The application of structural entropy in tissue based diagnosis
Background: Entropy belongs to the few basic measurable entities in nature. It measures the distance of a closed or open ‘statistical’ system from its present stage to its final stage, and analyzes the probability distribution of the included elements, independently from their meaning. The development can be predicted by use of an ‘ideal transformation’, i.e. additive formula (for example Shannon’s entropy) or by mathematical derivatives such as the more generalized q – entropy, for example Tsallis entropy. Herein, the internal structures of the system are described which include so – called macro – systems. They are created by individual elements or basic micro – systems, and transformed into essentials of tissue – based diagnosis.
Entropy and neighborhood: The basic entropy approaches consider a spatially force – independent system, i.e., the calculation of the elements’ probability distribution does not take into account the formation of macro – systems, or the position of the individual elements within the system or between individual elements. The receiver of an informative signal cannot distinguish whether it has been generated in the center or at the boundary of the system. Only the signal’s probability within the information chain and the formation of the chain are informative.
However, neighborhood plays an important role in development, maturation, degradation, and dissolution of biological systems. Most cells are generated by cellular division and neighboring cells are more similar in morphology and function than non-neighboring cells. This observation also holds true for ‘higher order’ biological systems such as animal colonies, forests, or even human societies. Thus, a potentially successful approach of estimating the development of a biological system should include neighborhood definitions and considerations.
Neighborhood conditioned (MST) entropy and entropy flow:
Any definition of a neighborhood condition is based upon the distances between different elements, called objects. The distances can be weighted by additional object features, might be ‘directed’, or might include certain ‘shadow’ conditions (hidden behind another object). The most frequently used algorithm has been introduced by Voronoi in 1902. It can be successfully formulated in graph theory and derived approaches. In microscopic morphology, the construction of weighted minimum spanning trees (MST) is a convincing approach.
Living biological systems are open and not closed. They exchange energy, information, and directives for future development with their environment. They have to stabilize their own entropy level against that of their environment. The mandatory entropy exchange or entropy flow from the individual element into its environment or vice versa reflects to the system’s stability and impact on its environment.
Tissue – based diagnosis and entropy:
Tissue – based diagnosis includes all technical procedures to ascertain a ‘medical diagnosis’, such as microscopic, electron microscopic investigations, gene analysis, proteomics, syntactic structure analysis, liquid biopsies, etc. Herein, the transformation and applicability of the entropy approach are described and discussed.
2. Kayser K. Digital Lung Pathology. Berlin Heidelberg New York: Springer; 1991.
3. Kayser K, Borkenfeld S, Carvalho R, Kayser G. Structure, Function, and Predictive Diagnosis Algorithms. Diagnostic Pathology; 2016. 8.
4. Kayser K, Gabius HJ. Graph theory and the entropy concept in histochemistry. Theoretical considerations, application in histopathology and the combination with receptor-specific approaches. Prog Histochem Cytochem; 1997. 32(2): 1-106.
5. Kayser K, Hoffgen H. Pattern recognition in histopathology by orders of textures. Med Inform (Lond). 1984; 9(1): 55-9.
6. Gabius HJ, Roth J. An introduction to the sugar code. Histochem Cell Biol. 2017; 147(2): 111-117.
7. Kaltner H, Toegel S, Caballero GG, Manning JC, Ledeen RW, Gabius HJ. Galectins- their network and roles in immunity tumor growth control. Histochem Cell Biol. 2017; 147(2): 239-256.
8. Toegel S, Bieder D, Andre S, Altmann F, Walzer SM, Kaltner H, Hofstaetter JG, Windhager R, Gabius HJ. Glycophenotyping of osteoarthritic cartilage and chondrocytes by RT-qPCR, mass spectrometry, histochemistry with plant/human lectins and lectin localization with a glycoprotein. Arthritis Res Ther. 2013; 15(5): 147.
9. Evans P, Wolf B. Collaboration rules. Harv Bus Rev. 2005; 83(7): 96-104.
10. Kayser K. Quantification of virtual slides: Approaches to analysis of content-based image information. J Pathol Inform. 2011; 2: 2.
11. Kayser K, Borkenfeld S, Goldmann T, Kayser G. To be at the right place at the right time. Diagn Pathol. 2011; 6: 2-9.
12. Kayser K, Görtler J, Giesel F, Kayser G. How to implement grid technology in tissue-based diagnosis: diagnostic surgical pathology. Expert Opin Med Diagn. 2008; 2(3): 323-337.
