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Related Concept Videos

Polar Coordinates: Problem Solving01:27

Polar Coordinates: Problem Solving

Directional radiation patterns are central to antenna analysis, as they illustrate how signal strength varies with direction. These patterns are often modeled using polar plots, where the radial distance from the origin represents signal intensity at a given angle. A commonly used idealized form is the four-lobed rose curve, which captures the concept of directional beams in a simplified mathematical form.The four-lobed rose curve, described by r = cos⁡(2θ), features four symmetric lobes, each...
Computed Tomography01:10

Computed Tomography

Tomography refers to imaging by sections. Computed tomography (CT) is a non-invasive imaging technique that uses computers to analyze several cross-sectional X-rays to reveal minute details about structures in the body.
The technique was invented in the 1970s and is based on the principle that as X-rays pass through the body, they are absorbed or reflected at different levels. In the technique, a patient lies on a motorized platform while a computerized axial tomography (CAT) scanner rotates...
Cylinders in Three-Dimensional Space01:28

Cylinders in Three-Dimensional Space

A cylindrical surface is generated when a two-dimensional profile curve is translated along a straight line in three-dimensional space. The translated copies of the curve form a surface composed of parallel rulings, each oriented in the same fixed direction. This construction allows many three-dimensional forms to be described using relatively simple planar equations.In Cartesian coordinates, a cylindrical surface is often recognized by an equation that omits one of the three variables. For...
Imaging Studies III: Computed Tomography01:27

Imaging Studies III: Computed Tomography

DefinitionComputed Tomography (CT) of the genitourinary (GU) tract is a non-invasive imaging modality that utilizes X-rays and computer processing to generate detailed cross-sectional images of the urinary system, encompassing the kidneys, ureters, bladder, and adjacent structures such as the adrenal glands.PurposeCT scans of the GU tract serve several diagnostic and therapeutic purposes, including:Diagnosis of Urinary Tract Diseases: Detects kidney stones, tumors, cysts, and congenital...
Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
The particle's location is described using a unit vector along the radial direction. Deriving the particle's position with respect to time...
Integration Applied to Polar Coordinates to Find Areas01:15

Integration Applied to Polar Coordinates to Find Areas

A rotating lawn sprinkler with an uneven spray pattern produces a variable reach as it distributes water in different directions. This directional variation in spray distance can be effectively described using polar coordinates, where the distance from the center is represented as a function of the angle of rotation. The path traced by the spray then forms a polar curve, which captures the irregularities in the sprinkler’s reach across the full rotation.To calculate the total area watered by...

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Longitudinal Morphological and Physiological Monitoring of Three-dimensional Tumor Spheroids Using Optical Coherence Tomography
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Published on: February 9, 2019

Estimation and statistical bounds for three-dimensional polar shapes in diffuse optical tomography.

Gregory Boverman1, Eric L Miller, Dana H Brooks

  • 1Biomedical Engineering Department, Rensselaer Polytechnic Institute, 7046 Jonsson Engineering Center, Troy, NY 12180, USA. boverg@rpi.edu

IEEE Transactions on Medical Imaging
|June 11, 2008
PubMed
Summary

This study presents a new method for directly reconstructing tumor shapes using diffuse optical tomography (DOT). The approach accurately estimates object boundaries and contrasts, improving medical imaging capabilities.

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Area of Science:

  • Biomedical Optics
  • Medical Imaging
  • Computational Science

Background:

  • Voxel-based diffuse optical tomography (DOT) reconstructions yield smooth images, hindering accurate tumor boundary and contrast estimation.
  • Quadratic regularization in DOT attenuates high spatial frequencies, complicating the localization of anomalies.

Purpose of the Study:

  • To develop a method for directly reconstructing the shape boundary of piecewise constant objects from diffuse optical measurements.
  • To improve the spatial resolution and accuracy of anomaly detection in DOT.

Main Methods:

  • Parametric modeling of object boundaries using a spherical harmonic basis.
  • Computation of measurement sensitivities with respect to shape parameters.
  • Utilized a projected Newton method for simultaneous optimization of object center and shape parameters.
  • Employed a finite-difference-based forward model for forward and adjoint field computation.

Main Results:

  • Successfully reconstructed simulated target shapes with high accuracy.
  • Achieved <10% error in object volume and absorption contrast for an eighth-order spherical harmonic model.
  • Demonstrated the ability to estimate small absorption contrasts (0.15 cm⁻¹) and volumes (4.82 cm³).
  • Quantified shape uncertainty using the Cramér-Rao lower bound and visualized 3D confidence regions.

Conclusions:

  • The developed shape reconstruction method directly estimates object boundaries and contrasts in DOT.
  • The approach offers significant improvements over traditional smooth reconstruction methods for anomaly localization.
  • The method shows robustness and potential for accurate tumor imaging in biomedical applications.