The Risk Function of Breast and Ovarian Cancers in the Avrami-Dobrzyński Cellular Phase-Transition Model

Specifying the role of genetic mutations in cancer development is crucial for effective screening or targeted treatments for people with hereditary cancer predispositions. Our goal here is to find the relationship between a number of cancerogenic mutations and the probability of cancer induction over the lifetime of cancer patients. We believe that the Avrami-Dobrzyński biophysical model can be used to describe this mechanism. Therefore, clinical data from breast and ovarian cancer patients were used to validate this model of cancer induction, which is based on a purely physical concept of the phase-transition process with an analogy to the neoplastic transformation. The obtained values of model parameters established using clinical data confirm the hypothesis that the carcinogenic process strongly follows fractal dynamics. We found that the model's theoretical prediction and population clinical data slightly differed for patients with the age below 30 years old, and that might point to the existence of an ancillary protection mechanism against cancer development. Additionally, we reveal that the existing clinical data predict breast or ovarian cancers onset two years earlier for patients with BRCA1/2 mutations.

The Radiation-Specific Components Generated in the Second Step of Sequential Reactions Have a Mountain-Shaped Function

A mathematical model for radiation hormesis below 100 mSv has previously been reported, but the origins of the formula used in the previous report were not provided. In the present paper, we first considered a sequential reaction model with identical rate constants. We showed that the function of components produced in the second step of this model agreed well with the previously reported function. Furthermore, in a general sequential reaction model with different rate constants, it was mathematically proved that the function representing the component produced in the second step is always mountain-shaped: the graph has a peak with one inflection point on either side, and such a component may induce radiation hormesis.

Biophysical Modeling of the Ionizing Radiation Influence on Cells Using the Stochastic (Monte Carlo) and Deterministic (Analytical) Approaches

This review article describes our simplified biophysical model for the response of a group of cells to ionizing radiation. The model, which is a product of 10 years of studies, acts as (a) a comprehensive stochastic approach based on the Monte Carlo simulation with a probability tree and (b) the thereof derived detailed deterministic models describing the selected biophysical and radiobiological phenomena in an analytical manner. Specifically, the presented model describes effects such as the risk of neoplastic transformation of cells relative to the absorbed radiation dose, the dynamics of tumor development, the priming dose effect (also called the Raper–Yonezawa effect) based on the introduced adaptive response approach, and the bystander effect. The model is also modifiable depending on users’ potential needs.

Medical management of acute radiation syndrome

Acute radiation syndrome (ARS) is a clinical syndrome involving four organ systems, resulting in the hematopoietic syndrome (HS), gastrointestinal subsyndrome (GIS), neurovascular subsyndrome (NVS) and cutaneous subsyndrome (CS). Since few healthcare providers have seen an ARS case, evidence-based recommendations are needed to guide medical management in a mass casualty scenario. The authors reviewed recommendations from evidence-based and narrative reviews by expert consultants to the World Health Organisation (WHO), a subsequent review of published HS cases, and infectious disease guidelines for management of febrile neutropenia. The WHO Consultancy applied a rigorous grading system to evaluate treatment strategies described in published ARS cases as of 2009, strategies to manage HS in unirradiated persons, results of ARS studies in animal models of ARS, and recommendations of prior expert panels. Major findings for HS were (a) no randomised controlled studies have been performed, (b) data are restricted by the lack of comparator groups, and (c) reports of countermeasures for management of injury to non-hematopoietic organs are often incomplete. Strength of recommendations ranged from strong to weak. Countermeasures of potential benefit include cytokines and for a subgroup of HS patients, hematopoietic stem cell transplantation. These recommendations did not change in a subsequent analysis of HS cases. Recommendations also included fluoroquinolones, bowel decontamination, serotonin receptor antagonists, loperamide and enteral nutrition for GIS; supportive care for NVS; and topical steroids, antihistamines and antibiotics, and surgical excision/grafting for CS. Also reviewed are critical care management guidelines, the role of mesenchymal stem cells for CS, the potential of a platelet-stimulating cytokine for HS, and the author's approach to clinical management of microbial infections associated with ARS based on published guidelines of infectious disease experts. Today's management of HS is supported by evidence-based guidelines. Management of non-HS subsyndromes is supported by a narrative review of the literature and recommendations of infectious disease societies.

