Decomposition of neurological multivariate time series by state space modelling.

Decomposition of multivariate time series data into independent source components forms an important part of preprocessing and analysis of time-resolved data in neuroscience. We briefly review the available tools for this purpose, such as Factor Analysis (FA) and Independent Component Analysis (ICA), then we show how linear state space modelling, a methodology from statistical time series analysis, can be employed for the same purpose. State space modelling, a generalization of classical ARMA modelling, is well suited for exploiting the dynamical information encoded in the temporal ordering of time series data, while this information remains inaccessible to FA and most ICA algorithms. As a result, much more detailed decompositions become possible, and both components with sharp power spectrum, such as alpha components, sinusoidal artifacts, or sleep spindles, and with broad power spectrum, such as FMRI scanner artifacts or epileptic spiking components, can be separated, even in the absence of prior information. In addition, three generalizations are discussed, the first relaxing the independence assumption, the second introducing non-stationarity of the covariance of the noise driving the dynamics, and the third allowing for non-Gaussianity of the data through a non-linear observation function. Three application examples are presented, one electrocardigram time series and two electroencephalogram (EEG) time series. The two EEG examples, both from epilepsy patients, demonstrate the separation and removal of various artifacts, including hum noise and FMRI scanner artifacts, and the identification of sleep spindles, epileptic foci, and spiking components. Decompositions obtained by two ICA algorithms are shown for comparison.

Optimal HRF and smoothing parameters for fMRI time series within an autoregressive modeling framework.

The analysis of time series obtained by functional magnetic resonance imaging (fMRI) may be approached by fitting predictive parametric models, such as nearest-neighbor autoregressive models with exogeneous input (NNARX). As a part of the modeling procedure, it is possible to apply instantaneous linear transformations to the data. Spatial smoothing, a common preprocessing step, may be interpreted as such a transformation. The autoregressive parameters may be constrained, such that they provide a response behavior that corresponds to the canonical haemodynamic response function (HRF). We present an algorithm for estimating the parameters of the linear transformations and of the HRF within a rigorous maximum-likelihood framework. Using this approach, an optimal amount of both the spatial smoothing and the HRF can be estimated simultaneously for a given fMRI data set. An example from a motor-task experiment is discussed. It is found that, for this data set, weak, but non-zero, spatial smoothing is optimal. Furthermore, it is demonstrated that activated regions can be estimated within the maximum-likelihood framework.

Evaluating the performance of Kalman-filter-based EEG source localization.

Electroencephalographic (EEG) source localization is an important tool for noninvasive study of brain dynamics, due to its ability to probe neural activity more directly, with better temporal resolution than other imaging modalities. One promising technique for solving the EEG inverse problem is Kalman filtering, because it provides a natural framework for incorporating dynamic EEG generation models in source localization. Here, a recently developed inverse solution is introduced, which uses spatiotemporal Kalman filtering tuned through likelihood maximization. Standard diagnostic tests for objectively evaluating Kalman filter performance are then described and applied to inverse solutions for simulated and clinical EEG data. These tests, employed for the first time in Kalman-filter-based source localization, check the statistical properties of the innovation and validate the use of likelihood maximization for filter tuning. However, this analysis also reveals that the filter's existing space- and time-invariant process model, which contains a single fixed-frequency resonance, is unable to completely model the complex spatiotemporal dynamics of EEG data. This finding indicates that the algorithm could be improved by allowing the process model parameters to vary in space.

Model driven EEG/fMRI fusion of brain oscillations.

