In vivo fiber tractography using DT-MRI data.

Fiber tract trajectories in coherently organized brain white matter pathways were computed from in vivo diffusion tensor magnetic resonance imaging (DT-MRI) data. First, a continuous diffusion tensor field is constructed from this discrete, noisy, measured DT-MRI data. Then a Frenet equation, describing the evolution of a fiber tract, was solved. This approach was validated using synthesized, noisy DT-MRI data. Corpus callosum and pyramidal tract trajectories were constructed and found to be consistent with known anatomy. The method's reliability, however, degrades where the distribution of fiber tract directions is nonuniform. Moreover, background noise in diffusion-weighted MRIs can cause a computed trajectory to hop from tract to tract. Still, this method can provide quantitative information with which to visualize and study connectivity and continuity of neural pathways in the central and peripheral nervous systems in vivo, and holds promise for elucidating architectural features in other fibrous tissues and ordered media.

Segmentation of gated Tl-SPECT images and computation of ejection fraction: a different approach.

BACKGROUND: We describe a set of image processing algorithms and mathematical models that can be advantageously used in schemes for the segmentation of thallium-201-single photon emission computed tomography (SPECT) images and for computation of left ventricular ejection fraction (EF). METHODS: The system consists of two independent blocs for image segmentation and computation of function. The former is based on a multiresolution elliptical coordinate transformation and dynamic contour tracking. Computation of EF is formulated on the basis of both the endocardial and epicardial contours, and we compare this formulation with that using only the endocardial border for images with low signal-to-noise ratios. The accuracy of border detection was validated against manual border tracing on FDG-PET images, simulated Tl-201-SPECT images where the true underlying borders were known, and actual Tl-201-SPECT images. Finally, we compared EFs computed for FDG-PET, technetium-99m-SPECT and Tl-201-SPECT with those obtained from planar gated blood pool imaging. RESULTS: The automatically obtained results always were within the manual uncertainty range. Agreement between myocardial volumes from positron emission tomography and automatically obtained values from the simulated Tl-201-SPECT images was excellent (r = 0.95, n = 32). Agreement between EFs from planar gated blood pool imaging and the other image modalities was good (FDG-PET: y = 5.89 + 1.21x, r = 0.92, see = 6.24, n = 19, Tc-99m-SPECT: y = -3.86 + 1.06x, r = 0.88, see = 7.78, n = 9, Tl-201-SPECT: y = 17.8 + 0.81x, r = 0.77, see = 7.44, n = 26). For noisy input data the combined use of information from epicardial and endocardial contours gives more accurate EF values than the traditional formula on the basis of the endocardial contour only. CONCLUSIONS: Alternate approaches for segmentation and computation of function have been presented and validated. They might also be advantageously incorporated into other existing techniques.

Determination of optimally resolving gel concentration and migration time (path) in gel electrophoresis.

The notion of a mathematically defined optimally resolving gel concentration for components of a pair of molecular species of any given size was developed by Rodbard et al. (Electrophoresis and Isoelectric Focusing on Polyacrylamide Gel, pp. 28-62, de Gruyter, Berlin, 1974) 21 years ago. The mathematical treatment was incorporated into a computer program (T-OPT) for mainframe computers which upon input of the slope and intercept on the mobility axis of the Ferguson plots of the two components, electrophoresis time and temperature, yielded plots of resolution vs gel concentration. The same algorithms were later incorporated into the program ELPHOFIT for personal computers. Ideality of diffusion spreading and zero initial zone width were assumed along with a Gaussian peak distribution and an equal area for both components. Moreover, these programs failed to respond to the practical question of the migration time (or path) required for the resolution at the optimal gel concentration, although an independent program predicting the course of resolution under the assumption of free diffusion band spreading in gels (DAR-001) had been devised by Rodbard for application in preparative elution-PAGE. The present work advances the technology for predicting resolving conditions by presenting a computer program which allows the user (i) to predict the gel concentration which is optimal for obtaining the desired degree of resolution at any migration time, (ii) to prescribe the minimal degree of resolution between two band distributions one wishes to achieve, and (iii) to predict the migration time (or path) required at the optimal gel concentration for the resolution of the two components. The program is written in MATLAB and can be used by any computer that supports MATLAB language.

A computer program for predicting recovery of SDS-protein in the automated HPGE-1000 apparatus.

The commercial automated gel electrophoresis apparatus (HPGE-1000 of LabIntelligence, Menlo Park, CA) allows one to recover the material migrating and visualized as a fluorescent-labeled band by electrophoresis into a collection cup located above the band at a right angle to the orientation of the separation path. The degree of recovery is a function of sample load (peak area), electrophoresis time at constant field strength, the mobility of the material and band width. Neglecting the latter, recovery of several SDS-proteins was measured as a function of the first three parameters. These measurements were used as a data base for a computer program capable of predicting, by interpolation of the experimental values, the time of electrophoresis needed to obtain a specified degree of recovery, or the degree of recovery obtained after a desired time of electrophoresis into the collection cup.

