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Management of Respiratory Motion Artefacts in 18F-fluorodeoxyglucose Positron Emission Tomography using an Amplitude-Based Optimal Respiratory Gating Algorithm
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Continuous gated first-passage processes.

Yuval Scher1, Aanjaneya Kumar2, M S Santhanam2

  • 1School of Chemistry, Center for the Physics & Chemistry of Living Systems, Ratner Institute for Single Molecule Chemistry, and the Sackler Center for Computational Molecular & Materials Science, Tel Aviv University, 6997801 Tel Aviv, Israel.

Reports on Progress in Physics. Physical Society (Great Britain)
|August 29, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a renewal framework to solve complex gated first-passage processes, offering analytical solutions for detection times previously unknown. The findings reveal universal properties and extend to higher dimensions.

Keywords:
diffusionfirst-passagegated reactionsintermittent sensingthreshold crossing

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Area of Science:

  • Physics
  • Mathematics
  • Physical Chemistry

Background:

  • Gated first-passage processes are crucial in many fields but lack analytical solutions for complex targets.
  • Problems like diffusion to gated intervals, disks, or spheres remain analytically intractable.

Purpose of the Study:

  • To develop a unified analytical framework for continuous gated first-passage processes.
  • To derive solutions for problems, including interval targets, that have previously evaded exact solutions.

Main Methods:

  • A novel renewal framework is presented to analyze gated first-passage processes.
  • The framework connects gated problem solutions to ungated dynamics.
  • The formalism is extended to higher dimensions.

Main Results:

  • The renewal framework provides unified solutions for various gated first-passage problems.
  • Solutions for interval targets, previously unsolved, are now obtainable.
  • The study reveals universal properties, asymptotic behaviors, and intermediate-time regimes.

Conclusions:

  • The developed framework offers analytical tools for continuous gated first-passage processes.
  • This work provides significant insights into the dynamics of these processes across diverse scientific domains.