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Time differentiation, convolution, integration, and periodicity are fundamental concepts in analyzing functions and signals over time. Each concept provides a unique perspective on how functions evolve, interact, and repeat, offering essential tools for various scientific and engineering applications.
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Updated: Oct 7, 2025

Visualizing Protein Kinase A Activity In Head-fixed Behaving Mice Using In Vivo Two-photon Fluorescence Lifetime Imaging Microscopy
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Using inverse Laplace transform in positronium lifetime imaging.

Kengo Shibuya1,2, Haruo Saito1, Hideaki Tashima2

  • 1Institute of Physics, Graduate School of Arts and Sciences, University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 153-8902, Japan.

Physics in Medicine and Biology
|January 10, 2022
PubMed
Summary
This summary is machine-generated.

Positronium (Ps) lifetime imaging can be improved using inverse Laplace transform (ILT) to separate lifetime components within voxels. This method enhances Positron Emission Tomography (PET) data accuracy, especially for disease-related changes.

Keywords:
Tikhonov regularizationhypoxia imaginginverse Laplace transformnumerical iterative algorithmoxygen partial pressurepositron emission tomographypositronium lifetime imaging

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Area of Science:

  • Medical imaging
  • Biophysics

Background:

  • Positronium (Ps) lifetime imaging offers novel biomedical insights from Positron Emission Tomography (PET).
  • Ps lifetime in vivo is sensitive to the surrounding physical and chemical microenvironments, reflecting disease states.
  • Limited sensitivity in Ps lifetime imaging often necessitates voxel merging, risking information loss.

Purpose of the Study:

  • To present a method for separating lifetime components within individual voxels to prevent data loss from averaging.
  • To evaluate the efficacy of numerical inverse Laplace transform (ILT) algorithms for this separation.
  • To improve the diagnostic utility of Ps lifetime imaging by preserving detailed information.

Main Methods:

  • Utilized inverse Laplace transform (ILT), specifically an iterative numerical ILT algorithm with Tikhonov regularization (CONTIN).
  • Applied the ILT method to separate positronium lifetime components within voxels.
  • Investigated the algorithm's ability to discriminate small lifetime differences, such as those related to oxygen saturation.

Main Results:

  • The developed method successfully separates lifetime components within voxels, avoiding information loss.
  • ILT enables voxel merging without compromising critical data on abnormal lifetime components (long or short).
  • The CONTIN algorithm demonstrated capability in discriminating subtle lifetime variations.

Conclusions:

  • Inverse Laplace Transform (ILT) can significantly enhance Ps lifetime imaging by compensating for sensitivity limitations.
  • This approach maximizes information extraction from PET scans, improving disease characterization.
  • ILT facilitates more accurate and detailed analysis of biological environments using Ps lifetime.