Karsten Tabelow

• Dr. rer. nat.
• Senior Researcher at Weierstrass Institute for Applied Analysis and Stochastics

Quantitative magnetic resonance imaging (qMRI) finds increasing application in neuro-science and clinical research due to its sensitivity to micro-structural properties of brain tissue, e.g. axon, myelin, iron and water concentration. We introduce the hMRI-toolbox, an easy-to-use open-source tool for handling and processing of qMRI data presented t...

Noise is a common issue for all magnetic resonance imaging (MRI) techniques such as diffusion MRI and obviously leads to variability of the estimates in any model describing the data. Increasing spatial resolution in MR experiments further diminish the signal-to-noise ratio (SNR). However, with low SNR the expected signal deviates from the true val...

We present a novel multi-shell position orientation adaptive smoothing (msPOAS) method for diffusion-weighted magnetic resonance data. Smoothing in voxel and diffusion gradient space is embedded in an iterative adaptive multiscale approach. The adaptive character avoids blurring of the inherent structures and preserves discontinuities. The simultan...

We present an implementation of a recently developed noise reduction algorithm for dMRI data, called multi-shell position orientation adaptive smoothing (msPOAS), as a toolbox for SPM. The method intrinsically adapts to the structures of different size and shape in dMRI and hence avoids blurring typically observed in non-adaptive smoothing. We give...

Data from functional magnetic resonance imaging (fMRI) consist of time series of brain images that are characterized by a low signal-to-noise ratio. In order to reduce noise and to improve signal detection, the fMRI data are spatially smoothed. However, the common application of a Gaussian filter does this at the cost of loss of information on spat...

Purpose: Identify differences between the acquisition-time efficient axisymmetric diffusion kurtosis imaging (DKI) model and standard DKI and their consequences on biophysical parameter estimates using standard DKI parameters as the ground truth. Methods: Noise-free, synthetic diffusion MRI (dMRI) human brain data are generated using standard DKI a...

In this paper we discuss the notion of research data for the field of mathematics and report on the status quo of research-data management and planning. A number of decentralized approaches are presented and compared to needs and challenges faced in three use cases from different mathematical subdisciplines. We highlight the importance of tailoring...

Purpose To compare the estimation accuracy of axisymmetric diffusion kurtosis imaging (DKI) and standard DKI in combination with Rician bias correction (RBC). Methods Axisymmetric DKI is more robust against noise‐induced variation in the measured signal than standard DKI because of its reduced parameter space. However, its susceptibility to Rician...

Multi-Parameter Mapping (MPM) is a comprehensive quantitative neuroimaging protocol that enables estimation of four physical parameters (longitudinal and effective transverse relaxation rates R1 and R2*, proton density PD, and magnetization transfer saturation MTsat) that are sensitive to microstructural tissue properties such as iron and myelin co...

This paper investigates a data assimilation approach for non-invasive quantification of intracranial pressure from partial displacement data, acquired through magnetic resonance elastography. Data assimilation is based on a parametrized-background data weak methodology, in which the state of the physical system -- tissue displacements and pressure...

Purpose To compare the estimation accuracy of axisymmetric diffusion kurtosis imaging (DKI) and standard DKI in combination with Rician bias correction (RBC) under the influence of noise. Methods Axisymmetric DKI is more robust against noise-induced variation in the measured signal than standard DKI because of its reduced parameter space. However,...

Multi-Parameter Mapping (MPM) is a comprehensive quantitative neuroimaging protocol that enables estimation of four physical parameters (longitudinal and effective transverse relaxation rates R1 and R2*, proton density PD, and magnetization transfer saturation MTsat) that are sensitive to microstructural tissue properties such as iron and myelin co...

In order to tackle the challenges caused by the variability in estimated MRI parameters (e.g., T 2 * and T 2 ) due to low SNR a number of strategies can be followed. One approach is postprocessing of the acquired data with a filter. The basic idea is that MR images possess a local spatial structure that is characterized by equal, or at least simila...

