The application of structural entropy in tissue based diagnosis

  • Gian Kayser Institute of Surgical Pathology, Medical Center – University of Freiburg, Faculty of Medicine, University of Freiburg, Germany
  • Jürgen Görtler IBM Global Markets, Systems, Frankfurt, Germany
  • Cleo Aron Weis Institute of Pathology, University Medical Centre Mannheim, University of Heidelberg, Mannheim, Germany
  • Stephan Borkenfeld IAT, Heidelberg, Germany
  • Klaus Kayser Charite - Berlin


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.


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How to Cite
KAYSER, Gian et al. The application of structural entropy in tissue based diagnosis. Diagnostic Pathology, [S.l.], v. 3, n. 1, aug. 2017. ISSN 2364-4893. Available at: <>. Date accessed: 20 sep. 2017. doi:

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