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PubMed1997

Statistical methods in computational anatomy.

This paper reviews recent developments by the Washington/Brown groups for the study of anatomical shape in the emerging new discipline of computational anatomy. Parametric representations of anatomical variation for computational anatomy are reviewed, restricted to the assumption of small deformations. The generation of covariance operators for probabilistic measures of anatomical variation on coordinatized submanifolds is formulated as an empirical procedure. Populations of brains are mapped to common coordinate systems, from which template coordinate systems are constructed which are closest to the population of anatomies in a minimum distance sense. Variation of several one-, two- and three-dimensional manifolds, i.e. sulci, surfaces and brain volumes are examined via Gaussian measures with mean and covariances estimated directly from maps of templates to targets. Methods are presented for estimating the covariances of vector fields from a family of empirically generated maps, posed as generalized spectrum estimation indexed over the submanifolds. Covariance estimation is made parametric, analogous to autoregressive modelling, by introducing small deformation linear operators for constraining the spectrum of the fields.

Algorithms↗

PubMed1998

Submicrovolt flicker electroretinogram: cycle-by-cycle recording of multiple harmonics with statistical estimation of measurement uncertainty.

PURPOSE: To study cycle-by-cycle recording of small-amplitude flicker-electroretinogram (ERG) responses and analyze results with robust statistical methods to estimate the measurement uncertainty. METHODS: Flicker ERGs at 32 Hz were recorded simultaneously from both eyes of patients with retinal degeneration. The ERG was amplified under wide-band (1-1000 Hz) conditions, digitized at 6144 Hz/eye, and multiplied point for point (192 points/cycle) by sine and cosine functions within each 1/32-second flash cycle to extract coefficients for six harmonic components of a discrete Fourier transform in real time. Amplitude windowing was not used, and all data were saved for subsequent statistical processing to identify and remove large-amplitude artifacts discretely and to search for quiet recording periods that minimized small-amplitude noise. RESULTS: Plots of amplitude and phase indicated far outlying noise points that were excised from the data. The SD of sequential intervals on a time line of the sine component identified quiet periods that minimized small-amplitude noise and improved measurement consistency. The SE of the response mean provided an estimate of measurement uncertainty. CONCLUSIONS: The harmonic components of many individual responses are captured quickly (e.g., 500 responses in 15.6 seconds) for post hoc statistical analysis, using mathematical algorithms that are precisely reproducible to facilitate comparison of results from all laboratories. Graphical time lines of responses allow separation of artifact transients from gaussian noise for elimination of noisy periods without disturbing the stored information. Statistical estimates of measurement uncertainty are determined on-line to allow immediate feedback during the recording session. Amplitude-phase plots of the multiple harmonic components, along with reconstructed analog waveforms, provide results in a readily assimilated manner for comparison of all testing sessions.

Electroretinography↗

PubMed1997

Fluctuation-driven directional flow in biochemical cycle: further study of electric activation of Na,K pumps.

Directional flow of information and energies is characteristic of many types of biochemical reactions, for instance, ion transport, energy coupling during ATP synthesis, and muscle contraction. Can a fluctuating force field, or a noise, induce such a directional flux? Previous work has shown that Na,K-ATPase of human erythrocyte can absorb free energy from an externally applied random-telegraph-noise (RTN) electric field to pump Rb+ up its concentration gradient. However, the RTN field used in these experiments was constant in amplitude and would not mimic fluctuating electric fields of a cell membrane. Here we show that electric fields which fluctuate both in life time and in amplitude, and thus, better mimicking the transmembrane electric fields of a cell, can also induce Rb+ pumping by Na,K-ATPase. A Gaussian-RTN-electric field, or a field with amplitude fluctuating according to the Gaussian distribution, with varied standard deviation (sigma), induced active pumping of Rb+ in human erythrocyte, which was completely inhibited by ouabain. Increased values for sigma led to a nonmonotonic reduction in pumping efficiency. A general formula for calculating the ion transport in a biochemical cycle induced by fluctuating electric field has been derived and applied to a simple four-state electroconformational coupling (ECC) model. It was found that the calculated efficiency in the energy coupling decreased with increasing sigma value, and this effect was relatively small and monotonic, whereas experimental data were more complex: monotonic under certain sets of conditions but nonmonotonic under different sets. The agreement in general features but disagreement in some fine features suggest that there are other properties of the electric activation process for Na,K-ATPase that cannot be adequately described by the simple ECC model, and further refinement of the ECC model is required.

