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Principles of doppler tomography

Technical Report:

Abstract

This paper shows how the radon transform can be used to determine vector fields. A scheme to determine the velocity field of a moving fluid by measurements with a continuous doppler signal is suggested. When the flow is confined to a bounded domain, as is the case in most applications, it can be uniquely decomposed into one gradiental and one rotational part. The former vanishes if the fluid is incompressible and source-free, and the latter can be completely reconstructed by the methods proposed in this paper if the domain is simply connected. Special attention is paid to laminar flow in a long cylindrical vessel with circular cross-section. Under such conditions the flow profile becomes parabolic, which makes the vessel recognizable as a typical `N-shaped` pattern in an image describing the rotation of the velocity field. The vessel yields the same doppler tomographic pattern, no matter how it is sectioned. The ideas presented should be applicable also when studying the flow in blood vessels, even if the flow profile in these is not quite parabolic. The discrepancies only make the `N-shape` somewhat distorted.
Authors:
Publication Date:
Aug 01, 1992
Product Type:
Technical Report
Report Number:
LUTFD2-TFMA-92-7002
Reference Number:
SCA: 990200; 550602; 550601; PA: AIX-25:003860; EDB-94:016827; ERA-19:006177; NTS-94:014810; SN: 93001120941
Resource Relation:
Other Information: PBD: Aug 1992
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; 62 RADIOLOGY AND NUCLEAR MEDICINE; DOPPLER EFFECT; TOMOGRAPHY; ARTERIES; BLOOD FLOW; FLUID FLOW; MATHEMATICS; 990200; 550602; 550601; MATHEMATICS AND COMPUTERS; EXTERNAL RADIATION IN DIAGNOSTICS; UNSEALED RADIONUCLIDES IN DIAGNOSTICS
OSTI ID:
10110303
Research Organizations:
Lund Univ. (Sweden). Dept. of Mathematics
Country of Origin:
Sweden
Language:
English
Other Identifying Numbers:
Other: ON: DE94609546; TRN: SE9300250003860
Availability:
OSTI; NTIS; INIS
Submitting Site:
SWDN
Size:
17 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Juhlin, P. Principles of doppler tomography. Sweden: N. p., 1992. Web.
Juhlin, P. Principles of doppler tomography. Sweden.
Juhlin, P. 1992. "Principles of doppler tomography." Sweden.
@misc{etde_10110303,
title = {Principles of doppler tomography}
author = {Juhlin, P}
abstractNote = {This paper shows how the radon transform can be used to determine vector fields. A scheme to determine the velocity field of a moving fluid by measurements with a continuous doppler signal is suggested. When the flow is confined to a bounded domain, as is the case in most applications, it can be uniquely decomposed into one gradiental and one rotational part. The former vanishes if the fluid is incompressible and source-free, and the latter can be completely reconstructed by the methods proposed in this paper if the domain is simply connected. Special attention is paid to laminar flow in a long cylindrical vessel with circular cross-section. Under such conditions the flow profile becomes parabolic, which makes the vessel recognizable as a typical `N-shaped` pattern in an image describing the rotation of the velocity field. The vessel yields the same doppler tomographic pattern, no matter how it is sectioned. The ideas presented should be applicable also when studying the flow in blood vessels, even if the flow profile in these is not quite parabolic. The discrepancies only make the `N-shape` somewhat distorted.}
place = {Sweden}
year = {1992}
month = {Aug}
}