13. Anza F, Vedral V. Information-theoretic equilibrium and observable thermalization. Sci Rep. 2017; 7: 44066.
14. Bailey K. Sociocybernetics and social entropy theory. Kybernetics. 2006; 35: 375-384.
15. Kayser K, Gabius HJ. The application of thermodynamic principles to histochemical and morphometric tissue research: principles and practical outline with focus on the glycosciences. Cell Tissue Res. 1999; 296(3): 443-55.
16. Kayser K, Hufnagl P, Kayser G, Zink S. Stratified sampling: Basic ideas and application in pathology. Elec J Pathol Histol. 1999; 5: 994-06.
17. Kayser K, Borkenfeld S, Carvalho R, Djenouni A, Kayser G. How to analyze Structure and Function in Tissue – based Diagnosis?. Diagnostic Pathology. 2016; 2.
18. Kayser K, Kayser G, Hufnagl P. The concept of structural entropy: basic idea and applications. Elec J Pathol Histol. 2002; 8: 024-06.
19. Kayser K, Hoshang SA, Metze K, Goldmann T, Vollmer E, Radziszowski D, Kosjerina Z, Mireskandari M, Kayser G. Texture- and object-related automated information analysis in histological still images of various organs. Anal Quant Cytol Histol. 2008; 30(6): 323-35.
20. Kayser K, Kayser G, Metze K. The concept of structural entropy in tissue based diagnosis. AQCH, 2007; 29(5): 296-308.
21. Pincus SM. Approximate entropy as a measure of system complexity. Proc Natl Acad Sci U S A. 1991; 88(6): 2297-2301.
22. Shannon C. A mathematical theory of communication. The Bell System Technical Journal. 1948; 27(3): 379-423.
23. Eigen M. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften. 1971; 58: 465-523.
24. Gibbs J. Elementary Principles in statistical Mechanics developed with especial reference to the rational. Foundation of Thermodynamics. New York: Yale University Press; 1902.
25. Tsallis C. Entropic nonextensivity: a possible measure of complexity. Chaos, Solitons and Fractals. 2002; 13: 371-391.
26. Gunduz G, Gunduz U. The mathematical analysis of the structure of some songs. Physica A. 2005; 357: 565-592.
27. Zhang Y, Yang Z, Li W. Analyses of urban ecosystem based on information entropy. Ecological Modelling. 2006; 197: 1-12.
28. Fradkov AL. Horizons of cybernetical physics. Philos Trans A Math Phys Eng Sci. 2006; 375:2088.
29. Souza AM, Nobre FD. Thermodynamic framework for the ground state of a simple quantum system. Phys Rev E. 2017; 95(1-1): 012111.
30. Beretta GP. Steepest entropy ascent model for far-nonequilibrium thermodynamics: unified implementation of the maximum entropy production principle. Phys Rev E Stat Nonlin Soft Matter Phys. 2014; 90(4): 042113.
31. Voß K. Entropie als statistisches Strukturmaß. Wiss Z Techn Univs Dresden. 1970; 19: 1415-1419.
32. Krige DG, Rand DS. Some basic considerations in the application of geostatistics to the valuation of ore in South African gold mines. J South Afr Inst Min Metal. 1976; 77: 383-391.
33. van Diest PJ, Kayser K, Meijer GA, Baak JP. Syntactic structure analysis. Pathologica, 1995; 87(3): 255-62.
34. Diosi L, Feldmann T, Kosloff R. On the exact identity between thermodynamic and informatic entropies in a unitary model of friction. Int J Quantum Information. 2006; 4: 99-104.
35. Naudts J. Generalized thermostatistics based on deformed exponential and logarithmic functions. Physica A,.2004; 340: 32-40.
36. Kayser K, Molnar B, Weinstein R. Virtual Microscopy: Fundamentals, Applications, Perspectives of Electronic Tissue-based Diagnosis. Berlin: VSV Interdisciplinary Medical Publishing; 2006.
37. Kayser K, Stute H, Bubenzer J, Paul J. , Combined morphometrical and syntactic structure analysis as tools for histomorphological insight into human lung carcinoma growth. Anal Cell Pathol. 1990; 2(3): 167-78.
38. Voß K, Süße H. Praktische Bildverarbeitung. München, Wien: Carl Hanser Verlag; 1991.
39. Kayser K, Stute H, Tacke M. Minimum spanning tree, integrated optical density and lymph node metastasis in bronchial carcinoma. Anal Cell Pathol. 1993; 5(4): 225-34.
40. Hu X, Wu DD. Data mining and predictive modeling of biomolecular network from biomedical literature databases. IEEE/ACM Trans Comput Biol Bioinform. 2007; 4(2): 251-63.