Biophysical Phenomena↗

PubMed2002

[Computerized analysis of craniography: new limits of the norm for static and dynamic forms].

Literature about normal parameters of Craniocorpography (CCG) is scant and poorly documented. Its results are variable according to the series. Our aim is to reach a criteria of normality for CCG in our reference population. We have prospectively made Romberg and Unterberger tests to 72 healthy volunteers (mean age 34.7 years old, SD 17.07, 55.6% men) using a computerized method of measurement and making its estimation by means of a statistical model widely accepted. All the studied variables observe the conditions of Gaussian distribution. The normal limits for lateral and antero-posterior oscillation were 9 centimeters, 12 centimeters for lateral sway and 59 degrees to the right and 46 degrees to the left for angular deviation. The computerized method of analysis has facilitated the detection of the limits of the light tracings, which together with the careful design of our study guarantees the validity of the results.

Adolescent↗

PubMed2004

What does measure the scaling exponent of the correlation sum in the case of human heart rate?

It is shown that in the case of human heart rate, the scaling behavior of the correlation sum (calculated by the Grassberger-Procaccia algorithm) is a result of the interplay of various factors: finite resolution of the apparatus (finite-size effects), a wide dynamic range of mean heart rate, the amplitude of short-time variability being a decreasing function of the mean heart rate. This is done via constructing a simple model of heart rhythm: a signal with functionally modulated Gaussian noise. This model reproduces the scaling behavior of the correlation sum of real medical data. The value of the scaling exponent depends on all the above-mentioned factors, and is a certain measure of short-time variability of the signal.

Algorithms↗

PubMed1999

Computer identification of musical instruments using pattern recognition with cepstral coefficients as features.

Cepstral coefficients based on a constant Q transform have been calculated for 28 short (1-2 s) oboe sounds and 52 short saxophone sounds. These were used as features in a pattern analysis to determine for each of these sounds comprising the test set whether it belongs to the oboe or to the sax class. The training set consisted of longer sounds of 1 min or more for each of the instruments. A k-means algorithm was used to calculate clusters for the training data, and Gaussian probability density functions were formed from the mean and variance of each of the clusters. Each member of the test set was then analyzed to determine the probability that it belonged to each of the two classes; and a Bayes decision rule was invoked to assign it to one of the classes. Results have been extremely good and are compared to a human perception experiment identifying a subset of these same sounds.

Algorithms↗

PubMed1999

Variational learning in nonlinear gaussian belief networks.

We view perceptual tasks such as vision and speech recognition as inference problems where the goal is to estimate the posterior distribution over latent variables (e.g., depth in stereo vision) given the sensory input. The recent flurry of research in independent component analysis exemplifies the importance of inferring the continuous-valued latent variables of input data. The latent variables found by this method are linearly related to the input, but perception requires nonlinear inferences such as classification and depth estimation. In this article, we present a unifying framework for stochastic neural networks with nonlinear latent variables. Nonlinear units are obtained by passing the outputs of linear gaussian units through various nonlinearities. We present a general variational method that maximizes a lower bound on the likelihood of a training set and give results on two visual feature extraction problems. We also show how the variational method can be used for pattern classification and compare the performance of these nonlinear networks with other methods on the problem of handwritten digit recognition.

Depth Perception↗

PubMed2001

Neural field model of receptive field restructuring in primary visual cortex.

