ASU Scholarship Showcase

Five immunocompetent C57BL/6-cBrd/cBrd/Cr (albino C57BL/6) mice were injected with GL261-luc2 cells, a cell line sharing characteristics of human glioblastoma multiforme (GBM). The mice were imaged using magnetic resonance (MR) at five separate time points to characterize growth and development of the tumor. After 25 days, the final tumor volumes of the mice varied from 12 mm³ to 62 mm³, even though mice were inoculated from the same tumor cell line under carefully controlled conditions. We generated hypotheses to explore large variances in final tumor size and tested them with our simple reaction-diffusion model in both a 3-dimensional (3D) finite difference method and a 2-dimensional (2D) level set method. The parameters obtained from a best-fit procedure, designed to yield simulated tumors as close as possible to the observed ones, vary by an order of magnitude between the three mice analyzed in detail. These differences may reflect morphological and biological variability in tumor growth, as well as errors in the mathematical model, perhaps from an oversimplification of the tumor dynamics or nonidentifiability of parameters. Our results generate parameters that match other experimental in vitro and in vivo measurements. Additionally, we calculate wave speed, which matches with other rat and human measurements.

Background:
Data assimilation refers to methods for updating the state vector (initial condition) of a complex spatiotemporal model (such as a numerical weather model) by combining new observations with one or more prior forecasts. We consider the potential feasibility of this approach for making short-term (60-day) forecasts of the growth and spread of a malignant brain cancer (glioblastoma multiforme) in individual patient cases, where the observations are synthetic magnetic resonance images of a hypothetical tumor.

Results:
We apply a modern state estimation algorithm (the Local Ensemble Transform Kalman Filter), previously developed for numerical weather prediction, to two different mathematical models of glioblastoma, taking into account likely errors in model parameters and measurement uncertainties in magnetic resonance imaging. The filter can accurately shadow the growth of a representative synthetic tumor for 360 days (six 60-day forecast/update cycles) in the presence of a moderate degree of systematic model error and measurement noise.

Conclusions:
The mathematical methodology described here may prove useful for other modeling efforts in biology and oncology. An accurate forecast system for glioblastoma may prove useful in clinical settings for treatment planning and patient counseling.

Two classes of scaling behaviours, namely the super-linear scaling of links or activities, and the sub-linear scaling of area, diversity, or time elapsed with respect to size have been found to prevail in the growth of complex networked systems. Despite some pioneering modelling approaches proposed for specific systems, whether there exists some general mechanisms that account for the origins of such scaling behaviours in different contexts, especially in socioeconomic systems, remains an open question. We address this problem by introducing a geometric network model without free parameter, finding that both super-linear and sub-linear scaling behaviours can be simultaneously reproduced and that the scaling exponents are exclusively determined by the dimension of the Euclidean space in which the network is embedded. We implement some realistic extensions to the basic model to offer more accurate predictions for cities of various scaling behaviours and the Zipf distribution reported in the literature and observed in our empirical studies. All of the empirical results can be precisely recovered by our model with analytical predictions of all major properties. By virtue of these general findings concerning scaling behaviour, our models with simple mechanisms gain new insights into the evolution and development of complex networked systems.

The development of non-volatile logic through direct coupling of spontaneous ferroelectric polarization with semiconductor charge carriers is nontrivial, with many issues, including epitaxial ferroelectric growth, demonstration of ferroelectric switching and measurable semiconductor modulation. Here we report a true ferroelectric field effect—carrier density modulation in an underlying Ge(001) substrate by switching of the ferroelectric polarization in epitaxial c-axis-oriented BaTiO₃ grown by molecular beam epitaxy. Using the density functional theory, we demonstrate that switching of BaTiO₃ polarization results in a large electric potential change in Ge. Aberration-corrected electron microscopy confirms BaTiO₃ tetragonality and the absence of any low-permittivity interlayer at the interface with Ge. The non-volatile, switchable nature of the single-domain out-of-plane ferroelectric polarization of BaTiO₃ is confirmed using piezoelectric force microscopy. The effect of the polarization switching on the conductivity of the underlying Ge is measured using microwave impedance microscopy, clearly demonstrating a ferroelectric field effect.

