The concept of entropy in histopathological diagnosis and targeted therapy

  • Klaus Kayser Charite - Berlin
  • Stephan Borkenfeld
  • Rita Carvalho
  • Gian Kayser



Targeted therapy has been developed to apply individual patient – specific drug regimes that are based upon specific bio-chemical intra-cellular pathways and usually related to cellular proliferation or apoptosis.

Entropy Definition and Concept 

Entropy is considered to be a physical entity similar to space and time. It quantifies the distribution of events and transport mechanisms in relation to the macrosystem for thermodynamic, chemical and biological processes which are analyzed by statistics, communication and information methods. It amounts the distance of a gross (macro) system from its final stage in heat theory; in biology the entropy flow measures its dynamics (distance from its environment) through the surface of an open macrosystem, for example of a society, an individual, an organ, a gene, cell, and others. A derivative of entropy is the so-called structural entropy that measures the distance of internal (enclosed) microstates in the macrosystem. It can be computed by quantification of internal (vascular) and external (outer) surfaces of solid tumors, and their proliferation.

Entropy and targeted Therapy 

The most frequently investigated pathways include onco and suppressor genes that display pathways with cellular surface receptors such as the epidermal growth factor receptor (EGFR), and others. The presence and signalling intensity of EFGR in a set of malignant tumors can be considered as microstate in a large compartment of the whole cancer (macrosystem). Thus entropy and structural entropy can measure and classify the internal dynamic structure of the investigated cancer and can be associated to the therapy response and patient’s survival.


The concept of entropy and structural entropy has been tested and applied on several cancer cell types including primary lung cancer and pulmonary metastases of colon cancer. The patients’ survival rates were closely associated with the corresponding entropies and entropy flows. These tests have been based upon visualization of proliferation (Ki-67). The extension of this entropy concept to be applied in targeted therapy of breast and lung cancer is under investigation.


The concept of conventional and structural entropy is a promising tool in search for understanding biological structures and their related functions, for  improved analysis of microstate dynamics in malignant tumors, and can serve for refinement of targeted therapy. 


Author Biography

Klaus Kayser, Charite - Berlin


1. Rakha, E.A., et al., HER2 testing in invasive breast cancer: should histological grade, type and oestrogen receptor status influence the decision to repeat testing? Histopathology, 2015. Accepted Article’, doi: 10.1111/his.12900.

2. Poulakaki, N., et al., Hormonal receptor status, Ki-67 and HER2 expression: Prognostic value in the recurrence of ductal carcinoma in situ of the breast? Breast, 2015. accepted article pii: S0960-9776(15)00232-5. doi: 10.1016/j.breast.2015.10.007.

3. Davis, J.E., et al., Her2 and Ki67 Biomarkers Predict Recurrence of Ductal Carcinoma in Situ. Appl Immunohistochem Mol Morphol, 2015. accepted publication: 2015 August PMID: 26317313.

4. Burrai, G.P., et al., Investigation of HER2 expression in canine mammary tumors by antibody-based, transcriptomic and mass spectrometry analysis: is the dog a suitable animal model for human breast cancer? Tumour Biol, 2015. appected publicaton: PMID: 26088453.

5. Spoerke, J.M., et al., Phosphoinositide 3-kinase (PI3K) pathway alterations are associated with histologic subtypes and are predictive of sensitivity to PI3K inhibitors in lung cancer preclinical models. Clin Cancer Res. 18(24): p. 6771-83.

6. Xu, J., et al., Targeting SHP2 for EGFR inhibitor resistant non-small cell lung carcinoma. Biochem Biophys Res Commun, 2013. 439. (4): p. 586-90.

7. Hicks, M., et al., Neoadjuvant dual HER2-targeted therapy with lapatinib and trastuzumab improves pathologic complete response in patients with early stage HER2-positive breast cancer: a meta-analysis of randomized prospective clinical trials. Oncologist. 20(4): p. 337-43.

8. Chatterjee, S. and M.J. Davies, Current management of diabetes mellitus and future directions in care. Postgrad Med J, 2015. 91(1081): p. 612-21.

