Least-squares Best-fit Research Articles

Registration of prostate histology images to ex vivo MR images via strand‐shaped fiducials

To present and evaluate a method for registration of whole-mount prostate digital histology images to ex vivo magnetic resonance (MR) images. Nine radical prostatectomy specimens were marked with 10 strand-shaped fiducial markers per specimen, imaged with T1- and T2-weighted 3T MRI protocols, sliced at 4.4-mm intervals, processed for whole-mount histology, and the resulting histological sections (3-5 per specimen, 34 in total) were digitized. The correspondence between fiducial markers on histology and MR images yielded an initial registration, which was refined by a local optimization technique, yielding the least-squares best-fit affine transformation between corresponding fiducial points on histology and MR images. Accuracy was quantified as the postregistration 3D distance between landmarks (3-7 per section, 184 in total) on histology and MR images, and compared to a previous state-of-the-art registration method. The proposed method and previous method had mean (SD) target registration errors of 0.71 (0.38) mm and 1.21 (0.74) mm, respectively, requiring 3 and 11 hours of processing time, respectively. The proposed method registers digital histology to prostate MR images, yielding 70% reduced processing time and mean accuracy sufficient to achieve 85% overlap on histology and ex vivo MR images for a 0.2 cc spherical tumor.

SU-E-U-04: MRI-Targeted, 3D TRUS-Guided Prostate Biopsy: Measurement of Inter-Modality Prostate Deformation and Rigid Registration Algorithm Performance

Purpose: To measure the target registration error (TRE) of two approaches for the rigid registration of magnetic resonance(MR) prostate images to 3D transrectal ultrasound(TRUS)images, in order to improve biopsy planning and guidance for prostate cancer diagnosis. Methods: Six T2‐weighted MRimages and six 3D‐TRUS images from six different subjects were acquired during an MRI‐targeted, 3D TRUS‐guided biopsy procedure. All image pairs had identifiable calcifications and/or cysts which were used as fiducials for registration validation. A total of 78 fiducials were identified and all images were segmented using a semi‐automated method. The MRimages were designated as the source images, and the 3D‐TRUS images were designated as the target images. The source images were rigidly registered to the corresponding target images using 3 different methods. The first method was a visual alignment (VA) performed interactively by the operator, the second was a surface‐based iterative‐closest‐point (ICP) method, and the third was least‐squares best fit (LSF) transformation based on a set of identified homologous landmark pairs. We calculated the RMS TREs for each method and compared the results using a two‐tailed paired t‐test for each combination. Results: The RMS TREs for VA, ICP and LSF were 5.07mm, 5.87mm and 3.10mm, respectively (p 2.5mm). This is likely due to the substantial shape distortion of the prostate, caused mainly by transducer pressure in the 3D‐TRUS images, and the pressure induced by the endorectal coil in the MRimages. These preliminary results indicate that, at most, an ideal rigid registration algorithm based on the operator's initialization (i.e. VA) would able to reduce the TRE by 1.97mm. The remaining error of 3.10mm would require a non‐rigid registration to correct for the deformation.

REDSHIFT EVOLUTION IN THE IRON ABUNDANCE OF THE INTRACLUSTER MEDIUM

Clusters of galaxies provide a closed box within which one can determine the chemical evolution of the gaseous baryons with cosmic time. We studied this metallicity evolution in the hot X-ray emitting baryons through an analysis of XMM-Newton observations of 29 galaxy clusters in the redshift range 0.3 < z < 1.3. Taken alone, this data set does not show evidence for significant evolution. However, when we also include a comparable sample of 115 clusters observed with Chandra (Maughan et al. 2008) and a lower redshift sample of 70 clusters observed with XMM at z < 0.3 (Snowden et al. 2008), there is definitive evidence for a decrease in the metallicity. This decrease is approximately a factor of two from z = 0 to z \approx 1, over which we find a least-squares best-fit line Z(z) / Z_{\odot} = (0.46 \pm 0.05) - (0.38 \pm 0.03)z. The greatest uncertainty in the evolution comes from poorly constrained metallicities in the highest redshift bin.

