The design of a reflectionless arterial prosthesis

We propose a new technique to characterize a reflectionless arterial prosthesis. The corresponding transmission and reflection coefficients are determined from the geometric and the elastic properties of the arterial wall, and the interaction between the latter and the prosthesis are studied accordingly.     

pH effect on cellular uptake of Sn(IV) chlorine e6 dichloride trisodium salt by cancer cells in vitro

The effects of pH value and presence of serum in an incubation medium on photosensitizer drug cellular uptake in MCF7 cancer cells have been investigated. The results showed that the presence of serum in an incubation medium reduced the drug cellular uptake at all pH values. It has been found that decreasing on pH values of the incubation medium increased the cellular uptake of the drug, demonstrating selective uptake of the sensitizer. The HepG2 liver cancer cells exhibited more drug cellular uptake than CCD-18CO normal colon cells, which assessed the selectivity uptake of photosensitizer on cancerous cells. The concentration of photosensitizer measured in 10⁶ cells showed a good correlation to the incubation time. Fluorescence and absorption spectroscopy been have used to examine the cells.     

An Effective Automatic Procedure for Testing Parameter Identifiability of HIV/AIDS Models

Realistic HIV models tend to be rather complex and many recent models proposed in the literature could not yet be analyzed by traditional identifiability testing techniques. In this paper, we check a priori global identifiability of some of these nonlinear HIV models taken from the recent literature, by using a differential algebra algorithm based on previous work of the author. The algorithm is implemented in a software tool, called DAISY (Differential Algebra for Identifiability of SYstems), which has been recently released (DAISY is freely available on the web site ). The software can be used to automatically check global identifiability of (linear and) nonlinear models described by polynomial or rational differential equations, thus providing a general and reliable tool to test global identifiability of several HIV models proposed in the literature. It can be used by researchers with a minimum of mathematical background.     

Empirical Study of an Adaptive Multiscale Model for Simulating Cardiac Conduction

We modify and empirically study an adaptive multiscale model for simulating cardiac action potential propagation along a strand of cardiomyocytes. The model involves microscale partial differential equations posed over cells near the action potential upstroke and macroscale partial differential equations posed over the remainder of the tissue. An important advantage of the modified model of this paper is that, unlike our original model, it does not require perfect alignment between myocytes and the macroscale computational grid. We study the effects of gap-junctional coupling, ephaptic coupling, and macroscale grid spacing on the accuracy of the multiscale model. Our simulations reveal that the multiscale method accurately reproduces both the wavespeed and the waveform, including both upstroke and recovery, of fully microscale models. They also reveal that perfect alignment between myocytes and the macroscale grid is not necessary to reproduce the dynamics of a traveling action potential. Further, our simulations suggest that the macroscale grid spacing used in an adaptive multiscale model need not be much finer than the spatial width of an action potential. These results are demonstrated to hold under high, low, and zero gap-junctional coupling regimes.     

Stochastic Analysis of the Motion of DNA Nanomechanical Bipeds

In this paper, we formulate and analyze a Markov process modeling the motion of DNA nanomechanical walking devices. We consider a molecular biped restricted to a well-defined one-dimensional track and study its asymptotic behavior. Our analysis allows for the biped legs to be of different molecular composition, and thus to contribute differently to the dynamics. Our main result is a functional central limit theorem for the biped with an explicit formula for the effective diffusivity coefficient in terms of the parameters of the model. A law of large numbers, a recurrence/transience characterization and large deviations estimates are also obtained. Our approach is applicable to a variety of other biological motors such as myosin and motor proteins on polymer filaments.     

Restricted Trees: Simplifying Networks with Bottlenecks

Suppose N is a phylogenetic network indicating a complicated relationship among individuals and taxa. Often of interest is a much simpler network, for example, a species tree T, that summarizes the most fundamental relationships. The meaning of a species tree is made more complicated by the recent discovery of the importance of hybridizations and lateral gene transfers. Hence, it is desirable to describe uniform well-defined procedures that yield a tree given a network N.