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Related Concept Videos

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the others.
NMR Spectrometers: Resolution and Error Correction01:14

NMR Spectrometers: Resolution and Error Correction

When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied first.
¹³C NMR: Distortionless Enhancement by Polarization Transfer (DEPT)01:20

¹³C NMR: Distortionless Enhancement by Polarization Transfer (DEPT)

When proton-coupled carbon-13 spectra are simplified by a broadband proton decoupling technique, structural information about the coupled protons is lost. Distortionless enhancement by polarization transfer (DEPT) is a technique that provides information on the number of hydrogens attached to each carbon in a molecule. While the DEPT experiment utilizes complex pulse sequences, the pulse delay and flip angle are specifically manipulated. The resulting signals have different phases depending on...
Double Resonance Techniques: Overview01:12

Double Resonance Techniques: Overview

Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by...
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Insensitive Nuclei Enhanced by Polarization Transfer (INEPT)

Insensitive Nuclei Enhanced by Polarization Transfer (INEPT) is an advanced Nuclear Magnetic Resonance (NMR) technique specifically designed to detect and enhance the signals of low-abundance nuclei, such as carbon-13 and nitrogen-15, in small molecules. The fundamental principle behind INEPT is the transfer of polarization from a more abundant and highly polarizable nucleus, typically hydrogen-1, to the low-abundance nucleus of interest. This process effectively boosts the NMR signal of the...

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Related Experiment Video

Updated: Jul 12, 2026

Proton Therapy Delivery and Its Clinical Application in Select Solid Tumor Malignancies
08:34

Proton Therapy Delivery and Its Clinical Application in Select Solid Tumor Malignancies

Published on: February 6, 2019

A single-field-each-peak optimization method for motion-robust proton LATTICE therapy.

Xin Tong1, Ya-Nan Zhu2, Nimita Shinde3

  • 1Department of Radiation Oncology, University of Kansas Medical Center, Kansas City, Kansas, USA.

Medical Physics
|July 10, 2026
PubMed
Summary

A new single-field-each-peak (SFEP) method improves proton LATTICE (pLATTICE) therapy by delivering each dose peak with one beam, enhancing robustness against motion and uncertainties. This approach maintains plan quality and offers superior peak localization compared to intensity-modulated proton therapy.

Keywords:
motion robustnessproton lattice therapyrange uncertainty

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Area of Science:

  • Medical Physics
  • Radiation Oncology
  • Computational Optimization

Background:

  • LATTICE therapy delivers spatially modulated radiation doses using high-dose peaks and low-dose valleys.
  • Proton LATTICE (pLATTICE) offers advanced treatment capabilities but conventional planning is sensitive to delivery uncertainties like motion and range variations.
  • These uncertainties can compromise the accuracy of proton dose deposition in pLATTICE treatments.

Purpose of the Study:

  • To introduce a novel single-field-each-peak (SFEP) optimization framework for robust pLATTICE delivery.
  • To enhance robustness against motion, range uncertainty, and anatomical variations by assigning each peak to a single beam field.
  • To preserve the characteristic spatially fractionated dose pattern of LATTICE therapy.

Main Methods:

  • SFEP optimization assigns each lattice peak to a single beam angle from candidate orientations.
  • The method is formulated as a mixed integer optimization problem, optimizing field selection and proton spot weights.
  • Solutions are derived using alternating direction method of multipliers and iterative convex relaxation techniques.

Main Results:

  • The SFEP method (NEW) consistently used single fields per peak, achieving comparable peak-to-valley dose ratio (PVDR) and conformity index (CI) to exhaustive search (ES).
  • SFEP demonstrated superior robustness against range and setup uncertainties compared to intensity-modulated proton therapy (IMPT)-based pLATTICE.
  • Motion-robust evaluations showed SFEP maintained more stable peak localization and coverage under simulated anatomical shifts than IMPT.

Conclusions:

  • The SFEP optimization approach provides a novel strategy for motion-robust pLATTICE delivery.
  • SFEP successfully delivers each peak with a single, optimally chosen field, maintaining plan quality.
  • This method exhibits superior robustness in peak localization and coverage compared to IMPT, addressing key challenges in pLATTICE.