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  • Open Access

Lifetime distribution of multiexponential recovery processes

Armin Afrough and Thomas Vosegaard*

  • Department of Chemistry and Interdisciplinary Nanoscience Center, Aarhus University, Aarhus C, Denmark

  • *Contact author: tv@chem.au.dk
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Phys. Rev. Applied 25, 034020 – Published 5 March, 2026

DOI: https://doi.org/10.1103/v4pb-vvd2

Abstract

Multiexponential recovery is a process where a transient signal recovers through multiple relaxation pathways to a nonzero steady-state value. Such processes are ubiquitous in science and technology—for example in longitudinal (T1) relaxation in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI). Existing schemes for extracting lifetime distributions from multiexponential recovery data are inaccurate or inefficient. They either impose unrealistic initial-condition constraints or require extensive late-time sampling. We present a robust inversion method that overcomes both limitations. The devised method determines the lifetime distribution by solving explicitly for the steady-state value and implicitly for the recovery factor—where the recovery factor defines the arbitrary starting point of the signal relative to the steady-state value. The method provides unprecedented accuracy even at shorter time windows and opens up new possibilities in research and industry. Several examples show the features of the method especially in nuclear magnetic resonance, food science, geoscience, and climate science.

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Phys. Rev. Applied 25, 034020– Published 5 March, 2026
  • Received 4 July 2025
  • Revised 11 November 2025
  • Accepted 23 January 2026
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