Generalized Mittag-Leffler Distributions and Processes for Applications in Astrophysics and Time Series Modeling

Geometric generalized Mittag-Leffler distributions having the Laplace transform $\frac{1}{1+\beta\log(1+t^\alpha)},00$ is introduced and its properties are discussed. Autoregressive processes with Mittag-Leffler and geometric generalized Mittag-Leffler marginal distributions are developed. Haubold and Mathai (2000) derived a closed form representation of the fractional kinetic equation and thermonuclear function in terms of Mittag-Leffler function. Saxena et al (2002, 2004a,b) extended the result and derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions. These results are useful in explaining various fundamental laws of physics. Here we develop first-order autoregressive time series models and the properties are explored. The results have applications in various areas like astrophysics, space sciences, meteorology, financial modeling and reliability modeling.Comment: 12 pages, LaTe

Microfluidic Perfusion for Regulating Diffusible Signaling in Stem Cells

Background Autocrine & paracrine signaling are widespread both in vivo and in vitro, and are particularly important in embryonic stem cell (ESC) pluripotency and lineage commitment. Although autocrine signaling via fibroblast growth factor-4 (FGF4) is known to be required in mouse ESC (mESC) neuroectodermal specification, the question of whether FGF4 autocrine signaling is sufficient, or whether other soluble ligands are also involved in fate specification, is unknown. The spatially confined and closed-loop nature of diffusible signaling makes its experimental control challenging; current experimental approaches typically require prior knowledge of the factor/receptor in order to modulate the loop. A new approach explored in this work is to leverage transport phenomena at cellular resolution to downregulate overall diffusible signaling through the physical removal of cell-secreted ligands. Methodology/Principal Findings We develop a multiplex microfluidic platform to continuously remove cell-secreted (autocrine\paracrine) factors to downregulate diffusible signaling. By comparing cell growth and differentiation in side-by-side chambers with or without added cell-secreted factors, we isolate the effects of diffusible signaling from artifacts such as shear, nutrient depletion, and microsystem effects, and find that cell-secreted growth factor(s) are required during neuroectodermal specification. Then we induce FGF4 signaling in minimal chemically defined medium (N2B27) and inhibit FGF signaling in fully supplemented differentiation medium with cell-secreted factors to determine that the non-FGF cell-secreted factors are required to promote growth of differentiating mESCs. Conclusions/Significance Our results demonstrate for the first time that flow can downregulate autocrine\paracrine signaling and examine sufficiency of extracellular factors. We show that autocrine\paracrine signaling drives neuroectodermal commitment of mESCs through both FGF4-dependent and -independent pathways. Overall, by uncovering autocrine\paracrine processes previously hidden in conventional culture systems, our results establish microfluidic perfusion as a technique to study and manipulate diffusible signaling in cell systems.National Institutes of Health (U.S.) (NIH grant No. EB007278)Swiss National Science FoundationSwiss National Science Foundatio

Understanding pharmacokinetics using realistic computational models of fluid dynamics: biosimulation of drug distribution within the CSF space for intrathecal drugs