41. Springelkamp H, Mishra A, Hysi PG, Gharahkhani P, Höhn R, Khor CC, Cooke Bailey JN, Luo X, Ramdas WD, Vithana E, Koh V, Yazar S, Xu L, Forward H,Kearns LS, Amin N, Iglesias AI, Sim KS, van Leeuwen EM, Demirkan A, van der Lee S, Loon SC, Rivadeneira F, Nag A, Sanfilippo PG, Schillert A, de Jong PT, Oostra BA, Uitterlinden AG, Hofman A; NEIGHBORHOOD Consortium, Zhou T, Burdon KP, Spector TD, Lackner KJ, Saw SM, Vingerling JR, Teo YY,Pasquale LR, Wolfs RC, Lemij HG, Tai ES, Jonas JB, Cheng CY, Aung T, Jansonius NM, Klaver CC, Craig JE, Young TL, Haines JL, MacGregor S, Mackey DA, Pfeiffer N, Wong TY, Wiggs JL, Hewitt AW, van Duijn CM, Hammond CJ. Meta-analysis of genome-wide association studies identifies novel loci that influence cupping and the glaucomatous process. Nat Commun. 2015; 5: 4883.
42. O'Callaghan JF. An alternative definition for neighborhood of a point. IEEE Trans Comput. 1975; 24: 1121-1125.
43. Zahn CT. Graph-theoretical methods for detecting and describing Gestalt clusters. IEEE Trans Comput. 1971; 20: 68-86.
44. Prewitt JMS, Wu SC. An application of pattern recognition to epithelial tissues. Computer Applications in Medical Care. Int: IEEE Computer Society; 1978.
45. Voronoi G. Nouvelles applications des parametres continus a la theorie des formes quadratiques, deuxieme memoire: recherches sur les paralleloedres primitifs. J Reine Angew Math. 1902; 134: 188-287.
46. Kayser K, Radziszowski D, Bzdyl P, Sommer R, Kayser G. Digitized pathology: theory and experiences in automated tissue-based virtual diagnosis. Rom J Morphol Embryol. 2006; 47(1): 21-8.
47. Kayser G, Kayser K. Quantitative pathology in virtual microscopy: history, applications, perspectives. Acta Histochem. 2013; 115(6): 527-32.
48. Kayser G, Baumhakel JD, Szoke T, Trojan I, Riede U, Werner M, Kayser K. Vascular diffusion density and survival of patients with primary lung carcinomas. Virchows Arch. 2003; 442(5): 462-7.
49. Kayser K, Kayser C, Rahn W, Bovin NV, Gabius HJ. Carcinoid tumors of the lung: immuno- and ligandohistochemistry, analysis of integrated optical density, syntactic structure analysis, clinical data, and prognosis of patients treated surgically. J Surg Oncol. 1996; 63(2): 99-106.
50. Kayser K, Zink S, Andre S, Schuring MP, Hecker E, Klar E, Bovin NV, Kaltner H, Gabius HJ. Primary colorectal carcinomas and their intrapulmonary metastases: clinical, glyco-, immuno- and lectin histochemical, nuclear and syntactic structure analysis with emphasis on correlation with period of occurrence of metastases and survival. APMIS. 2002; 110(6): 435-46.
51. Weyn B, Tjalma W, Van De Wouwer G, Van Daele A, Scheunders P, Jacob W, Van Marck E. Validation of nuclear texture, density, morphometry and tissue syntactic structure analysis as prognosticators of cervical carcinoma. Anal Quant Cytol Histol. 2000; 22(5): 373-82.
52. Becker RL Jr. Standardization and quality control of quantitative microscopy in pathology. J Cell Biochem Suppl. 1993; 17: 199-204.
53. Haroske G, Dimmer V, Meyer W, Kunze KD. DNA histogram interpretation based on statistical approaches. Anal Cell Pathol. 1997; 15(3): 157-73.
54. Haroske G, Meyer W, Theissig F, Schubert K, Kunze KD. Remote quantitation server for quality assurance in DNA ploidy analysis. Anal Quant Cytol Histol. 1998; 20(4): 302-12.
55. Kayser K. Analytical Lung Pathology. Heidelberg, New York: Springer; 1992.
56. Görtler J, Kayser K, Borkenfeld S, Carvalho R, Kayser G. Cognitive Algorithms and digitized Tissue – based Diagnosis. Diagnostic Pathology. 2017; 3(1): 248.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this journal agree to the following terms:
1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
4. In case of virtual slide publication the authors agree to copy the article in a structural modified version to the journal's VS archive.