Geometric distortion in clinical MRI systems - Part II: correction using a 3D phantom

In this paper, we present the correction of the geometric distortion measured in the clinical magnetic resonance imaging (MRI) systems reported in the preceding paper (Part 1) using a 3D method based on the phantom-mapped geometric distortion data. This method allows the correction to be made on phantom images acquired without or with the vendor correction applied. With the vendor's 2D correction applied, the method corrects for both the residual geometric distortion still present in the plane in which the correction method was applied (the axial plane) and the uncorrected geometric distortion along the axis non-nal to the plane. The evaluation of the effectiveness of the correction using this new method was carried out through analyzing the residual geometric distortion in the corrected phantom images. The results show that the new method can restore the distorted images in 3D nearly to perfection. For all the MRI systems investigated, the mean absolute deviations in the positions of the control points (along x-, y- and z-axes) measured on the corrected phantom images were all less than 0.2 mm. The maximum absolute deviations were all below similar to0.8 mm. As expected, the correction of the phantom images acquired with the vendor's correction applied in the axial plane performed equally well. Both the geometric distortion still present in the axial plane after applying the vendor's correction and the uncorrected distortion along the z-axis have all been restored. (C) 2004 Elsevier Inc. All rights reserved.

Application of central composite rotatable design to modelling the effect of some operating variables on the performance of the three-product cyclone

The central composite rotatable design (CCRD) was used to design an experimental program to model the effects of inlet pressure, feed density, and length and diameter of the inner vortex finder on the operational performance of a 150-min three-product cyclone. The ranges of values of the variables used in the design were: inlet pressure: 80-130 kPa, feed density: 30 60%; length of IVF below the OVF: 50-585 mm; diameter of IVF: 35-50 mm. A total of 30 tests were conducted, which is 51 less; an that required for a three-level full factorial design. Because the model allows confident performance prediction by interpolation over the range of data in the database, it was used to construct response surface graphs to describe the effects of the variables on the performance of the three-product cyclone. To obtain a simple and yet a realistic model, it was refitted using only the variable terms that are significant at greater than or equal to 90% confidence level. Considering the selected operating variables, the resultant model is significant and predicts the experimental data well. (c) 2005 Elsevier B.V. All rights reserved.

Green-Ampt approximations

The solution to the Green and Ampt infiltration equation is expressible in terms of the Lambert W-1 function. Approximations for Green and Ampt infiltration are thus derivable from approximations for the W-1 function and vice versa. An infinite family of asymptotic expansions to W-1 is presented. Although these expansions do not converge near the branch point of the W function (corresponds to Green-Ampt infiltration with immediate ponding), a method is presented for approximating W-1 that is exact at the branch point and asymptotically, with interpolation between these limits. Some existing and several new simple and compact yet robust approximations applicable to Green-Ampt infiltration and flux are presented, the most accurate of which has a maximum relative error of 5 x 10(-5)%. This error is orders of magnitude lower than any existing analytical approximations. (c) 2005 Elsevier Ltd. All rights reserved.

Rotary atomizer drop size distribution database

Wind tunnel measurements of drop Size distributions from Micronair A U4000 and A U5000 rotary atomizers were collected to develop a database for model use. The measurements varied tank mix, flow rate, air speed, and blade angle conditions, which were correlated by multiple regressions (average R-2 = 0.995 for A U4000 and 0.988 for AU5000). This database replaces an outdated set of rotary atomizer data measured in the 1980s by the USDA Forest Service and fills in a gap in data measured in the 1990s by the Spray Drift Task Force. Since current USDA Forest Service spray projects rely on rotary atomizers, the creation of the database (and its multiple regression interpolation) satisfies a need seen for ten years.

