| 1. |
- Carlsson, Tobias, 1975, et al.
(författare)
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Irreducible memory function and slow dynamics in disordered systems.
- 2007
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Ingår i: Phys. Rev. E. - 1539-3755. ; 75:031109, s. 1-8
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Tidskriftsartikel (refereegranskat)abstract
- We show how the irreducible memory function can be obtained in a rather straightforward way, and that it can be expressed in terms of two contributions representing two parallel decay channels. This representation should be useful for treating systems with a slow time dependence and where eventually some internal degrees of freedom enters in the relaxation process, and cuts off an underlying ideal ergodic to nonergodic transition. We also show how the irreducible memory function under certain mild conditions defines a regenerative stochastic process, or a two level stochastic system. This leads to a picture with dynamical heterogeneities, where the statistical properties asymptotically are ruled by limit processes. This can explain the universal behavior observed in many glass-forming systems.
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| 2. |
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| 3. |
- Mamontov, Eugen, 1955, et al.
(författare)
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Oncogenic hyperplasia caused by combination of various factors: A decision-support software for radionuclide therapy
- 2007
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Ingår i: Workshop "Mathematical Modelling and Analysis of Cancer Invasion of Tissues", Mar 26, 2007 - Mar 30, 2007, Dundee, Scotland.
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Konferensbidrag (refereegranskat)abstract
- The present work deals with the software based on the PhasTraM model [1] for oncogenic hyperplasia, the first stage of formation of any solid tumor. The work generalizes the related results of [2]-[6] and discusses application of the software for decision support in radionuclide therapy. The software capabilities to allow for combinations of various causes of oncogeny are emphasized. The causes comprise inflammation, immune dysfunction, and chronic psychological stress. The immune dysfunction is represented with hypogammaglobulenimia expressed in terms of the concentration of the immunoglobulin-G molecules. The level of chronic pychological stress is described with the concentration of the interleukin-6 molecules. The work considers how application of the software can support decisions on the specific radionuclide-therapy setting depending on the tissue-, organ-, and patient-specific data. This is illustrated by a number of numerical-simulation results, also the ones which include the effects of common and fractionation-based radionuclide-therapy modalities. A proper attention is paid to how specifically the input data can be prepared by prospective users of the software, i.e. the specialists who apply radionuclide therapy. The work also formulates a few directions for future research in connection with the features of the everyday work of the prospective users. REFERENCES: [1] E. Mamontov, K. Psiuk-Maksymowicz, A. Koptioug, 2006, Stochastic mechanics in the context of the properties of living systems, Mathl Comput. Modelling, 44(7-8) 595-607. [2] E. Mamontov, A. V. Koptioug, K. Psiuk-Maksymowicz, 2006, The minimal, phase-transition model for the cell-number maintenance by the hyperplasia-extended homeorhesis, Acta Biotheoretica, 54(2) 61-101. [3] K. Psiuk-Maksymowicz and E. Mamontov, 2006, The homeorhesis-based modelling and fast numerical analysis for oncogenic hyperplasia under radiotherapy, Mathl Comput. Modelling, Special Issue
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| 4. |
- Mamontov, Eugen, 1955, et al.
(författare)
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Stochastic mechanics in the context of the properties of living systems
- 2006
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Ingår i: Mathl Comput. Modelling. - : Elsevier BV. - 0895-7177 .- 1872-9479. ; 44:7-8, s. 595-607
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Tidskriftsartikel (refereegranskat)abstract
- Many features of living systems prevent the application of fundamental statistical mechanics (FSM) to study such systems. The present work focuses on some of these features. After discussing all the basic approaches of FSM, the work formulates an extension of the kinetic theory paradigm (based on the reduced one-particle distribution function) that exhibits all of the living-system properties considered. This extension appears to be a model within the generalized kinetic theory developed by N. Bellomo and his co-authors. In connection with this model, the work also stresses some other features necessary for making the model relevant to living systems. A mathematical formulation of homeorhesis is also derived. An example discussed in the work is a generalized kinetic equation coupled with a probability-density equation representing the varying component content of a living system. The work also suggests a few directions for future research. [All rights reserved Elsevier]
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| 5. |
- Mamontov, Eugen, 1955, et al.
