An Eulerian PDE Approach for Computing Tissue Thickness

Anthony J. Yezzi, Jerry Ladd Prince

Research output: Contribution to journalArticle

Abstract

We outline an Eulerian framework for computing the thickness of tissues between two simply connected boundaries that does not require landmark points or parameterizations of either boundary. Thickness is defined as the length of correspondence trajectories, which run from one tissue boundary to the other, and which follow a smooth vector field constructed in the region between the boundaries. A pair of partial differential equations (PDEs) that are guided by this vector field are then solved over this region, and the sum of their solutions yields the thickness of the tissue region. Unlike other approaches, this approach does not require explicit construction of any correspondence trajectories. An efficient, stable, and computationally fast solution to these PDEs is found by careful selection of finite differences according to an upwinding condition. The behavior and performance of our method is demonstrated on two simulations and two magnetic resonance imaging data sets in two and three dimensions. These experiments reveal very good performance and show strong potential for application in tissue thickness visualization and quantification.

Original languageEnglish (US)
Pages (from-to)1332-1339
Number of pages8
JournalIEEE Transactions on Medical Imaging
Volume22
Issue number10
DOIs
StatePublished - Oct 2003

Fingerprint

Partial differential equations
Tissue
Trajectories
Magnetic resonance
Parameterization
Visualization
Magnetic Resonance Imaging
Imaging techniques
Experiments

Keywords

  • Correspondence trajectory
  • Numerical methods
  • Partial differential equations (PDEs)
  • Thickness

ASJC Scopus subject areas

  • Biomedical Engineering
  • Radiology Nuclear Medicine and imaging
  • Radiological and Ultrasound Technology
  • Electrical and Electronic Engineering
  • Computer Science Applications
  • Computational Theory and Mathematics

Cite this

An Eulerian PDE Approach for Computing Tissue Thickness. / Yezzi, Anthony J.; Prince, Jerry Ladd.

In: IEEE Transactions on Medical Imaging, Vol. 22, No. 10, 10.2003, p. 1332-1339.

Research output: Contribution to journalArticle

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