ASU Scholarship Showcase

It is known that in classical fluids turbulence typically occurs at high Reynolds numbers. But can turbulence occur at low Reynolds numbers? Here we investigate the transition to turbulence in the classic Taylor-Couette system in which the rotating fluids are manufactured ferrofluids with magnetized nanoparticles embedded in liquid carriers. We find that, in the presence of a magnetic field transverse to the symmetry axis of the system, turbulence can occur at Reynolds numbers that are at least one order of magnitude smaller than those in conventional fluids. This is established by extensive computational ferrohydrodynamics through a detailed investigation of transitions in the flow structure, and characterization of behaviors of physical quantities such as the energy, the wave number, and the angular momentum through the bifurcations. A finding is that, as the magnetic field is increased, onset of turbulence can be determined accurately and reliably. Our results imply that experimental investigation of turbulence may be feasible by using ferrofluids. Our study of transition to and evolution of turbulence in the Taylor-Couette ferrofluidic flow system provides insights into the challenging problem of turbulence control.

The apolipoprotein E (APOE) e4 genotype is a powerful risk factor for late-onset Alzheimer’s disease (AD). In the Alzheimer’s Disease Neuroimaging Initiative (ADNI) cohort, we previously reported significant baseline structural differences in APOE e4 carriers relative to non-carriers, involving the left hippocampus more than the right—a difference more pronounced in e4 homozygotes than heterozygotes. We now examine the longitudinal effects of APOE genotype on hippocampal morphometry at 6-, 12- and 24-months, in the ADNI cohort. We employed a new automated surface registration system based on conformal geometry and tensor-based morphometry. Among different hippocampal surfaces, we computed high-order correspondences, using a novel inverse-consistent surface-based fluid registration method and multivariate statistics consisting of multivariate tensor-based morphometry (mTBM) and radial distance. At each time point, using Hotelling’s T² test, we found significant morphological deformation in APOE e4 carriers relative to non-carriers in the full cohort as well as in the non-demented (pooled MCI and control) subjects at each follow-up interval. In the complete ADNI cohort, we found greater atrophy of the left hippocampus than the right, and this asymmetry was more pronounced in e4 homozygotes than heterozygotes. These findings, combined with our earlier investigations, demonstrate an e4 dose effect on accelerated hippocampal atrophy, and support the enrichment of prevention trial cohorts with e4 carriers.

Many children born preterm exhibit frontal executive dysfunction, behavioral problems including attentional deficit/hyperactivity disorder and attention related learning disabilities. Anomalies in regional specificity of cortico-striato-thalamo-cortical circuits may underlie deficits in these disorders. Nonspecific volumetric deficits of striatal structures have been documented in these subjects, but little is known about surface deformation in these structures. For the first time, here we found regional surface morphological differences in the preterm neonatal ventral striatum. We performed regional group comparisons of the surface anatomy of the striatum (putamen and globus pallidus) between 17 preterm and 19 term-born neonates at term-equivalent age. We reconstructed striatal surfaces from manually segmented brain magnetic resonance images and analyzed them using our in-house conformal mapping program. All surfaces were registered to a template with a new surface fluid registration method. Vertex-based statistical comparisons between the two groups were performed via four methods: univariate and multivariate tensor-based morphometry, the commonly used medial axis distance, and a combination of the last two statistics. We found statistically significant differences in regional morphology between the two groups that are consistent across statistics, but more extensive for multivariate measures. Differences were localized to the ventral aspect of the striatum. In particular, we found abnormalities in the preterm anterior/inferior putamen, which is interconnected with the medial orbital/prefrontal cortex and the midline thalamic nuclei including the medial dorsal nucleus and pulvinar. These findings support the hypothesis that the ventral striatum is vulnerable, within the cortico-stiato-thalamo-cortical neural circuitry, which may underlie the risk for long-term development of frontal executive dysfunction, attention deficit hyperactivity disorder and attention-related learning disabilities in preterm neonates.

