The Influence of Cross-immunity on the Coexistence, Invasion and Evolution of Pathogen Strains

Several epidemic models with many co-circulating strains have shown that partial crossimmunity between otherwise identical strains of a pathogen can lead to three solutions: stable coexistence of all strains, stable coexistence of a subset of strains, coexistence of some or all strains in complex cycles. Here we step back to a three strain model to examine the mechanisms behind some of these solutions. Using a one-dimensional antigenic space, we consider a host population in which two strains are endemic and ask when it can be invaded by a third strain. If the function relating antigenic distance to cross-immunity is linear or a square-root this is always possible. If the function is parabolic it depends on the degree of antigenic similarity between strains and the basic reproductive number. We show that the differences between functional forms occur because their shape determines the importance of secondary infection. These results suggest that pathogens for which the relationship between antigenic distance and cross-immunity has a square-root form will exist as a cloud of strains without significant antigenic structuring. Conversely, pathogens for which the relationship is parabolic will exist in populations with strong antigenic structuring and the number of strains limited by the basic reproductive number. Furthermore, numerical simulation showssimulation shows that the maximum sustainable number of strains in such populations requires significant instantaneous changes in antigenic structure and cannot be achieved by a sequence of small point mutations alone

Antigenic distance and cross-immunity, invisibility and coexistence of pathogen strains in an epidemiological model with discrete antigenic space

In models of pathogen interaction and evolution discrete genotypes in the form of bit strings may be mapped to points in a discrete phenotype space based on similarity in antigenic structure. Cross-immunity between strains, that is the reduction in susceptibility to strain A conferred to a host by infection with strain B, can then be defined for pairs of points in the antigenic space by a specified function. Analysis of an SIR type model shows that, if two strains are at equilibrium, the shape of the cross-immunity function has a strong influence on the invasion and coexistence of a third strain and, consequently, the expected evolutionary pathway. A function that is constant except for discontinuities at the end points is expected to result in the accumulation of diversity until a pair of discordant strains occurs that can, depending on parameter values, exclude all other strains. For a function of the form f(h)=h^q, where h is the antigenic distance between two strains, invasion and coexistence is always possible if q1 invasion and coexistence may be impossible, depending on parameter values, and the pathogen population is expected to show significant antigenic structuring. In addition to illuminating the role of cross-immunity in pathogen evolution, this analysis indicates that the choice of cross-immunity function, the representation of immunity acquired from multiple previous infections and the number of elements used to characterize the antigenic space must be carefully considered in the development and interpretation of more sophisticated models of pathogen dynamics and evolution

Tetrahedral Image-to-Mesh Conversion Software for Anatomic Modeling of Arteriovenous Malformations

We describe a new implementation of an adaptive multi-tissue tetrahedral mesh generator targeting anatomic modeling of Arteriovenous Malformation (AVM) for surgical simulations. Our method, initially constructs an adaptive Body-Centered Cubic (BCC) mesh of high quality elements. Then, it deforms the mesh surfaces to their corresponding physical image boundaries, hence, improving the mesh fidelity and smoothness. Our deformation scheme, which builds upon the ITK toolkit, is based on the concept of energy minimization, and relies on a multi-material point-based registration. It uses non-connectivity patterns to implicitly control the number of the extracted feature points needed for the registration, and thus, adjusts the trade-off between the achieved mesh fidelity and the deformation speed. While many medical imaging applications require robust mesh generation, there are few codes available to the public. We compare our implementation with two similar open-source image-to-mesh conversion codes: (1) Cleaver from US, and (2) CGAL from EU. Our evaluation is based on five isotropic/anisotropic segmented images, and relies on metrics like geometric & topologic fidelity, mesh quality, gradation and smoothness. The implementation we describe is open- source and it will be available within: (i) the 3D Slicer package for visualization and image analysis from Harvard Medical School, and (ii) an interactive simulator for neurosurgical procedures involving vasculature using SOFA, a framework for real-time medical simulation developed by INRIA

Analytic Approaches to the Evolution of Polarised Parton Distributions at Small xx

The $Q^2$ evolution of polarised parton distributions at small $x$ is studied. Various analytic approximations are critically discussed. We compare the full evolution with that obtained from the leading-pole approximation to the splitting functions, and show that the validity of this approximation depends critically on the $x \to 0$ behaviour of the starting distributions. A new analytic solution which is valid at small $x$ is obtained, and its domain of applicability is discussed.Comment: 14 pages, LATeX, 4 figures availabe as .uu-fil

