UV-Photolithography Fabrication of Poly-Ethylene Glycol Hydrogels Encapsulated with Hepatocytes

The development of biomanufacturing technologies particularly, layered manufacturing has advanced cell encapsulation processes in an effort to mimic the cellular microenvironment for invitro studies. This paper illustrates an inexpensive UV-photolithographic method for encapsulation of human hepatocytes in three dimensional structures using poly-ethylene diacrylate (PEGDA) hydrogels as candidate substrates. In order to further develop this technology for layered fabrication, we have quantified the long-term effects of the photo-initiator concentration and UV light exposure on the metabolic rates of encapsulated human hepatocytes under a 21 day study. The photoinitator toxicity was observed immediately after polymerization with no significant cytotoxicity on a long term basis. A cellular viability is examined and reported for the UV photopolymerization process. Cell phenotype maintenance was observed by measuring the amount of urea produced over a 1 week time period. This photo encapsulation process may find use in the fabrication of spatially complex 3D scaffolds for tissue engineering applications, elucidation of the 3D structure-pharmacokinetic response relationship and the fabrication of complex multi-compartment liver tissue analog devices for drug screening applications.Mechanical Engineerin

Biomimetic Design and Fabrication of Interior Architecture of Tissue Scaffolds Using Solid Freeform Fabrication

Modeling, design and fabrication of tissue scaffolds with intricate architecture, porosity and pore size for desired tissue properties presents a challenge in tissue engineering. This paper will present the details of our development in designing and fabrication of the interior architecture of scaffolds using a novel design approach. The Interior Architecture Design (IAD) approach seeks to generate scaffold layered freeform fabrication tool path without forming complicated 3D CAD scaffold models. This involves: applying the principle of layered manufacturing to determine the scaffold individual layered process planes and layered contour; defining the 2D characteristic patterns of the scaffold building blocks (unit cells) to form the Interior Scaffold Pattern; and the generation of process tool path for freeform fabrication of these scaffolds with the specified interior architecture. Feasibility studies applying the IAD algorithm to example models and the generation of fabrication planning instructions will be presented.Mechanical Engineerin

Modelling and control of the flame temperature distribution using probability density function shaping

This paper presents three control algorithms for the output probability density function (PDF) control of the 2D and 3D flame distribution systems. For the 2D flame distribution systems, control methods for both static and dynamic flame systems are presented, where at first the temperature distribution of the gas jet flames along the cross-section is approximated. Then the flame energy distribution (FED) is obtained as the output to be controlled by using a B-spline expansion technique. The general static output PDF control algorithm is used in the 2D static flame system, where the dynamic system consists of a static temperature model of gas jet flames and a second-order actuator. This leads to a second-order closed-loop system, where a singular state space model is used to describe the dynamics with the weights of the B-spline functions as the state variables. Finally, a predictive control algorithm is designed for such an output PDF system. For the 3D flame distribution systems, all the temperature values of the flames are firstly mapped into one temperature plane, and the shape of the temperature distribution on this plane can then be controlled by the 3D flame control method proposed in this paper. Three cases are studied for the proposed control methods and desired simulation results have been obtained

Binomial coefficients, Catalan numbers and Lucas quotients

Let $p$ be an odd prime and let $a,m$ be integers with $a>0$ and $m \not\equiv0\pmod p$. In this paper we determine $\sum_{k=0}^{p^a-1}\binom{2k}{k+d}/m^k$ mod $p^2$ for $d=0,1$; for example, $$\sum_{k=0}^{p^a-1}\frac{\binom{2k}k}{m^k}\equiv\left(\frac{m^2-4m}{p^a}\right)+\left(\frac{m^2-4m}{p^{a-1}}\right)u_{p-(\frac{m^2-4m}{p})}\pmod{p^2},$$ where $(-)$ is the Jacobi symbol, and $\{u_n\}_{n\geqslant0}$ is the Lucas sequence given by $u_0=0$, $u_1=1$ and $u_{n+1}=(m-2)u_n-u_{n-1}$ for $n=1,2,3,\ldots$. As an application, we determine $\sum_{0<k<p^a,\, k\equiv r\pmod{p-1}}C_k$ modulo $p^2$ for any integer $r$, where $C_k$ denotes the Catalan number $\binom{2k}k/(k+1)$. We also pose some related conjectures.Comment: 24 pages. Correct few typo

