Mathematical and computational models of drug transport in tumours

The ability to predict how far a drug will penetrate into the tumour microenvironment within its pharmacokinetic (PK) lifespan would provide valuable information about therapeutic response. As the PK profile is directly related to the route and schedule of drug administration, an in silico tool that can predict the drug administration schedule that results in optimal drug delivery to tumours would streamline clinical trial design. This paper investigates the application of mathematical and computational modelling techniques to help improve our understanding of the fundamental mechanisms underlying drug delivery, and compares the performance of a simple model with more complex approaches. Three models of drug transport are developed, all based on the same drug binding model and parametrized by bespoke in vitro experiments. Their predictions, compared for a ‘tumour cord’ geometry, are qualitatively and quantitatively similar. We assess the effect of varying the PK profile of the supplied drug, and the binding affinity of the drug to tumour cells, on the concentration of drug reaching cells and the accumulated exposure of cells to drug at arbitrary distances from a supplying blood vessel. This is a contribution towards developing a useful drug transport modelling tool for informing strategies for the treatment of tumour cells which are ‘pharmacokinetically resistant’ to chemotherapeutic strategies

Statistical properties and statistical interaction for particles with spin: Hubbard model in one dimension and statistical spin liquid

We derive the statistical distribution functions for the Hubbard chain with infinite Coulomb repulsion among particles and for the statistical spin liquid with an arbitrary magnitude of the local interaction in momentum space. Haldane's statistical interaction is derived from an exact solution for each of the two models. In the case of the Hubbard chain the charge (holon) and the spin (spinon) excitations decouple completely and are shown to behave statistically as fermions and bosons, respectively. In both cases the statistical interaction must contain several components, a rule for the particles with the internal symmetry.Comment: (RevTex, 16 pages, improved version

Influence of a Uniform Current on Collective Magnetization Dynamics in a Ferromagnetic Metal

We discuss the influence of a uniform current, $\vec{j}$, on the magnetization dynamics of a ferromagnetic metal. We find that the magnon energy $\epsilon(\vec{q})$ has a current-induced contribution proportional to $\vec{q}\cdot \vec{\cal J}$, where $\vec{\cal J}$ is the spin-current, and predict that collective dynamics will be more strongly damped at finite ${\vec j}$. We obtain similar results for models with and without local moment participation in the magnetic order. For transition metal ferromagnets, we estimate that the uniform magnetic state will be destabilized for $j \gtrsim 10^{9} {\rm A} {\rm cm}^{-2}$. We discuss the relationship of this effect to the spin-torque effects that alter magnetization dynamics in inhomogeneous magnetic systems.Comment: 12 pages, 2 figure

NMR Self Diffusion and Relaxation Time Measurements for Poly (vinylidene fluoride) (PVDF) Based Polymer Gel Electrolytes Containing LiBF4 and Propylene Carbonate

Polymer gel electrolytes (PGEs) have been prepared using lithium tetrafluoroborate (LiBF4), propylene carbonate (PC) and poly (vinylidene fluoride) (PVDF). Self diffusion coefficients have been measured using pulse field gradient nuclear magnetic resonance (PFG-NMR) for the lithium cation, BF4 anion and solvent molecules using 7Li, 19F and 1H nuclei, respectively. It was found that lithium ion diffusion was slow compared to the much larger fluorinated BF4 anion, which is attributed to a large solvation shell around the lithium ions. The 7Li and 1H diffusion measurements also exhibited two unique environments for the diffusive species. The measurement of NMR transverse relaxation times has confirmed the presence of lithium ions in multiple phases as shown by the diffusion measurements

Quadrupolar and magnetic ordering in CeB6

The quadrupolar ordering in CeB_6 is explained in terms of the electrostatic interaction of quadrupolar moments arranged into a simple cubic lattice. The representation of magnetic and quadrupolar moments by means of quasispins of two kinds is employed. A linear increase of the quadrupolar transition temperature T_Q(H) with applied magnetic field and its further re-entrance are described using a generalized spherical model which is well adjusted to a particular problem of the quadrupolar ordering in CeB_6. The theory naturally explains the growing specific heat jump at T_Q(H) with increasing magnetic field. The role of the quadrupolar ordering in the formation of the magnetic ordering, as well as the possible critical experiments and applications to other rare-earth compounds, are discussed.Comment: 40 pages, 9 Postscript figures, to appear in Phys.Rev.

