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Pulse wave propagation models
- Speaker(s)
- Jan Poleszczuk
- Affiliation
- MiSDoMP i IBIB PAN
- Date
- Jan. 15, 2014, 2:15 p.m.
- Room
- room 5840
- Seminar
- Seminar of Biomathematics and Game Theory Group
During the seminar I will present the state of the art of mathematical
methods utilized in the modeling of the pulse wave propagation (PWP)
through the arterial tree.
In the spatially distributed approach, the whole arterial tree is divided into segments that are assumed to be straight compliant vessels (each segment may have different characteristics), some of which bifurcate into two subsequent smaller vessels. A typical blood vessel segment is modeled as an axisymmetric compliant cylinder with wall assumed to be impermeable (or permeable only to a small extent). The assumption about the axisymmetry allows to reduce the continuous flow into one spatial dimension, i.e. position along the vessel. The relation between pressure p and flow q for each vascular segment is derived from conservation of mass and the momentum equations by assuming fully developed incompressible Newtonian flow in a straight vessel.
In other approach, each arterial segment is lumped and spatial information about the flow is lost. This approach allows to express the system as the electrical circuit analog, with capacitors and resistors as the main components. Obviously, these models are simpler than the distributed ones and the mathematical complications are kept to a minimum. They can also yield useful insight into the behavior of the system under investigation.
In the spatially distributed approach, the whole arterial tree is divided into segments that are assumed to be straight compliant vessels (each segment may have different characteristics), some of which bifurcate into two subsequent smaller vessels. A typical blood vessel segment is modeled as an axisymmetric compliant cylinder with wall assumed to be impermeable (or permeable only to a small extent). The assumption about the axisymmetry allows to reduce the continuous flow into one spatial dimension, i.e. position along the vessel. The relation between pressure p and flow q for each vascular segment is derived from conservation of mass and the momentum equations by assuming fully developed incompressible Newtonian flow in a straight vessel.
In other approach, each arterial segment is lumped and spatial information about the flow is lost. This approach allows to express the system as the electrical circuit analog, with capacitors and resistors as the main components. Obviously, these models are simpler than the distributed ones and the mathematical complications are kept to a minimum. They can also yield useful insight into the behavior of the system under investigation.
