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Frequency-domain optical tomographic image reconstruction algorithm with the simplified spherical harmonics (SP3)

Hyun Keol Kim1, Ludguier D Montejo2, Jingfei Jia3

  • 1Department of Radiology, Columbia University, 660 W 168 St, New York, NY 10032, USA.

International Journal of Thermal Sciences = Revue Generale De Thermique
|October 25, 2017
PubMed
Summary

We developed a new model, the frequency-domain simplified spherical harmonics model with 3rd order absorption coefficients (FD-SP3), for accurate optical imaging of biological tissues. This efficient model reconstructs absorption and scattering coefficients faster and more precisely than previous methods.

Keywords:
biological tissueimage reconstructionradiative transfersimplified spherical harmonics

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Area of Science:

  • Biomedical Optics
  • Medical Imaging
  • Computational Physics

Background:

  • Accurate optical imaging of biological tissues is crucial for diagnosis and treatment.
  • Existing models for frequency-domain radiative transfer (FD-ERT) can be computationally intensive.
  • Simplified spherical harmonics models offer a balance between accuracy and computational efficiency.

Purpose of the Study:

  • To introduce a finite volume formulation of the frequency-domain simplified spherical harmonics model with n-th order absorption coefficients (FD-SPN).
  • To develop and evaluate an FD-SPN-based algorithm for reconstructing absorption and scattering coefficients in biological tissues.
  • To demonstrate the efficiency and accuracy of the FD-SP3 model for optical tomographic imaging of small-volume media.

Main Methods:

  • Finite volume formulation of the FD-SPN model.
  • Node-centered finite volume scheme for FD-SP3 discretization.
  • Restarted generalized minimum residual (GMRES) algorithm for solving the forward problem.
  • Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm for inverse problem solving.
  • Evaluation using numerical phantoms mimicking small-volume tissues.

Main Results:

  • The FD-SP3 model accurately approximates the FD-ERT (S12) solution, with low average errors in phase (<3.7%) and amplitude (<7.1%) of partial current at the boundary.
  • Absorption and scattering coefficient maps reconstructed using the FD-SP3 model showed higher accuracy compared to the SP1 model.
  • The FD-SP3 model demonstrated significantly lower CPU time compared to FD-ERT (S12).

Conclusions:

  • The FD-SP3 model provides an efficient and accurate method for optical tomographic imaging of small-volume biological tissues.
  • This model is suitable for imaging media with non-diffuse optical properties.
  • The FD-SP3 model offers a superior balance of computational speed and accuracy over FD-ERT (S12) and FD-SP1 models.