A processing method for weighing lysimeter data and comparison to micrometeorological ETo predictions

Weighing lysimeters make direct measurements of water loss from a growing crop and the soil surface around a crop (evapotranspiration, ET), and thus, provide basic data to validate other ET prediction methods. The objective of this study was the improvement of the lysimeter data processing to eliminate bad data and minimize the effect of random variations in the measurements. Also, grass evapotranspiration rates (ETo) were compared with evapotranspiration rates predicted from data taken at a nearby weather station that is part of the California Irrigation Management Information System (CIMIS). Hourly data for a 2-year period from a grass lysimeter located at Five Points, California were screened to remove questionable data and data taken on rainy days (38% of all data). The hourly ETo rate was calculated for the remaining data from lysimeter mass measurements using a seven-point Savitsky–Golay (S–G) approximation of the derivative at the central point. The data were plotted against the CIMIS hourly ETo predictions using the Pruitt–Doorenbos (PD) model and the least-squares best-fit line was close to the 1:1 line indicating that CIMIS PD predictions were reasonably accurate for this time period. Comparing the S–G method with a two-point finite difference method, the S–G method reduced the root-mean-squared error between lysimeter ETo and CIMIS predictions from 0.112 for the two-point method to 0.074 mm h −1. Slopes of zero-intercept, best-fit lines to CIMIS PD versus lysimeter ETo for data representing each hour during the day exceeded unity from 9:00 a.m. to 4:00 p.m. but were less than unity at other times. An improved daytime result was obtained with the CIMIS Penman–Monteith (PM) model. The daytime soil heat flux calculated by the PM model is not included in the PD model and could account for this improvement. Correlation of hourly CIMIS and lysimeter ETo was poor during the night so CIMIS hourly ETo predictions at this site could be improved by characterization of factors that would improve prediction of ETo at night. Daily CIMIS ETo predictions were in good agreement with daily lysimeter ETo measurements for ETo < 6 mm d −1 but tended to be smaller when ETo > 6 mm d −1.

Site attenuation and source parameters on the North Anatolian Fault zone, eastern Turkey estimated from the aftershocks of 13 March 1992 Erzincan earthquake

Site attenuation and source characteristics of 45 aftershocks of the 13 March 1992 Erzincan, eastern Turkey earthquake have been determined from SH-wave spectra using a least-squares best-fit method. Although the most of the seismograms were recorded on the ophiolitic rock sites and the average regional attenuation correction of Q(f) = 35 f0.83 was applied, the high fall-off rates γ ranging between 3.0 and 4.5 beyond the corner frequencies of 8–13 Hz were observed on the SH spectra. The site attenuation value, κ, has been calculated from the slope of the high frequency part of the SH spectra. It was found that κ varied in the range of 0.0124–0.0364 s and the average was 0.0246 s with a standard deviation of 0.0047 s. The high fall-off rates of observed spectra have decreased considerably as a result of site attenuation corrections and converged to an average value of 2.3. We concluded that the high fall-off rates of SH wave spectra are mainly controlled by highly deformed Miocene ophiolitic formations which covers a wide area in the North Anatolian Fault zone in the vicinity of Erzincan region. Using the spectra that were corrected for regional and site attenuation, and assuming a Brune's source model; seismic moment, source radius, and stress-drops of the aftershocks were computed. We found that stress-drops for some of the aftershocks in Erzincan area have slightly decreased after removal of site attenuation over SH wave observed spectra.

Determining finite longitudinal strains from oppositely-concave microfolds in and around porphyroblasts: a new quantitative method

This paper describes a precise new method for determining finite longitudinal strains in porphyroblastic metamorphic rocks, which makes use of oppositely-concave microfolds (OCMs) formed by heterogeneous strain of the matrix around porphyroblasts. The initial spacing between two foliation surfaces is measured inside a porphyroblast and compared to the spacing between the same two surfaces in the matrix, which results in a measure of extension ( e) experienced by the rock during and/or after porphyroblast nucleation. A natural example is provided by the well-known ‘millipede’ plagioclase porphyroblasts from the Robertson River Metamorphics in Queensland, Australia. Twenty-four measurements were made from 22 serial thin sections cut parallel to both the X- Z and X- Y planes of finite strain, giving an average extension of 1.72 parallel to the X-direction of finite strain. The least-squares best-fit line to a plot of initial length vs change in length gives an R 2 value of 0.998. A minimum estimate of maximum shortening (negative e) was also made by measuring the total lengths of S 1 folia that had been crenulated during OCM formation, giving a value of −0.54, which falls short of the −0.63 expected for constant-volume, plane-strain deformation. Because the OCM method is particularly suited to metapelites, results may provide new insight into mechanisms of folding and crenulation cleavage development, pressure-temperature-time-deformation histories, mass transport during deformation and metamorphism, and kinematic studies of porphyroblast behavior (rotation vs non-rotation) during ductile deformation.