Enlargement or reduction of digital images with minimum loss of information.

The purpose of this paper is to derive optimal spline algorithms for the enlargement or reduction of digital images by arbitrary (noninteger) scaling factors. In our formulation, the original and rescaled signals are each represented by an interpolating polynomial spline of degree n with step size one and Delta, respectively. The change of scale is achieved by determining the spline with step size Delta that provides the closest approximation of the original signal in the L(2)-norm. We show that this approximation can be computed in three steps: (i) a digital prefilter that provides the B-spline coefficients of the input signal, (ii) a resampling using an expansion formula with a modified sampling kernel that depends explicitly on Delta, and (iii) a digital postfilter that maps the result back into the signal domain. We provide explicit formulas for n=0, 1, and 3 and propose solutions for the efficient implementation of these algorithms. We consider image processing examples and show that the present method compares favorably with standard interpolation techniques. Finally, we discuss some properties of this approach and its connection with the classical technique of bandlimiting a signal, which provides the asymptotic limit of our algorithm as the order of the spline tends to infinity.

Fast wavelet transformation of EEG.

Wavelet transforms offer certain advantages over Fourier transform techniques for the analysis of EEG. Recent work has demonstrated the applicability of wavelets for both spike and seizure detection, but the computational demands have been excessive. We compare the quality of feature extraction of continuous wavelet transforms using standard numerical techniques, with more rapid algorithms utilizing both polynomial splines and multiresolution frameworks. We further contrast the difference between filtering with and without the use of surrogate data to model background noise, demonstrate the preservation of feature extraction with critical versus redundant sampling, and perform the analyses with wavelets of different shape. Comparison is made with windowed Fourier transforms, similarly filtered, at different data window lengths. We here report a dramatic reduction in computational time required to perform this analysis, without compromising the accuracy of feature extraction. It now appears technically feasible to filter and decompose EEG using wavelet transforms in real time with ordinary microprocessors.

Determination of fractional absorption of dietary calcium in humans.

Four dual-isotopic label methods for determining true fractional absorption of dietary calcium were compared in 23 subjects. The ratio of the integrals of oral label in a 24-h pooled urine to intravenous label in the same urine is called alpha 24h and was taken as the standard against which the others were compared. alpha Spot is the ratio of the fraction of oral label to the fraction of intravenous label in a single urine specimen; alpha Lag is the ratio of the level of oral label in blood 4 h after administration to the level of intravenous label in blood 2 h after administration. alpha Dec is obtained by deconvoluting response to the intravenous label from the response to the oral tracer. Results were as follows: alpha 24h = 0.273 +/- 0.124, alpha Dec = 0.300 +/- 0.101 (n = 14), alpha Spot = 0.359 +/- 0.179, and alpha Lag = 0.271 +/- 0.103. The Bland-Altman approach for comparison of methods was used to show that results for alpha Spot and alpha Lag can be expected, with a 95% confidence limit, to differ from the value of alpha 24h by 60 and 69%, respectively. The results for alpha Dec were shown to be not only indistinguishable from alpha 24h but identical from a theoretical perspective.

Relative efficiency of molecular sieving in solutions of four polymers.

The efficiency of size separations of polystyrene sulfate, 120-1085 nm radius, by molecular sieving in polymer solutions, expressed by the separation efficiency function S = M0 magnitude of dKR(R)/dR Te-KR(R)T [where M0 is the mobility in free solution, KR the retardation coefficient, R the geometric mean radius of the particle, KR(R) the retardation coefficient as a function of R, and the polymer concentration is T] increases from methylhydroxypropyl cellulose to polyvinyl alcohol to uncrosslinked polyacrylamide to agarose above its gelling temperature. Separations of DNA, in the size range of 3-21 nm radius, are by at least one order of magnitude more efficient than those of polystyrene sulfate in the size range of 120-1085 nm radius. A plot of S vs. R in the experimental range of T is constructed for the four polymer solutions; this allows one to select optimal media and concentrations for the sieving of particles in the desired range of molecular sizes.

Minimal electrophoresis time for DNA sequencing.

This study presents a mathematical approach that allows one to determine the shortest electrophoresis time and migration path length required for DNA sequencing. The calculation was applied to the capillary electrophoresis of a DNA sequencing separation and showed that acceptable resolution could be obtained using a shorter path length than anticipated.

Magnification mismatches between micrographs: corrective procedures and implications for structural analysis.

