UNITY: A low-field magnetic resonance neuroimaging initiative to characterize neurodevelopment in low and middle-income settings.

Measures of physical growth, such as weight and height have long been the predominant outcomes for monitoring child health and evaluating interventional outcomes in public health studies, including those that may impact neurodevelopment. While physical growth generally reflects overall health and nutritional status, it lacks sensitivity and specificity to brain growth and developing cognitive skills and abilities. Psychometric tools, e.g., the Bayley Scales of Infant and Toddler Development, may afford more direct assessment of cognitive development but they require language translation, cultural adaptation, and population norming. Further, they are not always reliable predictors of future outcomes when assessed within the first 12-18 months of a child's life. Neuroimaging may provide more objective, sensitive, and predictive measures of neurodevelopment but tools such as magnetic resonance (MR) imaging are not readily available in many low and middle-income countries (LMICs). MRI systems that operate at lower magnetic fields (< 100mT) may offer increased accessibility, but their use for global health studies remains nascent. The UNITY project is envisaged as a global partnership to advance neuroimaging in global health studies. Here we describe the UNITY project, its goals, methods, operating procedures, and expected outcomes in characterizing neurodevelopment in sub-Saharan Africa and South Asia.

Mapping average axon diameters in porcine spinal cord white matter and rat corpus callosum using d-PFG MRI.

Knowledge of microstructural features of nerve fascicles, such as their axon diameter, is crucial for understanding normal function in the central and peripheral nervous systems as well as assessing changes due to pathologies. In this study double-pulsed field gradient (d-PFG) filtered MRI was used to map the average axon diameter (AAD) in porcine spinal cord, which was then compared to AADs measured with optical microscopy of the same specimen, as a way to further validate this new MRI method. A novel 3D d-PFG acquisition scheme was used to obtain AADs in each voxel of a coronal slice of rat brain corpus callosum. AAD measurements were also acquired using optical microscopy performed on histological sections and validated using a glass capillary array phantom.

Double pulsed field gradient (double-PFG) MR imaging (MRI) as a means to measure the size of plant cells.

Measurement of diffusion in porous materials and biological tissues with the pulsed field gradient (PFG) MR techniques has proven useful in characterizing the microstructure of such specimens noninvasively. A natural extension of the traditional PFG technique comprises multiple pairs of diffusion gradients. This approach has been shown to provide the ability to characterize anisotropy at different length scales without the need to employ very strong gradients. In this work, the double-PFG imaging technique was used on a specimen involving a series of glass capillary arrays with different diameters. The experiments on the phantom demonstrated the ability to create a quantitative and accurate map of pore sizes. The same technique was subsequently employed to image a celery stalk. A diffusion tensor image (DTI) of the same specimen was instrumental in accurately delineating the regions of vascular tissue and determining the local orientation of cells. This orientation information was incorporated into a theoretical double-PFG framework and the technique was employed to estimate the cell size in the vascular bundles of the celery stalk. The findings suggest that the double-PFG MRI framework could provide important new information regarding the microstructure of many plants and other food products.

A novel MRI phantom to study interstitial fluid transport in the glymphatic system.

The glymphatic system is a recently discovered transport system, mediated by cerebral spinal fluid (CSF), that clears metabolic and cellular waste products in the brain. This system's function in the brain is analogous to that of the lymphatic system in the rest of the mammalian body. It is hypothesized that CSF clears harmful chemicals from the brain by flowing through interstitial spaces in the brain during sleep. While there is growing recognition of the critical role the glymphatic system plays in maintaining normal brain health and in explaining pathology, there are few noninvasive imaging methods that measure and characterize the efficacy of glymphatic transport in vivo. In this study we designed, constructed, and tested a glymphatic transport magnetic resonance imaging (MRI) flow phantom, which combines regions that mimic CSF-filled ventricles and brain interstitial space. We tested high- and low-q space diffusion MRI and diffusion tensor imaging (DTI) acquisitions to determine if they could detect, measure, and map interstitial glymphatic flows. The results suggest that, under certain flow conditions, diffusion-weighted MRI can detect the enhanced mixing that occurs during glymphatic clearance.

Elucidating the mechanisms and loci of neuronal excitation by transcranial magnetic stimulation using a finite element model of a cortical sulcus.