This article reviews progress and challenges in model driven EEG/fMRI fusion with a focus on brain oscillations. Fusion is the combination of both imaging modalities based on a cascade of forward models from ensemble of post-synaptic potentials (ePSP) to net primary current densities (nPCD) to EEG; and from ePSP to vasomotor feed forward signal (VFFSS) to BOLD. In absence of a model, data driven fusion creates maps of correlations between EEG and BOLD or between estimates of nPCD and VFFS. A consistent finding has been that of positive correlations between EEG alpha power and BOLD in both frontal cortices and thalamus and of negative ones for the occipital region. For model driven fusion we formulate a neural mass EEG/fMRI model coupled to a metabolic hemodynamic model. For exploratory simulations we show that the Local Linearization (LL) method for integrating stochastic differential equations is appropriate for highly nonlinear dynamics. It has been successfully applied to small and medium sized networks, reproducing the described EEG/BOLD correlations. A new LL-algebraic method allows simulations with hundreds of thousands of neural populations, with connectivities and conduction delays estimated from diffusion weighted MRI. For parameter and state estimation, Kalman filtering combined with the LL method estimates the innovations or prediction errors. From these the likelihood of models given data are obtained. The LL-innovation estimation method has been already applied to small and medium scale models. With improved Bayesian computations the practical estimation of very large scale EEG/fMRI models shall soon be possible.

A data-driven model of the generation of human EEG based on a spatially distributed stochastic wave equation.

We discuss a model for the dynamics of the primary current density vector field within the grey matter of human brain. The model is based on a linear damped wave equation, driven by a stochastic term. By employing a realistically shaped average brain model and an estimate of the matrix which maps the primary currents distributed over grey matter to the electric potentials at the surface of the head, the model can be put into relation with recordings of the electroencephalogram (EEG). Through this step it becomes possible to employ EEG recordings for the purpose of estimating the primary current density vector field, i.e. finding a solution of the inverse problem of EEG generation. As a technique for inferring the unobserved high-dimensional primary current density field from EEG data of much lower dimension, a linear state space modelling approach is suggested, based on a generalisation of Kalman filtering, in combination with maximum-likelihood parameter estimation. The resulting algorithm for estimating dynamical solutions of the EEG inverse problem is applied to the task of localising the source of an epileptic spike from a clinical EEG data set; for comparison, we apply to the same task also a non-dynamical standard algorithm.

Asymmetric control mechanisms of bimanual coordination: an application of directed connectivity analysis to kinematic and functional MRI data.

Mirror-symmetrical bimanual movement is more stable than parallel bimanual movement. This is well established at the kinematic level. We used functional MRI (fMRI) to evaluate the neural substrates of the stability of mirror-symmetrical bimanual movement. Right-handed participants (n=17) rotated disks with their index fingers bimanually, both in mirror-symmetrical and asymmetrical parallel modes. We applied the Akaike causality model to both kinematic and fMRI time-series data. We hypothesized that kinematic stability is represented by the extent of neural "cross-talk": as the fraction of signals that are common to controlling both hands increases, the stability also increases. The standard deviation of the phase difference for the mirror mode was significantly smaller than that for the parallel mode, confirming that the former was more stable. We used the noise-contribution ratio (NCR), which was computed using a multivariate autoregressive model with latent variables, as a direct measure of the cross-talk between both the two hands and the bilateral primary motor cortices (M1s). The mode-by-direction interaction of the NCR was significant in both the kinematic and fMRI data. Furthermore, in both sets of data, the NCR from the right hand (left M1) to the left (right M1) was more prominent than vice versa during the mirror-symmetrical mode, whereas no difference was observed during parallel movement or rest. The asymmetric interhemispheric interaction from the left M1 to the right M1 during symmetric bimanual movement might represent cortical-level cross-talk, which contributes to the stability of symmetric bimanual movements.

Increased myocardial contractility and enhanced exercise function in transgenic mice overexpressing either adenylyl cyclase 5 or 8.

