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Related Concept Videos

Dimensional Analysis03:40

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Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach is: the units of quantities must be subjected to the same mathematical operations as their associated numbers. This method can be applied to computations ranging from simple unit conversions to more complex and multi-step calculations involving several different quantities and their units.
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Dimensional analysis is a valuable technique in fluid mechanics for simplifying complex problems by reducing them into dimensionless groups. These groups capture the essential relationships between the variables involved, allowing researchers and engineers to analyze fluid flow without dealing with each variable individually. This approach reduces the number of independent variables, allowing for easier analysis and better understanding of physical phenomena.
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Dimensional analysis is a powerful tool that is used in physics and engineering to understand and predict the behavior of physical systems. The basic idea behind dimensional analysis is to express physical quantities in terms of fundamental dimensions such as the mass, length, and time. Derived dimensions like the velocity, acceleration, and force are derived from the combinations of these fundamental dimensions.
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The concept of dimension is important because every mathematical equation linking physical quantities must be dimensionally consistent, implying that mathematical equations must meet the following two rules. The first rule is that, in an equation, the expressions on each side of the equal sign must have the same dimensions. This is fairly intuitive since we can only add or subtract quantities of the same type (dimension). The second rule states that, in an equation, the arguments of any of the...
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In mechanical engineering, a three-dimensional force system is a system of forces acting in three dimensions, with forces applied along the x, y, and z coordinate axes. The three-dimensional force system is an important concept in mechanical engineering, as it allows engineers to understand and analyze the behavior of objects and structures in three dimensions. By understanding the forces acting on a system, engineers can design more efficient and effective mechanical systems that can withstand...
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A two-dimensional system in mechanical engineering involves the analysis of motion and forces in a plane. A two-dimensional force vector can be resolved into its components as:
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Related Experiment Video

Updated: Feb 7, 2026

Planar and Three-Dimensional Printing of Conductive Inks
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Reproducing two-dimensional mammograms with three-dimensional printed phantoms.

Andreu Badal1, Matthew Clark2, Bahaa Ghammraoui1

  • 1U.S. Food and Drug Administration, Center for Devices and Radiological Health, Office of Science and Engineering Laboratories, Division of Imaging, Diagnostics and Software Reliability, Silver Spring, Maryland, United States.

Journal of Medical Imaging (Bellingham, Wash.)
|July 24, 2018
PubMed
Summary

Researchers developed a 3-D printing method to create realistic breast phantoms for mammography quality testing. This technique improves early breast cancer detection by enabling more accurate evaluation of mammography systems.

Keywords:
breast phantomsmammographythree-dimensional printing

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Area of Science:

  • Medical Imaging
  • Biomedical Engineering
  • Materials Science

Background:

  • Mammography is the standard for breast cancer screening, relying on physical phantoms to test system performance.
  • Existing phantoms lack the anatomical complexity of real breasts, limiting their effectiveness.
  • Three-dimensional (3-D) printing offers potential for creating more realistic and anatomically accurate breast phantoms.

Purpose of the Study:

  • To present a reproducible methodology for designing and 3-D printing breast phantoms that mimic real mammographic attenuation profiles.
  • To evaluate different 3-D printing technologies and materials for their x-ray properties.
  • To enable the creation of patient-specific models for assessing anatomical variability in mammography.

Main Methods:

  • Developed open-source software to process mammography images into 3-D printable mesh objects encoding attenuation maps.
  • Utilized knowledge of imaging system parameters to convert pixel gray values to material attenuation.
  • Validated the methodology by comparing X-ray projections of printed phantoms with original mammograms using structural similarity index and root-mean-square error.

Main Results:

  • Successfully created 3-D printed breast phantoms replicating the attenuation profiles of real mammograms.
  • Characterized the X-ray properties of various 3-D printing materials and technologies.
  • Demonstrated the feasibility of producing anatomically realistic phantoms for mammography system evaluation.

Conclusions:

  • The proposed 3-D printing methodology provides a simple and reproducible way to create realistic breast phantoms.
  • These phantoms can enhance the bench testing of mammography systems, bringing them closer to clinical trial relevance.
  • This approach facilitates the assessment of anatomical variability's impact on mammography system performance.