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X-ray Diffraction of Biological Samples01:10

X-ray Diffraction of Biological Samples

X-ray diffraction or XRD is an analytical tool that utilizes X-rays to study ordered structures such as crystalline organic and inorganic samples, polycrystalline materials, proteins, carbohydrates, and drugs.
According to Bragg's law, when X-rays strike the sample positioned on a stage, the rays are  scattered by the electron clouds around the sample atoms. The  X-ray diffraction or scattering is caused by constructive interference of the X-ray waves that reflect off the internal crystal...
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In studying beam stress distribution, examining an elemental section is essential. To determine the average shearing stress on this face, the calculated shear is divided by the surface area. Importantly, shearing stresses on the beam's transverse and horizontal planes mirror each other, indicating a consistent stress distribution along the upper region of the beam. Notably, shearing stresses are absent at the beam's upper and lower surfaces due to the absence of applied forces in these areas.
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...

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Related Experiment Video

Updated: Jun 12, 2026

Quantitative Analysis of Cell Edge Dynamics during Cell Spreading
10:54

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Published on: May 22, 2021

Gaussian beam spread in biological tissues.

L I Grossweiner, J L Karagiannes, P W Johnson

    Applied Optics
    |June 18, 2010
    PubMed
    Summary

    Optical fiber laser measurements in tissue reveal that flux density decreases exponentially with distance. This finding applies to various incident light profiles, aiding optical modeling in biomedical applications.

    Area of Science:

    • Biomedical Optics
    • Photomedicine
    • Biophotonics

    Background:

    • Accurate modeling of light propagation in biological tissues is crucial for applications like photodynamic therapy and optical imaging.
    • Understanding light attenuation and distribution within tissues informs treatment efficacy and safety.
    • Previous models often simplify light source profiles, potentially limiting predictive accuracy.

    Purpose of the Study:

    • To measure and model flux density distributions in large tissue sections under specific laser wavelengths.
    • To validate a diffusion approximation model for light propagation with experimental data.
    • To establish a generalizable principle for light attenuation in tissue regardless of the incident beam profile.

    Main Methods:

    • Experimental measurement of flux density distributions using 633-nm and 1064-nm laser radiation delivered via optical fiber in large tissue sections.

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  • Development and application of a 2-D diffusion approximation model for light propagation.
  • Nonlinear regression analysis to fit experimental data with the diffusion model predictions.

    • Main Results:

    • Measured flux density distributions were successfully modeled using the 2-D diffusion approximation.
    • The radial average flux density was found to be exponentially attenuated.
    • This exponential attenuation held true for arbitrary incident irradiance profiles, not just Gaussian beams.

    Conclusions:

    • The diffusion approximation provides a robust framework for modeling light transport in tissue under fiber-optic illumination.
    • Exponential attenuation of radial average flux density is a fundamental characteristic of light propagation in large tissue sections.
    • These findings enhance the predictive capability of optical models for various biomedical applications involving light-tissue interactions.