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The measures of central tendency calculated from a data set may not reveal much about its intrinsic distribution. If a plot is made of the data set’s values, the mean and the median may not only differ, but also the plot may have more values on one side of the central tendencies. Such a data set is said to be skewed towards that side.
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Orthogonal trajectories describe the geometric relationship between two families of curves that intersect each other at right angles. One illustrative case involves a family of parabolas that open sideways along the x-axis. These curves share a common shape but differ by a scaling parameter, resulting in a set of curves that all pass through the origin and widen at different rates.Determining Orthogonal TrajectoriesTo identify the orthogonal trajectories for these parabolas, the first step...
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If the frequency distribution of a data set is more inclined towards smaller or larger values, the distribution is said to be skewed. If data values are skewed to the right, then the distribution is called positively skewed. Conversely, if the plot is skewed to the left, the distribution is called negatively skewed.
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Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...
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Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...
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In structural engineering, the equilibrium of a system is not only determined by its equations of equilibrium but also with the help of constraints. Constraints refer to restrictions on the motion of a system. The proper combinations of constraints can minimize the total number of constraints needed to maintain a system in mechanical equilibrium. When this happens, the system is said to be statically determinate. For such systems, the unknown reaction supports can be estimated using equilibrium...
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Imagen de asimetría de difusión mediante imagen de trayectoria Q-space con restricciones de positividad

Jun Li1, Zan Chen2, Zhaoyi Teng1

  • 1Zhejiang University of Technology, Xihu District, Hangzhou City,Zhejiang Province, ChinaHangzhou City, Hangzhou, Zhejiang, 310014, China.

Physics in medicine and biology
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PubMed
Resumen

Este estudio presenta la imagen de trayectoria Q-space con restricciones de tensor de asimetría (QTI-STC) para mejorar el análisis de RM de difusión. El nuevo método mejora la precisión y la robustez al incorporar información de difusión de orden superior, superando a las técnicas convencionales.

Palabras clave:
imagen de trayectoria Q-spaceresonancia magnética de difusiónprogramación semidefinidatensor de asimetría

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Área de la Ciencia:

  • Imagenología Médica
  • Biofísica
  • Neurociencia Computacional

Sus antecedentes:

  • La resonancia magnética de difusión (dMRI) caracteriza la microestructura tisular a través de la difusión del agua.
  • La imagen convencional de trayectoria Q-space (QTI) utiliza momentos de bajo orden, omitiendo potencialmente información de orden superior como los tensores de asimetría.
  • Esta omisión puede conducir a una representación incompleta de la asimetría de difusión y a un sesgo de estimación.

Objetivo del estudio:

  • Desarrollar un método avanzado de dMRI, imagen de trayectoria Q-space con restricciones de tensor de asimetría (QTI-STC).
  • Incorporar tensores de asimetría de orden superior y restricciones de positividad en el análisis de dMRI.
  • Introducir técnicas de filtrado novedosas (LF y QF) para el análisis mejorado de componentes de difusión.

Principales métodos:

  • Imagen de trayectoria Q-space propuesta con restricciones de tensor de asimetría (QTI-STC).
  • Se incorporaron tensores de asimetría de orden superior bajo restricciones de positividad.
  • Se introdujeron filtros lineales ponderados por traza (LF) y cuadráticos ponderados por traza (QF).

Principales resultados:

  • QTI-STC mitiga el sesgo de estimación al tener en cuenta la asimetría de orden superior.
  • Los filtros LF y QF mejoran las señales de alta difusión y suprimen las señales de baja difusión.
  • Los experimentos mostraron que QTI-STC produce estimaciones más cercanas a la verdad fundamental en datos sintéticos.

Conclusiones:

  • QTI-STC proporciona información de asimetría de difusión más precisa y completa en dMRI.
  • El método propuesto demuestra una robustez superior en condiciones de imagen ruidosas.
  • Este avance ofrece una caracterización mejorada de la microestructura tisular utilizando dMRI.