OBJECTIVE: This work aims to elucidate by what physical mechanisms and where stimulation occurs in the brain during transcranial magnetic stimulation (TMS), taking into account cortical geometry and tissue heterogeneity. METHODS: An idealized computer model of TMS was developed, comprising a stimulation coil, a cortical sulcus, and surrounding tissues. The distribution of the induced electric field was computed, and estimates of the relevant parameters were generated to predict the locus and type of neurons stimulated during TMS, assuming three different stimulation mechanisms. RESULTS: Tissue heterogeneity strongly affects the spatial distribution of the induced electric field and hence which stimulation mechanism is dominant and where it acts. Stimulation of neurons may occur in the gyrus, in the lip of the gyrus, and in the walls of the sulcus. The stimulated cells can be either pyramidal cells having medium to large caliber axons, or intracortical fibers of medium caliber. CONCLUSIONS: The results highlight the influence of cortical folding on the action of magnetic and electric fields on cortical tissue. SIGNIFICANCE: Tissue geometry and heterogeneity in electrical conductivity both must be taken into account to predict accurately stimulation loci and mechanism in TMS.

Detection of microscopic anisotropy in gray matter and in a novel tissue phantom using double Pulsed Gradient Spin Echo MR.

A double Pulsed Gradient Spin Echo (d-PGSE) MR experiment was used to measure and assess the degree of local diffusion anisotropy in brain gray matter, and in a novel "gray matter" phantom that consists of randomly oriented tubes filled with water. In both samples, isotropic diffusion was observed at a macroscopic scale while anisotropic diffusion was observed at a microscopic scale, however, the nature of the resulting echo attenuation profiles were qualitatively different. Gray matter, which contains multiple cell types and fibers, exhibits a more complicated echo attenuation profile than the phantom. Since microscopic anisotropy was observed in both samples in the low q regime comparable to that achievable in clinical scanner, it may offer a new potential contrast mechanism for characterizing gray matter microstructure in medical and biological applications.

Tissue heterogeneity as a mechanism for localized neural stimulation by applied electric fields.

We investigate the heterogeneity of electrical conductivity as a new mechanism to stimulate excitable tissues via applied electric fields. In particular, we show that stimulation of axons crossing internal boundaries can occur at boundaries where the electric conductivity of the volume conductor changes abruptly. The effectiveness of this and other stimulation mechanisms was compared by means of models and computer simulations in the context of transcranial magnetic stimulation. While, for a given stimulation intensity, the largest membrane depolarization occurred where an axon terminates or bends sharply in a high electric field region, a slightly smaller membrane depolarization, still sufficient to generate action potentials, also occurred at an internal boundary where the conductivity jumped from 0.143 S m(-1) to 0.333 S m(-1), simulating a white-matter-grey-matter interface. Tissue heterogeneity can also give rise to local electric field gradients that are considerably stronger and more focal than those impressed by the stimulation coil and that can affect the membrane potential, albeit to a lesser extent than the two mechanisms mentioned above. Tissue heterogeneity may play an important role in electric and magnetic 'far-field' stimulation.

Anisotropic phantom to calibrate high-q diffusion MRI methods.

A silicon oil-filled glass capillary array is proposed as an anisotropic diffusion MRI phantom. Together with a computational/theoretical pipeline these provide a gold standard for calibrating and validating high-q diffusion MRI experiments. The phantom was used to test high angular resolution diffusion imaging (HARDI) and double pulsed-field gradient (d-PFG) MRI acquisition schemes. MRI-based predictions of microcapillary diameter using both acquisition schemes were compared with results from optical microscopy. This phantom design can be used for quality control and quality assurance purposes and for testing and validating proposed microstructure imaging experiments and the processing pipelines used to analyze them.

Cartilage calcification studied by proton nuclear magnetic resonance microscopy.

A three-dimensional (3D) mineralizing culture system using hollow fiber bioreactors has been developed to study the early stages of endochondral ossification by proton nuclear magnetic resonance (NMR) microscopy. Chondrocytes harvested from the cephalic half of the sterna from 17-day-old chick embryos were terminally differentiated with 33 nM of retinoic acid for 1 week and mineralization was initiated by the addition of 1% beta-glycerophosphate to the culture medium. Histological sections taken after 6 weeks of development in culture confirmed calcification of the cartilage matrix formed in bioreactors. Calcium to phosphorus ratios (1.62-1.68) from X-ray microanalysis supported electron diffraction of thin tissue sections showing the presence of a poorly crystalline hydroxyapatite mineral phase in the cultures. After 4 weeks of culture, quantitative proton NMR images showed water proton magnetization transfer rate constants (km) were higher in premineralized cartilage compared with uncalcified cartilage, a result suggesting collagen enrichment of the matrix. Notably after 5 weeks mineral deposits formed in bioreactors principally in the collagen-enriched zones of the cartilage with increased km values. This caused marked reductions in water proton longitudinal (T1) and transverse (T2) relaxation times and water diffusion coefficients (D). These results support the hypothesis that mineralization proceeds in association with a collagen template. After 6 weeks of culture development, the water proton T2 values decreased by 13% and D increased by 7% in uncalcified areas, compared with the same regions of tissue examined 1 week earlier. These changes could be attributed to the formation of small mineral inclusions in the cartilage, possibly mediated by matrix vesicles, which may play an important role in cartilage calcification. In summary, NMR images acquired before and after the onset of mineralization of the same tissue provide unique insights into the matrix events leading to endochondral mineral formation.