(författare)
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The minimal, phase-transition model for the cell-number maintenance by the hyperplasia-extended homeorhesis
- 2006
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Ingår i: Acta Biotheoretica. - : Springer Science and Business Media LLC. - 0001-5342 .- 1572-8358. ; 54:2, s. 61-101
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Tidskriftsartikel (refereegranskat)abstract
- Oncogenic hyperplasia is the first and inevitable stage of formation of a (solid) tumor. This stage is also the core of many other proliferative diseases. The present work proposes the first minimal model that combines homeorhesis with oncogenic hyperplasia where the latter is regarded as a genotoxically activated homeorhetic dysfunction. This dysfunction is specified as the transitions of the fluid of cells from a fluid, homeorhetic state to a solid, hyperplastic-tumor state, and back. The key part of the model is a nonlinear reaction-diffusion equation (RDE) where the biochemical-reaction rate is generalized to the one in the well-known Schlögl physical theory of the non-equilibrium phase transitions. A rigorous analysis of the stability and qualitative aspects of the model, where possible, are presented in detail. This is related to the spatially homogeneous case, i.e. when the above RDE is reduced to a nonlinear ordinary differential equation. The mentioned genotoxic activation is treated as a prevention of the quiescent G0-stage of the cell cycle implemented with the threshold mechanism that employs the critical concentration of the cellular fluid and the nonquiescent-cell-duplication time. The continuous tumor morphogeny is described by a time-space-dependent cellular-fluid concentration. There are no sharp boundaries (i.e. no concentration jumps exist) between the domains of the homeorhesis- and tumor-cell populations. No presumption on the shape of a tumor is used. To estimate a tumor in specific quantities, the model provides the time-dependent tumor locus, volume, and boundary that also points out the tumor shape and size. The above features are indispensable in the quantitative development of antiproliferative drugs or therapies and strategies to prevent oncogenic hyperplasia in cancer and other proliferative diseases. The work proposes an analytical-numerical method for solving the aforementioned RDE. A few topics for future research are suggested.
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| 6. |
- Mamontov, Eugen, 1955, et al.
(författare)
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What stochastic mechanics are relevant to the study of living systems?
- 2005
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Ingår i: Proceedings of the Latvian Academy of Sciences. Section B: Natural, Exact and Applied Sciences. - Riga, Latvia : Latvian Academy of Sciences. - 1407-009X. ; 59:6, s. 255-262
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Tidskriftsartikel (refereegranskat)abstract
- Biologists have identified many features of living systems which cannot be studied by application of fundamental statistical mechanics (FSM). The present work focuses on some of these features. By discussing all the basic approaches of FSM, the work formulates the extension of the kinetic-theory paradigm (based on the reduced one-particle distribution function) that possesses all the considered properties of the living systems. This extension appears to be a model within the generalized-kinetic theory developed by N. Bellomo and his co-authors. In connection with this model, the work also stresses some other features necessary for making the model relevant to living systems. An example is discussed, which is a generalized kinetic equation coupled with the probability-density equation which represents the varying component content of a living system. The work also suggests directions for future research.
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| 7. |
- Psiuk-Maksymowicz, Krzysztof, 1980, et al.
(författare)
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Homeorhesis-based modelling and fast numerical analysis for oncogenic hyperplasia under radiotherapy
- 2008
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Ingår i: Mathl Comput. Modelling. - : Elsevier BV. - 0895-7177. ; 47:5-6, s. 580-596
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Tidskriftsartikel (refereegranskat)abstract
- A few previous works of the authors derived and discussed the space–time mathematical description, the PhasTraM model, for oncogenic hyperplasia regarded as a genotoxically activated homeorhetic dysfunction. The model is based on the fluid-to-solid-and-back transitions and nonlinear reaction–diffusion equations relevant to a series of the key biomedical facts, and some distinguishing features of living systems. The first computer-simulation results have also been reported. The present work generalizes the PhasTraM model for the effect of radiation therapies (RTs), both external and internal. The resulting model also includes the autocrine mechanism promoting oncogenic hyperplasia and the suppression of this process by certain drugs. The autocrine signalling is implemented by the transforming-growth-factor-α (TGF-α) molecules released by the cells and bound to the epidermal-growth-factor receptors (EGFRs) at the cell surface. The suppression can be carried out by a drug deactivating the mentioned molecules. The work also presents and discusses examples of the computer-simulation results for four different settings of the applied RT. A few directions for future research, as well as prospective applications of the model and developed software, are also discussed.
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