Quantitative photoluminescence of broad band absorbing melanins: a procedure to correct for inner filter and re-absorption effects

We report methods for correcting the photoluminescence emission and excitation spectra of highly absorbing samples for re-absorption and inner filter effects. We derive the general form of the correction, and investigate various methods for determining the parameters. Additionally, the correction methods are tested with highly absorbing fluorescein and melanin (broadband absorption) solutions; the expected linear relationships between absorption and emission are recovered upon application of the correction, indicating that the methods are valid. These procedures allow accurate quantitative analysis of the emission of low quantum yield samples (such as melanin) at concentrations where absorption is significant. (c) 2004 Elsevier B.V. All rights reserved.

A quantum yield map for synthetic eumelanin

The quantum yield of synthetic eumelanin is known to be extremely low and it has recently been reported to be dependent on excitation wavelength. In this paper, we present quantum yield as a function of excitation wavelength between 250 and 500 nm, showing it to be a factor of 4 higher at 250 nm than at 500 nm. In addition, we present a definitive map of the steady-state fluorescence as a function of excitation and emission wavelengths, and significantly, a three-dimensional map of the specific quantum yield: the fraction of photons absorbed at each wavelength that are subsequently radiated at each emission wavelength. This map contains clear features, which we attribute to certain structural models, and shows that radiative emission and specific quantum yield are negligible at emission wavelengths outside the range of 585 and 385 nm (2.2 and 3.2 eV), regardless of excitation wavelength. This information is important in the context of understanding melanin biofunctionality, and the quantum molecular biophysics therein. (c) 2005 American Institute of Physics.

Quantitative fluorescence excitation spectra of synthetic eumelanin

Previously reported excitation spectra for eumelanin are sparse and inconsistent. Moreover, these studies have failed to account for probe beam attenuation and emission reabsorption within the samples, making them qualitative at best. We report for the first time quantitative excitation spectra for synthetic eumelanin, acquired for a range of solution concentrations and emission wavelengths. Our data indicate that probe beam attenuation and emission reabsorption significantly affect the spectra even in low-concentration eumelanin solutions and that previously published data do not reflect the true excitation profile. We apply a correction procedure (previously applied to emission spectra) to account for these effects. Application of this procedure reconstructs the expected relationship of signal intensity with concentration, and the normalized spectra show a similarity in form to the absorption profiles. These spectra reveal valuable information regarding the photophysics and photochemistry of eumelanin. Most notably, an excitation peak at 365 urn (3.40 eV), whose position is independent of emission wavelength, is possibly attributable to a 5,6-dihydroxyindole-2-carboxylic acid (DHICA) component singly linked to a polymeric structure.

Towards structure-property-function relationships for eumelanin

We discuss recent progress towards the establishment of important structure-property-function relationships in eumelanins-key functional bio-macromolecular systems responsible for photoprotection and immune response in humans, and implicated in the development of melanoma skin cancer. We focus on the link between eumelanin's secondary structure and optical properties such as broad band UV-visible absorption and strong non-radiative relaxation; both key features of the photo-protective function. We emphasise the insights gained through a holistic approach combining optical spectroscopy with first principles quantum chemical calculations, and advance the hypothesis that the robust functionality characteristic of eumelanin is related to extreme chemical and structural disorder at the secondary level. This inherent disorder is a low cost natural resource, and it is interesting to speculate as to whether it may play a role in other functional bio-macromolecular systems.

Shift, scaling and derivative properties for the discrete cosine transform

A set of DCT domain properties for shifting and scaling by real amounts, and taking linear operations such as differentiation is described. The DCT coefficients of a sampled signal are subjected to a linear transform, which returns the DCT coefficients of the shifted, scaled and/or differentiated signal. The properties are derived by considering the inverse discrete transform as a cosine series expansion of the original continuous signal, assuming sampling in accordance with the Nyquist criterion. This approach can be applied in the signal domain, to give, for example, DCT based interpolation or derivatives. The same approach can be taken in decoding from the DCT to give, for example, derivatives in the signal domain. The techniques may prove useful in compressed domain processing applications, and are interesting because they allow operations from the continuous domain such as differentiation to be implemented in the discrete domain. An image matching algorithm illustrates the use of the properties, with improvements in computation time and matching quality.

