Abstract
The mathematical modeling of blood flow in the cardiovascular system has long history. Zero-dimensional (0D) and one-dimensional (1D) models contributeactively to the study of the human cardiovascular system. Usually, low-dimensional models consist of a system of time dependent equations that do not involve spatial derivatives, thus reducing the computational complexity compared to multi-dimensional models. Despite that more complex 3D cardiovascular models are available, there is a tendency of reintroducing the simpler 1D models, due to their capability of involving extensive segments of the cardiovascular system and providing boundary conditions for the advanced 3D models. The low-dimensional models can provide useful information to clinicians about the characteristics of blood flow at the level of individual incidents, patient-specific treatment, and can describe the general phenomena of circulatory physiology. The purpose of the current review is to discuss the recent advances and evolution of 0D and 1D models of human cardiovascular system.
Highlights
The cardiovascular system is the blood transport mechanism that enables the nutrient transport to the tissues and organs of the body and the removal of various waste and toxic substances [1]
Blood flow in the cardiovascular system obeys the laws of mass and momentum conservation and blood interaction with the arterial wall [2,3]
A special case of 0D modeling is that of local circulation characteristics in important vascular subsystem, such as cerebral, coronary, renal or lower extremity vessels where often multiple compartment models have been designed to include features such as anastomoses, auto-regulation effects and occasionally collapsible vessels and internal valves
Summary
The cardiovascular system is the blood transport mechanism that enables the nutrient transport to the tissues and organs of the body and the removal of various waste and toxic substances [1]. Blood flow in the cardiovascular system obeys the laws of mass and momentum conservation and blood interaction with the arterial wall [2,3]. Lumped parameter models assume a uniform distribution of the fundamental variables, pressure, flow and volume, within any particular compartment, organ or vessel at any time instant. The 0D models give rise to a coupled system of ordinary differential equations (ODEs), suitable for the assessment of global distributions of pressure, flow and blood volume over a range of physiological conditions. For each vascular compartment included in the models, two ODEs are applicable, representing conservation of mass and momentum, complemented by an algebraic equilibrium equation that relates compartment volume to pressure. Voltage in a circuit is the reason that current flow overcomes the electrical resistance.
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