Analytical computation of the eigenvalues and eigenvectors in DT-MRI.

In this paper a noniterative algorithm to be used for the analytical determination of the sorted eigenvalues and corresponding orthonormalized eigenvectors obtained by diffusion tensor magnetic resonance imaging (DT-MRI) is described. The algorithm uses the three invariants of the raw water spin self-diffusion tensor represented by a 3 x 3 positive definite matrix and certain math functions that do not require iteration. The implementation requires a positive definite mask to preserve the physical meaning of the eigenvalues. This algorithm can increase the speed of eigenvalue/eigenvector calculations by a factor of 5-40 over standard iterative Jacobi or singular-value decomposition techniques. This approach may accelerate the computation of eigenvalues, eigenvalue-dependent metrics, and eigenvectors especially when having high-resolution measurements with large numbers of slices and large fields of view.

The Donnan model derived from microstructure.

The ideal Donnan potential of an ionized polyelectrolyte medium is shown to be an approximate solution to a system of Poisson-Boltzmann (PB) equations for a periodic array of charged plates in an electrolyte bath. This result, derived using homogenization and scaling methods, demonstrates that the macrocontinuum, thermodynamic Donnan, and statistical mechanical PB models describe the same phenomenon: electrostatic repulsion between fixed-charged groups (albeit at different length scales). The Donnan approximation is accurate at low ionic strength (i.e., where the Debye length is much larger than the separation between charged plates), but is less faithful at physiologic and higher ionic strength. This work also provides a framework for relating theories of electrostatic repulsive interactions formulated at microscopic and macroscopic length scales.

Spatial transformations of diffusion tensor magnetic resonance images.

We address the problem of applying spatial transformations (or "image warps") to diffusion tensor magnetic resonance images. The orientational information that these images contain must be handled appropriately when they are transformed spatially during image registration. We present solutions for global transformations of three-dimensional images up to 12-parameter affine complexity and indicate how our methods can be extended for higher order transformations. Several approaches are presented and tested using synthetic data. One method, the preservation of principal direction algorithm, which takes into account shearing, stretching and rigid rotation, is shown to be the most effective. Additional registration experiments are performed on human brain data obtained from a single subject, whose head was imaged in three different orientations within the scanner. All of our methods improve the consistency between registered and target images over naïve warping algorithms.

Focal magnetic stimulation of an axon.

The induced electric field produced by a circular coil during magnetic stimulation of an axon is derived from Maxwell's equations. The foci and virtual cathodal and anodal regions are predicted as a function of coil radius and orientation. Two virtual anode and cathode pairs are predicted, one lying outside the coil's perimeter and predominant in the far field, and one lying within the perimeter of the coil which may stimulate the axon when the coil and nerve are in close proximity. When the coil is positioned tangent to the nerve, an orientation commonly used in clinical magnetic stimulation, the foci of the predominant cathode and anode pair are extremely sensitive to changes in coil placement. In addition, the radius of curvature of the activating function, a measure of the size of the virtual cathode at threshold, is predicted to decrease with decreasing coil diameter and distance to the nerve. These predictions may help explain observed variability in measurements of conduction velocity and latency during magnetic stimulation of peripheral axons.

A model of the stimulation of a nerve fiber by electromagnetic induction.

A model is presented to explain the physics of nerve stimulation by electromagnetic induction. Maxwell's equations predict the induced electric field distribution that is produced when a capacitor is discharged through a stimulating coil. A nonlinear Hodgkin-Huxley cable model describes the response of the nerve fiber to this induced electric field. Once the coil's position, orientation, and shape are given and the resistance, capacitance, and initial voltage of the stimulating circuit are specified, this model predicts the resulting transmembrane potential of the fiber as a function of distance and time. It is shown that the nerve fiber is stimulated by the gradient of the component of the induced electric field that is parallel to the fiber, which hyperpolarizes or depolarizes the membrane and may stimulate an action potential. Finally, it predicts complicated dynamics such as action potential annihilation and dispersion.

A theoretical model for magneto-acoustic imaging of bioelectric currents.