Effects of adhesion on the effective Young's modulus in glass slide/glue laminates

Bond-phase defects in laminates can affect the mechanical properties of laminate composites. The effects of adhesion area, number of glue spots, and bond thickness on the effective Young's modulus of adhered microscope glass slides have been investigated. Three different adhesive agents (super glue, epoxy cement, and epoxy resin) were used to explore the effect of bond-phase defects upon adhesion in laminates. The elastic moduli of single glass slides, unadhered glass slide pairs, glass slide/glue composite specimens and epoxy resin specimens were non-destructively determined by a sonic resonance technique. The change of Young's modulus of adhered glass slides was monitored while adhesion area per cent ranged from 0.35-100%. Trends in the Young's moduli of glass slide/glue composite specimens have been analysed by a least-squares best-fit procedure to two empirical equations. Qualitative explanations for the observed trends are discussed.

Structure of diphenanthro[1,2-b;2',1'-d]-furan at 191 K.

Diphenanthro[1,2-b;2',1'-d]furan crystallizes in space group Pnma (No. 62) with the mirror plane bisecting the molecule and passing through the furan O atom. Although exhibiting packing similar to that of dibenzofuran, this diphenanthrofuran showed no disorder of the sort found in that close molecular analog. The C atoms of the individual phenanthrene rings of the title compound have a mean deviation of 0.027 (21) A from the best least-squares plane describing the rings. The configuration and conformation of the individual phenanthrene rings in this diphenanthrofuran closely match the theoretical and experimental results for phenanthrene itself. Overall, this diphenanthrofuran molecule adopts a distinct V shape, the dihedral angle between the least-squares best-fit planes of the phenanthrene rings being 11.0 (1.2) degrees.

Automated Surface Wave Method: Field Testing

The spectral analysis of surface waves (SASW) method is a nondestructive in situ seismic testing method for determining shear wave velocity profiles of soil sites and stiffness profiles of pavement systems. The key steps involved are construction of an experimental dispersion curve from data collected in situ, and inversion of the dispersion curve to determine the stiffness profile. In this paper, an automated method for the construction of dispersion curves is discussed. Weighted least-squares best-fit solution is used to estimate the phase at each frequency with coherence as weighted function. By knowing the distance between the receivers and the phase at each frequency, phase velocity and wavelength associated with that frequency are calculated. These raw data are then combined using the least-absolute-value best-fit criterion to construct a dispersion curve. The inversion process for determination of stiffness profile from the dispersion curve is described in a companion paper.

Docking by least-squares fitting of molecular surface patterns

Molecular surfaces are fitted to each other by a new solution to the problem of docking a ligand into the active site of a protein molecule. The procedure constructs patterns of points on the surfaces and superimposes them upon each other using a least-squares best-fit algorithm. This brings the surfaces into contact and provides a direct measure of their local complementarity. The search over the ligand surface produces a large number of dockings, of which a small fraction having the best complementarity and the least steric hindrance are evaluated for electrostatic interaction energy. When applied to molecules taken from crystallographically observed complexes, this procedure consistently assigns the lowest electrostatic energies to correct dockings. On independently determined structures, the ability of the method to discern correct dockings depends on how much conformational difference there is between the free and complexed forms of the molecules. The procedure is found to be fast enough on contemporary workstation computers to permit many conformations to be considered, and tolerant enough to make rather coarse bond dihedral sampling a practicable way to overcome the problem of structural flexibility.

THE ATTENUATION OF THE PERIODIC TABLE

Unique among models of nuclear structure, the face-centered-cubic (FCC) lattice model predicts the attenuation of the periodic table at Z&lt;110 and the impossibility of superheavy nuclei. The total binding energies of superheavy nuclei in the FCC model (109&lt;Z&lt;127) were calculated on the basis of parameters obtained from a least-squares best-fit for 914 nuclei (Z&lt;99). No indication of increased stability was found for any of the transuranic elements.

