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Inverse trigonometric functions are fundamental mathematical tools that reverse the actions of standard trigonometric functions. While trigonometric functions map angles to ratios, inverse trigonometric functions perform the opposite operation by mapping a ratio back to its corresponding angle. These functions are essential in various applications, particularly in determining angles when given specific distances, such as calculating elevation angles in navigation and engineering.For a function...
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Inverse Hyperbolic Functions and Their Derivatives01:25

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The shape of a suspension bridge cable hanging under its own weight is described by a catenary curve, which is modeled using the hyperbolic cosine function. This mathematical model accurately captures the balance between gravity and tension acting along the cable. When a particular vertical position on the cable is known, the corresponding horizontal position can be determined using the inverse hyperbolic cosine function, allowing for a detailed analysis of the cable's geometry.Inverse...
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A ship tracking an approaching aircraft relies on geometric measurements to find out the aircraft’s position relative to the observer. By measuring the slant distance to the aircraft and the angle of elevation, the horizontal and vertical components of the distance can be obtained using trigonometric relationships. This geometric approach provides a basis for analyzing how the observed angle changes as the aircraft moves closer to the ship.To examine the mathematical behavior of the angle...
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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Appropriate Objective Functions for Quantifying Iris Mechanical Properties Using Inverse Finite Element Modeling.

Anup D Pant1, Syril K Dorairaj2, Rouzbeh Amini3

  • 1Department of Biomedical Engineering, The University of Akron, Akron, OH 44325 e-mail: .

Journal of Biomechanical Engineering
|March 24, 2018
PubMed
Summary
This summary is machine-generated.

Determining iris mechanical properties in vivo is crucial for glaucoma research. Using inverse finite element modeling, objective functions incorporating local displacement values improve accuracy, especially with measurement errors.

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Area of Science:

  • Ophthalmology
  • Biomechanics
  • Medical Imaging

Background:

  • Quantifying iris mechanical properties offers insights into glaucoma pathophysiology.
  • Ex vivo studies reveal differences in glaucomatous versus normal irises, but are limited for clinical applications.
  • In vivo mechanical property assessment is essential for diagnosis and treatment development.

Purpose of the Study:

  • To evaluate objective functions for inverse finite element (FE) modeling of in vivo iris mechanics.
  • To determine the most reliable criterion for estimating iris mechanical properties using clinical biometrics.
  • To assess the impact of measurement errors on the performance of different objective functions.

Main Methods:

  • Inverse finite element (FE) modeling approach was employed.
  • Five objective functions based on iris biometrics (iris chord length [CL] and iris concavity [CV]) were evaluated.
  • The study considered scenarios with and without clinical measurement errors.

Main Results:

  • In the absence of measurement error, a combination of iris CL and CV serves as a suitable objective function.
  • With the introduction of measurement errors, objective functions utilizing numerous local displacement values yield more reliable outcomes.
  • The choice of objective function significantly impacts the accuracy of in vivo iris mechanical property estimation.

Conclusions:

  • Accurate in vivo quantification of iris mechanical properties is achievable through inverse FE modeling.
  • Objective functions incorporating local displacement data enhance reliability in the presence of measurement errors.
  • This approach holds potential for improving glaucoma diagnosis and guiding treatment strategies.