We introduce how biophysical modeling in pharmaceutical research and development, combining physiological observations at the tissue, organ and system level with selected drug physiochemical properties, may contribute to a greater and non-intuitive understanding of drug pharmacokinetics and therapeutic design. Based on rich first-principle knowledge combined with experimental data at both conception and calibration stages, and leveraging our insights on disease processes and drug pharmacology, biophysical modeling may provide a novel and unique opportunity to interactively characterize detailed drug transport, distribution, and subsequent therapeutic effects. This innovative approach is exemplified through a three-dimensional (3D) computational fluid dynamics model of the spinal canal motivated by questions arising during pharmaceutical development of one molecular therapy for spinal cord injury. The model was based on actual geometry reconstructed from magnetic resonance imaging data subsequently transformed in a parametric 3D geometry and a corresponding finite-volume representation. With dynamics controlled by transient Navier–Stokes equations, the model was implemented in a commercial multi-physics software environment established in the automotive and aerospace industries. While predictions were performed in silico, the underlying biophysical models relied on multiple sources of experimental data and knowledge from scientific literature. The results have provided insights into the primary factors that can influence the intrathecal distribution of drug after lumbar administration. This example illustrates how the approach connects the causal chain underlying drug distribution, starting with the technical aspect of drug delivery systems, through physiology-driven drug transport, then eventually linking to tissue penetration, binding, residence, and ultimately clearance. Currently supporting our drug development projects with an improved understanding of systems physiology, biophysical models are being increasingly used to characterize drug transport and distribution in human tissues where pharmacokinetic measurements are difficult or impossible to perform. Importantly, biophysical models can describe emergent properties of a system, i.e. properties not identifiable through the study of the system’s components taken in isolation

The imperative for controlled mechanical stresses in unraveling cellular mechanisms of mechanotransduction

BACKGROUND: In vitro mechanotransduction studies are designed to elucidate cell behavior in response to a well-defined mechanical signal that is imparted to cultured cells, e.g. through fluid flow. Typically, flow rates are calculated based on a parallel plate flow assumption, to achieve a targeted cellular shear stress. This study evaluates the performance of specific flow/perfusion chambers in imparting the targeted stress at the cellular level. METHODS: To evaluate how well actual flow chambers meet their target stresses (set for 1 and 10 dyn/cm(2 )for this study) at a cellular level, computational models were developed to calculate flow velocity components and imparted shear stresses for a given pressure gradient. Computational predictions were validated with micro-particle image velocimetry (μPIV) experiments. RESULTS: Based on these computational and experimental studies, as few as 66% of cells seeded along the midplane of commonly implemented flow/perfusion chambers are subjected to stresses within ±10% of the target stress. In addition, flow velocities and shear stresses imparted through fluid drag vary as a function of location within each chamber. Hence, not only a limited number of cells are exposed to target stress levels within each chamber, but also neighboring cells may experience different flow regimes. Finally, flow regimes are highly dependent on flow chamber geometry, resulting in significant variation in magnitudes and spatial distributions of stress between chambers. CONCLUSION: The results of this study challenge the basic premise of in vitro mechanotransduction studies, i.e. that a controlled flow regime is applied to impart a defined mechanical stimulus to cells. These results also underscore the fact that data from studies in which different chambers are utilized can not be compared, even if the target stress regimes are comparable

Microfluidic Endothelium for Studying the Intravascular Adhesion of Metastatic Breast Cancer Cells

BACKGROUND:The ability to properly model intravascular steps in metastasis is essential in identifying key physical, cellular, and molecular determinants that can be targeted therapeutically to prevent metastatic disease. Research on the vascular microenvironment has been hindered by challenges in studying this compartment in metastasis under conditions that reproduce in vivo physiology while allowing facile experimental manipulation. METHODOLOGY/PRINCIPAL FINDINGS:We present a microfluidic vasculature system to model interactions between circulating breast cancer cells with microvascular endothelium at potential sites of metastasis. The microfluidic vasculature produces spatially-restricted stimulation from the basal side of the endothelium that models both organ-specific localization and polarization of chemokines and many other signaling molecules under variable flow conditions. We used this microfluidic system to produce site-specific stimulation of microvascular endothelium with CXCL12, a chemokine strongly implicated in metastasis. CONCLUSIONS/SIGNIFICANCE:When added from the basal side, CXCL12 acts through receptor CXCR4 on endothelium to promote adhesion of circulating breast cancer cells, independent of CXCL12 receptors CXCR4 or CXCR7 on tumor cells. These studies suggest that targeting CXCL12-CXCR4 signaling in endothelium may limit metastases in breast and other cancers and highlight the unique capabilities of our microfluidic device to advance studies of the intravascular microenvironment in metastasis