Quantitative structural analysis from electron micrographs of biological macromolecules inevitably requires the synthesis of data from many parts of the same micrograph and, ultimately, from multiple micrographs. Higher resolutions require the inclusion of progressively more data, and for the particles analyzed to be consistent to within ever more stringent limits. Disparities in magnification between micrographs or even within the field of one micrograph, arising from lens hysteresis or distortions, limit the resolution of such analyses. A quantitative assessment of this effect shows that its severity depends on the size of the particle under study: for particles that are 100 nm in diameter, for example, a 2% discrepancy in magnification restricts the resolution to approximately 5 nm. In this study, we derive and describe the properties of a family of algorithms designed for cross-calibrating the magnifications of particles from different micrographs, or from widely differing parts of the same micrograph. This approach is based on the assumption that all of the particles are of identical size: thus, it is applicable primarily to cryo-electron micrographs in which native dimensions are precisely preserved. As applied to icosahedral virus capsids, this procedure is accurate to within 0.1-0.2%, provided that at least five randomly oriented particles are included in the calculation. The algorithm is stable in the presence of noise levels typical of those encountered in practice, and is readily adaptable to non-isometric particles. It may also be used to discriminate subpopulations of subtly different sizes.

Advances in DNA electrophoresis in polymer solutions.

DNA electrophoresis in gels and solutions of agarose and polyacrylamide was objectively evaluated with regard to separation efficiency at optimal polymer concentrations. In application to DNA fragments, polyacrylamide gels were superior for separating fragments of less than 7800 bp, and agarose gels are the best choice for larger fragments. Agarose solutions are nearly as good as polyacrylamide gels for small DNA (< 300 bp). Agarose solutions have a higher efficiency than polyacrylamide solutions for DNA of less than 1200 bp. Separation efficiency sharply decreases with increasing length of DNA. Retardation in polyacrylamide solutions was found to depend on polymer length in a biphasic fashion. The choice of resolving polymer concentrations depends on the progressive stretching of DNA in proportion to polymer concentration. The rate of that stretching appears higher in polyacrylmide solution than in gels or in liquid or gelled agarose. Application of polymer solutions to capillary electrophoresis raises further problems concerning agarose plugs, DNA interactions with the polymers, operation at low field strength and long durations as well as detection sensitivity.

Computerized methods for analyzing two-dimensional agarose gel electropherograms.

Previous methods interpret zonal or polydisperse gel patterns of two-dimensional Serwer-type gels in terms of size and free mobility (surface net charge density). These two parameters have been determined for each component without quantitatively measuring the abundance of the components. The present study advances these previous methods by determining the relative concentration of each component by computer evaluation of densitometrically analyzed gel patterns. Suitable procedures and their underlying algorithms are presented. The mathematical routines are implemented in a user-friendly software package, called GelFit and designed for a Macintosh personal computer. The program input consists of digitized images of gel staining patterns exemplified by those obtained from electrophoresis of native subcellular-sized particles. The data are processed through the following steps: (i) Noise reduction and calibration. (ii) Geometrical transformation of the pattern onto a rectangular size/free mobility coordinate system using rationales of the extended Ogston model. (iii) Analysis of the transformed image to determine density maxima, density profiles along iso-free-mobility or iso-size lines, curve fitting of one-dimensional profiles or two-dimensional surfaces using Gaussian functions and curve stripping of surfaces to determine the possible number of particle populations.

The distribution of particles characterized by size and free mobility within polydisperse populations of protein-polysaccharide conjugates, determined from two-dimensional agarose electropherograms.

New approaches for the characterization of polydisperse particle populations are presented*. The investigated samples contain virus-sized protein-polysaccharide conjugates which had previously been prepared as immunogens against bacterial meningitis (Hib). The analysis is based on two-dimensional agarose electrophoresis (Serwer-type). This method, like the one of O'Farrell, achieves a separation according to size and charge. It relies on a different principle, however, and is applicable to nondenatured particles which are 100 to more than 1000 times larger in mass than regular uncrosslinked proteins. Data from stained gel patterns are evaluated by the computer program ELPHOFIT, which makes it possible to standardize the gel and to construct a nomogram which defines every position on the gel in terms of particle size and free mobility (related to surface net charge density). The output of ELPHOFIT, consisting of nomogram parameters, is transferred to the image processing program GELFIT. This software is used to evaluate the computer images obtained by digitizing the stained gel patterns: (i) The nomogram is electronically superimposed on the computer image. (ii) The gel pattern is transformed from a curvilinear to a rectangular coordinate system of particle size and free mobility. The center of gravity as well as density maxima are given in coordinates of particle size and free mobility. Ranges of grey levels can be accentuated by adding 16 pseudocolors. (iii) Using surface-stripping techniques, GELFIT provides an estimate for the number of major subpopulations within each preparation. (iv) Numerical values for the distribution of particle size and free mobility are determined. Using program IMAGE, the quantitative physical assessment of a given conjugate preparation is presented in the form of a computer-generated three-dimensional plot, the shape of which serves to identify and characterize the preparation visually. The data analysis based on digitized two-dimensional gel patterns is automated to an extent that a technician can perform routine evaluations. It uses the Macintosh II personal computer.

On the uniqueness of quasi-static solutions of some linear models of left ventricular mechanics.

We review two models describing the material properties of heart muscle: the fluid-fiber model and the fluid-fiber-collagen model. We show that the fluid-fiber description gives rise to non-uniqueness when used in ventricular modeling while the fluid-fiber-collagen description does not. We derive a general cavity pressure-volume relation for an extended class family of linear models of the heart's left ventricle.