Biomedical subjects
Publications and source records attributed to R P Millane.
Models for the probability density functions of the Fourier amplitude of images are derived. The densities are based on a simple model of an image made up of independent objects and incorporates the observed behavior of the circularly averaged power spectrum versus spatial frequency. The density function over all spatial frequencies gives a good fit to spectral amplitude data from a variety of images.
The circularly averaged power spectra of natural image ensembles tend to have a power-law dependence on spatial frequency with an exponent of approximately -2. This phenomenon has been attributed to object occlusion, the presence of edges, and scaling of object sizes (self-similarity) in natural scenes, although the relative importance of these properties is still unclear. A detailed examination of the effects of occlusion, edges, and self-similarity on the behavior of the power spectrum is conducted using a simple model of natural images. Numerical simulations show that edges and self-similarity are necessary for a power-law power spectrum over a wide range of spatial frequencies. Object occlusion is not an essential factor. A theoretical analysis for images containing nonoccluding objects supports these results.
The ground state entropy density of the antiferromagnetic Ising model on a triangular lattice is considered in the infinite volume limit as a function of boundary conditions on a finite triangular domain. The ground states of this domain do not map to a dimer covering and so cannot be classified into string sectors. A parametrized boundary condition is identified that allows the entropy density to be tuned to values between nondegeneracy and maximal degeneracy. The results are compared to those for a rectangular periodic domain for which the ground states can be classified into string sectors.
A method is presented for fluorescence optical diffusion tomography in turbid media using multiple-frequency data. The method uses a frequency-domain diffusion equation model to reconstruct the fluorescent yield and lifetime by means of a Bayesian framework and an efficient, nonlinear optimizer. The method is demonstrated by using simulations and laboratory experiments to show that reconstruction quality can be improved in certain problems through the use of more than one frequency. A broadly applicable mutual information performance metric is also presented and used to investigate the advantages of using multiple modulation frequencies compared with using only one.
A nonlinear, Bayesian optimization scheme is presented for reconstructing fluorescent yield and lifetime, the absorption coefficient, and the diffusion coefficient in turbid media, such as biological tissue. The method utilizes measurements at both the excitation and the emission wavelengths to reconstruct all unknown parameters. The effectiveness of the reconstruction algorithm is demonstrated by simulation and by application to experimental data from a tissue phantom containing the fluorescent agent Indocyanine Green.
An image whose region of support is smaller than its bounding rectangle can, in principle, be reconstructed from a subset of the Nyquist samples. However, determining such a sampling set that gives a stable reconstruction is a difficult and computationally intensive problem. An algorithm is developed for determining periodic nonuniform sampling patterns that is orders of magnitude faster than existing algorithms. The speedup is achieved by using a sequential selection algorithm and heuristic metrics for the quality of sampling sets that are fast to compute, as opposed to the more rigorous linear algebraic metrics that have been used previously. Simulations show that the sampling sets determined using the new algorithm give image reconstructions that are of accuracy comparable with those determined by other slower algorithms.
Phase dominance refers to the observation that the phase of the Fourier transform of an image carries more information than does the amplitude. We show that apparent counterexamples to phase dominance are not in fact counterexamples since the phase functions used are not independent of the true phase function. Phase dominance appears to be a general phenomenon.
Optical diffusion tomography is a method for reconstructing three-dimensional optical properties from light that passes through a highly scattering medium. Computing reconstructions from such data requires the solution of a nonlinear inverse problem. The situation is further complicated by the fact that while reconstruction algorithms typically assume exact knowledge of the optical source and detector coupling coefficients, these coupling coefficients are generally not available in practical measurement systems. A new method for estimating these unknown coupling coefficients in the three-dimensional reconstruction process is described. The joint problem of coefficient estimation and three-dimensional reconstruction is formulated in a Bayesian framework, and the resulting estimates are computed by using a variation of iterative coordinate descent optimization that is adapted for this problem. Simulations show that this approach is an accurate and efficient method for simultaneous reconstruction of absorption and diffusion coefficients as well as the coupling coefficients. A simple experimental result validates the approach.
A detailed analysis is made of the statistics and diffraction by a general, finite, two-dimensional ideal paracrystal. The statistics of the diagonal chain through the ideal paracrystal are derived, and the special cases of square and hexagonal ideal paracrystals are considered. Expressions for the diffraction are derived and characteristics of diffraction patterns are discussed in terms of the different parameters of the model for square and hexagonal ideal paracrystals. The variation of peak widths with scattering angle along different directions in reciprocal space is examined.
A simple physical model of the relationship between crystallite size and disorder for paracrystalline materials is presented, based on the spiral paracrystal and distortion of the lattice cells. Simulations show that the model leads to relationships similar to the alpha* rule. Average crystallite sizes predicted by the model are in agreement with experimental data and also allow crystallite-size distributions to be proposed. The model provides a more satisfactory and complete explanation of this relationship than do current descriptions.
Water molecules within a monolayer or so of macromolecular surfaces are often located in well-defined positions and have restricted mobility. These ordered water molecules play a role in stabilizing polysaccharide ordered structures and intermolecular interactions that are the basis of the rheological properties utilized in food systems. X-ray fiber diffraction can be used to determine the three-dimensional structures of polysaccharides in solid, but well-hydrated, polycrystalline fibers. In favorable cases, difference Fourier synthesis can be used to locate ordered water molecules in these systems, allowing one to visualize their functionally important interactions. These studies provide relevant evidence regarding water interactions in more hydrated systems and in solution. The functionality of ordered water in some polysaccharides used in food systems, as well as in some connective tissue glycosaminoglycans where the ordered water has been defined in considerable detail, as determined by fiber diffraction, is described in this chapter. These structures allow one to derive some general features of the role of ordered water in such systems.