We present a mathematical model and a tool chain for the numerical simulation of TEM images of semiconductor quantum dots (QDs). This includes elasticity theory to obtain the strain profile coupled with the Darwin–Howie–Whelan equations, describing the propagation of the electron wave through the sample. We perform a simulation study on indium gall...

This book discusses the modeling and analysis of magnetic resonance imaging (MRI) data acquired from the human brain. The data processing pipelines described rely on R. The book is intended for readers from two communities: Statisticians who are interested in neuroimaging and looking for an introduction to the acquired data and typical scientific p...

Functional magnetic resonance imaging (fMRI) maps brain activity by detecting changes in image intensity related to neural activity by the blood oxygenation level-dependent (BOLD) contrast. Functional MRI data essentially consists of time series of 3D images associated with a description of the experimental conditions. The chapter outlines an analy...

Diffusion-weighted Magnetic Resonance Imaging (dMRI) has long proven to be a versatile tool for the in vivo microstructural investigation of the human brain (Le Bihan 2003), the spinal cord (Clark et al. 1999), or even muscle tissue (Sinha et al. 2006). In contrast to conventional weighted MRI or functional MRI discussed in the preceding Chap. 4, i...

There exist a large variety of data formats used in medical imaging in general and specifically for functional magnetic resonance imaging, diffusion-weighted imaging, or multiparameter mapping. Medical imaging data typically contain the actual data and additionally some metadata. This may be the data dimensionality, the spatial extension of the ima...

Unlike conventional weighted MRI, leading to \(T_1\)-, \(T_2\)-, \(T_2^\star \)-, or proton density (\(P\!D\)) weighted images in arbitrary units, quantitative MRI (qMRI) aims to estimate absolute physical metrics. One example is dMRI considered in Chap. 5. qMRI is of increasing interest in neuroscience and clinical research for its greater specifi...

Since its invention in the early 70s by Lauterbur (Lauterbur 1973; Mansfield and Grannell 1973) and Mansfield (Mansfield 1977), for which they shared the 2003 Nobel prize in Physiology and Medicine, magnetic resonance imaging (MRI) has evolved into a versatile tool for the in vivo examination of tissue. MRI is based on the nuclear magnetic resonanc...

The hMRI toolbox is an open-source toolbox for the calculation of quantitative MRI parameter maps from a series of weighted imaging data, and optionally additional calibration data. The multi-parameter mapping (MPM) protocol, incorporating calibration data to correct for spatial variation in the scanner's transmit and receive fields, is the most co...

Neuroscience and clinical researchers are increasingly interested in quantitative magnetic resonance imaging (qMRI) due to its sensitivity to micro-structural properties of brain tissue such as axon, myelin, iron and water concentration. We introduce the hMRI-toolbox, an open-source, easy-to-use tool available on GitHub, for qMRI data handling and...

The reconstruction of geometric properties of semiconductor quantum dots (QDs) from imaging of bulk‐like samples (thickness 100‐300 nm) by transmission electron microscopy (TEM) is a difficult problem. A direct reconstruction by solving the tomography problem is not feasible due to the limited image resolution (0.5‐1 nm), the highly nonlinear behav...

Image reconstruction from noisy data has a long history of methodological development and is based on a variety of ideas. In this paper we introduce a new method called patch-wise adaptive smoothing, that extends the Propagation-Separation approach by using comparisons of local patches of image intensities to define local adaptive weighting schemes...

Mathematical models are the foundation of numerical simulation of optoelectronic devices. We present a concept for a machine-actionable as well as human-understandable representation of the mathematical knowledge they contain and the domain-specific knowledge they are based on. We propose to use theory graphs to formalize mathematical models and mo...

Attempts for in-vivo histology require a high spatial resolution that comes with the price of a decreased signal-to-noise ratio. We present a novel iterative and multi-scale smoothing method for quantitative Magnetic Resonance Imaging (MRI) data that yield proton density, apparent transverse and longitudinal relaxation, and magnetization transfer m...