9. Pozdeyev, N., et al., Targeting the NF-kappaB Pathway as a Combination Therapy for Advanced Thyroid Cancer. PLoS One, 2015. 10(8): p. e0134901.

10. Sharma, G., et al., Nanoparticle based insulin delivery system: the next generation efficient therapy for Type 1 diabetes. J Nanobiotechnology, 2015. 13(1): p. 74.

11. Sharma, R., MR imaging in carotid artery atherosclerosis plaque characterization. Magn Reson Med Sci, 2002. 1(4): p. 217-32.

12. van der Torren, C.R., et al., Innate and adaptive immunity to human beta cell lines: implications for beta cell therapy. Diabetologia, 2015. preaccepted: PMID: 26489735.

13. Esposito, A., et al., Liquid biopsies for solid tumors: Understanding tumor heterogeneity and real time monitoring of early resistance to targeted therapies. Pharmacol Ther, 2015. accepted: pii: S0163-7258(15)00220-X. doi: 10.1016/.

14. Hokkanen, A., et al., Microfluidic sampling system for tissue analytics. Biomicrofluidics. 9(5): p. 054109.

15. Konishi, H., et al., Microarray Technology and Its Applications for Detecting Plasma microRNA Biomarkers in Digestive Tract Cancers. Methods Mol Biol. 1368: p. 99-109.

16. Ma, M., et al., "Liquid biopsy"-ctDNA detection with great potential and challenges. Ann Transl Med. 3(16): p. 235.

17. Salvianti, F., M. Pazzagli, and P. Pinzani, Single circulating tumor cell sequencing as an advanced tool in cancer management. Expert Rev Mol Diagn: p. 1-13.

18. Schweizer, M.T. and E.S. Antonarakis, Liquid biopsy: Clues on prostate cancer drug resistance. Sci Transl Med. 7(312): p. 312fs45.

19. Sestini, S., et al., Circulating microRNA signature as liquid-biopsy to monitor lung cancer in low-dose computed tomography screening. Oncotarget. 6(32): p. 32868-77.

20. Aarthy, R., et al., Role of Circulating Cell-Free DNA in Cancers. Mol Diagn Ther. 19(6): p. 339-50.

21. Passiglia, F., et al., Prognostic and predictive biomarkers for targeted therapy in NSCLC: for whom the bell tolls? Expert Opin Biol Ther. 15(11): p. 1553-66.

22. Si, M.J., et al., Role of MRI in the early diagnosis of tubal ectopic pregnancy. Eur Radiol, 2015. accepted: PMID: 26373758

23. Sun, K., et al., Plasma DNA tissue mapping by genome-wide methylation sequencing for noninvasive prenatal, cancer, and transplantation assessments. Proc Natl Acad Sci U S A. 112(40): p. E5503-12.

24. The Oxforf Englsih Dictionary. 2015, Oxford University Press.

25. Bartels, P.H., et al., Cell recognition by multivariate gray value analysis in digitized images. Acta Cytol, 1971. 15(3): p. 284-8.

26. Bartels, P.H., et al., Tissue architecture analysis in prostate cancer and its precursors: An innovative approach to computerized histometry. Eur Urol, 1999. 35(5-6): p. 484-91.

27. Kayser, K., Neighborhood Condition and Application of Syntactic Structure Analysis in Histo-Pathology. Acta Stereol, 1987. 6:(2): p. 373-384.

28. Kayser, K., et al., Application of attributed graphs in diagnostic pathology. Anal Quant Cytol Histol, 1996. 18(4): p. 286-92.

29. Kayser, K., et al., Texture and object related image analysis in microscopic images. Diagnostic Pathology, 2015. 1.

30. Kayser, K. and H.J. Gabius, 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): p. 1-106.

31. Kayser, K. and H.J. Gabius, 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): p. 443-55.

32. Kayser, K. and H. Hoffgen, Pattern recognition in histopathology by orders of textures. Med Inform (Lond), 1984. 9(1): p. 55-9.

33. Kayser, K., et al., Texture- and object-related automated information analysis in histological still images of various organs. Anal Quant Cytol Histol, 2008. 30(6): p. 323-35.

