A spatially-distributed continuous mathematical model of solid tumor growth and treatment by fractionated radiotherapy is presented. The model explicitly accounts for three time and space-dependent factors that influence the efficiency of radiotherapy fractionation schemes—tumor cell repopulation, reoxygenation and redistribution of proliferative states. A special algorithm is developed, aimed at finding the fractionation schemes that provide increased tumor cure probability under the constraints of maximum normal tissue damage and maximum fractional dose. The optimization procedure is performed for varied radiosensitivity of tumor cells under the values of model parameters, corresponding to different degrees of tumor malignancy. The resulting optimized schemes consist of two stages. The first stages are aimed to increase the radiosensitivity of the tumor cells, remaining after their end, sparing the caused normal tissue damage. This allows to increase the doses during the second stages and thus take advantage of the obtained increased radiosensitivity. Such method leads to significant expansions in the curative ranges of the values of tumor radiosensitivity parameters. Overall, the results of this study represent the theoretical proof of concept that non-uniform radiotherapy fractionation schemes may be considerably more effective that uniform ones, due to the time and space-dependent effects.

The efficacy of antitumor radiotherapy can be enhanced by utilizing nonradioactive nanoparticles that emit secondary radiation when activated by a primary beam. They consist of small volumes of a radiosensitizing substance embedded within a polymer layer, which is coated with tumor-specific antibodies. The efficiency of nanosensitizers relies on their successful delivery to the tumor, which depends on their size. Increasing their size leads to a higher concentration of active substance; however, it hinders the penetration of nanosensitizers through tumor capillaries, slows down their movement through the tissue, and accelerates their clearance. In this study, we present a mathematical model of tumor growth and radiotherapy with the use of intravenously administered tumor-specific nanosensitizers. Our findings indicate that their optimal size for achieving maximum tumor radiosensitization following a single injection of their fixed total volume depends on the permeability of the tumor capillaries. Considering physiologically plausible spectra of capillary pore radii, with a nanoparticle polymer layer width of 7 nm, the optimal radius of nanoparticles falls within the range of 13–17 nm. The upper value is attained when considering an extreme spectrum of capillary pores.

The results of a scientometric analysis of publications of scientific chemical organizations for 2015–2019, presented in the Web of Science database, are given. Seven groups of scientific categories are considered in the analysis: chemistry, electrochemistry, green & sustainable science & technology, materials sciences, nanotechnology, polymers, and quantum calculations. For each group, the contribution of articles published in journals of different quartiles has been estimated. It is shown that the role of international cooperation in the creation of articles depends significantly on the subject area. Keywords characterizing each of the subject areas analyzed have been determined.

A spatially distributed mathematical model is presented that simulates the growth of a non-invasive tumour undergoing treatment by fractionated proton therapy with the use of non-radioactive tumour-specific nanosensitizers. Nanosensitizers are injected intravenously before each irradiation to increase the locally deposited dose via a chain of reactions with therapeutic protons. Modelling simulations show that the use of nanosensitizers allows increasing treatment efficacy. However, their effect is restricted by the necessity of decreasing the energy deposited in tumour in order to comply to the normal damage restrictions. Normalization of tumour microvasculature that accompanies the treatment, also compromises nanosensitizers effect as it impairs their inflow in tumour. It is shown that spatial optimization of irradiation, with conservation of total dose deposited in tumour, can increase tumour cell damage for each single irradiation. However, eventually it may not lead to the overall increase of treatment efficacy, in terms of minimization of the number of remaining viable tumour cells, due to the influence of tumour cell repopulation between irradiations. It is suggested that an efficient way towards minimization of tumour cell repopulation may be the faster suppression of angiogenesis by eradication of metabolically deprived tumour cells. This method can be efficient even despite the fact that it would also cause the decrease of supply of nanosensitizers into the tumour.

Antiangiogenic therapy (AAT) is an indirect oncological modality that is aimed at the disruption of cancer cell nutrient supply. Invasive tumors have been shown to possess inherent resistance to this treatment, while compactly growing benign tumors react to it by shrinking. It is generally accepted that AAT by itself is not curative. This study presents a mathematical model of non-invasive tumor growth with a physiologically justified account of microvasculature alteration and the biomechanical aspects of importance during tumor growth and AAT. In the untreated setting, the model reproduces tumor growth with saturation, where the maximum tumor volume depends on the level of angiogenesis. The outcomes of the AAT simulations depend on the tumor size at the moment of treatment initiation. If it is close to the stable size of an avascular tumor grown in the absence of angiogenesis, then the tumor is rapidly stabilized by AAT. The treatment of large tumors is accompanied by the displacement of normal tissue due to tumor shrinkage. During this, microvasculature undergoes distortion, the degree of which depends on the displacement distance. As it affects tumor nutrient supply, the stable size of a tumor that undergoes AAT negatively correlates with its size at the beginning of treatment. For sufficiently large initial tumors, the long-term survival of tumor cells is compromised by competition with normal cells for the severely limited inflow of nutrients, which makes AAT effectively curative.

An off-lattice agent-based model of tumor growth is presented, which describes a tumor as a network of proliferating cells, whose dynamics depend on the stress generated by intercellular bonds. A numerical method is introduced that ensures the smooth dynamics of the cell network and allows for relative numerical cheapness while reproducing the effects typical of more complex approaches such as the elongation of cells toward low-pressure regions and their tendency to maximize the contact area. Simulations of free tumor growth, restricted only by the stress generated within the tumor, demonstrate the influence of the tissue hydraulic conductivity and strength of cell–cell interactions on tumor shape and growth rate. Simulations of compact tumor growth within normal tissue show that strong interaction between tumor cells is a major factor limiting tumor growth. Moreover, the effects of normal tissue size and strength of normal cell interactions on tumor growth are ambiguous and depend on the value of tissue hydraulic conductivity. Simulations of tumor growth in normal tissue with the account of nutrients yield different growth regimes, including growth without saturation for at least several years with the formation of large necrotic cores in cases of low tissue hydraulic conductivity and sufficiently high nutrient supply, which qualitatively correlates with known clinical data.