MR-Based Electrical Property Reconstruction Using Physics-Informed Neural Networks

Tech ID: 33248 / UC Case 2023-860-0


Electrical properties (EP), such as permittivity and conductivity, dictate the interactions between electromagnetic waves and biological tissue. EP are biomarkers for pathology characterization, such as cancer. Imaging of EP helps monitor the health of the tissue and can provide important information in therapeutic procedures. Magnetic resonance (MR)-based electrical properties tomography (MR-EPT) uses MR measurements, such as the magnetic transmit field B1+, to reconstruct EP. These reconstructions rely on the calculations of spatial derivatives of the measured B1+. However, the numerical approximation of derivatives leads to noise amplifications introducing errors and artifacts in the reconstructions. Recently, a supervised learning-based method (DL-EPT) has been introduced to reconstruct robust EP maps from noisy measurements. Still, the pattern-matching nature of this method does not allow it to generalize for new samples since the network’s training is done on a limited number of simulated data pairs, which makes it unrealistic in clinical applications. Thus, there is a need for a robust and realistic method for EP map construction.


Researchers at the University of California, Santa Barbara, have created a physics-informed deep learning framework that can accurately reconstruct EP at an arbitrarily high spatial resolution from incomplete, noisy MR measurements. This invention applies Fourier neural network algorithms constrained by the Helmholtz equation to effectively de-noise magnetic field measurements. Two separate Fourier neural networks efficiently estimate the magnetic field and EP at any location. This technology marks the first time that EP and magnetic field values can be reconstructed simultaneously from incomplete noisy measurements, indicating further potential to improve other MR-based reconstruction methods, such as Helmholtz-EPT and convection-reaction EPT. Greater success in generating these EP maps translates to better diagnostic/prognostic tools and better-informed treatment options.


  • Accurately reconstructs EP maps using physics-informed deep learning from incomplete, noisy MR measurements
  • Instrumental for further improvements in MR-based reconstruction methods


  • Biotech
      o Diagnostics
      o MR-based methods

Patent Status

Country Type Number Dated Case
Patent Cooperation Treaty Published Application WO 2024/081966 04/18/2024 2023-860

Additional Patent Pending

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  • Liu, Ziyue
  • Yu, Xinling
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Other Information


MRI, cancer, neural network, de-noise, EP maps, Diagnostic/prognostic tools, Magnetic field measurements, Pathology characterization, Electrical properties tomography (MR-EPT), Magnetic transmit field B1+

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