34. Kayser, K. and G. Kayser, Virtual Microscopy and Automated Diagnosis in Virtual Microscopy and Virtual Slides in Teaching, Diagnosis and Research, J. Gu and R. Ogilvie, Editors. 2005, Taylor Francis: Boca Raton.

35. Kayser, K., et al., Phenotype and genotype associations of lung carcinoma with atypical adenomatoid hyperplasia, squamous cell dysplasia, and chromosome alterations in non-neoplastic bronchial mucosa. Rom J Morphol Embryol, 2005. 46(1): p. 5-10.

36. Pinter, C.C., A Book of Set Theory 2014, Mineola, New York: Dover Publications.

37. Kayser, K., et al., AI (artificial intelligence) in histopathology--from image analysis to automated diagnosis. Folia Histochem Cytobiol, 2009. 47(3): p. 355-61.

38. Kayser, K. and O. Hagemeyer, Stage related morphometry of sarcoid granulomas and inflammatory cell types in broncho-alveolar lavage. Anal Cell Pathol, 1991. 3(6): p. 335-42.

39. Kayser, K., et al., How to measure diagnosis-associated information in virtual slides. Diagn Pathol, 2011. 6: p. S9.

40. Kayser, K., B. Molnar, and R. Weinstein, Virtual Microscopy: Fundamentals, Applications, Perspectives of Electronic Tissue-based Diagnosis. 2006, Berlin: VSV Interdisciplinary Medical Publishing. 206.

41. Eigen, M., Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften, 1971. 58(10): p. 465-523.

42. Eigen, M., Selforganization in molecular and cellular networks. Neurochem Int, 1980. 2C: p. 25.

43. Eigen, M., The origin of genetic information: viruses as models. Gene, 1993. 135(1-2): p. 37-47.

44. Eigen, M., On the origin of biological information. Biophys Chem, 1994. 50(1-2): p. 1.

45. Eigen, M., Selection and the origin of information. Int Rev Neurobiol, 1994. 37: p. 35-46; discussion 47-50.

46. Eigen, M., Natural selection: a phase transition? Biophys Chem, 2000. 85(2-3): p. 101-23.

47. Eigen, M., Viruses: evolution, propagation, and defense. Nutr Rev, 2000. 58(2 Pt 2): p. S5-16; discussion S63-73.

48. Eigen, M., W.C. Gardiner, Jr., and P. Schuster, Hypercycles and compartments. Compartments assists--but do not replace--hypercyclic organization of early genetic information. J Theor Biol, 1980. 85(3): p. 407-11.

49. Eigen, M., R. Winkler-Oswatitsch, and A. Dress, Statistical geometry in sequence space: a method of quantitative comparative sequence analysis. Proc Natl Acad Sci U S A, 1988. 85(16): p. 5913-7.

50. Epstein, I.R. and M. Eigen, Selection and self-organization of self-reproducing macromolecules under the constraint of constant flux. Biophys Chem, 1979. 10(2): p. 153-60.

51. Desgranges, C. and J. Delhommelle, Many-Body Effects on the Thermodynamics of Fluids, Mixtures, and Nanoconfined Fluids. J Chem Theory Comput. 11(11): p. 5401-14.

52. Ilievski, E., et al., Complete Generalized Gibbs Ensembles in an Interacting Theory. Phys Rev Lett. 115(15): p. 157201.

53. Latouche, C. and V. Barone, Computational Chemistry Meets Experiments for Explaining the Behavior of Bibenzyl: A Thermochemical and Spectroscopic (Infrared, Raman, and NMR) Investigation. J Chem Theory Comput. 10(12): p. 5586-92.

54. Taye, M.A., Exact analytical thermodynamic expressions for a Brownian heat engine. Phys Rev E Stat Nonlin Soft Matter Phys. 92(3-1): p. 032126.

55. Shannon, C., Mathematische Grundlagen der Informationstheorie. 1976, München: Oldenbourg.

56. Gell-Mann, M.a.C.T., ed. Nonextensive Entropy: Interdisciplinary Applications. 2004, Oxford University Press:: Oxford.

57. Tsallis, C., . , Introduction to Nonextensive Statistical Mechanics. 210, Berlin: Springer.

58. 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: p. 188-287.