Receptive fields (RF) in the visual cortex can change their size depending on the state of the individual. This reflects a changing visual resolution according to different demands on information processing during drowsiness. So far, however, the possible mechanisms that underlie these size changes have not been tested rigorously. Only qualitatively has it been suggested that state-dependent lateral geniculate nucleus (LGN) firing patterns (burst versus tonic firing) are mainly responsible for the observed cortical receptive field restructuring. Here, we employ a neural field approach to describe the changes of cortical RF properties analytically. Expressions to describe the spatiotemporal receptive fields are given for pure feedforward networks. The model predicts that visual latencies increase nonlinearly with the distance of the stimulus location from the RF center. RF restructuring effects are faithfully reproduced. Despite the changing RF sizes, the model demonstrates that the width of the spatial membrane potential profile (as measured by the variance sigma of a gaussian) remains constant in cortex. In contrast, it is shown for recurrent networks that both the RF width and the width of the membrane potential profile generically depend on time and can even increase if lateral cortical excitatory connections extend further than fibers from LGN to cortex. In order to differentiate between a feedforward and a recurrent mechanism causing the experimental RF changes, we fitted the data to the analytically derived point-spread functions. Results of the fits provide estimates for model parameters consistent with the literature data and support the hypothesis that the observed RF sharpening is indeed mainly driven by input from LGN, not by recurrent intracortical connections.

Electroencephalography↗

PubMed2003

Using statistical image models for objective evaluation of spot detection in two-dimensional gels.

Protein spot detection is central to the analysis of two-dimensional electrophoresis gel images. There are many commercially available packages, each implementing a protein spot detection algorithm. Despite this, there have been relatively few studies comparing the performance characteristics of the different packages. This is in part due to the fact that different packages employ different sets of user-adjustable parameters. It is also partly due to the fact that the images are complex. To carry out an evaluation, "ground truth" data specifying spot position, shape and intensities needs to be defined subjectively on selected test images. We address this problem by proposing a method of evaluation using synthetic images with unambiguous interpretation. The characteristics of the spots in the synthetic images are determined from statistical models of the shape, intensity, size, spread and location of real spot data. The distribution of parameters is described using a Gaussian mixture model obtained from training images. The synthetic images allow us to investigate the effects of individual image properties, such as signal-to-noise ratios and degree of spot overlap, by measuring quantifiable outcomes, e.g. accuracy of spot position, false positive and false negative detection. We illustrate the approach by carrying out quantitative evaluations of spot detection on a number of widely used analysis packages.

Algorithms↗

PubMed2004

Gaussian mixture models of ECoG signal features for improved detection of epileptic seizures.

PURPOSE: To investigate the potential for improving the performance of the Osorio-Frei seizure detection algorithm (OFA) by incorporating multiple FIR filters operating in parallel and Gaussian mixture models (GMM) for ECoG features distributions, thus creating "hybrid" system. METHODS: The "hybrid" algorithm decomposes the signal into four subbands, using wavelets, after which relevant features are extracted for each subband. Following these steps, multivariate GMM are developed for seizure and non-seizure states, using training segments. State classification is based on thresholding of the likelihood ratio of seizure vs. non-seizure data. Multiple comparisons are performed between this "hybrid" and a modified version of the OFA suitable for this purpose, using as indices false positives (FP), false negatives (FN) and speed of detection. RESULTS: GMM improved speed of detection over the modified OFA at negligible FP levels. The average detection delay from expert visually placed electrographic onset over all seizures was reduced from 4.8 s for modified OFA to 1.8 s for GMM (p < 0.002) Individualized training by subject proved superior to group-based training. CONCLUSIONS: This work introduces multi-feature extraction from ECoG signals together with use of Gaussian mixtures to model them, as tools to improve automated seizure detection. At the clinical level, this approach appears to increase warning time and with it the window during which safety measures and seizure blockage may be implemented, at an affordable computational cost and with negligible FP rate.

Algorithms↗

PubMed2003

Nonlinear coded excitation method for ultrasound contrast imaging.

