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Related Concept Videos

Parametric Surfaces01:30

Parametric Surfaces

A parametric surface in three-dimensional space is defined through a vector-valued function\begin{equation*}\mathbf{r}(u, v) = x(u, v)\mathbf{i} + y(u, v)\mathbf{j} + z(u, v)\mathbf{k}\end{equation*}where u and v are parameters within a specified domain D in the uv-plane. The functions x(u, v), y(u, v), and z(u, v) define the coordinates of points on the surface. As u and v vary over D, the position vector r(u, v) traces a continuous surface in space. This parametric representation is essential...
Mesh Analysis01:20

Mesh Analysis

Mesh analysis is a valuable method for simplifying circuit analysis using mesh currents as key circuit variables. Unlike nodal analysis, which focuses on determining unknown voltages, mesh analysis applies Kirchhoff's voltage law (KVL) to find unknown currents within a circuit. This method is particularly convenient in reducing the number of simultaneous equations that need to be solved.
A fundamental concept in mesh analysis is the definition of meshes and mesh currents. A mesh is a closed...
Tangent Planes to a Parametric Surface01:22

Tangent Planes to a Parametric Surface

A tangent plane provides a linear approximation to a curved surface at a specific point, capturing the local behavior of the surface. It can be understood as the plane that just touches the surface at that point and is defined by the tangent directions of curves lying on the surface. These tangent directions arise naturally when the surface is described parametrically, allowing systematic construction of the plane.For a surface expressed in parametric form, the position of any point is...
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Mesh analysis becomes simpler when analyzing circuits with current sources, whether independent or dependent. The presence of current sources reduces the number of equations required for analysis. Two cases illustrate this:
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Related Experiment Video

Updated: Jun 9, 2026

Precision Measurements and Parametric Models of Vertebral Endplates
10:35

Precision Measurements and Parametric Models of Vertebral Endplates

Published on: September 17, 2019

Parametric FE mesh generation: application to the cervical spine.

F Galbusera1, C M Bellini, H N Aziz

  • 1IRCCS Istituto Ortopedico Galeazzi, Milano - Italy.

Journal of Applied Biomaterials & Biomechanics : JABB
|August 27, 2010
PubMed
Summary
This summary is machine-generated.

A new algorithm generates 3D hexahedral finite element (FE) meshes for schematic geometries, enabling faster biomechanical analysis of spinal segments and facilitating research into surgical procedures.

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Area of Science:

  • Computational mechanics
  • Biomechanical modeling
  • Finite element analysis

Background:

  • Generating accurate finite element (FE) meshes for complex anatomical structures is computationally intensive.
  • Schematic geometries simplify model creation but may limit detailed biomechanical investigations.

Purpose of the Study:

  • To present a voxel-based reconstruction algorithm for generating fully hexahedral FE meshes of schematic geometries.
  • To enable the creation of parameterized FE models for efficient biomechanical analysis.

Main Methods:

  • A voxel-based algorithm reconstructs 3D hexahedral FE meshes from volumetric data defined by surfaces.
  • The algorithm was applied to create a parameterized FE model of the C3-C7 spinal segment.
  • Non-linear simulations were performed under various loading conditions (flexion-extension, lateral bending, axial rotation).

Main Results:

  • The FE model generated accurate moment-rotation curves and ranges of motion for the C3-C7 spinal segment.
  • Principal and coupled rotations were determined for lateral bending and axial rotation.
  • Intradiscal pressure in the nucleus pulposus was computed for all intervertebral levels.

Conclusions:

  • The developed algorithm successfully generates parameterized FE models of schematic spinal structures.
  • The parameterized models facilitate biomechanical investigations of spinal mechanics, pathologies, and surgical interventions like fusion and disc arthroplasty.