We investigate high-dimensional nonlinear dynamical systems exhibiting multiple resonances under adiabatic parameter variations. Our motivations come from experimental considerations where time-dependent sweeping of parameters is a practical approach to probing and characterizing the bifurcations of the system. The question is whether bifurcations so detected are faithful representations of the bifurcations intrinsic to the original stationary system. Utilizing a harmonically forced, closed fluid flow system that possesses multiple resonances and solving the Navier-Stokes equation under proper boundary conditions, we uncover the phenomenon of the early effect. Specifically, as a control parameter, e.g., the driving frequency, is adiabatically increased from an initial value, resonances emerge at frequency values that are lower than those in the corresponding stationary system. The phenomenon is established by numerical characterization of physical quantities through the resonances, which include the kinetic energy and the vorticity field, and a heuristic analysis based on the concept of instantaneous frequency. A simple formula is obtained which relates the resonance points in the time-dependent and time-independent systems. Our findings suggest that, in general, any true bifurcation of a nonlinear dynamical system can be unequivocally uncovered through adiabatic parameter sweeping, in spite of a shift in the bifurcation point, which is of value to experimental studies of nonlinear dynamical systems.

In this paper, we develop a new automated surface registration system based on surface conformal parameterization by holomorphic 1-forms, inverse consistent surface fluid registration, and multivariate tensor-based morphometty (mTBM). First, we conformally map a surface onto a planar rectangle space with holomorphic 1-forms. Second, we compute surface conformal representation by combining its local conformal factor and mean curvature and linearly scale the dynamic range of the conformal representation to form the feature image of the surface. Third, we align the feature image with a chosen template image via the fluid image registration algorithm, which has been extended into the curvilinear coordinates to adjust for the distortion introduced by surface parameterization. The inverse consistent image registration algorithm is also incorporated in the system to jointly estimate the forward and inverse transformations between the study and template images. This alignment induces a corresponding deformation on the surface. We tested the system on Alzheimer's Disease Neuroimaging Initiative (ADNI) baseline dataset to study AD symptoms on hippocampus. In our system, by modeling a hippocampus as a 3D parametric surface, we nonlinearly registered each surface with a selected template surface. Then we used mTBM to analyze the morphometry difference between diagnostic groups. Experimental results show that the new system has better performance than two publicly available subcortical surface registration tools: FIRST and SPHARM. We also analyzed the genetic influence of the Apolipoprotein E(is an element of)4 allele (ApoE4), which is considered as the most prevalent risk factor for AD. Our work successfully detected statistically significant difference between ApoE4 carriers and non-carriers in both patients of mild cognitive impairment (MCI) and healthy control subjects. The results show evidence that the ApoE genotype may be associated with accelerated brain atrophy so that our work provides a new MRI analysis tool that may help presymptomatic AD research.

We investigate fundamental nonlinear dynamics of ferrofluidic Taylor-Couette flow - flow confined be-tween two concentric independently rotating cylinders - consider small aspect ratio by solving the ferro-hydrodynamical equations, carrying out systematic bifurcation analysis. Without magnetic field, we find steady flow patterns, previously observed with a simple fluid, such as those containing normal one- or two vortex cells, as well as anomalous one-cell and twin-cell flow states. However, when a symmetry-breaking transverse magnetic field is present, all flow states exhibit stimulated, finite two-fold mode. Various bifurcations between steady and unsteady states can occur, corresponding to the transitions between the two-cell and one-cell states. While unsteady, axially oscillating flow states can arise, we also detect the emergence of new unsteady flow states. In particular, we uncover two new states: one contains only the azimuthally oscillating solution in the configuration of the twin-cell flow state, and an-other a rotating flow state. Topologically, these flow states are a limit cycle and a quasiperiodic solution on a two-torus, respectively. Emergence of new flow states in addition to observed ones with classical fluid, indicates that richer but potentially more controllable dynamics in ferrofluidic flows, as such flow states depend on the external magnetic field.

