Related papers: A Three-dimensional tumor growth model and its bou…
In this work we analyse a PDE-ODE problem modelling the evolution of a Glioblastoma, which includes an anisotropic nonlinear diffusion term with a diffusion velocity increasing with respect to vasculature. First, we prove the existence of…
Stability and boundedness analysis for vector nonlinear systems with variable delays and coefficients remains challenging due to the conservatism of existing methods. Moreover, estimates of the transient behavior of solution norms remain…
The landscape of computational modeling in cancer systems biology is diverse, offering a spectrum of models and frameworks, each with its own trade-offs and advantages. Ideally, models are meant to be useful in refining hypotheses, to…
We study a free boundary problem modeling multi-layer tumor growth with a small time delay $\tau$, representing the time needed for the cell to complete the replication process. The model consists of two elliptic equations which describe…
The mathematical modeling of tumor growth leads to singular stiff pressure law limits for porous medium equations with a source term. Such asymptotic problems give rise to free boundaries, which, in the absence of active motion, are…
We present a mathematical model describing the time development of a population of tumors subject to mutual angiogenic inhibitory signaling. Based on biophysical derivations, it describes organism-scale population dynamics under the…
Evaluating structural uncertainties associated with seismic imaging and target horizons can be of critical importance for decision-making related to oil and gas exploration and production. An important breakthrough for industrial…
Automation of brain tumor segmentation in 3D magnetic resonance images (MRIs) is key to assess the diagnostic and treatment of the disease. In recent years, convolutional neural networks (CNNs) have shown improved results in the task.…
In this paper, we propose a tumor growth model to incorporate and investigate the spatial effects of autophagy. The cells are classified into two phases: normal cells and autophagic cells, whose dynamics are also coupled with the nutrients.…
This paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth describing evolutions driven by long-range interactions. These integro-partial differential equations model cell-to-cell…
Some existing models of the atherosclerosis development are discussed and a new improved mathematical model, which takes into account new experimental results about diverse roles of macrophages in atherosclerosis, is proposed. Using technic…
During the last decades, medical observations and multiscale data concerning tumor growth are mounting. At the same time, contemporary imaging techniques well established in clinical practice, provide a variety of information on real-time,…
In this paper we study a model describing the growth of necrotic tumors in different regimes of vascularisation. The tumor consists of a necrotic core of death cells and a surrounding nonnecrotic shell. The corresponding mathematical…
We present a robust computational framework for Hele-Shaw tumor growth with necrotic cores, a problem identified as the incompressible limit of the Porous Media Equation. Simulating this system presents a fundamental challenge: while the…
Equivocal 3D lesion segmentation exhibits high inter-observer variability. Conventional deterministic models ignore this aleatoric uncertainty, producing over-confident masks that obscure clinical risks. Conversely, while generative methods…
This paper aims at proving asymptotic stability of the radial stationary solution of a free boundary problem modeling the growth of nonnecrotic tumors with fluid-like tissues. In a previous paper we considered the case where the nutrient…
The three-body problem is famously chaotic, with no closed-form analytical solutions. However, hierarchical systems of three or more bodies can be stable over indefinite timescales. A system is considered hierarchical if the bodies can be…
Computational techniques which establish the stability of an evolution-boundary algorithm for a model wave equation with shift are incorporated into a well-posed version of the initial-boundary value problem for gravitational theory in…
Tomographic image reconstruction with deep learning is an emerging field, but a recent landmark study reveals that several deep reconstruction networks are unstable for computed tomography (CT) and magnetic resonance imaging (MRI).…
Here, we investigate the linear spatial stability of a parallel two-dimensional compressible boundary layer on an adiabatic plate by considering 2D and 3D disturbances. We employ the Compound Matrix Method for the first time for…