<i>Numerical Recipes, The Art of Scientific Computing</i>

Press, William H.; Flannery, Brian P.; Teukolsky, Saul A.; Vetterling, William T.; Gould, Harvey

doi:10.1119/1.14981

Cited by 4,229 publications

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“…For the Laplacian method, we tried both 1mm iso-tropic and 0.5mm iso-tropic voxels. The Laplacian method uses a grid based relaxation process (Press et al, 1991) to solve the Laplace equation and the thickness PDE. The cortex varies between 1 and 4.5mm in different parts of the brain (Fischl and Dale, 2000;von Economo, 1929), which means that with 1mm iso-tropic voxels the grey matter might be only 1 -4 voxels wide.…”

Section: Discussionmentioning

confidence: 99%

“…Laplacian approaches (Hutton et al, 2008;Acosta et al, 2009;Cardoso et al, 2011), solve the Laplace equation (Jones et al, 2000) using boundary value relaxation (Press et al, 1991) or matrix methods (Haidar et al, 2005), calculate thickness by integrating the tangent to the Laplacian scalar field (Jones et al, 2000), summing the Euclidean distance from neighbouring voxels on the same streamline, or using a partial differential equation (Yezzi and Prince, 2003) with boundaries set to zero (Yezzi and Prince, 2003), half the mean voxel dimension (Diep et al, 2007) or using Lagrangian initialisation (Bourgeat et al, 2008;Acosta et al, 2009). In contrast, the registration based approach of Das et al (2009) uses a greedy diffeomorphic registration algorithm to warp the WM segment to match the GM+WM segment.…”

Section: Introductionmentioning

confidence: 99%

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A comparison of voxel and surface based cortical thickness estimation methods

et al. 2011

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Cortical thickness estimation performed in-vivo via magnetic resonance imaging is an important technique for the diagnosis and understanding of the progression of neurodegenerative diseases. Currently, two different computational paradigms exist, with methods generally classified as either surface or voxel-based. This paper provides a much needed comparison of the surface-based method FreeSurfer and two voxel-based methods using clinical data. We test the effects of computing regional statistics using two different atlases and demonstrate that this makes a significant difference to the cortical thickness results. We assess reproducibility, and show that FreeSurfer has a regional standard deviation of thickness difference on same day scans that is significantly lower than either a Laplacian or Registration based method and discuss the trade off between reproducibility and segmentation accuracy caused by bending energy constraints. We demonstrate that voxel-based methods can detect similar patterns of group-wise differences as well as FreeSurfer in typical applications such as producing group-wise maps of statistically significant thickness change, but that regional statistics can vary between methods. We use a Support Vector Machine to classify patients against controls and did not find statistically significantly different results with voxel based methods compared to FreeSurfer. Finally we assessed longitudinal performance and concluded that currently FreeSurfer provides the most plausible measure of change over time, with further work required for voxel based methods.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A comparison of voxel and surface based cortical thickness estimation methods

et al. 2011

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“…General features of self-sustaining limit cycles, like a steady amplitude that decreases with increasing frequency can be observed (note that the amplitude is fixed here so that, in relative terms, velocity increases). 5 We numerically estimated velocity after smoothing the position data via a polynomial filter (fifth-order Savitzky-Golay, frame size 35; Press et al 1994) …”

Section: Vector Fieldsmentioning

confidence: 99%

Deterministic and stochastic features of rhythmic human movement

2005

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The dynamics of rhythmic movement has both deterministic and stochastic features. We advocate a recently established analysis method that allows for an unbiased identification of both types of system components. The deterministic components are revealed in terms of drift coefficients and vector fields, while the stochastic components are assessed in terms of diffusion coefficients and ellipse fields. The general principles of the procedure and its application are explained and illustrated using simulated data from known dynamical systems. Subsequently, we exemplify the method's merits in extracting deterministic and stochastic aspects of various instances of rhythmic movement, including tapping, wrist cycling and forearm oscillations. In particular, it is shown how the extracted numerical forms can be analysed to gain insight into the dependence of dynamical properties on experimental conditions.