The emission properties of GeSn heterostructure pin diodes have been investigated. The devices contain thick (400–600 nm) Ge_1-y Sn_y i-layers spanning a broad compositional range below and above the crossover Sn concentration y_c where the Ge_1-y Sn_y alloy becomes a direct-gap material. These results are made possible by an optimized device architecture containing a single defected interface thereby mitigating the deleterious effects of mismatch-induced defects. The observed emission intensities as a function of composition show the contributions from two separate trends: an increase in direct gap emission as the Sn concentration is increased, as expected from the reduction and eventual reversal of the separation between the direct and indirect edges, and a parallel increase in non-radiative recombination when the mismatch strains between the structure components is partially relaxed by the generation of misfit dislocations. An estimation of recombination times based on the observed electroluminescence intensities is found to be strongly correlated with the reverse-bias dark current measured in the same devices.

Predicting the timing of a castrate resistant prostate cancer is critical to lowering medical costs and improving the quality of life of advanced prostate cancer patients. We formulate, compare and analyze two mathematical models that aim to forecast future levels of prostate-specific antigen (PSA). We accomplish these tasks by employing clinical data of locally advanced prostate cancer patients undergoing androgen deprivation therapy (ADT). While these models are simplifications of a previously published model, they fit data with similar accuracy and improve forecasting results. Both models describe the progression of androgen resistance. Although Model 1 is simpler than the more realistic Model 2, it can fit clinical data to a greater precision. However, we found that Model 2 can forecast future PSA levels more accurately. These findings suggest that including more realistic mechanisms of androgen dynamics in a two population model may help androgen resistance timing prediction.

The compositional dependence of the lowest direct and indirect band gaps in Ge_1-ySn_y alloys has been determined from room-temperature photoluminescence measurements. This technique is particularly attractive for a comparison of the two transitions because distinct features in the spectra can be associated with the direct and indirect gaps. However, detailed modeling of these room temperature spectra is required to extract the band gap values with the high accuracy required to determine the Sn concentration y_c at which the alloy becomes a direct gap semiconductor. For the direct gap, this is accomplished using a microscopic model that allows the determination of direct gap energies with meV accuracy. For the indirect gap, it is shown that current theoretical models are inadequate to describe the emission properties of systems with close indirect and direct transitions. Accordingly, an ad hoc procedure is used to extract the indirect gap energies from the data. For y < 0.1 the resulting direct gap compositional dependence is given by ΔE₀ = −(3.57 ± 0.06)y (in eV). For the indirect gap, the corresponding expression is ΔE_ind = −(1.64 ± 0.10)y (in eV). If a quadratic function of composition is used to express the two transition energies over the entire compositional range 0 ≤ y ≤ 1, the quadratic (bowing) coefficients are found to be b₀ = 2.46 ± 0.06 eV (for E0) and b_ind = 1.03 ± 0.11 eV (for E_ind). These results imply a crossover concentration y_c = $0.073 [+0.007 over -0.006], much lower than early theoretical predictions based on the virtual crystal approximation, but in better agreement with predictions based on large atomic supercells.

Given a complex geospatial network with nodes distributed in a two-dimensional region of physical space, can the locations of the nodes be determined and their connection patterns be uncovered based solely on data? We consider the realistic situation where time series/signals can be collected from a single location. A key challenge is that the signals collected are necessarily time delayed, due to the varying physical distances from the nodes to the data collection centre. To meet this challenge, we develop a compressive-sensing-based approach enabling reconstruction of the full topology of the underlying geospatial network and more importantly, accurate estimate of the time delays. A standard triangularization algorithm can then be employed to find the physical locations of the nodes in the network. We further demonstrate successful detection of a hidden node (or a hidden source or threat), from which no signal can be obtained, through accurate detection of all its neighbouring nodes. As a geospatial network has the feature that a node tends to connect with geophysically nearby nodes, the localized region that contains the hidden node can be identified.

Recent works revealed that the energy required to control a complex network depends on the number of driving signals and the energy distribution follows an algebraic scaling law. If one implements control using a small number of drivers, e.g. as determined by the structural controllability theory, there is a high probability that the energy will diverge. We develop a physical theory to explain the scaling behaviour through identification of the fundamental structural elements, the longest control chains (LCCs), that dominate the control energy. Based on the LCCs, we articulate a strategy to drastically reduce the control energy (e.g. in a large number of real-world networks). Owing to their structural nature, the LCCs may shed light on energy issues associated with control of nonlinear dynamical networks.

Earth-abundant sustainable inorganic thin-film solar cells, independent of precious elements, pivot on a marginal material phase space targeting specific compounds. Advanced materials characterization efforts are necessary to expose the roles of microstructure, chemistry, and interfaces. Herein, the earth-abundant solar cell device, Cu₂ZnSnS_(4-x)Se_x, is reported, which shows a high abundance of secondary phases compared to similarly grown Cu₂ZnSnSe₄.