ArticleMagnetic resonance in medicine2024
Diffusional kurtosis time dependence and the water exchange rate for the multi-compartment Kärger model.
Article in Magnetic resonance in medicine, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 15 papers.
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15 citing papers in PubMed.
- Localization-driven exchange contrast in diffusion exchange spectroscopy.Journal of magnetic resonance (San Diego, Calif. : 1997) · 2026Article
- Monte Carlo Assessment of Accuracy for Mean Kärger Model Water Exchange Rate Estimates From Diffusional Kurtosis Time Dependence.NMR in biomedicine · 2026Article
- Passive water exchange between multiple sites can explain why apparent exchange rate constants depend on ionic and osmotic conditions in gray matter.Magnetic resonance letters · 2026Article
- Article
- Motion and Flow Robust Free-Breathing Diffusion Kurtosis Imaging of the Kidney.NMR in biomedicine · 2025Article
- Non-monotonic time- and frequency-dependent diffusion kurtosis in the human brain revealed by pulsed and oscillating gradient experiments.Magnetic resonance in medicine · 2025Article
- Correcting pulse duration effects in the diffusional kurtosis of the multi-compartment Kärger model.Magnetic resonance in medicine · 2025Article
- Passive water exchange between multiple sites can explain why apparent exchange rate constants depend on ionic and osmotic conditions in gray matter.bioRxiv : the preprint server for biology · 2025Article
- Linear rotationally invariant kurtosis measures from double diffusion encoding MRI.Magnetic resonance imaging · 2025Article
- In vivo cortical microstructure mapping using high-gradient diffusion MRI accounting for intercompartmental water exchange effects.NeuroImage · 2025Article
- Diffusion MRI with double diffusion encoding and variable mixing times disentangles water exchange from transient kurtosis.Scientific reports · 2025Article
- Mean Kärger Model Water Exchange Rate in Brain.Imaging neuroscience (Cambridge, Mass.) · 2024Article
- Investigating exchange, structural disorder, and restriction in gray matter via water and metabolites diffusivity and kurtosis time-dependence.Imaging neuroscience (Cambridge, Mass.) · 2024Article
- Revisiting the interpretation of axon diameter mapping using higher-order signal representations.Imaging neuroscience (Cambridge, Mass.)Article
- Microstructure.jl: A Julia package for probabilistic microstructure model fitting with diffusion MRI.Imaging neuroscience (Cambridge, Mass.)Article
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Abstract
purposeTo demonstrate an analytic formula giving the time dependence of the diffusional kurtosis for the Kärger model (KM) with an arbitrary number of exchanging compartments and its application in estimating the mean KM water exchange rate. THEORY AND
methodsThe general formula for the kurtosis is derived from a power series solution for the multi-compartment KM. A lower bound on the exchange rate is established from the observation that the kurtosis is always a logarithmically convex function of time. Both the kurtosis time dependence and the lower bound are illustrated with numerical calculations. The lower bound is also applied to previously published data for the time dependence of the kurtosis in both brain and tumors.
resultsThe kurtosis for the multi-compartment KM is given by a sum in which each term is associated with an eigenvector of the exchange rate matrix. The lower bound is determined from the most negative value for the logarithmic derivative of the kurtosis with respect to time. In the cerebral cortex, the lower bound is found to vary from 15 to 76 s
conclusionThe time dependence of the kurtosis for the multi-compartment KM has a simple analytic solution that allows a lower bound for the mean KM water exchange rate to be determined directly from experiment. This may be useful in tissues with complex microstructure that is difficult to model explicitly.
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