On the asymptotics of dimers on tori

We study asymptotics of the dimer model on large toric graphs. Let $\mathbb L$ be a weighted $\mathbb{Z}^2$-periodic planar graph, and let $\mathbb{Z}^2 E$ be a large-index sublattice of $\mathbb{Z}^2$. For $\mathbb L$ bipartite we show that the dimer partition function on the quotient $\mathbb{L}/(\mathbb{Z}^2 E)$ has the asymptotic expansion $\exp[A f_0 + \text{fsc} + o(1)]$, where $A$ is the area of $\mathbb{L}/(\mathbb{Z}^2 E)$, $f_0$ is the free energy density in the bulk, and $\text{fsc}$ is a finite-size correction term depending only on the conformal shape of the domain together with some parity-type information. Assuming a conjectural condition on the zero locus of the dimer characteristic polynomial, we show that an analogous expansion holds for $\mathbb{L}$ non-bipartite. The functional form of the finite-size correction differs between the two classes, but is universal within each class. Our calculations yield new information concerning the distribution of the number of loops winding around the torus in the associated double-dimer models.Comment: 48 pages, 18 figure

Proportional hazards models with continuous marks

For time-to-event data with finitely many competing risks, the proportional hazards model has been a popular tool for relating the cause-specific outcomes to covariates [Prentice et al. Biometrics 34 (1978) 541--554]. This article studies an extension of this approach to allow a continuum of competing risks, in which the cause of failure is replaced by a continuous mark only observed at the failure time. We develop inference for the proportional hazards model in which the regression parameters depend nonparametrically on the mark and the baseline hazard depends nonparametrically on both time and mark. This work is motivated by the need to assess HIV vaccine efficacy, while taking into account the genetic divergence of infecting HIV viruses in trial participants from the HIV strain that is contained in the vaccine, and adjusting for covariate effects. Mark-specific vaccine efficacy is expressed in terms of one of the regression functions in the mark-specific proportional hazards model. The new approach is evaluated in simulations and applied to the first HIV vaccine efficacy trial.Comment: Published in at http://dx.doi.org/10.1214/07-AOS554 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Radio continuum and polarization study of SNR G57.2+0.8 associated with magnetar SGR1935+2154

We present a radio continuum and linear polarization study of the Galactic supernova remnant G57.2+0.8, which may host the recently discovered magnetar SGR1935+2154. The radio SNR shows the typical radio continuum spectrum of a mature supernova remnant with a spectral index of $\alpha = -0.55 \pm 0.02$ and moderate polarized intensity. Magnetic field vectors indicate a tangential magnetic field, expected for an evolved SNR, in one part of the SNR and a radial magnetic field in the other. The latter can be explained by an overlapping arc-like feature, perhaps a pulsar wind nebula, emanating from the magnetar. The presence of a pulsar wind nebula is supported by the low average braking index of 1.2, we extrapolated for the magnetar, and the detection of diffuse X-ray emission around it. We found a distance of 12.5 kpc for the SNR, which identifies G57.2+0.8 as a resident of the Outer spiral arm of the Milky Way. The SNR has a radius of about 20 pc and could be as old as 41,000 years. The SNR has already entered the radiative or pressure-driven snowplow phase of its evolution. We compared independently determined characteristics like age and distance for both, the SNR and SGR1935+2154, and conclude that they are physically related.Comment: accepted by The Astrophysical Journal, 16 pages, 10 figure