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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
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In most main group element compounds, the valence electrons of the isolated atoms combine to form chemical bonds that satisfy the octet rule. For instance, the four valence electrons of carbon overlap with electrons from four hydrogen atoms to form CH4. The one valence electron leaves sodium and adds to the seven valence electrons of chlorine to form the ionic formula unit NaCl (Figure 1a). Transition metals do not normally bond in this fashion. They primarily form coordinate covalent bonds, a...
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The human heart is made up of three layers of tissue that are surrounded by the pericardium, a membrane that protects and confines the heart. The outermost layer, closest to the pericardium, is the epicardium. The pericardial cavity separates the pericardium from the epicardium. Beneath the epicardium is the myocardium, the middle layer, and the endocardium, the innermost layer. There are four chambers of the heart: the right atrium, the right ventricle, the left atrium, and the left ventricle.
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Understanding the motion of particles is a fundamental aspect of classical mechanics, and the choice of the coordinate system plays a pivotal role in unraveling the complexities of their dynamics.
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The Cartesian coordinate plane is a fundamental structure in mathematics that enables the visualization of relationships between numerical values in two dimensions. It is formed by two intersecting number lines: a horizontal x-axis and a vertical y-axis. These axes meet at the origin, the point where both values are zero. Their intersection divides the plane into four quadrants labeled in a counterclockwise direction starting from the upper right.An ordered pair of numbers represents every...
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Related Experiment Video

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Author Spotlight: Workflow for Integrating POCUS Data into EHR for Managing Heart Failure Patients
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Universal ventricular coordinates: A generic framework for describing position within the heart and transferring

Jason Bayer1, Anton J Prassl2, Ali Pashaei1

  • 1LIRYC Electrophysiology and Heart Modeling Institute, Bordeaux Fondation, avenue du Haut-Lévèque, Pessac 33600, France; IMB Bordeaux Institute of Mathematics, University of Bordeaux, 351 cours de la Libération, Talence 33405, France.

Medical Image Analysis
|February 8, 2018
PubMed
Summary

Universal Ventricular Coordinates (UVC) provide a standardized method for mapping any biventricular heart. This novel approach enables fast and accurate data transfer between diverse cardiac geometries, aiding comparative studies.

Keywords:
CoordinatesDeformationMappingVolumetric meshes

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Area of Science:

  • Computational biology
  • Medical imaging
  • Cardiovascular research

Background:

  • Comparing diverse cardiac anatomies is challenging.
  • A standardized coordinate system for ventricles is needed for data transfer and analysis.

Purpose of the Study:

  • Introduce Universal Ventricular Coordinates (UVC) for any biventricular heart.
  • Demonstrate UVC's utility in transferring various data types between cardiac meshes.

Main Methods:

  • Developed UVC using four intuitive coordinates derived from Laplace's equation solutions.
  • Applied UVC to map scalar, vector, and tensor data between four ventricular meshes from three species.
  • Utilized KD tree for efficient node searching during data transfer.

Main Results:

  • UVC enabled rapid data transfer (minutes) between disparate ventricular meshes.
  • Mapping accuracy showed minimal distance errors (less than element size).
  • Transferred fiber directions exhibited <5° difference, demonstrating gradient transfer capability.

Conclusions:

  • UVC offers a robust framework for inter-heart data transfer.
  • The system facilitates comparative analysis and quantitative studies across different cardiac geometries.
  • Complex structures like papillary muscles require additional definitions beyond the UVC framework.