Radiative relaxation in synthetic pheomelanin

We report a detailed photoluminescence study of cysteinyldopa-melanin ( CDM), the synthetic analogue of pheomelanin. Emission spectra are shown to be a far more sensitive probe of CDM's spectroscopic behavior than are absorption spectra. Although CDM and dopa-melanin ( DM, the synthetic analogue of eumelanin) have very similar absorption spectra, we find that they have very different excitation and emission characteristics; CDM has two distinct photoluminescence peaks that do not shift with excitation wavelength. Additionally, our data suggest that the radiative quantum yield of CDM is excitation energy dependent, an unusual property among biomolecules that is indicative of a chemically disordered system. Finally, we find that the radiative quantum yield for CDM is similar to 0.2%, twice that of DM, although still extremely low. This means that 99.8% of the energy absorbed by CDM is dissipated via nonradiative pathways, consistent with its role as a pigmentary photoprotectant.

Quantitative scattering of melanin solutions

The optical scattering coefficient of a dilute, well-solubilized eumelanin solution has been accurately measured as a function of incident wavelength, and found to contribute < 6% of the total optical attenuation between 210 and 325 nm. At longer wavelengths (325-800 nm), the scattering was less than the minimum sensitivity of our instrument. This indicates that ultraviolet and visible optical density spectra can be interpreted as true absorption with a high degree of confidence. The scattering coefficient versus wavelength was found to be consistent with Rayleigh theory for a particle radius of 38 6 1 nm. Our results shed important light on the role of melanins as photoprotectants.

Why people underestimate y when extrapolating in linear functions

E. L. DeLosh, J. R. Busemeyer, and M. A. McDaniel (1997) found that when learning a positive, linear relationship between a continuous predictor (x) and a continuous criterion (y), trainees tend to underestimate y on items that ask the trainee to extrapolate. In 3 experiments, the authors examined the phenomenon and found that the tendency to underestimate y is reliable only in the so-called lower extrapolation region-that is, new values of x that lie between zero and the edge of the training region. Existing models of function learning, such as the extrapolation-association model (DeLosh et al., 1997) and the population of linear experts model (M. L. Kalish, S. Lewandowsky, & J. Kruschke, 2004), cannot account for these results. The authors show that with minor changes, both models can predict the correct pattern of results.

XSophe, a computer simulation software suite for the analysis of electron paramagnetic resonance spectra

The XSophe computer simulation software suite consisting of a daemon, the XSophe interface and the computational program Sophe is a state of the art package for the simulation of electron paramagnetic resonance spectra. The Sophe program performs the computer simulation and includes a number of new technologies including; the SOPHE partition and interpolation schemes, a field segmentation algorithm, homotopy, parallelisation and spectral optimisation. The SOPHE partition and interpolation scheme along with a field segmentation algorithm greatly increases the speed of simulations for most systems. Multidimensional homotopy provides an efficient method for accurately tracing energy levels and hence tracing transitions in the presence of energy level anticrossings and looping transitions and allowing computer simulations in frequency space. Recent enhancements to Sophe include the generalised treatment of distributions of orientational parameters, termed the mosaic misorientation linewidth model and a faster more efficient algorithm for the calculation of resonant field positions and transition probabilities. For complex systems the parallelisation enables the simulation of these systems on a parallel computer and the optimisation algorithms in the suite provide the experimentalist with the possibility of finding the spin Hamiltonian parameters in a systematic manner rather than a trial-and-error process. The XSophe software suite has been used to simulate multifrequency EPR spectra (200 MHz to 6 00 GHz) from isolated spin systems (S > ~½) and coupled centres (Si, Sj _> I/2). Griffin, M.; Muys, A.; Noble, C.; Wang, D.; Eldershaw, C.; Gates, K.E.; Burrage, K.; Hanson, G.R."XSophe, a Computer Simulation Software Suite for the Analysis of Electron Paramagnetic Resonance Spectra", 1999, Mol. Phys. Rep., 26, 60-84.