OBJECTIVE: ss-adrenergic receptors (ssARs) are powerful regulators of cardiac function in vivo, activating heterotrimeric G proteins and the effector molecule adenylyl cyclase (AC). Interestingly, cardiac-specific overexpression of different AC isoforms leads to variable changes in cardiac function. Whether AC overexpression affects intrinsic cardiac contractility in an isoform-specific fashion determining a change in exercise capacity is currently unknown. METHODS: To address this issue, we performed load-independent measurements of cardiac systolic and diastolic function by pressure-volume (PV) loop analysis in intact wild-type mice (WT) and transgenic mice overexpressing the AC isoforms 5 or 8. RESULTS: Here we show that cardiac overexpression of either AC5 or AC8 transgenic mice determined an increase in intrinsic cardiac contractility. Interestingly, AC8 transgenic mice displayed a significantly greater increase in cardiac contractility and improved active phase of relaxation. Despite these differences detected by PV loop analysis, both AC5 and AC8 mice showed a marked increase in exercise capacity on treadmill testing. CONCLUSIONS: Our results demonstrate that load-independent measurements of cardiac function are needed to compare different groups of genetically-modified mouse models and to detect subtle AC isoform-specific changes in cardiac performance.

Tissue inhibitor of metalloproteinase-3 deficiency inhibits blood pressure elevation and myocardial microvascular remodeling induced by chronic administration of Nomega-nitro-L-arginine methyl ester in mice.

Hypertension is a major risk factor for cardiovascular disease. Thus, prevention of hypertension and consequent organ damage is important for reducing its incidence. In the present study, we examined the involvement of tissue inhibitor of metalloproteinase-3 (Timp-3) in N(omega)-nitro-L-arginine methyl ester (L-NAME)-induced hypertension and accompanying vascular remodeling in mice. L-NAME was orally administered to wild-type (WT) and Timp-3 knockout (KO) mice for 6 weeks, blood pressure was monitored, and histological changes in myocardial arteries were examined. After L-NAME administration, blood pressure was lower in Timp-3 KO mice than in WT mice. The coronary arteries of WT and Timp-3 KO mice were similar after L-NAME treatment and showed no differences compared to untreated control mice. However, cardiac microvessels differed histologically between WT and Timp-3 KO mice. Vascular walls were less thickened in Timp-3 KO than in WT mice, and fibrotic changes were significantly reduced in Timp-3 KO mice. Moreover, the L-NAME-induced production of reactive oxygen species in cardiac microvessels was lower in Timp-3 KO than in WT mice. These results indicate that Timp-3 plays an important role in L-NAME-induced hypertension and myocardial vascular remodeling. Our findings suggest that Timp-3 may be a novel therapeutic target for the treatment of hypertension and consequent organ damage.

Akaike causality in state space. Instantaneous causality between visual cortex in fMRI time series.

We present a new approach of explaining instantaneous causality in multivariate fMRI time series by a state space model. A given single time series can be divided into two noise-driven processes, a common process shared among multivariate time series and a specific process refining the common process. By assuming that noises are independent, a causality map is drawn using Akaike noise contribution ratio theory. The method is illustrated by an application to fMRI data recorded under visual stimulation.

Tissue inhibitor of metalloproteinase-3 plays important roles in the kidney following unilateral ureteral obstruction.

Tissue inhibitor of metalloproteinase-3 (Timp-3), an inhibitor of matrix-degrading enzymes, is an important molecule for maintenance of the extracellular matrix. In this study, we generated Timp-3-deficient mice and used them to examine the effect of Timp-3-deficiency on blood pressure and to investigate the role of Timp-3 in the kidney following unilateral ureteral obstruction. The blood pressure and heart rate of Timp-3-deficient mice were not significantly different from those of wild-type mice. On the other hand, the obstructed kidneys of Timp-3-deficient mice developed more severe hydronephrosis than those of wild-type animals. Matrix metalloproteinase activities assessed by in situ zymography and transforming growth factor-beta expression were elevated in Timp-3-deficient mice. The renal tissues were thinner and the ratio of renal medulla to cortex was significantly lower in the obstructed Timp-3-deficient kidneys. These findings indicate that Timp-3-deficiency does not substantially affect the blood pressure in mice, and that Timp-3 plays an important role in the maintenance of renal macrostructure after unilateral ureteral obstruction.

Modelling non-stationary variance in EEG time series by state space GARCH model.

We present a new approach to modelling non-stationarity in EEG time series by a generalized state space approach. A given time series can be decomposed into a set of noise-driven processes, each corresponding to a different frequency band. Non-stationarity is modelled by allowing the variances of the driving noises to change with time, depending on the state prediction error within the state space model. The method is illustrated by an application to EEG data recorded during the onset of anaesthesia.

