold, where they
stick to the walls and grow in a nutrient to form a network of blood vessels
within the scaffold, which itself dissolves over a few months,
leaving behind a functioning liver.
The researchers are Jay Vacanti at Massachusetts
General Hospital in Boston, a transplant surgeon who grew a human ear from
cartilage cells on the back of a mouse in 1997, and Jeffrey Borenstein at
Draper Lab, a micro-engineering expert.
New Scientist, April 27, 2002
Web 91. The death of our son Seth Speken: http://www.med-malpractice.com/howto.htm. Use of fractal compression (ISI FIFs) to show detailed medical images. In support of malpractice suit by Dr. Ralph Speken, M.D., in the death in hospital of his son Seth. For more details about this site and a related one, see: Homepage.
End of part M01 of M01 of section 11.
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