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

Late-onset GM2 gangliosidosis: magnetic resonance imaging, diffusion tensor imaging, and correlational fiber tractography differentiate Tay-Sachs and Sandhoff diseases

GM2 gangliosidosis is lysosomal storage disorder caused by deficiency of the heterodimeric enzyme β-hexosaminidase A. Tay-Sachs disease is caused by variants in HEXA encoding the α-subunit and Sandhoff disease is caused by variants in HEXB encoding the β-subunit. Due to shared clinical and biochemical findings, the two have been considered indistinguishable. We applied T1-weighted volumetric analysis, diffusion tensor imaging (DTI), and correlational fiber tractography to assess phenotypic differences in these two diseases. 51 T1-weighted and 40 DTI scans from 19 Late-Onset GM2 patients with either late-onset Sandhoff disease (LOSD), or late-onset Tay-Sachs (LOTS) were included and compared to 1033 neurotypical control volumetric MRI scans. LOTS patients had significantly smaller cerebellum volume compared to neurotypical controls (p < 0.0001) and LOSD patients (p < 0.0001). There was no statistical difference for the volume of any structure between LOSD and neurotypical controls. DTI analysis showed LOTS patients had higher mean diffusivity (MD) in the left cerebellum (p = 0.003703), right cerebellum (p = 0.003435), superior cerebellar peduncle (p = 0.007332), and vermis (p = 0.01007) compared to LOSD. LOTS patients had lower fractional anisotropy (FA) in the left cerebellum (p = 0.005537), right cerebellum (p = 0.01905), SCP (p = 0.02844), and vermis (p = 0.02469) when compared to LOSD. Correlational fiber tractography identified fiber tracts in cerebellar pathways with higher FA and lower MD in LOSD patients compared to LOTS patients. Our study shows neurobiologic differences between these two related disorders. To our knowledge, this is the first study using correlational tractography in a lysosomal storage disorder. This result indicates a greater burden of cerebellar pathology in LOTS patients compared with LOSD patients.

Metabolic Energy is Stored in a Homeostatic Trans-Membrane Water Barochemical Gradient

Trans-membrane water transport and co-transport is ubiquitous in cell biology. Integrated over all the cell's H2O transporters and co-transporters, the rate of homeostatic, bidirectional trans-cytolemmal water "exchange" is synchronized with the metabolic rate of the crucial Na+,K+-ATPase (NKA) enzyme: the active trans-membrane water cycling (AWC) phenomenon. Is AWC futile, or is it consequential? Conservatively representative literature metabolomic and proteinomic results enable comprehensive free energy (ΔG) calculations for the many transport reactions with known water stoichiometries. Including established intracellular pressure (Pi) magnitudes, these reveal an outward trans-membrane H2O barochemical ΔG gradient comparable to that of the well-known inward Na+ electrochemical ΔG gradient. For most co-influxers, these two gradients are finely balanced to maintain intracellular metabolite concentration values near their consuming enzyme Michaelis constants. Our analyses include glucose, glutamate-, gamma-aminobutyric acid (GABA), and lactate- transporters. 2%-4% Pi alterations can lead to disastrous metabolite concentrations. 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 trans-membrane pressure gradients. A feedback loop inherent in the opposing Na+ electrochemical and H2O barochemical gradients regulates AQP-catalyzed water flux as integral to AWC. A re-consideration of the underlying nature of Pi is also necessary. AWC is not a futile cycle but is inherent to the cell's "NKA system"-a new, fundamental aspect of biology. Metabolic energy is stored in the trans-membrane water barochemical gradient.

In vivo human neurite exchange imaging (NEXI) at 500 mT/m diffusion gradients

Evaluating tissue microstructure and membrane integrity in the living human brain through diffusion-water exchange imaging is challenging due to requirements for a high signal-to-noise ratio and short diffusion times dictated by relatively fast exchange processes. The goal of this work was to demonstrate the feasibility of in vivo imaging of tissue micro-geometries and water exchange within the brain gray matter using the state-of-the-art Connectome 2.0 scanner equipped with an ultra-high-performance gradient system (maximum gradient strength=500 mT/m, maximum slew rate=600 T/m/s). We performed diffusion MRI measurements in 15 healthy volunteers at multiple diffusion times (13-30 ms) and b -values up to 17.5 ms/μm2. The anisotropic Kärger model was applied to estimate the exchange time between intra-neurite and extracellular water in gray matter. The estimated exchange time across the cortical ribbon was around (median±interquartile range) 13±8 ms on Connectome 2.0, substantially faster than that measured using an imaging protocol compatible with Connectome 1.0-alike systems on the same cohort. Our investigation suggested that the NEXI exchange time estimation using a Connectome 1.0 compatible protocol was more prone to residual noise floor biases due to the small time-dependent signal contrasts across diffusion times when the exchange is fast (≤20 ms). Furthermore, spatial variation of exchange time was observed across the cortex, where the motor cortex, somatosensory cortex and visual cortex exhibit longer exchange times compared to other cortical regions. Non-linear fitting for the anisotropic Kärger model was accelerated 100 times using a GPU-based pipeline compared to the conventional CPU-based approach. This study highlighted the importance of the chosen diffusion times and measures to address Rician noise in dMRI data, which can have a substantial impact on the estimated NEXI exchange time and require extra attention when comparing NEXI results between various hardware setups.