Mathematical models are the foundation of numer- ical simulation of optoelectronic devices. We present a concept for a machine-actionable as well as human-understandable rep- resentation of the mathematical knowledge they contain and the domain-specific knowledge they are based on. We propose to use theory graphs to formalize mathematical models an...

Mathematical modeling and simulation (MMS) has now been established as an essential part of the scientific work in many disciplines. It is common to categorize the involved numerical data and to some extent the corresponding scientific software as research data. But both have their origin in mathematical models, therefore any holistic approach to r...

The presentation is about the effects of low signal-to-noise ration in magnetic resonance imaging (MRI) and on methods to deal with the resulting estimation bias in data models like the diffusion tensor model or the multi-paramter maps in relaxometry.

The generation and processing of research data for modeling and simulation is an important part of the scientific work at WIAS. Together with scientific software it plays an essential role for the transfer of mathematical research results to industry or to other scientific disciplines. In the face of the emerging digital science agenda research dat...

Contains R-functions to perform an fMRI analysis as described in Tabelow et al. (2006) <DOI:10.1016/j.neuroimage.2006.06.029>, Polzehl et al. (2010) <DOI:10.1016/j.neuroimage.2010.04.241>, Tabelow and Polzehl (2011) <DOI:10.18637/jss.v044.i11>.

Mathematical modeling and simulation (MMS) has now been established as an essential part of the scientific work in many disciplines and application areas. It is common to categorize the involved numerical data and to some extend the corresponding scientific software as research data. Both have their origin in mathematical models. In this contributi...

In contrast to classical T1, T2, or PD-weighted imaging which acquires intensity values in arbitrary units, quantitative imaging (qMRI) has the clear advantage of providing absolute values comparable across sites and time. Multi-Parameter Mapping (MPM; Weiskopf, 2013; Lutti, 2014) is a framework for qMRI that simultaneously measures the proton dens...

Estimation of learning curves is ubiquitously based on proportions of correct responses within moving trial windows. Thereby, it is tacitly assumed that learning performance is constant within the moving windows, which, however, is often not the case. In the present study we demonstrate that violations of this assumption lead to systematic errors i...

Random and systematic errors of learning curve estimation with and without accounting for session breaks. Simulations were carried out as in Fig 4. (A) Bias, (B) standard deviation (SD), (C) mean absolute error (MAE), and (D) coverage probabilities of confidence intervals of the estimated learning curves for four different window sizes (11, 19, 31,...

Individual learning curves based on the constant model (conv). Learning curves (black lines) for the 20 individual rodents (R01 to R20) with 95%-confidence intervals (thin grey lines) derived from a constant model (conv) with a window of 19 trials moving across trials and session borders.—The three experimental sessions are separated by different b...

Individual learning curves based on the constant model (sep). Learning curves (black lines) for the 20 individual rodents (R01 to R20) with 95%-confidence intervals (thin grey lines) derived from a constant model employed in a session-wise moving window analysis. Windows consisted of 19 trials.—The three experimental sessions are separated by diffe...

Behavioral and physiological data archive. This RAR format file includes all analyzed behavioral and physiological data in ASCII format. It also contains the file Data-Documentation-001.rtf which explains the layout of the data. (RAR)

We analyze the pulsatile signal component of dynamic echo planar imaging data from the brain by modeling the dependence between local temporal and spatial signal variability. The resulting magnetic resonance advection imaging maps depict the location of major arteries. Color direction maps allow for visualization of the direction of blood vessels....

In vivo histology aims to extract biologically relevant metrics from MRI data. In neuroimaging this includes characterising white matter fibres in terms of orientation, distribution and g-ratio, or determining the cortical myelo- and cyto-architecture. It has been shown, both theoretically and experimentally, that the signal decay in gradient recal...