A theoretical model of magneto-acoustic current imaging is derived, based on fundamental equations of continuum mechanics and electromagnetism. In electrically active tissue, the interaction between an applied magnetic field, B, and action currents, J, creates a pressure distribution. In the near field limit, this pressure obeys Poisson's equation, with a source term (delta x J).B. The displacement and pressure fields are calculated for a dipole (q), oriented either parallel or perpendicular to the applied magnetic field (B), at the center of an elastic, conducting sphere (radius a, shear modulus G). Surface displacements are on the order of qB/(4 pi Ga), which is about 1 nm for typical biological parameters. If the applied magnetic field is changing with time, eddy currents induced in the tissue may be larger than the action currents themselves. The frequency of the pressure and displacement arising from these eddy currents, however, is twice the frequency of the applied magnetic field, so it may be possible to eliminate this artifact by filtering or lock-in techniques. Magneto-acoustic and biomagnetic measurements both image delta x J in a similar way, although magneto-acoustic current imaging has the disadvantage that acoustic properties vary among tissues to a greater degree than do magnetic properties.

The activating function for magnetic stimulation derived from a three-dimensional volume conductor model.

A three-dimensional volume conductor model of magnetic stimulation is proposed that relates transmembrane potential of an axon to the induced electric field in a uniform volume conductor. This model validates assumptions used to derive a one-dimensional cable model of magnetic stimulation (Roth & Basser, IEEE Trans. Biomed. Eng., vol. 37, pp. 588-597, 1990) of unmyelinated axons. The three-dimensional volume conductor model reduces to this one-dimensional cable equation forced by the activating function, -delta EzA/delta z.

Cable equation for a myelinated axon derived from its microstructure.

A simplified cable equation that describes the subthreshold behaviour of a myelinated axon is derived from its microstructure. Specifically, a microcontinuum cable model of a composite axon is homogenised, yielding a familiar macrocontinuum cable equation of electrotonus, for which the space and time constants depend on microstructural electrical parameters. Activating functions for magnetic and electrical stimulation can be incorporated into this homogenised cable equation as sources or sinks of transmembrane potential. An integral solution to the forced cable equation is also presented for the subthreshold regime. Errors are introduced when myelin membrane resistance is assumed to be infinite.

Stimulation of a myelinated nerve axon by electromagnetic induction.

A model of electromagnetic stimulation predicts the transmembrane potential distribution along a myelinated nerve axon and the volume of stimulated tissue within a limb. Threshold stimulus strength is shown to be inversely proportional to the square of the axon diameter. It is inversely proportional to pulse duration for short pulses and independent of pulse duration for long ones. These results are also predicted by dimensional analysis. Two dimensionless numbers, Sem, the ratio of the induced transmembrane potential to the axon's threshold potential, and Tc/T, the ratio of the pulse duration to the membrane time constant, summarise the dependence of threshold stimulus strength on pulse duration and axon diameter.

The dynamics of a hydrogel strip.

A hydrogel strip relaxes when it is stretched. The decay in tensile stress can be ascribed primarily to strain-induced swelling of the polymer network--a result that follows from a continuum model of the gel-solvent system. An equation of motion and a linear constitutive law of the polymer network, Darcy's law, and the conservation of mass of the network and interstitial fluid are solved with boundary and initial conditions appropriate for a stress-relaxation experiment. This model predicts that the time constant of decay depends inversely upon the square of the thickness of the sample. This result is confirmed by experiments. In addition, the network shear modulus, mu, bulk modulus, k, and hydraulic permeability, 1/f, which are estimated by non-linear regression, all agree with measurements obtained using other methods.

Role of myelin plasticity in oscillations and synchrony of neuronal activity.

Conduction time is typically ignored in computational models of neural network function. Here we consider the effects of conduction delays on the synchrony of neuronal activity and neural oscillators, and evaluate the consequences of allowing conduction velocity (CV) to be regulated adaptively. We propose that CV variation, mediated by myelin, could provide an important mechanism of activity-dependent nervous system plasticity. Even small changes in CV, resulting from small changes in myelin thickness or nodal structure, could have profound effects on neuronal network function in terms of spike-time arrival, oscillation frequency, oscillator coupling, and propagation of brain waves. For example, a conduction delay of 5ms could change interactions of two coupled oscillators at the upper end of the gamma frequency range (∼100Hz) from constructive to destructive interference; delays smaller than 1ms could change the phase by 30°, significantly affecting signal amplitude. Myelin plasticity, as another form of activity-dependent plasticity, is relevant not only to nervous system development but also to complex information processing tasks that involve coupling and synchrony among different brain rhythms. We use coupled oscillator models with time delays to explore the importance of adaptive time delays and adaptive synaptic strengths. The impairment of activity-dependent myelination and the loss of adaptive time delays may contribute to disorders where hyper- and hypo-synchrony of neuronal firing leads to dysfunction (e.g., dyslexia, schizophrenia, epilepsy).