Recent Progress of Research and Applications of Fractal and Its Theories in Medicine_Journal of Biomedical Engineering

Authors：

CAICongbo ,  WANGPing

Department of Anatomy and Histology, Medical School, Ningbo University, Ningbo 315211, China;

Corresponding author：

WANGPing, Email: pinoav@hotmail.com

Keywords：

fractal; fractal surface; bionic; fractal dimension; medical application

DOI：

10.7507/1001-5515.20140218

Video：

Export PDF Favorites Scan Get Citation

Abstract Full text Figures/Tables Video References Cited by

Fractal, a mathematics concept, is used to describe an image of self-similarity and scale invariance. Some organisms have been discovered with the fractal characteristics, such as cerebral cortex surface, retinal vessel structure, cardiovascular network, and trabecular bone, etc. It has been preliminarily confirmed that the three-dimensional structure of cells cultured in vitro could be significantly enhanced by bionic fractal surface. Moreover, fractal theory in clinical research will help early diagnosis and treatment of diseases, reducing the patient's pain and suffering. The development process of diseases in the human body can be expressed by the fractal theories parameter. It is of considerable significance to retrospectively review the preparation and application of fractal surface and its diagnostic value in medicine. This paper gives an application of fractal and its theories in the medical science, based on the research achievements in our laboratory.

Citation： CAICongbo, WANGPing. Recent Progress of Research and Applications of Fractal and Its Theories in Medicine. Journal of Biomedical Engineering, 2014, 31(5): 1155-1159. doi: 10.7507/1001-5515.20140218 Copy

