A cell kinetic model of granulopoiesis under radiation exposure: extension from rodents to canines and humans

Effects of Flash Radiotherapy on Blood Lymphocytes in Humans and Small Laboratory Animals

A mathematical model, which describes the level of surviving lymphocytes in the blood after ultra-high (FLASH) and lower dose rates of partial-body irradiation, is developed. The model is represented by simple analytic formulae that involve a few parameters, namely, physiologic parameters (characteristics of the blood flow through the blood circulatory system and its irradiated part), a biophysical parameter (a characteristic of the blood lymphocytes radiosensitivity), and the physical parameters (characteristics of irradiation). The model predicts that the level of surviving blood lymphocytes increases as the dose rate increases and approaches the limiting level of (1 - vR), where vR is the fraction of the blood volume in the irradiated part of the blood circulatory system. The model also predicts that the level of surviving blood lymphocytes after the same exposure is higher for lower vR. It is found that FLASH irradiation in humans with doses of 10 to 40 Gy and with exposure times significantly less (<1 s) than the blood circulation time (∼60 s) leads to the maximal blood lymphocyte sparing. Simple formula, which determines effective dose rates for optimal blood lymphocyte sparing, is derived in the framework of the developed model. For the dose range specified above, the obtained modeling prediction of the range of effective dose rates for optimal blood lymphocyte sparing in humans (namely, N ≥40 Gy/s) coincides with the dose rate range in FLASH radiation therapy. It is revealed that the respective effective dose rates for mice are higher than those for humans (for the same dose range) due to the shorter blood circulation time in mice than in humans. Proceeding from the findings obtained in this paper, a hypothesis elucidating the mechanisms of the abscopal effect of FLASH radiation therapy (namely, an antitumor response on metastases located outside of irradiated part of a body) is proposed.

Modeling Reveals the Dependence of Hippocampal Neurogenesis Radiosensitivity on Age and Strain of Rats

Cognitive dysfunction following radiation treatment for brain cancers in both children and adults have been correlated to impairment of neurogenesis in the hippocampal dentate gyrus. Various species and strains of rodent models have been used to study radiation-induced changes in neurogenesis and these investigations have utilized only a limited number of doses, dose-fractions, age and time after exposures conditions. In this paper, we have extended our previous mathematical model of radiation-induced hippocampal neurogenesis impairment of C57BL/6 mice to delineate the time, age, and dose dependent alterations in neurogenesis of a diverse strain of rats. To the best of our knowledge, this is the first predictive mathematical model to be published about hippocampal neurogenesis impairment for a variety of rat strains after acute or fractionated exposures to low linear energy transfer (low LET) radiation, such as X-rays and γ-rays, which are conventionally used in cancer radiation therapy. We considered four compartments to model hippocampal neurogenesis and its impairment following radiation exposures. Compartments include: (1) neural stem cells (NSCs), (2) neuronal progenitor cells or neuroblasts (NB), (3) immature neurons (ImN), and (4) glioblasts (GB). Additional consideration of dose and time after irradiation dependence of microglial activation and a possible shift of NSC proliferation from neurogenesis to gliogenesis at higher doses is established. Using a system of non-linear ordinary differential equations (ODEs), characterization of rat strain and age-related dynamics of hippocampal neurogenesis for unirradiated and irradiated conditions is developed. The model is augmented with the description of feedback regulation on early and late neuronal proliferation following radiation exposure. Predictions for dose-fraction regimes compared to acute radiation exposures, along with the dependence of neurogenesis sensitivity to radiation on age and strain of rats are discussed. A major result of this work is predictions of the rat strain and age dependent differences in radiation sensitivity and sub-lethal damage repair that can be used for predictions for arbitrary dose and dose-fractionation schedules.

Dynamical modeling approach to risk assessment for radiogenic leukemia among astronauts engaged in interplanetary space missions

A recently developed biologically motivated dynamical model of the assessment of the excess relative risk (ERR) for radiogenic leukemia among acutely/continuously irradiated humans (Smirnova, 2015, 2017) is applied to estimate the ERR for radiogenic leukemia among astronauts engaged in long-term interplanetary space missions. Numerous scenarios of space radiation exposure during space missions are used in the modeling studies. The dependence of the ERR for leukemia among astronauts on several mission parameters including the dose equivalent rates of galactic cosmic rays (GCR) and large solar particle events (SPEs), the number of large SPEs, the time interval between SPEs, mission duration, the degree of astronaut's additional shielding during SPEs, the degree of their additional 12-hour's daily shielding, as well as the total mission dose equivalent, is examined. The results of the estimation of ERR for radiogenic leukemia among astronauts, which are obtained in the framework of the developed dynamical model for various scenarios of space radiation exposure, are compared with the corresponding results, computed by the commonly used linear model. It is revealed that the developed dynamical model along with the linear model can be applied to estimate ERR for radiogenic leukemia among astronauts engaged in long-term interplanetary space missions in the range of applicability of the latter. In turn, the developed dynamical model is capable of predicting the ERR for leukemia among astronauts for the irradiation regimes beyond the applicability range of the linear model in emergency cases. As a supplement to the estimations of cancer incidence and death (REIC and REID) (Cucinotta et al., 2013, 2017), the developed dynamical model for the assessment of the ERR for leukemia can be employed on the pre-mission design phase for, e.g., the optimization of the regimes of astronaut's additional shielding in the course of interplanetary space missions. The developed model can also be used on the phase of the real-time responses during the space mission to make the decisions on the operational application of appropriate countermeasures to minimize the risks of occurrences of leukemia, especially, for emergency cases.

