Parameter inversion of a polydisperse system in small-angle scattering.

A general method to invert parameter distributions of a polydisperse system using data acquired from a small-angle scattering (SAS) experiment is presented. The forward problem, i.e. calculating the scattering intensity given the distributions of any causal parameters of a theoretical model, is generalized as a multi-linear map, characterized by a high-dimensional Green tensor that represents the complete scattering physics. The inverse problem, i.e. finding the maximum-likelihood estimation of the parameter distributions (in free form) given the scattering intensity (either a curve or an image) acquired from an experiment, is formulated as a constrained nonlinear programming (NLP) problem. This NLP problem is solved with high accuracy and efficiency via several theoretical and computational enhancements, such as an automatic data scaling for accuracy preservation and GPU acceleration for large-scale multi-parameter systems. Six numerical examples are presented, including both synthetic tests and solutions to real neutron and X-ray data sets, where the method is compared with several existing methods in terms of their generality, accuracy and computational cost. These examples show that SAS inversion is subject to a high degree of non-uniqueness of solution or structural ambiguity. With an ultra-high accuracy, the method can yield a series of near-optimal solutions that fit data to different acceptable levels.

Longitudinal regional brain volume changes quantified in normal aging and Alzheimer's APP x PS1 mice using MRI.

In humans, mutations of amyloid precursor protein (APP) and presenilins (PS) 1 and 2 are associated with amyloid deposition, brain structural change and cognitive decline, like in Alzheimer's disease (AD). Mice expressing these proteins have illuminated neurodegenerative disease processes but, unlike in humans, quantitative imaging has been little used to systematically determine their effects, or those of normal aging, on brain structure in vivo. Accordingly, we investigated wildtype (WT) and TASTPM mice (expressing human APP(695(K595N, M596L)) x PS1(M146V)) longitudinally using MRI. Automated global and local image registration, allied to a standard digital atlas, provided pairwise segmentation of 13 brain regions. We found the mature mouse brain, unlike in humans, enlarges significantly from 6-14 months old (WT 3.8+/-1.7%, mean+/-SD, P<0.0001). Significant changes were also seen in other WT brain regions, providing an anatomical benchmark for comparing other mouse strains and models of brain disorder. In TASTPM, progressive amyloidosis and astrogliosis, detected immunohistochemically, reflected even larger whole brain changes (5.1+/-1.4%, P<0.0001, transgenexage interaction P=0.0311). Normalising regional volumes to whole brain measurements revealed significant, prolonged, WT-TASTPM volume differences, suggesting transgene effects establish at <6 months old of age in most regions. As in humans, gray matter-rich regions decline with age (e.g. thalamus, cerebral cortex and caudoputamen); ventricles and white matter (corpus callosum, corticospinal tract, fornix system) increase; in TASTPMs such trends often varied significantly from WT (especially hippocampus). The pervasive, age-related structural changes between WT and AD transgenic mice (and mouse and human) suggest subtle but fundamental species differences and AD transgene effects.

Analysis of serial magnetic resonance images of mouse brains using image registration.

The aim of this paper is to investigate techniques that can identify and quantify cross-sectional differences and longitudinal changes in vivo from magnetic resonance images of murine models of brain disease. Two different approaches have been compared. The first approach is a segmentation-based approach: Each subject at each time point is automatically segmented into a number of anatomical structures using atlas-based segmentation. This allows cross-sectional and longitudinal analyses of group differences on a structure-by-structure basis. The second approach is a deformation-based approach: Longitudinal changes are quantified by the registration of each subject's follow-up images to that subject's baseline image. In addition the baseline images can be registered to an atlas allowing voxel-wise analysis of cross-sectional differences between groups. Both approaches have been tested on two groups of mice: A transgenic model of Alzheimer's disease and a wild-type background strain, using serial imaging performed over the age range from 6-14 months. We show that both approaches are able to identify longitudinal and cross-sectional differences. However, atlas-based segmentation suffers from the inability to detect differences across populations and across time in regions which are much smaller than the anatomical regions. In contrast to this, the deformation-based approach can detect statistically significant differences in highly localized areas.

Modeling epithelial cell behavior and organization.

We propose an individual cell based model for epithelial cell interactions. The model includes biological processes such as cell division, differentiation, adhesion, and death. Cell types include stem, transit amplifying, intermediate, mature, and dead. Stem and transit amplifying cells are allowed to divide provided they are on the basement membrane. In particular, the roles of differential adhesion and cell division during the development are discussed. The typical ordered structure of a healthy epithelium is shown to arise provided differential adhesion and cell division are modeled appropriately.