Metabolic activity diffusion imaging (MADI): I. Metabolic, cytometric modeling and simulations

Charles S. Springer, Eric M. Baker, Xin Li, Brendan Moloney, Gregory J. Wilson, Martin M. Pike, Thomas M. Barbara, William D. Rooney, Jeffrey H. Maki

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Evidence mounts that the steady-state cellular water efflux (unidirectional) first-order rate constant (kio [s−1]) magnitude reflects the ongoing, cellular metabolic rate of the cytolemmal Na+, K+-ATPase (NKA), cMRNKA (pmol [ATP consumed by NKA]/s/cell), perhaps biology's most vital enzyme. Optimal 1H2O MR kio determinations require paramagnetic contrast agents (CAs) in model systems. However, results suggest that the homeostatic metabolic kio biomarker magnitude in vivo is often too large to be reached with allowable or possible CA living tissue distributions. Thus, we seek a noninvasive (CA-free) method to determine kio in vivo. Because membrane water permeability has long been considered important in tissue water diffusion, we turn to the well-known diffusion-weighted MRI (DWI) modality. To analyze the diffusion tensor magnitude, we use a parsimoniously primitive model featuring Monte Carlo simulations of water diffusion in virtual ensembles comprising water-filled and -immersed randomly sized/shaped contracted Voronoi cells. We find this requires two additional, cytometric properties: the mean cell volume (V [pL]) and the cell number density (ρ [cells/μL]), important biomarkers in their own right. We call this approach metabolic activity diffusion imaging (MADI). We simulate water molecule displacements and transverse MR signal decays covering the entirety of b-space from pure water (ρ = V = 0; kio undefined; diffusion coefficient, D0) to zero diffusion. The MADI model confirms that, in compartmented spaces with semipermeable boundaries, diffusion cannot be described as Gaussian: the nanoscopic D (Dn) is diffusion time-dependent, a manifestation of the “diffusion dispersion”. When the “well-mixed” (steady-state) condition is reached, diffusion becomes limited, mainly by the probabilities of (1) encountering (ρ, V), and (2) permeating (kio) cytoplasmic membranes, and less so by Dn magnitudes. Importantly, for spaces with large area/volume (A/V; claustrophobia) ratios, this can happen in less than a millisecond. The model matches literature experimental data well, with implications for DWI interpretations.

Original languageEnglish (US)
Article numbere4781
JournalNMR in biomedicine
Issue number1
StatePublished - Jan 2023


  • DWI
  • Monte Carlo permeability
  • Voronoi cells
  • membrane
  • random walks
  • stochastic
  • water

ASJC Scopus subject areas

  • Molecular Medicine
  • Radiology Nuclear Medicine and imaging
  • Spectroscopy


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