Theory of heterogeneous relaxation in compartmentalized tissues

Daniel Barsky, Benno Pütz, Klaus Schulten

Research output: Contribution to journalArticlepeer-review


A new model of compartmentalized relaxation that-which occurs for spins (protons) exchanging between compartments of different relaxation rates-is presented. This model generalizes previous ones by allowing spatially dependent relaxation within compartments. Solutions for the diffusion-Bloch equations are found via an efficient numerical technique known as the generalized moment expansion, and they agree well with the solutions to the standard two-site exchange equations (TSEE) for many typical situations. Specific models are developed for liposomes, red blood cells, capillaries, and arteries with respect to applied contrast agents. A parameter derived from tissue characteristics is introduced to predict the nature of the solutions. A new method is proposed for using contrast agents to detect capillaries, which exploits their high surface-to-volume ratio relative to the other elements of the vasculature.

Original languageEnglish (US)
Pages (from-to)666-675
Number of pages10
JournalMagnetic Resonance in Medicine
Issue number5
StatePublished - May 1997
Externally publishedYes


  • capillary deletion
  • contrast agents
  • generalized moment expansion
  • two-site exchange

ASJC Scopus subject areas

  • Radiology Nuclear Medicine and imaging
  • Radiological and Ultrasound Technology


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