Related papers: A Model of Blood Flow in a Circulation Network
We study a coupled system of Navier-Stokes equation and the equation of conservation of mass in a one-dimensional network. The system models the blood circulation in arterial networks. A special feature of the system is that the equations…
One-dimensional (1D) blood flow simulations are extensively used in cardiovascular research due to their computational efficiency and effectiveness in analyzing pulse wave dynamics. Despite their versatility and simplicity, there is a lack…
We develop two mathematical lumped parameter models for blood pressure distribution in the Fontan blood flow circulation: an ODE based spatially homogeneous model and a PDE based spatially inhomogeneous model. We present numerical…
In this paper we will address the problem of developing mathematical models for the numerical simulation of the human circulatory system. In particular, we will focus our attention on the problem of haemodynamics in large human arteries.
Numerical model of the peripheral circulation and dynamical model of the large vessels and the heart are discussed in this paper. They combined together into the global model of blood circulation. Some results of numerical simulations…
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by…
We consider a boundary value problem for the system of equations describing the stationary motion of a viscous nonhomogeneous asymmetric fluid in a bounded planar domain having a $C^2$ boundary. We use a stream-function formulation after…
We present experimental evidence of multiple blood flow configurations in a relatively simple microfluidic network under constant inlet conditions. We provide evidence of multistability and unsteady dynamics and find good agreement with a…
In this article, we review the mathematical modeling for the vascular system.
We consider the initial boundary value problem for a model system of one-dimensional equations which describe unsteady polytropic motions of a mixture of viscous compressible fluids. We prove the global existence and uniqueness theorem for…
It is well known that in the computational fluid dynamics simulations related to the cardiovascular system the enforcement of outflow boundary conditions is a crucial point. In fact, they highly affect the computed flow and a wrong setup…
The blood vascular system consists of blood vessels such as arteries, arterioles, capillaries and veins that convey blood throughout the body. The pressure difference which exists between the ends of the vessels provides the living force…
One-dimensional blood flow models take the general form of nonlinear hyperbolic systems but differ greatly in their formulation. One class of models considers the physically conserved quantities of mass and momentum, while another class…
This paper deals with an initial and boundary value problem for a system coupling equation and boundary condition both of Cahn-Hilliard type; an additional convective term with a forced velocity field, which could act as a control on the…
A new two-dimensional model for blood flows in arteries with arbitrary cross sections is derived. The model consists of a system of balance laws for conservation of mass and balance of momentum in the axial and angular directions. The…
We show the solvability of a multidimensional Muskat type initial boundary value problem. The proposed mathematical model describing the transport phenomena of non-homogeneous flow in porous media, relies on a generalized formulation of the…
For the string baryon model "triangle" the initial-boundary value problem is stated and solved in general. This problem implies defining a classical motion of the system on the base of given initial position and initial velocities of string…
In this paper, we are concerned with the simulation of blood flow in microvascular networks and the surrounding tissue. To reduce the computational complexity of this issue, the network structures are modeled by a one-dimensional graph,…
Internal haemorrhage, often leading to cardio-vascular arrest happens to be one of the prime sources of high fatality rates in mammals. We propose a simplistic model of fluid flow to specify the location of the haemorrhagic spots, which, if…
To address the issue of computational efficiency related to the modelling of blood flow in complex networks, we derive a family of nonlinear lumped-parameter models for blood flow in compliant vessels departing from a well-established…