Skin Response to Single and Fractionated Irradiation: Dynamic Modeling Approach

A biologically motivated mathematical model of the dynamics of swine skin epidermis after single acute irradiation () is extended to describe the effects of fractionated irradiation on this vital body system. The extended model, as the initial one, is a system of nonlinear ordinary differential equations whose variables and parameters have clear biological meaning. The performed studies of the model reveal a correlation between the dynamics of the dimensionless concentration of corneal cells of the upper skin layer and the dynamics of the fraction of the area of swine skin epidermis without moist desquamation under fractionated irradiation similar to that after single acute irradiation (). On the basis of these results, the formula, which allows computation of the dynamics of the moist desquamation in irradiated skin proceeding from the respective dynamics of skin epidermal cells, is proposed. It is demonstrated that the modeling predictions of the moist reaction in swine skin under fractionated irradiation in the wide range of total doses agree, on qualitative and quantitative levels, with the respective experimental data. All this bears witness to the validity of employment of the developed model, after appropriate identification, in the investigation and prediction of the effects of fractionated irradiation on skin epidermis in humans.

Dynamics of acutely irradiated skin epidermal epithelium in swine: modeling studies

A mathematical model, which describes the dynamics of acutely irradiated skin epidermal epithelium in swine, is developed. This model embodies the key mechanisms of regulation of skin epidermal epithelium and the principal stages of development of its cells (basal, prickle, and corneal). The model is implemented as a system of nonlinear ordinary differential equations, whose variables and parameters have clear biological meaning. The modeling results for the dose- and time-dependent changes in basal and prickle cell populations are in a good agreement with relevant experimental data. The correlation between the experimental data on the dynamics of moist reaction in acutely irradiated swine skin epidermal epithelium and the corresponding modeling results on the dynamics of corneal cells is revealed. Proceeding from this, the threshold level of corneal cells, which indicates the appearance of the moist reaction, is found. All this bears witness to the validity of employment of the developed model, after appropriate identification, in the investigation and prediction of radiation effects on skin epidermal epithelium in humans.

Evaluation of the gamma-H2AX assay for radiation biodosimetry in a swine model

There is a paucity of large animal models to study both the extent and the health risk of ionizing radiation exposure in humans. One promising candidate for such a model is the minipig. Here, we evaluate the minipig for its potential in γ-H2AX-based biodosimetry after exposure to ionizing radiation using both Cs137 and Co60 sources. γ-H2AX foci were enumerated in blood lymphocytes and normal fibroblasts of human and porcine origin after ex vivo γ-ray irradiation. DNA double-strand break repair kinetics in minipig blood lymphocytes and fibroblasts, based on the γ-H2AX assay, were similar to those observed in their human counterparts. To substantiate the similarity observed between the human and minipig we show that minipig fibroblast radiosensitivity was similar to that observed with human fibroblasts. Finally, a strong γ-H2AX induction was observed in blood lymphocytes following minipig total body irradiation. Significant responses were detected 3 days after 1.8 Gy and 1 week after 3.8 and 5 Gy with residual γ-H2AX foci proportional to the initial radiation doses. These findings show that the Gottingen minipig provides a useful in vivo model for validation of γ-H2AX biodosimetry for dose assessment in humans.

Comparative analysis of the dynamics of thrombocytopoietic, granulocytopoietic, and erythropoietic systems in irradiated humans: a modeling approach

Biologically motivated mathematical models, which describe the dynamics of the thrombocytopoietic, granulocytopoietic, and erythropoietic systems in irradiated humans, are thoroughly investigated. These models are the systems of nonlinear ordinary differential equations, whose variables and constant parameters have clear biological meaning. The modeling studies reveal general regularities and peculiarities of the dynamics of the aforementioned hematopoietic lines in acutely and chronically irradiated humans. It is shown that the predictions of the models qualitatively and quantitatively agree with the respective clinical data for humans exposed to acute and chronic irradiation in wide ranges of doses and dose rates. Moreover, the "lethal" dose rate of chronic irradiation, which is evaluated in the framework of the granulocytopoiesis model, coincides with the real minimal dose rate of lethal chronic irradiation for humans. As for the thrombocytopoiesis and erythropoiesis models, the respective "lethal" dose rates of chronic irradiation are very close to the real one for humans. All this bears witness to the validity of employment of the developed models in the investigation and prediction of radiation effects on human hematopoiesis.