Related papers: Sub-voxel perfusion modeling in terms of coupled 3…
We present a new method for modeling tissue perfusion on the capillary scale. The microvasculature is represented by a network of one-dimensional vessel segments embedded in the extra-vascular space. Vascular and extra-vascular space…
Tumor growth beyond a critical size relies on the development of a functional vascular network, which ensures adequate oxygen and nutrient supply. In this work, we present a modeling framework based on an optimization-based 3D-1D coupling…
We consider a multiscale approach based on immersed methods for the efficient computational modeling of tissues composed of an elastic matrix (in two or three-dimensions) and a thin vascular structure (treated as a co-dimension two…
We propose and analyze a hierarchy of three models of blood perfusion through a tissue surrounding a thin arteriole or venule. Our goal is to rigorously link 3D-3D Darcy--Stokes, 3D-1D Darcy--Poiseuille, and 1D Green's function methods…
In the context of micro-circulation, the coexistence of two distinct length scales - the vascular radius and the tissue/organ scale - with a substantial difference in magnitude, poses significant challenges. To handle slender inclusions and…
The paper deals with modeling the liver perfusion intended to improve quantitative analysis of the tissue scans provided by the contrast-enhanced computed tomography (CT). For this purpose, we developed a model of dynamic transport of the…
In this paper, we derive an effective model for transport processes in periodically perforated elastic media, taking into account, e.g., cyclic elastic deformations as they occur in lung tissue due to respiratory movement. The underlying…
In this paper, a multiscale constitutive framework for one-dimensional blood flow modeling is presented and discussed. By analyzing the asymptotic limits of the proposed model, it is shown that different types of blood propagation phenomena…
Diffusion models have become a popular approach for image generation and reconstruction due to their numerous advantages. However, most diffusion-based inverse problem-solving methods only deal with 2D images, and even recently published 3D…
Many inverse problems are ill-posed and need to be complemented by prior information that restricts the class of admissible models. Bayesian approaches encode this information as prior distributions that impose generic properties on the…
We present and analyse a model for cell signalling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces, and both inter- and intracellular signalling. Using techniques from the theory of…
This paper considers particle propagation in a cylindrical molecular communication channel, e.g. a simplified model of a blood vessel. Emitted particles are influenced by diffusion, flow, and a vertical force induced e.g. by gravity or…
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…
Diffusion models have emerged as the new state-of-the-art generative model with high quality samples, with intriguing properties such as mode coverage and high flexibility. They have also been shown to be effective inverse problem solvers,…
Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…
In recent years, 3D vision has become a crucial field within computer vision, powering a wide range of applications such as autonomous driving, robotics, augmented reality, and medical imaging. This field relies on accurate perception,…
The paper gives a description of wave propagation in discrete-periodic one-dimensional media with block structure. For one-dimensional problems mathematical models are proposed that describe block structures in the form of a mass chain or…
Diffusion models are a special type of generative model, capable of synthesising new data from a learnt distribution. We introduce DISPR, a diffusion-based model for solving the inverse problem of three-dimensional (3D) cell shape…
The goal of this paper is to investigate the validity of a hybrid embedded/homogenized in-silico approach for modeling perfusion through solid tumors. The rationale behind this novel idea is that only the larger blood vessels have to be…
We propose and analyze a family of models describing blood perfusion through a tissue surrounding a thin blood vessel. Our goal is to rigorously establish convergence results among 3D-3D Darcy--Stokes, 3D-1D Darcy--Poiseuille, and 1D…