Diffraction patterns from oriented polycrystalline specimens of fibrous polymers sometimes contain features indicating that the constituent microcrystallites are disordered. Such disorder affects the relationship between the crystal structure and the diffracted intensities. Therefore, the effects of disorder must be considered when determining structures from fibre diffraction data. Theory is developed here that describes the intensities diffracted by disordered polycrystalline fibres, and is used to calculate diffraction patterns from stimulated specimens with various kinds of disorder. The results show how Bragg and continuous diffraction are distributed on such diffraction patterns, and implications for structure determination are discussed.
A model of cardiac impulse propagation through the atrioventricular node is described. The model is based on a synthesis of various experimentally determined characteristics of atrioventricular nodal conduction. The model can be set up to mimic a particular patient's atrioventricular node, by using data collected during routine electrophysiological studies. It can also be used as a component in a larger model of the cardiac conduction system, to simulate cardiac arrhythmias.
Classical A-DNA helices with h = 0.25 nm may represent the greatest mass per unit length attainable by polynucleotide duplexes. The X-ray diffraction pattern from polycrystalline and well-oriented fibers of calf thymus DNA in its A-form has been carefully re-examined. Indexing on the basis of a C-face-centered monoclinic unit cell of dimensions a = 2.170 nm, b = 3.990 nm, c = 2.803 nm and beta = 96.82 degrees is superior to alternatives that have been proposed. Two right-handed. Watson-Crick base-paired, helical DNA chains with 2 X 11 nucleotides per 2.803 nm pitch, each carrying C3'-endo furanose rings, pass through the unit cell. The crystallography requires the two chains in the duplex to be antiparallel and conformationally identical but the 11 nucleotides in each pitch may be distinct. However, a secondary structure with a mononucleotide asymmetric unit provides as good an X-ray agreement as one with 11 distinct nucleotides. This relative lack of variability is quite different from what is observed in fibrous B-DNAs.
The alpha-form of poly[d(A)].poly[d(T)], observed in fibers at high (greater than 80%) relative humidity, is a 10-fold double-helical structure of pitch 3.2 nm. This new X-ray analysis shows that the two strands of the double helix are of the same kind conformationally and both B-like in containing C-2'-endo-puckered deoxyribose rings. Nevertheless, the two strands are different enough for the overall morphology of the duplex to resemble that of the heteromerous model for the drier (beta) form of poly[d(A)].poly[d(T)] in which one strand has C-2'-endo rings and the other C-3'-endo. Since the orientations of the bases in poly[d(A)].poly[d(T)] are persistently different from those of classical B-DNA it is likely that there will be local bending (about 10 degrees) at the junctions between general sequence tracts and the oligo[d(A)].oligo[d(T)] tracts that occur in some native DNAs. The conclusions about the structure of alpha-poly[d(A)].poly[d(T)] are reinforced by independent analyses of similar X-ray diffraction patterns from poly[d(A)].poly[d(U)] and poly[d(A-I)].poly[d(C-T)].
DNA-RNA and DNA-DNA duplexes are even more polymorphic than observed previously. DNA-RNA hybrids can have secondary structures like A-DNA or A-RNA, but double helices of the synthetic DNA-RNA hybrids poly(dA) X poly(rU) and poly(dI) X poly(rC), respectively, form 11-fold and 10-fold double-helical structures in which the two chains have quite different conformations. Extensive X-ray fiber diffraction analyses show that in both structures the DNA chains have C-2'-endo-puckered furanose rings, while the anti-parallel RNA chains have C-3'-endo-puckered rings. The bidirectional properties of such duplexes may be important in the transfer of biological information from nucleic acids.
A chemically simple polynucleotide duplex, poly d(AT):poly d(AT), has been trapped in a fibrous form with a complex helical secondary structure with a large (7.4 nm) axial repeat 24 nucleotides long. The motif which is repeated by the symmetry elements is a hexanucleotide in which two residues (both TpA) have the less common gauche minus conformation at C3'-O3' and consequently distinctive phosphate orientations. This reinforces earlier conclusions that PypPu nucleotides tend to have different shapes from PupPy nucleotides and that DNA surfaces may signal what base sequences lie beneath them. The morphological differences between this pleiomeric DNA polymer and closely-related, but more symmetrical allomorphs are just as great as those observed in short DNA fragments in crystals.
Analysis of the X-ray diffraction pattern from an oriented, polycrystalline fiber of a potassium chondroitin 4-sulfate proteoglycan shows that the polysaccharide chains have a left-handed 3-fold helical secondary structure stabilized by intra- and intermolecular hydrogen bonds. Two antiparallel chains pass through each trigonal unit cell, which has dimensions a = b = 1.385 nm, c = 2.776 nm and space group symmetry P3(2)21. The cations and water molecules in the crystals are not all periodic and only one potassium ion and four water molecules per disaccharide were located by difference Fourier methods. Sodium chondroitin 4-sulfate forms an analogous structure with polyanions of similar geometry. However, the packing arrangements in the two salts are quite different, presumably because of the different co-ordination preference of K+ and Na+. Thus the relatively small differences between these two cations are greatly amplified by the idiosyncratic polymer networks they promote.