Statistical Theory of Spin Relaxation and Diffusion in Solids

A comprehensive theoretical description is given for the spin relaxation and diffusion in solids. The formulation is made in a general statistical-mechanical way. The method of the nonequilibrium statistical operator (NSO) developed by D. N. Zubarev is employed to analyze a relaxation dynamics of a spin subsystem. Perturbation of this subsystem in solids may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between the particles or with a thermal bath (lattice). The generalized kinetic equations were derived previously for a system weakly coupled to a thermal bath to elucidate the nature of transport and relaxation processes. In this paper, these results are used to describe the relaxation and diffusion of nuclear spins in solids. The aim is to formulate a successive and coherent microscopic description of the nuclear magnetic relaxation and diffusion in solids. The nuclear spin-lattice relaxation is considered and the Gorter relation is derived. As an example, a theory of spin diffusion of the nuclear magnetic moment in dilute alloys (like Cu-Mn) is developed. It is shown that due to the dipolar interaction between host nuclear spins and impurity spins, a nonuniform distribution in the host nuclear spin system will occur and consequently the macroscopic relaxation time will be strongly determined by the spin diffusion. The explicit expressions for the relaxation time in certain physically relevant cases are given.Comment: 41 pages, 119 Refs. Corrected typos, added reference

Complex geomorphologic assemblage of terrains in association with the banded terrain in Hellas basin, Mars

Hellas basin acts as a major sink for the southern highlands of Mars and is likely to have recorded several episodes of sedimentation and erosion. The north-western part of the basin displays a potentially unique Amazonian landscape domain in the deepest part of Hellas, called “banded terrain”, which is a deposit characterized by an alternation of narrow band shapes and inter-bands displaying a sinuous and relatively smooth surface texture suggesting a viscous flow origin. Here we use high-resolution (HiRISE and CTX) images to assess the geomorphological interaction of the banded terrain with the surrounding geomorphologic domains in the NW interior of Hellas to gain a better understanding of the geological evolution of the region as a whole. Our analysis reveals that the banded terrain is associated with six geomorphologic domains: a central plateau named Alpheus Colles, plain deposits (P1 and P2), reticulate (RT1 and RT2) and honeycomb terrains. Based on the analysis of the geomorphology of these domains and their cross-cutting relationships, we show that no widespread deposition post-dates the formation of the banded terrain, which implies that this domain is the youngest and latest deposit of the interior of Hellas. Therefore, the level of geologic activity in the NW Hellas during the Amazonian appears to have been relatively low and restricted to modification of the landscape through mechanical weathering, aeolian and periglacial processes. Thermophysical data and cross-cutting relationships support hypotheses of modification of the honeycomb terrain via vertical rise of diapirs such as ice diapirism, and the formation of the plain deposits through deposition and remobilization of an ice-rich mantle deposit. Finally, the observed gradual transition between honeycomb and banded terrain suggests that the banded terrain may have covered a larger area of the NW interior of Hellas in the past than previously thought. This has implications on the understanding of the evolution of the deepest part of Hellas

Observation of hard scattering in photoproduction events with a large rapidity gap at HERA

Events with a large rapidity gap and total transverse energy greater than 5 GeV have been observed in quasi-real photoproduction at HERA with the ZEUS detector. The distribution of these events as a function of the $\gamma p$ centre of mass energy is consistent with diffractive scattering. For total transverse energies above 12 GeV, the hadronic final states show predominantly a two-jet structure with each jet having a transverse energy greater than 4 GeV. For the two-jet events, little energy flow is found outside the jets. This observation is consistent with the hard scattering of a quasi-real photon with a colourless object in the proton.Comment: 19 pages, latex, 4 figures appended as uuencoded fil

Horizontal Branch Stars: The Interplay between Observations and Theory, and Insights into the Formation of the Galaxy

We review HB stars in a broad astrophysical context, including both variable and non-variable stars. A reassessment of the Oosterhoff dichotomy is presented, which provides unprecedented detail regarding its origin and systematics. We show that the Oosterhoff dichotomy and the distribution of globular clusters (GCs) in the HB morphology-metallicity plane both exclude, with high statistical significance, the possibility that the Galactic halo may have formed from the accretion of dwarf galaxies resembling present-day Milky Way satellites such as Fornax, Sagittarius, and the LMC. A rediscussion of the second-parameter problem is presented. A technique is proposed to estimate the HB types of extragalactic GCs on the basis of integrated far-UV photometry. The relationship between the absolute V magnitude of the HB at the RR Lyrae level and metallicity, as obtained on the basis of trigonometric parallax measurements for the star RR Lyrae, is also revisited, giving a distance modulus to the LMC of (m-M)_0 = 18.44+/-0.11. RR Lyrae period change rates are studied. Finally, the conductive opacities used in evolutionary calculations of low-mass stars are investigated. [ABRIDGED]Comment: 56 pages, 22 figures. Invited review, to appear in Astrophysics and Space Scienc