1.	BIZZARRI M, PASQUALATO A, CUCINA A, et al. Physical forces and non linear dynamics mould fractal cell shape: quantitative morphological parameters and cell phenotype[J]. Histol Histopathol, 2013, 28(2): 155-174.
2.	HUANG Z, PAN J, CHEN G, et al. Fractal analysis of two-photon microscopic images for diagnosis of nasopharyngeal cancer[J]. Scanning, 2012, 34(6): 399-403.
3.	ESTEBAN FJ, PADILLA N, SANZ-CORTÉS M, et al. Fractal-dimension analysis detects cerebral changes in preterm infants with and without intrauterine growth restriction[J]. Neuroimage, 2010, 53(4): 1225-1232.
4.	NITYANANDAM A, PARTHASARATHY S, TARABYKIN V. Postnatal subventricular zone of the neocortex contributes GFAP+ cells to the rostral migratory stream under the control of Sip1[J]. Dev Biol, 2012, 366(2): 341-356.
5.	HAITAO S, NING L, LIJUN G, et al. Fractal dimension analysis of MDCT images for quantifying the morphological changes of the pulmonary artery tree in patients with pulmonary hypertension[J]. Korean J Radiol, 2011, 12(3): 289-296.
6.	CYMBERKNOP L J, LEGNANI W, BARRA J G, et al. Fractal dimension as an index of left ventricular ischaemia: a pilot study[J]. Physiol Meas, 2013, 34(1): 83-97.
7.	SANGHERA B, BANERJEE D, KHAN A, et al. Reproducibility of 2D and 3D fractal analysis techniques for the assessment of spatial heterogeneity of regional blood flow in rectal cancer[J]. Radiology, 2012, 263(3): 865-873.
8.	VASILESCU C, GIZA D E, PETRISOR P, et al. Morphometrical differences between resectable and non-resectable pancreatic cancer: a fractal analysis[J]. Hepatogastroenterology, 2012, 59(113): 284-288.
9.	AMER M E, HEO M S, BROOKS S L, et al. Anatomical variations of trabecular bone structure in intraoral radiographs using fractal and particles count analyses[J]. Imaging Sci Dent, 2012, 42(1): 5-12.
10.	ALBERICH-BAYARRI A, MARTI-BONMATI L, ANGELES PÉREZ M, et al. Assessment of 2D and 3D fractal dimension measurements of trabecular bone from high-spatial resolution magnetic resonance images at 3 T[J]. Med Phys, 2010, 37(9): 4930-4937.
11.	MENG Z, HASHMI SM, ELIMELECH M. Aggregation rate and fractal dimension of fullerene nanoparticles via simultaneous multiangle static and dynamic light scattering measurement[J]. J Colloid Interface Sci, 2013, 392: 27-33.
12.	SHIBUICHI S, ONDA T, SATOH N, et al. Super water- and Oil-Repellent surfaces resulting from fractal structure[J]. J Colloid Interface Sci, 1998, 208(1): 287-294.
13.	FANG W, MAYAMA H, TSUJII K. Spontaneous formation of fractal structures on triglyceride surfaces with reference to their super water-repellent properties[J]. J Phys Chem B, 2007, 111(3): 564-571.
14.	QIAN A R, LI D, HAN J, et al. Fractal dimension as a measure of altered actin cytoskeleton in MC3T3-E1 cells under simulated microgravity using 3-D/2-D clinostats[J]. IEEE Trans Biomed Eng, 2012, 59(5): 1374-1380.
15.	FERNÁNDEZ E, JELINEK H F. Use of fractal theory in neuroscience: methods, advantages, and potential problems[J]. Methods, 2001, 24(4): 309-321.
16.	王萍,王仁芳,方文军.粗糙表面对神经胶质细胞三维立体形状的影响[J].中国生物医学工程学报,2009,28(2):280-284.
17.	SOFRONIEW M V. Transgenic techniques for cell ablation or molecular deletion to investigate functions of astrocytes and other GFAP-expressing cell types[J]. Methods Mol Biol, 2012, 814: 531-544.
18.	MENDONÇA J E, VILELA M C, BITTENCOURT H, et al. GFAP expression in astrocytes of suprachiasmatic nucleus and medial preoptic area are differentially affected by malnutrition during rat brain development[J]. Nutr Neurosci, 2004, 7(4): 223-234.
19.	CHEKHONIN V P, BAKLAUSHEV V P, YUSUBALIEVA G M, et al. Targeted delivery of liposomal nanocontainers to the peritumoral zone of glioma by means of monoclonal antibodies against GFAP and the extracellular loop of Cx43[J]. Nanomedicine, 2012, 8(1): 63-70.
20.	WANG P, LI L, ZHANG C, et al. Effects of fractal surface on C6 glioma cell morphogenesis and differentiation in vitro[J]. Biomaterials, 2010, 31(24): 6201-6206.
21.	REISHOFER G, KOSCHUTNIG K, ENZINGER C, et al. Fractal dimension and vessel complexity in patients with cerebral arteriovenous malformations[J]. PLoS One, 2012, 7(7): e41148.
22.	KING R D, GEORGE A T, JEON T, et al. Characterization of atrophic changes in the cerebral cortex using fractal dimensional analysis[J]. Brain Imaging Behav, 2009, 3(2): 154-166.
23.	SNG C C, SABANAYAGAM C, Lamoureux EL, et al. Fractal analysis of the retinal vasculature and chronic kidney disease[J]. Nephrol Dial Transplant, 2010, 25(7): 2252-2258.
24.	CHEUNG C Y, THOMAS G N, TAY W, et al. Retinal vascular fractal dimension and its relationship with cardiovascular and ocular risk factors[J]. Am J Ophthalmol, 2012, 154(4): 663-674.
25.	LIEW G, MITCHELL P, ROCHTCHINA E, et al. Fractal analysis of retinal microvasculature and coronary heart disease mortality[J]. Eur Heart J, 2011, 32(4): 422-429.
26.	RANGAYYAN R M, OLOUMI F, NGUYEN T M. Fractal analysis of contours of breast masses in mammograms via the power spectra of their signatures[J]. Conf Proc IEEE Eng Med Biol Soc, 2010,10(2): 6737-6740.
27.	FUSELER J W, BEDENBAUGH A, YEKKALA K, et al. Fractal and image analysis of the microvasculature in normal intestinal submucosa and intestinal polyps in Apc(Min/+) mice[J]. Microsc Microanal, 2010, 16(1): 73-79.
28.	RAGUSO G, ANCONA A, CHIEPPA L, et al. Application of fractal analysis to mammography[J].Conf Proc IEEE Eng Med Biol Soc, 2010,10(2): 3182-3185.
29.	KOH K J, PARK H N, KIM K A. Prediction of age-related osteoporosis using fractal analysis on panoramic radiographs[J]. Imaging Sci Dent, 2012, 42(4): 231-235.
30.	ALMAN A C, JOHNSON L R, CALVERLEY D C, et al. Diagnostic capabilities of fractal dimension and mandibular cortical width to identify men and women with decreased bone mineral density[J]. Osteoporos Int, 2012, 23(5): 1631-1636.
31.	MILOVANOVIC P, DJURIC M, RAKOCEVIC Z. Age-dependence of power spectral density and fractal dimension of bone mineralized matrix in atomic force microscope topography images: potential correlates of bone tissue age and bone fragility in female femoral neck trabeculae[J]. J Anat, 2012, 221(5): 427-433.