Mathematical derivations. Mathematical proofs and investigation of the proposed procedure regarding the tuning parameter κ. (PDF)

Signal detection in functional magnetic resonance imaging (fMRI) inherently involves the problem of testing a large number of hypotheses. A popular strategy to address this multi- plicity is the control of the false discovery rate (FDR). In this work we consider the case where prior knowledge is available to partition the set of all hypotheses into...

The underlying pathophysiology of neurological complications in patients with hemolytic-uremic syndrome (HUS) remains unclear. It was recently attributed to a direct cytotoxic effect of Shiga toxin 2 (Stx2) in the thalamus. Conventional MRI of patients with Stx2-caused HUS revealed - despite severe neurological symptoms - only mild alterations if a...

Background Common symptoms of multiple sclerosis (MS) such as gait ataxia, poor coordination of the hands, and intention tremor are usually the result of dysfunctionality in the cerebellum. Magnetic resonance imaging (MRI) has frequently failed to detect cerebellar damage in the form of inflammatory lesions in patients presenting with symptoms of c...

Diffusion Kurtosis Imaging (DKI) is more sensitive to microstructural differences and can be related to more specific micro-scale metrics (e.g., intra-axonal volume fraction) than diffusion tensor imaging (DTI), offering exceptional potential for clinical diagnosis and research into the white and gray matter. Currently DKI is acquired only at low s...

We present a method for local estimation of the signal-dependent noise level in magnetic resonance images. The procedure uses a multi-scale approach to adaptively infer on local neighborhoods with similar data distribution. It exploits a maximum-likelihood estimator for the local noise level. The validity of the method was evaluated on repeated dif...

Noise in MRI effects analysis in neuroscientific problems or clinical applications. The estimation of the noise power thus serves as a measure of the quality of MRI data. On the other hand its estimates is directly used in a number of data enhancing methods to differentiate noise variation from structural differences. Most estimation methods rely o...

Although spatial smoothing of fMRI data can serve multiple purposes, increasing the sensitivity of activation detection is probably its greatest benefit. However, this increased detection power comes with a loss of specificity when non-adaptive smoothing (i.e. the standard in most software packages) is used. Simulation studies and analysis of exper...

Recent studies suggest that Diffusion Kurtosis Imaging (DKI) is more sensitive to gray microstructure than the well-known diffusion tensor imaging (DTI). However, DKI suffers from a low signal-to-noise ratio (SNR), since it is based on multiple and high b-value data. Thus, in-vivo high-resolution DKI with small voxel sizes has not been available on...

In this paper we develop a tensor mixture model for diffusion weighted imaging data using an automatic model order selection criterion for the number of tensor components in a voxel. We show that the weighted orientation distribution function for this model can be expanded into a mixture of angular central Gaussian distributions. We investigate pro...

We introduce an algorithm for diffusion weighted magnetic resonance imaging data enhancement based on structural adaptive smoothing in both voxel space and diffusion-gradient space. The method, called POAS, does not refer to a specific model for the data, like the diffusion tensor or higher order models. It works by embedding the measurement space...

Structural adaptive smoothing provides a new concept of edge-preserving non-parametric smoothing methods. In imaging it employs qualitative assumption on the underlying homogeneity structure of the image. The chapter describes the main principles of the approach and discusses applications ranging from image denoising to the analysis of functional a...

The purpose of the package fmri is the analysis of single subject functional magnetic resonance imaging (fMRI) data. It provides fMRI analysis from time series modeling by a linear model to signal detection and publication quality images. Specifically, it implements structural adaptive smoothing methods with signal detection for adaptive noise redu...

The special volume on 'Magnetic Resonance Imaging in R' features articles and packages related to a variety of imaging modalities: functional MRI, diffusion-weighted MRI, dynamic contrast-enhanced MRI, dynamic susceptibility-contrast MRI and structural MRI. The papers describe the methodology, software implementation and provide comprehensive examp...

