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We examine a lattice model of tumor growth where survival of tumor cells depends on the supplied nutrients. When such a supply is random, the extinction of tumors belongs to the directed percolation universality class. However, when the…
We study a time-fractional Fisher-KPP equation involving a Riemann-Liouville fractional derivative acting on the diffusion term, as derived by Angstmann and Henry (Entropy, 22:1035, 2020). The model captures memory effects in diffusive…
Recent evidence suggests that nongenetic (epigenetic) mechanisms play an important role at all stages of cancer evolution. In many cancers, these mechanisms have been observed to induce dynamic switching between two or more cell states,…
Mechanical models for tumor growth have been used extensively in recent years for the analysis of medical observations and for the prediction of cancer evolution based on imaging analysis. This work deals with the numerical approximation of…
We propose a mathematical model for the growth and treatment dynamics of Undifferentiated Pleomorphic Sarcoma (UPS) based on a system of nonlinear differential equations. The model integrates Gompertz-type tumor growth with surface-area…
Understanding cancer cell differentiation is essential for advancing its detection, diagnosis, and treatment. Mathematical models significantly contribute to this by providing a theoretical framework to understand the complex interactions…
We explore the sensitivity of several core-level spectroscopic methods to the underlying atomistic structure by using the water molecule as our test system. We first define a metric that measures the magnitude of spectral change as a…
Anomalous heat diffusion is investigated for biological tissues displaying a fractal structure and long-term thermal memory, which is modeled via a fractional derivative. For increasing values of the fractional derivation order, the tissue…
The work presents a study of the non-linear mathematical model of tumor growth, proposed by Kolev and Zubik-Kowal (2011). The model is described by a system composed of four partial differential equations that represent the evolution of the…
The limits of TDF (time, dose, and fractionation) and linear quadratic models have been known for a long time. Medical physicists and physicians are required to provide fast and reliable interpretations regarding the delivered doses or any…
Radiation therapy outcomes are decided by two key parameters, dose and timing, whose best values vary substantially across patients. This variability is especially critical in the treatment of brain cancer, where fractionated or staged…
The normal tissue complication probability (NTCP) is a measure for the estimated side effects of a given radiation treatment schedule. Here we use a stochastic logistic birth death process to define an organ specific and patient specific…
Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border, and surface diffusion…
Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed…
Numerical simulations are performed on a stochastic model based on Monte Carlo damage simulation process and Markov Chain Monte Carlo techniques to investigate the formation and evaluation of isolated and multiple DNA damage and cellular…
The surrogate-based analysis and optimization of thermal damage in living biological tissue by laser irradiation are discussed in this paper. Latin Hypercube Sampling (LHS) and Response Surface Model (RSM) are applied to study…
In a previous work, we presented a model that integrates cancer cell differentiation and immunotherapy, analysing a particular therapy against cancer stem cells by cytotoxic cell vaccines. As every biological system is exposed to random…
Cancer cells are widely known to be protected from apoptosis, which is a major hurdle to successful anti-cancer therapy. Over-expression of several anti-apoptotic proteins, or mutations in pro-apoptotic factors, has been recognized to…
To deal with permanent deformations and residual stresses, we consider a morphoelastic model for the scar formation as the result of wound healing after a skin trauma. Next to the mechanical components such as strain and displacements, the…
Analytical expressions for the elastic and dynamic form factors (FFs) are derived in the shell model (SM) with a potential well of finite depth. The consideration takes into account the motion of the target-nucleus center of mass (CM).…