1. BIZZARRI M, PASQUALATO A, CUCINA A, et al. Physical forces and non linear dynamics mould fractal cell shape: quantitative morphological parameters and cell phenotype[J]. Histol Histopathol, 2013, 28(2): 155-174.
2. HUANG Z, PAN J, CHEN G, et al. Fractal analysis of two-photon microscopic images for diagnosis of nasopharyngeal cancer[J]. Scanning, 2012, 34(6): 399-403.
3. ESTEBAN FJ, PADILLA N, SANZ-CORTÉS M, et al. Fractal-dimension analysis detects cerebral changes in preterm infants with and without intrauterine growth restriction[J]. Neuroimage, 2010, 53(4): 1225-1232.
4. NITYANANDAM A, PARTHASARATHY S, TARABYKIN V. Postnatal subventricular zone of the neocortex contributes GFAP+ cells to the rostral migratory stream under the control of Sip1[J]. Dev Biol, 2012, 366(2): 341-356.
5. HAITAO S, NING L, LIJUN G, et al. Fractal dimension analysis of MDCT images for quantifying the morphological changes of the pulmonary artery tree in patients with pulmonary hypertension[J]. Korean J Radiol, 2011, 12(3): 289-296.
6. CYMBERKNOP L J, LEGNANI W, BARRA J G, et al. Fractal dimension as an index of left ventricular ischaemia: a pilot study[J]. Physiol Meas, 2013, 34(1): 83-97.
7. SANGHERA B, BANERJEE D, KHAN A, et al. Reproducibility of 2D and 3D fractal analysis techniques for the assessment of spatial heterogeneity of regional blood flow in rectal cancer[J]. Radiology, 2012, 263(3): 865-873.
8. VASILESCU C, GIZA D E, PETRISOR P, et al. Morphometrical differences between resectable and non-resectable pancreatic cancer: a fractal analysis[J]. Hepatogastroenterology, 2012, 59(113): 284-288.
9. AMER M E, HEO M S, BROOKS S L, et al. Anatomical variations of trabecular bone structure in intraoral radiographs using fractal and particles count analyses[J]. Imaging Sci Dent, 2012, 42(1): 5-12.
10. ALBERICH-BAYARRI A, MARTI-BONMATI L, ANGELES PÉREZ M, et al. Assessment of 2D and 3D fractal dimension measurements of trabecular bone from high-spatial resolution magnetic resonance images at 3 T[J]. Med Phys, 2010, 37(9): 4930-4937.
11. MENG Z, HASHMI SM, ELIMELECH M. Aggregation rate and fractal dimension of fullerene nanoparticles via simultaneous multiangle static and dynamic light scattering measurement[J]. J Colloid Interface Sci, 2013, 392: 27-33.
12. SHIBUICHI S, ONDA T, SATOH N, et al. Super water- and Oil-Repellent surfaces resulting from fractal structure[J]. J Colloid Interface Sci, 1998, 208(1): 287-294.
13. FANG W, MAYAMA H, TSUJII K. Spontaneous formation of fractal structures on triglyceride surfaces with reference to their super water-repellent properties[J]. J Phys Chem B, 2007, 111(3): 564-571.
14. QIAN A R, LI D, HAN J, et al. Fractal dimension as a measure of altered actin cytoskeleton in MC3T3-E1 cells under simulated microgravity using 3-D/2-D clinostats[J]. IEEE Trans Biomed Eng, 2012, 59(5): 1374-1380.
15. FERNÁNDEZ E, JELINEK H F. Use of fractal theory in neuroscience: methods, advantages, and potential problems[J]. Methods, 2001, 24(4): 309-321.
16. 王萍,王仁芳,方文军.粗糙表面对神经胶质细胞三维立体形状的影响[J].中国生物医学工程学报,2009,28(2):280-284.