Evaluating frequency-wise directed connectivity of BOLD signals applying relative power contribution with the linear multivariate time-series models.

In this article, we propose a statistical method to evaluate directed interactions of functional magnetic-resonance imaging (fMRI) data. The multivariate autoregressive (MAR) model was combined with the relative power contribution (RPC) in this analysis. The MAR model was fitted to the data to specify the direction of connections, and the RPC quantifies the strength of connections. As the RPC is computed in the frequency domain, we can evaluate the connectivity for each frequency component. From this, we can establish whether the specified connections represent low- or high-frequency connectivity, which cannot be examined solely using the estimated MAR coefficients. We applied this analysis method to fMRI data obtained during visual motion tasks, confirming previous reports of bottom-up connectivity around the frequency corresponding to the block experimental design. Furthermore, we used the MAR model with exogenous variables (MARX) to extend our understanding of these data, and to show how the input to V1 transfers to higher cortical areas.

Possible involvement of enhanced intestinal microsomal triglyceride transfer protein (MTP) gene expression in acceleration of lipid absorption by a western-type diet in apolipoprotein E knockout mice.

Evidence has been accumulating that triglyceride (TG)-rich lipoproteins are atherogenic. Microsomal TG transfer protein (MTP) is essential for the synthesis of both chylomicron in the intestine and very low density lipoprotein in the liver. To investigate whether a western-type diet, a so-called atherogenic diet, alters intestinal lipid absorption via change in intestinal MTP expression, the effects of two different diet regimes in apolipoprotein-E knockout (apoE KO) mice were examined. Male apoE KO mice aged 6 weeks were fed a western-type diet or a chow diet for 5 weeks. Then, measurement of plasma TG levels after oral fat-loading and analysis of jejunal MTP gene expression were performed. Both the maximum level and the 0-8 h area under the curve (AUC) of the increase in TG levels in the western-type diet-fed mice were almost three times greater than those in the chow diet-fed mice. MTP gene expression, determined by reverse transcriptase-polymerase chain reaction (RT-PCR), was obviously enhanced in the western-type diet-fed mice compared to the chow diet-fed mice. These results suggest that the enhancement of intestinal MTP gene expression is involved in the accelerated lipid absorption in the western-type diet-fed mice.

A solution to the dynamical inverse problem of EEG generation using spatiotemporal Kalman filtering.

We present a new approach for estimating solutions of the dynamical inverse problem of EEG generation. In contrast to previous approaches, we reinterpret this problem as a filtering problem in a state space framework; for the purpose of its solution, we propose a new extension of Kalman filtering to the case of spatiotemporal dynamics. The temporal evolution of the distributed generators of the EEG can be reconstructed at each voxel of a discretisation of the gray matter of brain. By fitting linear autoregressive models with neighbourhood interactions to EEG time series, new classes of inverse solutions with improved resolution and localisation ability can be explored. For the purposes of model comparison and parameter estimation from given data, we employ a likelihood maximisation approach. Both for instantaneous and dynamical inverse solutions, we derive estimators of the time-dependent estimation error at each voxel. The performance of the algorithm is demonstrated by application to simulated and clinical EEG recordings. It is shown that by choosing appropriate dynamical models, it becomes possible to obtain inverse solutions of considerably improved quality, as compared to the usual instantaneous inverse solutions.

Recursive penalized least squares solution for dynamical inverse problems of EEG generation.

In the dynamical inverse problem of electroencephalogram (EEG) generation where a specific dynamics for the electrical current distribution is assumed, we can impose general spatiotemporal constraints onto the solution by casting the problem into a state space representation and assuming a specific class of parametric models for the dynamics. The Akaike Bayesian Information Criterion (ABIC), which is based on the Type II likelihood, was used to estimate the parameters and evaluate the model. In addition, dynamic low-resolution brain electromagnetic tomography (LORETA), a new approach for estimating the current distribution is introduced. A recursive penalized least squares (RPLS) step forms the main element of our implementation. To obtain improved inverse solutions, dynamic LORETA exploits both spatial and temporal information, whereas LORETA uses only spatial information. A considerable improvement in performance compared to LORETA was found when dynamic LORETA was applied to simulated EEG data, and the new method was applied also to clinical EEG data.