Tay-Sachs and Sandhoff Diseases: Diffusion tensor imaging and correlational fiber tractography findings differentiate late-onset GM2 Gangliosidosis

GM2 gangliosidosis is lysosomal storage disorder caused by deficiency of the heterodimeric enzyme β-hexosaminidase A. Tay-Sachs disease is caused by variants in HEXA encoding the α-subunit and Sandhoff disease is caused by variants in HEXB encoding the β-subunit. Due to shared clinical and biochemical findings, the two have been considered indistinguishable. We applied diffusion tensor imaging (DTI) and correlational fiber tractography to assess phenotypic differences in these two diseases. 40 DTI scans from 16 Late-Onset GM2 patients (NCT00029965) with either Sandhoff (n = 4), or Tay-Sachs (n = 12) disease. DTI metrics including fractional anisotropy (FA), mean diffusivity (MD), radial diffusivity (RD), axial diffusivity (AD), and quantitative anisotropy (QA) were calculated in fiber tracts throughout the whole brain, arcuate fasciculus, corpus callosum, and cerebellum. Correlational tractography was also performed to identify fiber tracts with group wide differences in DTI metrics between Tay-Sachs and Sandhoff patients. A linear mixed effects model was used to analyze the differences between Tay-Sachs and Sandhoff patients. Tay-Sachs patients had higher MD in the left cerebellum (p = 0.003703), right cerebellum (p = 0.003435), superior cerebellar peduncle (SCP, p = 0.007332), and vermis (p = 0.01007). Sandhoff patients had higher FA in the left cerebellum (p = 0.005537), right cerebellum (p = 0.01905), SCP (p = 0.02844), and vermis (p = 0.02469). Correlational fiber tractography identified fiber tracts almost exclusively in cerebellar pathways with higher FA and QA, and lower MD, AD, and RD in Sandhoff patients compared to Tay-Sachs patients. Our study shows neurobiological differences between these two related disorders. To our knowledge, this is the first study using correlational tractography in a lysosomal storage disorder demonstrating these differences. This result indicates a greater burden of cerebellar pathology in Tay-Sachs patients compared with Sandoff patients.

Restriction-induced time-dependent transcytolemmal water exchange: Revisiting the Kӓrger exchange model

The Kӓrger model and its derivatives have been widely used to incorporate transcytolemmal water exchange rate, an essential characteristic of living cells, into analyses of diffusion MRI (dMRI) signals from tissues. The Kӓrger model consists of two homogeneous exchanging components coupled by an exchange rate constant and assumes measurements are made with sufficiently long diffusion time and slow water exchange. Despite successful applications, it remains unclear whether these assumptions are generally valid for practical dMRI sequences and biological tissues. In particular, barrier-induced restrictions to diffusion produce inhomogeneous magnetization distributions in relatively large-sized compartments such as cancer cells, violating the above assumptions. The effects of this inhomogeneity are usually overlooked. We performed computer simulations to quantify how restriction effects, which in images produce edge enhancements at compartment boundaries, influence different variants of the Kӓrger-model. The results show that the edge enhancement effect will produce larger, time-dependent estimates of exchange rates in e.g., tumors with relatively large cell sizes (>10 μm), resulting in overestimations of water exchange as previously reported. Moreover, stronger diffusion gradients, longer diffusion gradient durations, and larger cell sizes, all cause more pronounced edge enhancement effects. This helps us to better understand the feasibility of the Kärger model in estimating water exchange in different tissue types and provides useful guidance on signal acquisition methods that may mitigate the edge enhancement effect. This work also indicates the need to correct the overestimated transcytolemmal water exchange rates obtained assuming the Kärger-model.

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): II. Noninvasive, high-resolution human brain mapping of sodium pump flux and cell metrics

We introduce a new ¹ H₂ O magnetic resonance approach: metabolic activity diffusion imaging (MADI). Numerical diffusion-weighted imaging decay simulations characterized by the mean cellular water efflux (unidirectional) rate constant (k_io ), mean cell volume (V), and cell number density (ρ) are produced from Monte Carlo random walks in virtual stochastically sized/shaped cell ensembles. Because of active steady-state trans-membrane water cycling (AWC), k_io reflects the cytolemmal Na⁺ , K⁺ ATPase (NKA) homeostatic cellular metabolic rate (^c MR_NKA ). A digital 3D "library" contains thousands of simulated single diffusion-encoded (SDE) decays. Library entries match well with disparate, animal, and human experimental SDE decays. The V and ρ values are consistent with estimates from pertinent in vitro cytometric and ex vivo histopathological literature: in vivo V and ρ values were previously unavailable. The library allows noniterative pixel-by-pixel experimental SDE decay library matchings that can be used to advantage. They yield proof-of-concept MADI parametric mappings of the awake, resting human brain. These reflect the tissue morphology seen in conventional MRI. While V is larger in gray matter (GM) than in white matter (WM), the reverse is true for ρ. Many brain structures have k_io values too large for current, invasive methods. For example, the median WM k_io is 22s^-1 ; likely reflecting mostly exchange within myelin. The k_io •V product map displays brain tissue ^c MR_NKA variation. The GM activity correlates, quantitatively and qualitatively, with the analogous resting-state brain ¹⁸ FDG-PET tissue glucose consumption rate (^t MR_glucose ) map; but noninvasively, with higher spatial resolution, and no pharmacokinetic requirement. The cortex, thalamus, putamen, and caudate exhibit elevated metabolic activity. MADI accuracy and precision are assessed. The results are contextualized with literature overall homeostatic brain glucose consumption and ATP production/consumption measures. The MADI/PET results suggest different GM and WM metabolic pathways. Preliminary human prostate results are also presented.