The human body is an open, self-regulating system that responds as a whole to changes in the external environment. Its reliability is ensured by the redundancy of the structure, the presence of control systems and the ability to adapt and compensate for impaired functions, duplication and interaction of all systems with each other. As an open system, the body is studied at various levels: molecular, subcellular, cellular, tissue, etc., which makes it possible to analyze, predict and control processes of various natures occurring in it. From a practical viewpoint, of particular importance are processes occurring directly in the tissues of the body, studied at the cellular level, taking into account molecular and subcellular processes. For example, these are the processes of growth/degradation, regeneration, remodeling, healing of biological tissuesBiological tissue and others, many of which can be classified as biotribological. These include regeneration of articular cartilage of synovial joints, healing of bone fractures and muscle tears, wear and osseointegration of implants, migration of pathological cells, etc. An important role in the study of biotribological processBiotribological processes is played by mathematical models that take into account the most important features of tissues at different levels of detail. Their research makes it possible to assess the current state and predict the dynamics of tissue development under various external conditions, which is of interest from the development of personalized biomedical technologies viewpoint. This chapter is devoted to the analysis of the reaction–diffusion type mathematical models, which are widely used to study various processes occurring in biological tissues. Such models have been shown to be effective for predicting the evolution of a large number of biotribological processes under various tissue states and environmental conditions. However, as a rule, they use many parameters, which contradicts the well-known “principle of simplicity” and can lead to unrealistic or loss of real solutions to nonlinear problems. In addition, estimates of state parameters in most cases are determined because of complex experimental studies within the framework of different nature experiments, which does not allow them to be considered parameters of a specific tissue. To eliminate these problems, “digital twins” of tissue processes can be used, designed based on the “reaction–diffusion” type mathematical models and express information about the state of tissues in real time.

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Features and Problems for Biotribological Processes Modeling in Biological Tissues

  • Aleksandr M. Poliakov,
  • Vladimir I. Pakhaliuk,
  • Aleksandr I. Ryzhkov

摘要

The human body is an open, self-regulating system that responds as a whole to changes in the external environment. Its reliability is ensured by the redundancy of the structure, the presence of control systems and the ability to adapt and compensate for impaired functions, duplication and interaction of all systems with each other. As an open system, the body is studied at various levels: molecular, subcellular, cellular, tissue, etc., which makes it possible to analyze, predict and control processes of various natures occurring in it. From a practical viewpoint, of particular importance are processes occurring directly in the tissues of the body, studied at the cellular level, taking into account molecular and subcellular processes. For example, these are the processes of growth/degradation, regeneration, remodeling, healing of biological tissuesBiological tissue and others, many of which can be classified as biotribological. These include regeneration of articular cartilage of synovial joints, healing of bone fractures and muscle tears, wear and osseointegration of implants, migration of pathological cells, etc. An important role in the study of biotribological processBiotribological processes is played by mathematical models that take into account the most important features of tissues at different levels of detail. Their research makes it possible to assess the current state and predict the dynamics of tissue development under various external conditions, which is of interest from the development of personalized biomedical technologies viewpoint. This chapter is devoted to the analysis of the reaction–diffusion type mathematical models, which are widely used to study various processes occurring in biological tissues. Such models have been shown to be effective for predicting the evolution of a large number of biotribological processes under various tissue states and environmental conditions. However, as a rule, they use many parameters, which contradicts the well-known “principle of simplicity” and can lead to unrealistic or loss of real solutions to nonlinear problems. In addition, estimates of state parameters in most cases are determined because of complex experimental studies within the framework of different nature experiments, which does not allow them to be considered parameters of a specific tissue. To eliminate these problems, “digital twins” of tissue processes can be used, designed based on the “reaction–diffusion” type mathematical models and express information about the state of tissues in real time.