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

In vivo neuropil density from anatomical MRI and machine learning

Brain energy budgets specify metabolic costs emerging from underlying mechanisms of cellular and synaptic activities. While current bottom-up energy budgets use prototypical values of cellular density and synaptic density, predicting metabolism from a person's individualized neuropil density would be ideal. We hypothesize that in vivo neuropil density can be derived from magnetic resonance imaging (MRI) data, consisting of longitudinal relaxation (T1) MRI for gray/white matter distinction and diffusion MRI for tissue cellularity (apparent diffusion coefficient, ADC) and axon directionality (fractional anisotropy, FA). We present a machine learning algorithm that predicts neuropil density from in vivo MRI scans, where ex vivo Merker staining and in vivo synaptic vesicle glycoprotein 2A Positron Emission Tomography (SV2A-PET) images were reference standards for cellular and synaptic density, respectively. We used Gaussian-smoothed T1/ADC/FA data from 10 healthy subjects to train an artificial neural network, subsequently used to predict cellular and synaptic density for 54 test subjects. While excellent histogram overlaps were observed both for synaptic density (0.93) and cellular density (0.85) maps across all subjects, the lower spatial correlations both for synaptic density (0.89) and cellular density (0.58) maps are suggestive of individualized predictions. This proof-of-concept artificial neural network may pave the way for individualized energy atlas prediction, enabling microscopic interpretations of functional neuroimaging data.

A Futile Cycle?: Tissue Homeostatic Trans-Membrane Water Co-Transport: Kinetics, Thermodynamics, Metabolic Consequences

The phenomenon of active trans-membrane water cycling (AWC) has emerged in little over a decade. Here, we consider H2O transport across cell membranes from the origins of its study. Historically, trans-membrane water transport processes were classified into: A) compensating bidirectional fluxes ("exchange"), and B) unidirectional flux ("net flow") categories. Recent literature molecular structure determinations and molecular dynamic (MD) simulations indicate probably all the many different hydrophilic substrate membrane co-transporters have membrane-spanning hydrophilic pathways and co-transport water along with their substrates, and that they individually catalyze category A and/or B water flux processes, although usually not simultaneously. The AWC name signifies that, integrated over the all the cell's co-transporters, the rate of homeostatic, bidirectional trans-cytolemmal water exchange (category A) is synchronized with the metabolic rate of the crucial Na+,K+-ATPase (NKA) enzyme. A literature survey indicates the stoichiometric (category B) water/substrate ratios of individual co-transporters are often very large. The MD simulations also suggest how different co-transporter reactions can be kinetically coupled molecularly. Is this (Na+,K+-ATPase rate-synchronized) cycling futile, or is it consequential? Conservatively representative literature metabolomic and proteinomic results enable comprehensive free energy analyses of the many transport reactions with known water stoichiometries. Free energy calculations, using literature intracellular pressure (Pi) values reveals there is an outward trans-membrane H2O barochemical gradient of magnitude comparable to that of the well-known inward Na+ electrochemical gradient. For most co-influxers, these gradients are finely balanced to maintain intracellular metabolite concentration values near their consuming enzyme Michaelis constants. The thermodynamic analyses include glucose, glutamate-, gamma-aminobutyric acid (GABA), and lactate- transporters. 2%-4% Pi alterations can lead to disastrous concentration levels. For the neurotransmitters glutamate- and GABA, very small astrocytic Pi changes can allow/disallow synaptic transmission. Unlike the Na+ and K+ electrochemical steady-states, the H2O barochemical steady-state is in (or near) chemical equilibrium. The analyses show why the presence of aquaporins (AQPs) does not dissipate the trans-membrane pressure gradient. A feedback loop inherent in the opposing Na+ electrochemical and H2O barochemical gradients regulates AQP-catalyzed water flux as an integral AWC aspect. These results also require a re-consideration of the underlying nature of Pi. Active trans-membrane water cycling is not futile, but is inherent to the cell's "NKA system" - a new, fundamental aspect of biology.

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

Evidence mounts that the steady-state cellular water efflux (unidirectional) first-order rate constant (k_io [s^-1 ]) 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 H₂ 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, D₀ ) 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.