Quantitative Validation

• Simulating an image relies on a Beer-Lambert law implementation;
• Solving the Beer-Lambert law relies on Linear Attenuation Coefficients; (μ)
• μ is not known for given incident energies;
• μ is computed using Mass Attenuation Coefficients (μ/ρ) and material density (ρ).
• Are the values used in gVirtualXRay accurate?
  • Compare values computed in gVirtualXRay with those from the literature.
• Are the Beer-Lambert law implementations accurate?
  • Compare values computed in gVirtualXRay with theoretical ones.
• Are the simulated images accurate?
  • Compare images computed using gVirtualXRay with those using a state-of-the-art Monte Carlo software, e.g.
  

Density for Different Materials (human tissues) from the Literature

Image from W. Schneider, T. Bortfeld, and W. Schlegel, “Correlation between CT numbers and tissue parameters needed for Monte Carlo simulations of clinical dose distributions,” Physics in Medicine & Biology, vol. 45, no. 2, p. 459, 2000. doi:10.1088/0031-9155/45/2/314

Density for Different Materials (human tissues) computed by gVirtualXRay

Image from http://gvirtualxray.sourceforge.net/validation/validation_02/density.php

Mass Attenuation Coefficients

• Any tissue can be described by its Hounsfiled Unit (HU):
  • HU(material) = 1000 x (μ(material) - μ(water)) / μ(water)
• Given a HU value for any simulated object;
  • If μ(water) is known for any energy,
  • then μ(material) for any HU and for any energy can be computed:
    • μ(material, E) = μ(water, E) x (1 + HU(material)/1000)
• Mass attenuation coefficients (μ/ρ) for various human tissues can be found in the literature;
• The density (ρ) for various human tissues can be found in the literature.
• Linear attenuation coefficients can therefore be computed for various human tissues and
• used to solve the Beer-Lambert law

Mass Attenuation Coefficients: Tissue, Soft (ICRU-44)

• 

  Image from https://physics.nist.gov/PhysRefData/XrayMassCoef/ComTab/tissue.html

• μ(water) from literature is provided at given energies only: Interpolation needed for missing energies

  • 

    Image computed with gVirtualXRay using linear interpolation

  • 

    Image computed with gVirtualXRay using interpolation in the log scale

Mass Attenuation Coefficients: Bone, Cortical (ICRU-44)

• 

  Image from https://physics.nist.gov/PhysRefData/XrayMassCoef/ComTab/bone.html

• μ(water) from literature is provided at given energies only: Interpolation needed for missing energies

  • 

    Image computed with gVirtualXRay using linear interpolation

  • 

    Image computed with gVirtualXRay using interpolation in the log scale

Not a good match as the peaks are not visible in μ(water)

This is now a good match

Going back to previous slide

• Simulating an image relies on a Beer-Lambert law implementation;
• Solving the Beer-Lambert law relies on Linear Attenuation Coefficients; (μ)
• μ is not known for given incident energies;
• μ is computed using Mass Attenuation Coefficients (μ/ρ) and material density (ρ).
• Are the values used in gVirtualXRay accurate?
  • Compare values computed in gVirtualXRay with those from the literature.

Going back to previous slide

• Simulating an image relies on a Beer-Lambert law implementation;
• Solving the Beer-Lambert law relies on Linear Attenuation Coefficients; (μ)
• μ is not known for given incident energies;
• μ is computed using Mass Attenuation Coefficients (μ/ρ) and material density (ρ).
• Are the values used in gVirtualXRay accurate?
  • Compare values computed in gVirtualXRay with those from the literature.
  • YES

More testing

• Are the Beer-Lambert law implementations accurate?
  • Compare values computed in gVirtualXRay with theoretical ones.
• Are the simulated images accurate?
  • Compare images computed using gVirtualXRay with those using a state-of-the-art Monte Carlo software, e.g.
  

Test case

• Simulated object

  

  Simulated object

  • Cube: edge length of 3 cm, made of soft tissue (HU = 52).
  • Cylinder: height of 3 m, diameter of 2 cm, made of bone (HU = 1330).

• Incident beam:

Beer-Lambert Law: Polychromatism Case

• Use material properties from the literature;
• The energy, I_out, (in MeV) transmitted orthogonally throw the middle of cube and cylinder should be:
  • I_out = I_out(0.1) + I_out(0.2) + I_out(0.3), with
  • I_out(0.1) = 10 x 0.1 x e^{-( 3.346E-01 x 2 + 1.799E-01 x 1)}
  • I_out(0.2) = 10 x 0.1 x e^{-( 2.361E-01 x 2 + 1.443E-01 x 1)}
  • I_out(0.3) = 10 x 0.1 x e^{-( 2.008E-01 x 2 + 1.249E-01 x 1)}
  • I_out = 4.359
• On GPU, the energy, I_outgpu, is: 4.353.
  • The relative error is:
  • |I_out - I_outgpu| / I_out = 0.1%

Gate vs. gVirtualXRay

We simulate a test case twice:

• Using a Monte Carlo method for particle physics implemented in GATE;
• Using our GPU implementation.

GATE is an opensource software developed by an international collaboration. Its focus is on Monte Carlo simulation in medical imaging and radiotherapy. GATE makes use of the Geant4 libraries. Geant 4 is CERN’s Monte Carlo simulation platform dedicated to particle physics in nuclear research. CERN is the European Organization for Nuclear Research.

Gate vs. gVirtualXRay: Point Source

Simulation parameters

Image computed with GATE (2 weeks of computations on supercomputer)

Image computed with gVirtualXRay (less than 1 sec. of computations on GPU)

Normalised cross-correlation (NCC) = 99.747%

Profiles

Gate vs. gVirtualXRay: Uncentered Source

The source is translated by a vector: -5.0 0.5 0.5 cm

Image computed with GATE (2 weeks of computations on supercomputer)

Image computed with gVirtualXRay (less than 1 sec. of computations on GPU)

Normalised cross-correlation (NCC) = 99.656%

Profiles

Gate vs. gVirtualXRay: Cube Source

The source is a 1x1x1 cm cube.

Image computed with GATE (2 weeks of computations on supercomputer)

Image computed with gVirtualXRay (less than 1 sec. of computations on GPU)

Normalised cross-correlation (NCC) = 99.743%

Profiles

Unit tests

• More validation test available, see http://gvirtualxray.sourceforge.net/validation/validation_tests.php
• To check that your system provides the results you expect,
• Run the unit tests
  • See next topic

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