The radiation adaptive response and priming dose influence: the quantification of the Raper-Yonezawa effect and its three-parameter model for postradiation DNA lesions and mutations

The priming dose effect, called also the Raper-Yonezawa effect or simply the Yonezawa effect, is a special case of the radiation adaptive response phenomenon (radioadaptation), which refers to: (a) faster repair of direct DNA lesions (damage), and (b) DNA mutation frequency reduction after irradiation, by applying a small priming (conditioning) dose prior to the high detrimental (challenging) one. This effect is observed in many (but not all) radiobiological experiments which present the reduction of lesion, mutation or even mortality frequency of the irradiated cells or species. Additionally, the multi-parameter model created by Dr. Yonezawa and collaborators tried to explain it theoretically based on experimental data on the mortality of mice with chronic internal irradiation. The presented paper proposes a new theoretical approach to understanding and explaining the priming dose effect: it starts from the radiation adaptive response theory and moves to the three-parameter model, separately for two previously mentioned situations: creation of fast (lesions) and delayed damage (mutations). The proposed biophysical model was applied to experimental data-lesions in human lymphocytes and chromosomal inversions in mice-and was shown to be able to predict the Yonezawa effect for future investigations. It was also found that the strongest radioadaptation is correlated with the weakest cellular radiosensitivity. Additional discussions were focussed on more general situations where many small priming doses are used.

Modeling of single cell cancer transformation using phase transition theory: application of the Avrami equation

The nucleation and growth theory, described by the Avrami equation (also called Johnson-Mehl-Avrami-Kolmogorov equation), and usually used to describe crystallization and nucleation processes in condensed matter physics, was applied in the present paper to cancer physics. This can enhance the popular multi-hit model of carcinogenesis to volumetric processes of single cell's DNA neoplastic transformation. The presented approach assumes the transforming system as a DNA chain including many oncogenic mutations. Finally, the probability function of the cell's cancer transformation is directly related to the number of oncogenic mutations. This creates a universal sigmoidal probability function of cancer transformation of single cells, as observed in the kinetics of nucleation and growth, a special case of a phase transition process. The proposed model, which represents a different view on the multi-hit carcinogenesis approach, is tested on clinical data concerning gastric cancer. The results also show that cancer transformation follows DNA fractal geometry.

REVIEW OF QUANTITATIVE MECHANISTIC MODELS OF RADIATION-INDUCED NON-TARGETED EFFECTS (NTE)

Quantitative mechanistic modeling of the biological effects of ionizing radiation has a long rich history. Initially, it was dominated by target theory, which quantifies damage caused by traversal of cellular targets like DNA by ionizing tracks. The discovery that mutagenesis, death and/or altered behavior sometimes occur in cells that were not themselves traversed by any radiation tracks but merely interacted with traversed cells was initially seen as surprising. As more evidence of such 'non-targeted' or 'bystander' effects accumulated, the importance of their contribution to radiation-induced damage became more recognized. Understanding and modeling these processes is important for quantifying and predicting radiation-induced health risks. Here we review the variety of mechanistic mathematical models of nontargeted effects that emerged over the past 2-3 decades. This review is not intended to be exhaustive, but focuses on the main assumptions and approaches shared or distinct between models, and on identifying areas for future research.

Radiation adaptive response and cancer: From the statistical physics point of view

Elements of statistical physics formalism were applied to mutagenic and carcinogenic processes associated with cellular DNA; these are lesion (damage) creation, mutation creation, and cellular neoplastic (cancer) transformation. The probabilities of all state changes were strictly related to potential barrier heights between energetic states of DNA molecules. Barriers can be modified when radiation adaptive response mechanisms are applied, which are associated with a radiobiological quantity called radiosensitivity. It was discussed that radiosensitivity is determined by the cell's response to radiation resulting in three potential dose-response scenarios: linear, threshold, or hormetic. The type of dose-response is of critical importance in the development of radiation protection standards and individual radiation risk assessment. It is shown that the different scenarios describe different limits of the same underlying phenomena and the cell can respond in a linear, threshold, or hormetic way regarding its radiosensitivity. Finally, the dissipative adaptation mechanism is discussed in the context of proliferating cancer cells.

Modeling Cell Reactions to Ionizing Radiation: From a Lesion to a Cancer

This article focuses on the analytic modeling of responses of cells in the body to ionizing radiation. The related mechanisms are consecutively taken into account and discussed. A model of the dose- and time-dependent adaptive response is considered for 2 exposure categories: acute and protracted. In case of the latter exposure, we demonstrate that the response plateaus are expected under the modelling assumptions made. The expected total number of cancer cells as a function of time turns out to be perfectly described by the Gompertz function. The transition from a collection of cancer cells into a tumor is discussed at length. Special emphasis is put on the fact that characterizing the growth of a tumor (ie, the increasing mass and volume), the use of differential equations cannot properly capture the key dynamics-formation of the tumor must exhibit properties of the phase transition, including self-organization and even self-organized criticality. As an example, a manageable percolation-type phase transition approach is used to address this problem. Nevertheless, general theory of tumor emergence is difficult to work out mathematically because experimental observations are limited to the relatively large tumors. Hence, determination of the conditions around the critical point is uncertain.