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Related Concept Videos

Spherical Coordinates01:23

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Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
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A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have  equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
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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...
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Bone Structure01:55

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Within the skeletal system, the structure of a bone, or osseous tissue, can be exemplified in a long bone, like the femur, where there are two types of osseous tissue: cortical and cancellous.
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Quantitative Hardness Measurement by Instrumented AFM-indentation
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Measuring bone stiffness using spherical indentation.

Oliver R Boughton1,2, Shaocheng Ma1,2, Sarah Zhao1

  • 1The MSk Lab, Imperial College London, Charing Cross Hospital, London, United Kingdom.

Plos One
|July 13, 2018
PubMed
Summary
This summary is machine-generated.

Spherical indentation is a repeatable method for measuring human cortical bone stiffness. However, it did not reliably predict bone elastic modulus compared to compression testing, suggesting scale-dependent properties influence results.

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Area of Science:

  • Biomaterials Science
  • Orthopaedic Engineering
  • Materials Science

Background:

  • Bone material properties are crucial for assessing fracture risk and implant fixation in orthopaedics and dentistry.
  • Bone's anisotropic and hierarchical nature means its measured properties vary with the scale of measurement.
  • Millimetre-scale assessment is relevant for clinical problems like fracture risk and implant stability.

Purpose of the Study:

  • To investigate the reliability of spherical-tip indentation for measuring the apparent elastic modulus of human cortical bone at the millimetre scale.
  • To compare indentation measurements with established mechanical compression testing.

Main Methods:

  • Cortical bone samples were obtained from human femoral necks (n=19).
  • Spherical indentation (1.5 mm diameter ruby tip) was performed across multiple locations on each sample.
  • Mechanical compression testing was conducted on the same samples.
  • Repeatability of indentation was assessed, and correlation between indentation and compression was analyzed.

Main Results:

  • Spherical indentation demonstrated repeatability for measurements at the same location (mean coefficient of repeatability: 0.4 GPa).
  • Significant variation in indentation modulus was observed between different locations on the bone samples (mean coefficient of repeatability: 3.1 GPa).
  • No significant correlation was found between indentation and compression testing results for bone elastic modulus (r = 0.33, p = 0.17).

Conclusions:

  • Spherical-tip indentation is a repeatable technique for assessing human cortical bone's elastic modulus.
  • The technique, as applied, could not reliably predict bone elastic modulus measured by compression testing.
  • Differences may stem from indentation probing micro-scale properties versus compression testing assessing millimetre-scale properties; further refinement of indentation techniques is warranted.