Coded excitation with compression on receive is used in medical ultrasound (US) imaging to increase signal-to-noise ratio (SNR) and penetration depth. We performed a computer simulation study to investigate if chirped pulse excitation can be applied in US contrast agent imaging to increase SNR and contrast-to-tissue ratio (CTR) and, thus, reduce contrast agent destruction and tissue harmonics. A new nonlinear compression technique is proposed that selectively compresses the second harmonic component of the response. We compared a chirp of 9.4-micros duration, 2-MHz centre frequency, 45% relative bandwidth to a Gaussian pulse with equal centre frequency and bandwidth. For peak pressures between 50 and 300 kPa, we found for resonant bubbles an increase in response between 10 and 13 dB. Moreover, the axial resolution after compression was comparable to axial resolution of conventional imaging. This effect was relatively insensitive to peak excitation pressure and was largest for bubbles having resonance frequency around the centre frequency of the excitation.

Capsules↗

PubMed2003

Group imaging of task-related changes in cortical synchronisation using nonparametric permutation testing.

Synthetic aperture magnetometry (SAM) is a nonlinear beamformer technique for producing 3D images of cortical activity from magnetoencephalography data. We have previously shown how SAM images can be spatially normalised and averaged to form a group image. In this paper we show how nonparametric permutation methods can be used to make robust statistical inference about group SAM data. Data from a biological motion direction discrimination experiment were analysed using both a nonparametric analysis toolbox (SnPM) and a conventional parametric approach utilising Gaussian field theory. In data from a group of six subjects, we were able to show robust group activation at the P < 0.05 (corrected) level using the nonparametric methods, while no significant clusters were found using the conventional parametric approach. Activation was found using SnPM in several regions of right occipital-temporal cortex, including the superior temporal sulcus, V5/MT, the fusiform gyrus, and the lateral occipital complex.

Adult↗

PubMed1975

The stages of osmotic haemolysis.

The haemolysis of individual human erythrocytes has been observed using an inverted microscope and cine-camera. 2. With each permeant (glycerol, propylene glycol, ethylene glycol, urea and water) haemolysis is a multistage process. The stages are swelling, popping, reduction in volume possibly accompanied by ion leakage and, finally, haemoglobin leakage. 3. The classical haemolysis time (Th) is made up of a swelling time (Tsw) and a stress time (Tst). Tst is not negligible and with the faster permeants it may occupy more than 75% of the haemolysis time. 4. The stress time can also be divided into two parts: a K+ leak time (TK) during which the cell shrinks and a time (THb) during which haemoglobin is leaving the cell. THb occupies a substantial part of Th, from 25 to 65%, and is relatively longer in fast haemolysis. 5. There is a wide spread in the permeability coefficient to glycerol in a population of erythrocytes. The distribution is compatible with a Gaussian distribution. The mean permeability is 1-79 X 10(-6) cm/sec and the S.D. is +/0 0-45 X 10(-6) cm/sec. 6. The correlation between haemolysis time and swelling time for individual erythrocytes is poor, especially for fast haemolysis. Consequently, a measure of the distribution of haemolysis time does not give a related distribution of the swelling time or of the calculated permeability for individual erythrocytes.

Cell Membrane Permeability↗

PubMed2002

White and black blood volumetric angiographic filtering: ellipsoidal scale-space approach.

Prefiltering is a critical step in three-dimensional (3-D) segmentation of the blood vessel and its display (see the recent book by Suri et al.). This paper presents a scale-space approach for filtering the white blood and black blood angiographic volumes and its implementation issues. The raw MR angiographic volume is first converted to isotropic volume followed by 3-D higher order separable Gaussian derivative convolution with known scales to generate edge volume. The edge volume is then run by the directional processor at each voxel where the eigenvalues of the 3-D ellipsoid are computed. The vessel score per voxel is then estimated based on these three eigenvalues which suppress the nonvasculature and background structures yielding the filtered volume. The filtered volume is ray-cast to generate the maximum intensity projection images for display. The performance of the system is evaluated by computing the mean, variance, signal-to-noise ratio (SNR), and contrast-to-noise ratio (CNR) images. The system is run over 20 patient studies from different areas of the body such as the brain, abdomen, kidney, knee, and ankle. The computer program takes around 150 s of processing time per study for a data size of 512 x 512 x 194, which includes the complete performance evaluation. We also compare our strategy with the recently published MR filtering algorithms by Alexander et al. and Sun et al.