17. SOFRONIEW M V. Transgenic techniques for cell ablation or molecular deletion to investigate functions of astrocytes and other GFAP-expressing cell types[J]. Methods Mol Biol, 2012, 814: 531-544.
18. MENDONÇA J E, VILELA M C, BITTENCOURT H, et al. GFAP expression in astrocytes of suprachiasmatic nucleus and medial preoptic area are differentially affected by malnutrition during rat brain development[J]. Nutr Neurosci, 2004, 7(4): 223-234.
19. CHEKHONIN V P, BAKLAUSHEV V P, YUSUBALIEVA G M, et al. Targeted delivery of liposomal nanocontainers to the peritumoral zone of glioma by means of monoclonal antibodies against GFAP and the extracellular loop of Cx43[J]. Nanomedicine, 2012, 8(1): 63-70.
20. WANG P, LI L, ZHANG C, et al. Effects of fractal surface on C6 glioma cell morphogenesis and differentiation in vitro[J]. Biomaterials, 2010, 31(24): 6201-6206.
21. REISHOFER G, KOSCHUTNIG K, ENZINGER C, et al. Fractal dimension and vessel complexity in patients with cerebral arteriovenous malformations[J]. PLoS One, 2012, 7(7): e41148.
22. KING R D, GEORGE A T, JEON T, et al. Characterization of atrophic changes in the cerebral cortex using fractal dimensional analysis[J]. Brain Imaging Behav, 2009, 3(2): 154-166.
23. SNG C C, SABANAYAGAM C, Lamoureux EL, et al. Fractal analysis of the retinal vasculature and chronic kidney disease[J]. Nephrol Dial Transplant, 2010, 25(7): 2252-2258.
24. CHEUNG C Y, THOMAS G N, TAY W, et al. Retinal vascular fractal dimension and its relationship with cardiovascular and ocular risk factors[J]. Am J Ophthalmol, 2012, 154(4): 663-674.
25. LIEW G, MITCHELL P, ROCHTCHINA E, et al. Fractal analysis of retinal microvasculature and coronary heart disease mortality[J]. Eur Heart J, 2011, 32(4): 422-429.
26. RANGAYYAN R M, OLOUMI F, NGUYEN T M. Fractal analysis of contours of breast masses in mammograms via the power spectra of their signatures[J]. Conf Proc IEEE Eng Med Biol Soc, 2010,10(2): 6737-6740.
27. FUSELER J W, BEDENBAUGH A, YEKKALA K, et al. Fractal and image analysis of the microvasculature in normal intestinal submucosa and intestinal polyps in Apc(Min/+) mice[J]. Microsc Microanal, 2010, 16(1): 73-79.
28. RAGUSO G, ANCONA A, CHIEPPA L, et al. Application of fractal analysis to mammography[J].Conf Proc IEEE Eng Med Biol Soc, 2010,10(2): 3182-3185.
29. KOH K J, PARK H N, KIM K A. Prediction of age-related osteoporosis using fractal analysis on panoramic radiographs[J]. Imaging Sci Dent, 2012, 42(4): 231-235.
30. ALMAN A C, JOHNSON L R, CALVERLEY D C, et al. Diagnostic capabilities of fractal dimension and mandibular cortical width to identify men and women with decreased bone mineral density[J]. Osteoporos Int, 2012, 23(5): 1631-1636.
31. MILOVANOVIC P, DJURIC M, RAKOCEVIC Z. Age-dependence of power spectral density and fractal dimension of bone mineralized matrix in atomic force microscope topography images: potential correlates of bone tissue age and bone fragility in female femoral neck trabeculae[J]. J Anat, 2012, 221(5): 427-433.

Journal of Biomedical Engineering

Recent Progress of Research and Applications of Fractal and Its Theories in Medicine

Abstract Full text Figures/Tables Video References Cited by

Previous Article

Next Article

Format

Content