Quantum interference terms in nonmesonic weak decay of Λ\Lambda-hypernuclei within a RPA formalism

Single and double coincidence nucleon spectra in the $\Lambda$-hypernuclei weak decay are evaluated and discussed using a microscopic formalism. Nuclear matter is employed together with the local density approximation which allows us to analyze the $^{12}_{\Lambda}C$ hypernucleus non-mesonic weak decay. Final state interactions (FSI) are included via the first order (in the nuclear residual interaction) terms to the RPA, where the strong residual interaction is modelled by a Bonn potential. At this level of approximation, these FSI are pure quantum interference terms between the primary decay $(\Lambda N \to NN)$ and $(\Lambda N \to NN \to NN)$, where the strong interaction is responsible for the last piece in the second reaction. Also the Pauli exchange contributions are explicitly evaluated. We show that the inclusion of Pauli exchange terms is important. A comparison with data is made. We conclude that the limitations in phase space in the RPA makes this approximation inadequate to reproduce the nucleon spectra. This fact, does not allow us to draw a definite conclusion about the importance of the interference terms.Comment: 39 pages, 10 figure

Quantum State During and after O(4)O(4)-Symmetric Bubble Nucleation with Gravitaional Effects

We extend our previous analysis of the quantum state during and after $O(4)$-symmetric bubble nucleation to the case including gravitational effects. We find that there exists a simple relationship between the case with and without gravitational effects. In a special case of a conformally coupled scalar field which is massless except on the bubble wall, the state is found to be conformally equivalent to the case without gravity.Comment: 31 pages plain Tex file, uuencoded postscript figure file is available from [email protected] upon request, KUNS126

Nonmesonic Weak Decay of Λ\Lambda Hypernuclei within a Nuclear Matter Formalism

The nonmesonic weak decay of $\Lambda$ hypernuclei using nonrelativistic nuclear matter is studied. As the basic building block we use the Polarization Propagator Method developed by Oset and Salcedo. It is shown that the exact calculation of exchange terms is required. Using the Local Density Approximation we evaluate the nonmesonic decay width for $^{12}_{\Lambda}C$ and compare the result with a finite nucleus calculation, obtaining a qualitative agreement.Comment: 28 pages, 3 figure

General Solutions for Tunneling of Scalar Fields with Quartic Potentials in de Sitter Space

The tunneling rates for scalar fields with quartic potentials in de Sitter space in the limit of no gravitational back reaction are calculated numerically and the results are fitted by analytic formulae.Comment: (Contours in Figure 1 corrected, two-dimensional fitting coefficient corrected, references added.), 16 pages, KUNS 124

Endoscopic Endonasal Transclival Approaches: Case Series & Outcomes for Different Clival Regions

Objective Transclival endoscopic endonasal approaches to the skull base are novel with few published cases.We report our institution’s experience with this technique and discuss outcomes according to the clival region involved. Design Retrospective case series. Setting Tertiary care academic medical center Participants All patients who underwent endoscopic endonasal transclival approaches for skull base lesions from 2008 to 2012. Main Outcome Measures Pathologies encountered, mean intraoperative time, intraoperative complications, gross total resection, intraoperative cerebrospinal fluid (CSF) leak, postoperative CSF leak, postoperative complications, and postoperative clinical course. Results A total of 49 patients underwent 55 endoscopic endonasal transclival approaches. Pathology included 43 benign and 12 malignant lesions. Mean follow-up was 15.4 months. Mean operative time was 167.9 minutes, with one patient experiencing an intraoperative internal carotid artery injury. Of the 15 cases with intraoperative cerebrospinal fluid (CSF) leaks, 1 developed postoperative CSF leak (6.7%). There were six other postoperative complications: four systemic complications, one case of meningitis, and one retropharyngeal abscess. Gross total resection was achieved for all malignancies approached with curative intent. Conclusions This study provides evidence that endoscopic endonasal transclival approaches are a safe and effective strategy for the surgical management of a variety of benign and malignant lesions

A New Window for the Treatment of Posterior Cerebral Artery, Superior Cerebellar Artery, and Basilar Apex Aneurysm: The Expanded Endoscopic Endonasal Approach

To explore the feasibility of an endoscopic endonasal transclival approach to treat aneurysms arising in the basilar apex, posterior cerebral arteries, and superior cerebellar arteries