A state-space model of the hemodynamic approach: nonlinear filtering of BOLD signals.

In this paper, a new procedure is presented which allows the estimation of the states and parameters of the hemodynamic approach from blood oxygenation level dependent (BOLD) responses. The proposed method constitutes an alternative to the recently proposed Friston [Neuroimage 16 (2002) 513] method and has some advantages over it. The procedure is based on recent groundbreaking time series analysis techniques that have been, in this case, adopted to characterize hemodynamic responses in functional magnetic resonance imaging (fMRI). This work represents a fundamental improvement over existing approaches to system identification using nonlinear hemodynamic models and is important for three reasons. First, our model includes physiological noise. Previous models have been based upon ordinary differential equations that only allow for noise or error to enter at the level of observation. Secondly, by using the innovation method and the local linearization filter, not only the parameters, but also the underlying states of the system generating responses can be estimated. These states can include things like a flow-inducing signal triggered by neuronal activation, de-oxyhemoglobine, cerebral blood flow and volume. Finally, radial basis functions have been introduced as a parametric model to represent arbitrary temporal input sequences in the hemodynamic approach, which could be essential to understanding those brain areas indirectly related to the stimulus. Hence, thirdly, by inferring about the radial basis parameters, we are able to perform a blind deconvolution, which permits both the reconstruction of the dynamics of the most likely hemodynamic states and also, to implicitly reconstruct the underlying synaptic dynamics, induced experimentally, which caused these states variations. From this study, we conclude that in spite of the utility of the standard discrete convolution approach used in statistical parametric maps (SPM), nonlinear BOLD phenomena and unspecific input temporal sequences must be included in the fMRI analysis.

Vascular-targeted overexpression of G protein-coupled receptor kinase-2 in transgenic mice attenuates beta-adrenergic receptor signaling and increases resting blood pressure.

Cardiovascular regulation is tightly controlled by signaling through G protein-coupled receptors (GPCRs). beta-Adrenergic receptors (ARs) are GPCRs that regulate inotropy and chronotropy in the heart and mediate vasodilation, which critically influences systemic vascular resistance. GPCR kinases (GRKs), including GRK2 (or betaARK1), phosphorylate and desensitize agonist-activated betaARs. Myocardial GRK2 levels are increased in heart failure and data suggest that vascular levels may also be elevated in hypertension. Therefore, we generated transgenic mice with vascular smooth muscle (VSM) targeted overexpression of GRK2, using a portion of the SM22alpha promoter, to determine its impact on vascular betaAR regulation. VSM betaAR signaling, as determined by adenylyl cyclase and mitogen-activated protein (MAP) kinase activation assays, was attenuated when GRK2 was overexpressed 2- to 3-fold. In vivo vasodilation in response to betaAR stimulation using isoproterenol was attenuated and conscious resting mean arterial blood pressure was elevated from 96 +/- 2 mm Hg in nontransgenic littermate control (NLC) mice (n = 9) to 112 +/- 3 mm Hg and 117 +/- 2 mm Hg in two different lines of SM22alpha-GRK2 transgenic mice (n = 7 and n = 5, respectively; p < 0.05). Interestingly, medial VSM thickness was increased 30% from 29.8 +/- 1.6 microm in NLC mice (n = 6) to 39.4 +/- 1.6 microm in SM22alpha-GRK2 mice (n = 7) (p < 0.05) and vascular GRK2 overexpression was sufficient to cause cardiac hypertrophy. These data indicate that we have developed a unique mouse model of hypertension, providing insight into the contribution that vascular betaAR signaling makes toward resting blood pressure and overall cardiovascular regulation. Moreover, they suggest that GRK2 plays an important role in vascular control and may represent a novel therapeutic target for hypertension.