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

Abstract

Evidence mounts that the steady-state cellular water efflux (unidirectional) first-order rate constant (k io [s À1 ]) magnitude reflects the ongoing, cellular metabolic rate of the cytolemmal Na + , K + -ATPase (NKA), c MR NKA (pmol [ATP consumed by NKA]/s/cell), perhaps biology's most vital enzyme. Optimal 1 H 2 O MR k io determinations require paramagnetic contrast agents (CAs) in model systems. However, results suggest that the homeostatic metabolic k io 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 k io 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; k io undefined; diffusion coefficient, D 0 ) to zero diffusion. The MADI model confirms that, in compartmented spaces with semipermeable boundaries, diffusion cannot be described as Gaussian: the nanoscopic D (D n ) 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 (k io ) cytoplasmic membranes, and less so by D n 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.

Metabolic activity diffusion imaging (MADI): II. Noninvasive, high‐resolution human brain mapping of sodium pump flux and cell metrics

“…For these, the vendor software numerically calculates b = γ 2 M 2 enc Δ ap , where M enc is the PFG (zeroth) moment (~δG), and Δ ap is the apparent diffusion time. The quantities b and Δ are defined and elaborated in the companion paper 12 …”

“…However, the companion paper 12 reviews, and explains why, the most accurate k io measurements are made only in such model systems, using paramagnetic Gd (III) chelate contrast agents (CAs). For a fundamental reason, measuring in vivo k io accurately with CAs is quite difficult, if at all possible 12 . Furthermore, for the brain, where the normal blood–brain barrier (BBB) prevents CA extravasation, the situation is especially dire.…”

“…For these and CA environmental/safety reasons, 12 we have developed a completely noninvasive (CA‐free) approach, metabolic activity diffusion imaging (MADI), based on D‐w 1 H 2 O imaging (DWI), to directly measure k io , as well as two fundamental cytometric parameters: V, the mean cell volume (Equation (1)), and ρ , the cell (number) density, also not previously accessible. The companion paper 12 details the conception, hypotheses, derivation, and execution of MADI modeling of DWI signal decays. We take advantage of the diffusion tensor (DT) magnitude, rather than its much more commonly used anisotropy (review 18 ).…”

Water exchange rates measure active transport and homeostasis in neural tissue

“…NMR does so by directly encoding and measuring signals from protons ( 1 H) on water, and following their evolution as intra- and extra-cellular water pools mix. NMR findings suggest that there is a component of water exchange linked to Na + / K + –ATPase activity (15–21). Continual Na + / K + –ATPase activity accounts for about half the energy budget of CNS tissue (22) — approximately 2 ×10 5 ATP molecules per second per µ m 3 of neural tissue (22).…”

“…Another MR method uses diffusion measurements to distinguish between intracellular and extracellular water based on their differing mobilities or apparent diffusivities and observes exchange by varying the timescale of diffusion encoding (27, 28). This method was recently shown to be sensitive to active water exchange (20, 21). However, effects of restriction and exchange both vary with diffusion encoding time and are difficult to separate using one-dimensional diffusion measurements (29).…”