Algorithms↗

PubMed2001

Noise correction for the exact determination of apparent diffusion coefficients at low SNR.

Noise in MR image data increases the mean signal intensity of image regions due to the usually performed magnitude reconstruction. Diffusion-weighted imaging (DWI) is especially affected by high noise levels for several reasons, and a decreasing SNR at increasing diffusion weighting causes systematic errors when calculating apparent diffusion coefficients (ADCs). Two different methods are presented to correct biased signal intensities due to the presence of complex noise: 1) with Gaussian intensity distribution, and 2) with arbitrary intensity distribution. The performance of the correction schemes is demonstrated by numerical simulations and DWI measurements on two different MR systems with different noise characteristics. These experiments show that noise significantly influences the determination of ADCs. Applying the proposed correction schemes reduced the bias of the determined ADC to less than 10% of the bias without correction. Magn Reson Med 45:448-453, 2001.

Artifacts↗

PubMed2005

Estimation of coupling between oscillators from short time series via phase dynamics modeling: limitations and application to EEG data.

We demonstrate in numerical experiments that estimators of strength and directionality of coupling between oscillators based on modeling of their phase dynamics [D. A. Smirnov and B. P. Bezruchko, Phys. Rev. E 68, 046209 (2003)] are widely applicable. Namely, although the expressions for the estimators and their confidence bands are derived for linear uncoupled oscillators under the influence of independent sources of Gaussian white noise, they turn out to allow reliable characterization of coupling from relatively short time series for different properties of noise, significant phase nonlinearity of the oscillators, and nonvanishing coupling between them. We apply the estimators to analyze a two-channel human intracranial epileptic electroencephalogram (EEG) recording with the purpose of epileptic focus localization.

Artifacts↗

PubMed2005

A general framework for nonlinear multigrid inversion.

A variety of new imaging modalities, such as optical diffusion tomography, require the inversion of a forward problem that is modeled by the solution to a three-dimensional partial differential equation. For these applications, image reconstruction is particularly difficult because the forward problem is both nonlinear and computationally expensive to evaluate. In this paper, we propose a general framework for nonlinear multigrid inversion that is applicable to a wide variety of inverse problems. The multigrid inversion algorithm results from the application of recursive multigrid techniques to the solution of optimization problems arising from inverse problems. The method works by dynamically adjusting the cost functionals at different scales so that they are consistent with, and ultimately reduce, the finest scale cost functional. In this way, the multigrid inversion algorithm efficiently computes the solution to the desired fine-scale inversion problem. Importantly, the new algorithm can greatly reduce computation because both the forward and inverse problems are more coarsely discretized at lower resolutions. An application of our method to Bayesian optical diffusion tomography with a generalized Gaussian Markov random-field image prior model shows the potential for very large computational savings. Numerical data also indicates robust convergence with a range of initialization conditions for this nonconvex optimization problem.

Algorithms↗

PubMed2006

Precise segmentation of multimodal images.

We propose new techniques for unsupervised segmentation of multimodal grayscale images such that each region-of-interest relates to a single dominant mode of the empirical marginal probability distribution of grey levels. We follow the most conventional approaches in that initial images and desired maps of regions are described by a joint Markov-Gibbs random field (MGRF) model of independent image signals and interdependent region labels. However, our focus is on more accurate model identification. To better specify region borders, each empirical distribution of image signals is precisely approximated by a linear combination of Gaussians (LCG) with positive and negative components. We modify an expectation-maximization (EM) algorithm to deal with the LCGs and also propose a novel EM-based sequential technique to get a close initial LCG approximation with which the modified EM algorithm should start. The proposed technique identifies individual LCG models in a mixed empirical distribution, including the number of positive and negative Gaussians. Initial segmentation based on the LCG models is then iteratively refined by using the MGRF with analytically estimated potentials. The convergence of the overall segmentation algorithm at each stage is discussed. Experiments show that the developed techniques segment different types of complex multimodal medical images more accurately than other known algorithms.

Algorithms↗