Use of Full Diffraction Spectra, Both Experimental and Calculated, in Quantitative Powder Diffraction Analysis

The use of the full powder diffraction trace over a selected diffraction range for quantitative analysis has advantages over using single peaks in that it compensates for the effects of peak overlap and low levels of preferred orientation. Using a data base composed of experimental and calculated traces, the phase composition of an unknown may be determined by determining the least-squares best-fit sum of the appropriate data base patterns to the pattern of the unknown. Weight fractions are calculated from the pattern weighting factors using the reference-intensity-ratio method.

Quantitative X-Ray Powder Diffraction Method Using the Full Diffraction Pattern

AbstractA new quantitative X-ray powder diffraction (QXRPD) method has been developed to analyze polyphase crystalline mixtures. The unique approach employed in this method is the utilization of the full diffraction pattern of a mixture and its reconstruction as a weighted sum of diffraction patterns of the component phases. To facilitate the use of the new method, menu-driven interactive computer programs with graphics have been developed for the VAX series of computers. The analyst builds a reference database of component diffraction patterns, corrects the patterns for background effects, and determines the appropriate reference intensity ratios. This database is used to calculate the weight fraction of each phase in a mixture by fitting its diffraction pattern with a least-squares best-fit weighted sum of selected database reference patterns.The new QXRPD method was evaluated using oxides found in ceramics, corrosion products, and other materials encountered in the laboratory. Experimental procedures have been developed for sample preparation and data collection for reference samples and unknowns. Prepared mixtures have been used to demonstrate the very good results that can be obtained with this method.

42] Two simple programs for the analysis of data from enzyme-linked immunosorbent assays (ELISA) on a programmable desk-top calculator

This chapter discusses two simple programs for use with an inexpensive programmable calculator that rapidly and accurately converts raw data generated from enzyme-linked immunosorbent assays (ELISA) directly into antigen concentration. The first program computes and compares effective doses (ED 50 ) between a standard and each unknown sample assayed. The (ED 50 ) from the unknown sample is then multiplied by a concentration factor that yields the unknown concentration. The second program linearizes the sigmoidal enzyme-linked immunosorbent assay titration curve using a logit-log transformation of the data, in order to compute unknown concentration values. Both the programs employ stringent limit conditions to decrease “nonsense” calculations. Data is then processed by a least-squares best-fit linear regression analysis. While these programs have been designed for use with a competitive fibrinogen ELISA (that is, absorbance is inversely proportional to the amount of antigen in a well), both may be used with direct (that is, absorbance a [antigen]) ELISA test systems.

Two simple programs for the analysis of data from enzyme-linked immunosorbent (ELISA) assays on a programmable desk-top calculator

We have designed two programs for use with an inexpensive programmable calculator which rapidly and accurately convert raw data generated from enzyme-linked immunosorbent assays directly into antigen concentration. The first program computes and compares effective doses (ED 50)'s between a standard and each unknown sample assayed. The ED 50 from the unknown sample is then multiplied by a concentration factor which yields the unknown concentration. The second program linearizes the sigmoidal enzyme-linked immunosorbent assay titration curve using a logit-log transformation of the data in order to compute unknown concentration values. Both programs employ stringent limit conditions to decrease “nonsense” calculations. Data are then processed by a least-squares best-fit linear regression analysis.

Pioneer 9 and Ogo 5 observations of an interplanetary multiple shock ensemble on February 2, 1969

A multiple shock system was observed upstream (0.13 AU) of the earth by Pioneer 9 on February 2, 1969. The same system was observed at earth by Ogo 5 and was reported separately in the literature. This paper compares the two sets of observations in still further detail. Both magnetic-field and plasma data are used in a least-squares best-fit method to compute the characteristics of the fast forward shock wave (Pioneer 9 only) and two fast reverse shock waves. Nearly all major features (shock, piston, and tangential discontinuity) retained their characteristics during the transit of the shock ensemble from Pioneer 9 to Ogo 5. The genesis of the ensemble is believed to be due to a complex stream-stream interaction. A substantial density increase (including a large rise of alpha/proton abundance) at Ogo 5, but unobserved at Pioneer 9, is explained by a sudden meridional shift to a flow from below the ecliptic plane while the streams were en route to earth. This study demonstrates a spatial and temporal plasma inhomogeneity which is superimposed on the persistent major features.