We investigate the dynamics of ferrofluidic wavy vortex flows in the counter-rotating Taylor-Couette system, with a focus on wavy flows with a mixture of the dominant azimuthal modes. Without external magnetic field flows are stable and pro-grade with respect to the rotation of the inner cylinder. More complex behaviors can arise when an axial or a transverse magnetic field is applied. Depending on the direction and strength of the field, multi-stable wavy states and bifurcations can occur. We uncover the phenomenon of flow pattern reversal as the strength of the magnetic field is increased through a critical value. In between the regimes of pro-grade and retrograde flow rotations, standing waves with zero angular velocities can emerge. A striking finding is that, under a transverse magnetic field, a second reversal in the flow pattern direction can occur, where the flow pattern evolves into pro-grade rotation again from a retrograde state. Flow reversal is relevant to intriguing phenomena in nature such as geomagnetic reversal. Our results suggest that, in ferrofluids, flow pattern reversal can be induced by varying a magnetic field in a controlled manner, which can be realized in laboratory experiments with potential applications in the development of modern fluid devices.

Chronic manganese (Mn) exposure is associated with neuromotor and neurocognitive deficits, but the exact mechanism of Mn neurotoxicity is still unclear. With the advent of magnetic resonance imaging (MRI), in-vivo analysis of brain structures has become possible. Among different sub-cortical structures, the basal ganglia (BG) has been investigated as a putative anatomical biomarker in MR-based studies of Mn toxicity. However, previous investigations have yielded inconsistent results in terms of regional MR signal intensity changes. These discrepancies may be due to the subtlety of brain alterations caused by Mn toxicity, coupled to analysis techniques that lack the requisite detection power. Here, based on brain MRI, we apply a 3D surface-based morphometry method on 3 bilateral basal ganglia structures in school-age children chronically exposed to Mn through drinking water to investigate the effect of Mn exposure on brain anatomy. Our method successfully pinpointed significant enlargement of many areas of the basal ganglia structures, preferentially affecting the putamen. Moreover, these areas showed significant correlations with fine motor performance, indicating a possible link between altered basal ganglia neurodevelopment and declined motor performance in high Mn exposed children.

The apolipoprotein E (APOE) e4 allele is the most prevalent genetic risk factor for Alzheimer's disease (AD). Hippocampal volumes are generally smaller in AD patients carrying the e4 allele compared to e4 noncarriers. Here we examined the effect of APOE e4 on hippocampal morphometry in a large imaging database—the Alzheimer's Disease Neuroimaging Initiative (ADNI). We automatically segmented and constructed hippocampal surfaces from the baseline MR images of 725 subjects with known APOE genotype information including 167 with AD, 354 with mild cognitive impairment (MCI), and 204 normal controls. High-order correspondences between hippocampal surfaces were enforced across subjects with a novel inverse consistent surface fluid registration method. Multivariate statistics consisting of multivariate tensor-based morphometry (mTBM) and radial distance were computed for surface deformation analysis. Using Hotelling's T2 test, we found significant morphological deformation in APOE e4 carriers relative to noncarriers in the entire cohort as well as in the nondemented (pooled MCI and control) subjects, affecting the left hippocampus more than the right, and this effect was more pronounced in e4 homozygotes than heterozygotes. Our findings are consistent with previous studies that showed e4 carriers exhibit accelerated hippocampal atrophy; we extend these findings to a novel measure of hippocampal morphometry. Hippocampal morphometry has significant potential as an imaging biomarker of early stage AD.

Alzheimer's disease (AD) is a progressive brain disease. Accurate detection of AD and its prodromal stage, mild cognitive impairment (MCI), are crucial. There is also a growing interest in identifying brain imaging biomarkers that help to automatically differentiate stages of Alzheimer's disease. Here, we focused on brain structural networks computed from diffusion MRI and proposed a new feature extraction and classification framework based on higher order singular value decomposition and sparse logistic regression. In tests on publicly available data from the Alzheimer's Disease Neuroimaging Initiative, our proposed framework showed promise in detecting brain network differences that help in classifying different stages of Alzheimer's disease.