Development of a coupled modeling for tumor growth, angiogenesis, oxygen delivery, and phenotypic heterogeneity.

Analysis of the evolution and growth dynamics of tumors is crucial for understanding cancer and the development of individually optimized therapies. During tumor growth, a hypoxic microenvironment around cancer cells caused by excessive non-vascular tumor growth induces tumor angiogenesis that plays a key role in the ensuing tumor growth and its progression into higher stages. Various mathematical simulation models have been introduced to simulate these biologically and physically complex hallmarks of cancer. Here, we developed a hybrid two-dimensional computational model that integrates spatiotemporally different components of the tumor system to investigate both angiogenesis and tumor growth/proliferation. This spatiotemporal evolution is based on partial diffusion equations, the cellular automation method, transition and probabilistic rules, and biological assumptions. The new vascular network provided by angiogenesis affects tumor microenvironmental conditions and drives individual cells to adapt themselves to spatiotemporal conditions. Furthermore, some stochastic rules are involved besides microenvironmental conditions. Overall, the conditions promote some commonly observed cellular states, i.e., proliferative, migrative, quiescent, and cell death, depending on the condition of each cell. Altogether, our results offer a theoretical basis for the biological evidence that regions of the tumor tissue near blood vessels are densely populated by proliferative phenotypic variants, while poorly oxygenated regions are sparsely populated by hypoxic phenotypic variants.

Magnonic contribution in thermal conductance of a nanostructure in the presence of magnon-phonon interaction.

Using Green's function method, we study thermal transport properties of magnons transmitting through a magnetic nanowire at a certain temperature. In a small part of the nanowire in the middle, we are supposed to have two types of local and nonlocal magnon-phonon interactions. The self-energies for this part due to the other parts of the wire are analytically derived. First, we calculate the phonon mode-dependent magnon transmission coefficient in the classical canonical ensemble. Then, by taking an average of the phonon modes, we obtain the total magnon transmission coefficient and use it for computing magnon thermal conductance. We use the model to investigate four configurations of magnetic nanowires composed of ferromagnetic and/or antiferromagnetic parts. The results show that, when the scattering region has an antiferromagnetic alignment, the magnons transfer in the structure more weakly than for ferromagnetic alignment. There is a phonon-assisted mechanism for tunneling of magnons which are transmitted through the gap or between magnon quasifrequencies of the scattering region. Generally, in the same values for local and nonlocal strengths of magnon-phonon interaction, the nonlocal one has a greater effect on the magnonic thermal transport properties. We found the fitting functions in order to relate the macroscopic quantities of the magnon transmission coefficient and thermal conductivity to microscopic parameters of the strengths of the local and nonlocal magnon-phonon interaction.

Phononic properties of a periodic nanostructure including vacuum gap in the presence of effective interatomic interactions.

Using the harmonic approximation and Green's function technique, we investigate the contribution of phonons to heat transport across a narrow vacuum gap by an extended mass-spring chain model. We base the investigation on the van Beest-Kramer-van Santen potential that applies to two cases of simple and alternating mass systems at a finite temperature. Employing this model, we show that in specific values of interaction strengths, incoming phonon frequency, and gap distance, the phonon transmission across the vacuum gap can be improved. Finally, the thermal conductance of the system is computed as a function of interaction strength, gap distance, and temperature. These calculations reveal a suitable fitting function that can provide valuable insight into determining the internal interaction strengths from this quantity or controlling it by variation of the gap distance.