Diffusion weighted imaging (DWI) is a magnetic resonance (MR) based method to investigate water diffusion in tissue like the human brain. Inference focuses on integral properties of the tissue microstructure. The acquired data are usually modeled using the diffusion tensor model, a three-dimensional Gaussian model for the diffusion process. Since t...

R is a language and environment for statistical computing and graphics. It can be considered an alternative implementation of the S language developed in the 1970s and 1980s for data analysis and graphics (Becker and Chambers, 1984; Becker et al., 1988). The R language is part of the GNU project and offers versions that compile and run on almost ev...

Functional neuroimaging methods hold promise for the identification of cognitive function and communication capacity in some severely brain-injured patients who may not retain sufficient motor function to demonstrate their abilities. We studied seven severely brain-injured patients and a control group of 14 subjects using a novel hierarchical funct...

Functional Magnetic Resonance Imaging inherently involves noisy measurements and a severe multiple test problem. Smoothing is usually used to reduce the effective number of multiple comparisons and to locally integrate the signal and hence increase the signal-to-noise ratio. Here, we provide a new structural adaptive segmentation algorithm (AS) tha...

Bildgebende Verfahren haben sich in den letzten Jahren einen festen Platz in der Medizin erobert und die medizinische Forschung und Diagnostik revolutioniert. Sie ermöglichen Ärzten und Forschern einen Einblick in lebendes Gewebe. Mit der fortschreitenden technischen Entwicklung liefern die Verfahren immer höhere Auflösungen, schärfere Bilder und m...

Diffusion weighted imaging has become and will certainly continue to be an important tool in medical research and diagnostics. Data obtained with diffusion weighted imaging are characterized by a high noise level. Thus, estimation of quantities like anisotropy indices or the main diffusion direction may be significantly compromised by noise in clin...

Increasing the spatial resolution in functional Magnetic Resonance Imaging (fMRI) inherently lowers the signal-to-noise ratio (SNR). In order to still detect functionally significant activations in high-resolution images, spatial smoothing of the data is required. However, conventional non-adaptive smoothing comes with a reduced effective resolutio...

Project MATHEON A3

There exists a variety of software tools for analyzing functional Magnetic Resonance Imaging data. A very popular one is the freely available SPM package by the Functional Imaging Laboratory at the Wellcome Department of Imaging Neuroscience. In order to enhance the signal-to-noise ratio it provides the possibility to smooth the data in a pre-proce...

An important problem of the analysis of functional magnetic resonance imaging (fMRI) experiments is to achieve some noise reduction of the data without blurring the shape of the activation areas. As a novel solution to this problem, recently the propagation-separation (PS) approach has been proposed. PS is a structure adaptive smoothing method that...

Diffusion Tensor Imaging (DTI) data is characterized by a high noise level. Thus, estimation errors of quantities like anisotropy indices or the main diffusion direction used for fiber tracking are relatively large and may significantly confound the accuracy of DTI in clinical or neuroscience applications. Besides pulse sequence optimization, noise...

This article describes the usage of the R package fmri to analyze single time series BOLD fMRI (blood-oxygen-level dependent functional magnetic resonance imaging) data using structure adaptive smoothing procedures (Propagation- Separation approach) as described in (Tabelow et al., 2006). See (J. Polzehl and K. Tabelow, 2006) for an extended docume...

Electrophysiological and activity-dependent gene expression studies of birdsong have contributed to the understanding of the neural representation of natural sounds. However, we have limited knowledge about the overall spatial topography of song representation in the avian brain. Here, we adapt the noninvasive functional MRI method in mildly sedate...

Digital imaging has become omnipresent in the past years with a bulk of applications ranging from medical imaging to photography. When pushing the limits of resolution and sensitivity noise has ever been a major issue. However, commonly used non-adaptive filters can do noise reduction at the cost of a reduced effective spatial resolution only. Here...

This document describes the usage of the R package fmri to analyse functional Magnetic Resonance Imaging (fMRI) data with structure adaptive smoothing procedures (Propagation-Separation (PS) approach) as described in [7].