59. Voss, K. and H. Süsse, Praktische Bildverarbeitung. 1991: München, Wien: Carl Hanser Verlag.

60. O'Callaghan, J.F., An alternative definition for neighborhood of a point. IEEE Trans Comput, 1875. 24: p. 1121-1125.

61. Giblin, P., Graphs, Surfaces and Homology. 1977, New York: Halsted Press.

62. Kayser, K., et al., Pulmonary metastases of breast carcinomas: ligandohistochemical, nuclear, and structural analysis of primary and metastatic tumors with emphasis on period of occurrence of metastases and survival. J Surg Oncol, 1998. 69(3): p. 137-46.

63. Kayser, K., et al., Correlation of expression of binding sites for synthetic blood group A-, B- and H-trisaccharides and for sarcolectin with survival of patients with bronchial carcinoma. Eur J Cancer, 1994. 30A(5): p. 653-7.

64. Kayser, K., et al., TNM stage, immunohistology, syntactic structure analysis and survival in patients with small cell anaplastic carcinoma of the lung. J Cancer Res Clin Oncol, 1987. 113(5): p. 473-80.

65. Kayser, K., et al., 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): p. 435-46.

66. Gabius, H.J., et al., Reverse lectin histochemistry: design and application of glycoligands for detection of cell and tissue lectins. Histol Histopathol, 1993. 8(2): p. 369-83.

67. Prigogine, I., Introduction to Thermodynamics of Irreversible Processes, 2nd ed. 1961, New Yorck: John Wiley & Sons Inc, .

68. Kayser, K., C. Kremer, and M. Tacke, Integrated optical density and entropiefluss (current of entropy) in bronchial carcinoma. In Vivo, 1993. 7(4): p. 387-91.

69. Kayser, K., et al., Digitized pathology: theory and experiences in automated tissue-based virtual diagnosis. Rom J Morphol Embryol, 2006. 47(1): p. 21-8.

70. Kayser, K., et al., Glycohistochemical properties of malignancies of lung and pleura. Int J Oncol, 1998. 12(5): p. 1189-94.

71. van Diest, P.J., J.C. Fleege, and J.P. Baak, Syntactic structure analysis in invasive breast cancer: analysis of reproducibility, biologic background, and prognostic value. Hum Pathol, 1992. 23(8): p. 876-83.

72. van Diest, P.J., et al., Syntactic structure analysis. Pathologica, 1995. 87(3): p. 255-62.

73. Kayser, K., M. Ernst, and J. Bubenzer, Expression of transferrin- and interleukin-2-receptors, and HLA-DR in human lung carcinoma. Exp Pathol, 1991. 41(1): p. 37-43.

74. Kayser, K., et al., Expression of endogenous lectins (galectins, receptors for ABH-epitopes) and the MIB-1 antigen in esophageal carcinomas and their syntactic structure analysis in relation to post-surgical tumor stage and lymph node involvement. Anticancer Res, 2001. 21(2B): p. 1439-44.

75. Kayser, K. and W. Schlegel, Pattern recognition in histo-pathology: basic considerations. Methods Inf Med, 1982. 21(1): p. 15-22.

76. Kayser K, B.S., Carvalho R, Kayser G, How to create and implement diagnosis assistants in tissue-based diagnosis (surgical pathology)? Diagnostic Pathology, 2015. 1: in press.

77. Sharma H, Z.N., Lohmann S, Kayser K, Hellwich O, Hufnagl P, A review of graph-based methods for image analysis in digital histopathology. Diagnostic Pathology, 2015. 1:61.

78. Groot, S.D., Thermodynamik irreversibler Prozesse. Hochschultaschenbücher 18 /18a. 1960, Mannheim: Bibliographisches Institut.

79. Bridgewater, J.S., P.O. Boykin, and V.P. Roychowdhury, Statistical mechanical load balancer for the web. Phys Rev E Stat Nonlin Soft Matter Phys, 2005. 71(4 Pt 2): p. 046133.
How to Cite
KAYSER, Klaus et al. The concept of entropy in histopathological diagnosis and targeted therapy. Diagnostic Pathology, [S.l.], dec. 2015. ISSN 2364-4893. Available at: <>. Date accessed: 12 dec. 2018. doi:

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