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“…Similarly, linear regression of the fraction of labeled undivided cells, f lu (t), provided values for c alone, with the intercept depending on a combination of kinetic parameters including the lifetime of the dying cells, T R . Independent estimates of T G2M and estimates of T S were obtained using equation 9, which was fitted using the Levenburg-Marquardt nonlinear least squares algorithm (36). The ratio of the slopes of f lu (t) and f ld (t) was used to compute the fraction of cells entering G 2 /M that divide, r. The values of T S , T G2M , and r were combined as in equation 6 to determine T R .…”

Section: Fitting Methodsmentioning

confidence: 99%

Estimating cell death in G₂M using bivariate BrdUrd/DNA flow cytometry

et al. 2005

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Background: In an accompanying paper (Asmuth et al.) it was found necessary to include cell death explicitly to estimate parameters of cell proliferation. The use of bivariate flow cytometry to estimate the phase durations and the doubling times of cells labeled with thymidine analogues is well established. However, these methods of analysis do not consider the possibility of cell death. This report demonstrates that estimating cell death in G 2 /M is possible. Methods: Mathematical models for the experimental quantities, the fraction of labeled undivided cells, the fraction of labeled divided cells, and the relative movement were developed. These models include the possibility that, of the cells with G 2 /M DNA content, only a certain fraction will divide, with the remainder dying after some time T R . Simulation studies were conducted to test the possibility of using simple methods to estimate phase durations and cell death rates. Results: Cell death alters the estimates of phase transit times in a rather complex manner that depends on the lifetime of the doomed cells. However, it is still possible to obtain estimates of the phase durations of cells in S and G 2 /M and the death rates of cells in G 2 /M. Conclusions: The methods presented herein provide a new way to characterize cell populations that includes cell death rates and common measurements of cell proliferation. q 2005 Wiley-Liss, Inc.Key terms: cell cycle; phase durations; population growth; bromodeoxyuridineThe identification of DNA-synthesizing cells through the use of halogenated analogues of thymidine, such as bromodeoxyuridine, is a well-established procedure (1-6). Beyond merely measuring the S-phase fraction, the combination of DNA and halogenated thymidine analogue bivariate cytometry permits the more challenging measurement of dynamic quantities, including phase durations of S (T S )and G 2 /M (T G2M ) and a measurement of the doubling time of the population, the potential doubling time (T pot ) (7-21). These quantities have proved to be useful in a variety of applications including extensive analyses of clinical data (22)(23)(24)(25)(26)(27)(28)(29).However, the effects of cell death on these estimates have largely been ignored. In the accompanying paper it was observed that cell loss was critical in assessing the progression of T lymphocytes infected with human immunodeficiency virus (30). Moreover, the biological significance of T pot , a measurement of overall cell proliferation, is somewhat obscure. As defined operationally by Steel (31), T pot is a measurement of the difference between the observed doubling time of a cell population and that predicted by the duration of DNA synthesis time and the S-phase fraction. In the absence of evidence to the contrary, cell death was assumed to be random, with all cells in a population being equally likely to die. As explored by , violation of the random death assumption leads to very different values for T pot . In this paper, the effects of cell death in G 2 /M are considered and a method for ...

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Numerical Recipes, The Art of Scientific Computing

Cited by 4,229 publications

References 0 publications

A comparison of voxel and surface based cortical thickness estimation methods

A comparison of voxel and surface based cortical thickness estimation methods

Deterministic and stochastic features of rhythmic human movement

Estimating cell death in G₂M using bivariate BrdUrd/DNA flow cytometry

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Numerical Recipes, The Art of Scientific Computing

Cited by 4,229 publications

References 0 publications

A comparison of voxel and surface based cortical thickness estimation methods

A comparison of voxel and surface based cortical thickness estimation methods

Deterministic and stochastic features of rhythmic human movement

Estimating cell death in G2M using bivariate BrdUrd/DNA flow cytometry

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Estimating cell death in G₂M using bivariate BrdUrd/DNA flow cytometry