Biomedical subjects

Rob M Heethaar

Publications and source records attributed to Rob M Heethaar.

5 recordsLinked to original sources

PubMed2006

DENSE and HARP: two views on the same technique of phase-based strain imaging.

PURPOSE: To discuss differences between displacement encoding with stimulated echoes (DENSE) and the harmonic phase (HARP) in imaging and reconstruction strategies. MATERIALS AND METHODS: HARP and DENSE are presented in their historical context: while the HARP method was developed from the framework of myocardial tagging, DENSE arose from the framework of stimulated echo and displacement encoding using bipolar gradients. Both techniques have evolved since their introduction, thereby becoming more similar over time and losing their distinct features. Newly introduced improvements have successfully been applied in both methods. Differences between both methods are discussed point by point. RESULTS: From this discussion it follows that almost all apparent differences are in fact nonexistent. CONCLUSION: In the literature, both techniques are still regarded as distinctly different techniques, where a more general treatment of the technique is justified. Once it is realized that both frameworks are easily merged, the benefits are 1) less confusion about the (dis)advantages of either technique, and 2) understanding of phase-based strain imaging that is more general than HARP or DENSE alone.

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PubMed2005

The spatiotemporal MEG covariance matrix modeled as a sum of Kronecker products.

The single Kronecker product (KP) model for the spatiotemporal covariance of MEG residuals is extended to a sum of Kronecker products. This sum of KP is estimated such that it approximates the spatiotemporal sample covariance best in matrix norm. Contrary to the single KP, this extension allows for describing multiple, independent phenomena in the ongoing background activity. Whereas the single KP model can be interpreted by assuming that background activity is generated by randomly distributed dipoles with certain spatial and temporal characteristics, the sum model can be physiologically interpreted by assuming a composite of such processes. Taking enough terms into account, the spatiotemporal sample covariance matrix can be described exactly by this extended model. In the estimation of the sum of KP model, it appears that the sum of the first 2 KP describes between 67% and 93%. Moreover, these first two terms describe two physiological processes in the background activity: focal, frequency-specific alpha activity, and more widespread non-frequency-specific activity. Furthermore, temporal nonstationarities due to trial-to-trial variations are not clearly visible in the first two terms, and, hence, play only a minor role in the sample covariance matrix in terms of matrix power. Considering the dipole localization, the single KP model appears to describe around 80% of the noise and seems therefore adequate. The emphasis of further improvement of localization accuracy should be on improving the source model rather than the covariance model.

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PubMed2004

The coupled dipole model: an integrated model for multiple MEG/EEG data sets.

Often MEG/EEG is measured in a few slightly different conditions to investigate the functionality of the human brain. This kind of data sets show similarities, though are different for each condition. When solving the inverse problem (IP), performing the source localization, one encounters the problem that this IP is ill-posed: constraints are necessary to solve and stabilize the solution to the IP. Moreover, a substantial amount of data is needed to avoid a signal to noise ratio (SNR) that is too poor for source localizations. In the case of similar conditions, this common information can be exploited by analyzing the data sets simultaneously. The here proposed coupled dipole model (CDM) provides an integrated method in which these similarities between conditions are used to solve and stabilize the inverse problem. The coupled dipole model is applicable when data sets contain common sources or common source time functions. The coupled dipole model uses a set of common sources and a set of common source time functions (STFs) to model all conditions in one single model. The data of each condition are mathematically described as a linear combination of these common spatial and common temporal components. This linear combination is specified in a coupling matrix for each data set. The coupled dipole model was applied in two simulation studies and in one experimental study. The simulations show that the errors in the estimated spatial and temporal parameters decrease compared to the standard separate analyses. A decrease in position error of a factor of 10 was shown for the localization of two nearby sources. In the experimental application, the coupled dipole model was shown to be necessary to obtain a plausible solution in at least 3 of 15 conditions investigated. Moreover, using the CDM, a direct comparison between parameters in different conditions is possible, whereas in separate models, the scaling of the amplitude parameters varies in general from data set to data set.

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PubMed2003

A mathematical approach to the temporal stationarity of background noise in MEG/EEG measurements.

The general spatiotemporal covariance matrix of the background noise in MEG/EEG signals is huge. To reduce the dimensionality of this matrix it is modeled as a Kronecker product of a spatial and a temporal covariance matrix. When the number of time samples is larger than, say, J = 500, the iterative Maximum Likelihood estimation of these two matrices is still too time-consuming to be useful on a routine basis. In this study we looked for methods to circumvent this computationally expensive procedure by using a parametric model with subject-dependent parameters. Such a model would additionally help with interpreting MEG/EEG signals. For the spatial covariance, models have been derived already and it has been shown that measured MEG/EEG signals can be understood spatially as random processes, generated by random dipoles. The temporal covariance, however, has not been modeled yet, therefore we studied the temporal covariance matrix in several subjects. For all subjects the temporal covariance shows an alpha oscillation and vanishes for large time lag. This gives rise to a temporal noise model consisting of two components: alpha activity and additional random noise. The alpha activity is modeled as randomly occurring waves with random phase and the covariance of the additional noise decreases exponentially with lag. This model requires only six parameters instead of 12 J(J + 1). Theoretically, this model is stationary but in practice the stationarity of the matrix is highly influenced by the baseline correction. It appears that very good agreement between the data and the parametric model can be obtained when the baseline correction window is taken into account properly. This finding implies that the background noise is in principle a stationary process and that nonstationarities are mainly caused by the nature of the preprocessing method. When analyzing events at a fixed sample after the stimulus (e.g., the SEF N20 response) one can take advantage of this nonstationarity by optimizing the baseline window to obtain a low noise variance at this particular sample.

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PubMed2003

In vivo measurement of the brain and skull resistivities using an EIT-based method and realistic models for the head.

In vivo measurements of equivalent resistivities of skull (rho(skull)) and brain (rho(brain)) are performed for six subjects using an electric impedance tomography (EIT)-based method and realistic models for the head. The classical boundary element method (BEM) formulation for EIT is very time consuming. However, the application of the Sherman-Morrison formula reduces the computation time by a factor of 5. Using an optimal point distribution in the BEM model to optimize its accuracy, decreasing systematic errors of numerical origin, is important because cost functions are shallow. Results demonstrate that rho(skull)/rho(brain) is more likely to be within 20 and 50 rather than equal to the commonly accepted value of 80. The variation in rho(brain)(average = 301 omega x cm, SD = 13%) and rho(skull)(average = 12230 omega x cm, SD = 18%) is decreased by half, when compared with the results using the sphere model, showing that the correction for geometry errors is essential to obtain realistic estimations. However, a factor of 2.4 may still exist between values of rho(skull)/rho(brain) corresponding to different subjects. Earlier results show the necessity of calibrating rho(brain) and rho(skull) by measuring them in vivo for each subject, in order to decrease errors associated with the electroencephalogram inverse problem. We show that the proposed method is suited to this goal.

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