Dynamic metabolomic data analysis: a tutorial review

In metabolomics, time-resolved, dynamic or temporal data is more and more collected. The number of methods to analyze such data, however, is very limited and in most cases the dynamic nature of the data is not even taken into account. This paper reviews current methods in use for analyzing dynamic metabolomic data. Moreover, some methods from other fields of science that may be of use to analyze such dynamic metabolomics data are described in some detail. The methods are put in a general framework after providing a formal definition on what constitutes a 'dynamic' method. Some of the methods are illustrated with real-life metabolomics examples.

Data processing for noninvasive continuous glucose monitoring with a multisensor device

BACKGROUND

Impedance spectroscopy has been shown to be a candidate for noninvasive continuous glucose monitoring in humans. However, in addition to glucose, other factors also have effects on impedance characteristics of the skin and underlying tissue.

METHOD

Impedance spectra were summarized through a principal component analysis and relevant variables were identified with Akaike's information criterion. In order to model blood glucose, a linear least-squares model was used. A Monte Carlo simulation was applied to examine the effects of personalizing models.

RESULTS

The principal component analysis was able to identify two major effects in the impedance spectra: a blood glucose-related process and an equilibration process related to moisturization of the skin and underlying tissue. With a global linear least-squares model, a coefficient of determination (R²) of 0.60 was achieved, whereas the personalized model reached an R² of 0.71. The Monte Carlo simulation proved a significant advantage of personalized models over global models.

CONCLUSION

A principal component analysis is useful for extracting glucose-related effects in the impedance spectra of human skin. A linear global model based on Solianis Multisensor data yields a good predictive power for blood glucose estimation. However, a personalized linear model still has greater predictive power.

Two novel PET image restoration methods guided by PET-MR kernels: Application to brain imaging

PURPOSE

Post-reconstruction positron emission tomography (PET) image restoration methods that take advantage of available anatomical information can play an important role in accurate quantification of PET images. However, when using anatomical information, the resulting PET image may lose resolution in certain regions where the anatomy does not agree with the change in functional activity. In this work, this problem is addressed by using both magnetic resonance (MR) and filtered PET images to guide the denoising process.

METHODS

In this work, two novel post-reconstruction methods for restoring PET images using the subject's registered T1-weighted MR image are proposed. The first method is based on a representation of the image using basis functions extracted from T1-weighted MR and filtered PET image. The coefficients for these basis functions are estimated using a sparsity-penalized least squares objective function. The second method is a noniterative fast method that uses guided kernel filtering in combination with twicing to restore the noisy PET image. When applied after conventional PVE correction, these methods can be considered as voxel-based MR-guided partial volume effect (PVE) correction methods.

RESULTS

Using simulation analyses of [ 18 F]FDG PET images of the brain with lesions, the proposed methods are compared to other denoising methods through different figures of merit. The results show promising improvements in image quality as well as reduction in bias and variance of the lesions. We also show the application of the proposed methods on real [ 18 F]FDG data.

CONCLUSION

Two methods for restoring PET images were proposed. The methods were evaluated on simulation and real brain images. Most MR-guided PVE correction methods are only based on segmented T1-weighted images and their accuracy is very sensitive to segmentation errors, especially in regions of abnormalities and lesions. However, both proposed methods can use the T1-weighted image without segmentation. The simplicity and the very low computational cost of the second method make it suitable for clinical applications and large data studies. The proposed methods can be naturally extended to PVE correction and denoising of other functional modalities using corresponding anatomical information.

Comparison of basis functions and q-space sampling schemes for robust compressed sensing reconstruction accelerating diffusion spectrum imaging

Time constraints placed on magnetic resonance imaging often restrict the application of advanced diffusion MRI (dMRI) protocols in clinical practice and in high throughput research studies. Therefore, acquisition strategies for accelerated dMRI have been investigated to allow for the collection of versatile and high quality imaging data, even if stringent scan time limits are imposed. Diffusion spectrum imaging (DSI), an advanced acquisition strategy that allows for a high resolution of intra-voxel microstructure, can be sufficiently accelerated by means of compressed sensing (CS) theory. CS theory describes a framework for the efficient collection of fewer samples of a data set than conventionally required followed by robust reconstruction to recover the full data set from sparse measurements. For an accurate recovery of DSI data, a suitable acquisition scheme for sparse q-space sampling and the sensing and sparsifying bases for CS reconstruction need to be selected. In this work we explore three different types of q-space undersampling schemes and two frameworks for CS reconstruction based on either Fourier or SHORE basis functions. After CS recovery, diffusion and microstructural parameters and orientational information are estimated from the reconstructed data by means of state-of-the-art processing techniques for dMRI analysis. By means of simulation, diffusion phantom and in vivo DSI data, an isotropic distribution of q-space samples was found to be optimal for sparse DSI. The CS reconstruction results indicate superior performance of Fourier-based CS-DSI compared to the SHORE-based approach. Based on these findings we outline an experimental design for accelerated DSI and robust CS reconstruction of the sparse measurements that is suitable for the application within time-limited studies.

Model Comparison Metrics Require Adaptive Correction if Parameters Are Discretized: Proof-of-Concept Applied to Transient Signals in Dynamic PET

Linear parametric neurotransmitter PET (lp-ntPET) is a novel kinetic model that estimates the temporal characteristics of a transient neurotransmitter component in PET data. To preserve computational simplicity in estimation, the parameters of the nonlinear term that describe this transient signal are discretized, and only a limited set of values for each parameter are allowed. Thus, linear estimation can be performed. Linear estimation is implemented using predefined basis functions that incorporate the discretized parameters. The implementation of the model using discretized parameters poses unique challenges for significance testing. Significance testing employs model comparison metrics to determine the significance of the improvement of the fit accomplished by including a basis function, i.e. it determines the presence of a transient signal in the PET data. A false positive occurs when the bases overfit data that do not contain a transient component. The number of parameters in a model, p, is necessary to determine the degrees of freedom in the model. In turn, p is crucial for the calculation of model selection metrics and controlling the false positive rate (FPR). In this work, we first explore the effect of parameter discretization on FPR by fitting simulated null data with varying numbers of bases. We demonstrate the dependence of FPR on number of bases. Then, we propose a correction to the number of parameters in the model, p^eff , which adapts to the number of bases used. Implementing model selection with p^eff maintains a stable FPR independent of number of bases.

Basis function model to extract the combined confocal and fall-off function from multiple optical coherence tomography A-scans

Significance

Many derivatives of optical coherence tomography (OCT) rely on the depth-dependent information of the sample in the image. System depth-dependent effects, such as the confocal effect and the sensitivity fall-off, should be corrected to improve the accuracy of the images and information derived from them.

Aim

We developed a new single-shot method to extract the combined confocal and fall-off functions and remove system-generated depth-dependent effects from OCT images.

Approach

The combined function is modeled as a linear combination of basis functions whose coefficients are found from two or more A-scans (or B-scans) of a sample that are vertically shifted within the imaging range. No prior knowledge of the OCT system parameters or assumed form for the confocal and fall-off functions is needed.

Results

The method was derived and validated with simulations and OCT images of a phantom, a biological sample, and human retina. Improvement over the Ratio Fit method was demonstrated.

Conclusions

The improvement in the extraction of the combined confocal and fall-off effects by this method should lead to improved medical diagnosis through more accurate attenuation coefficient calculations. The method enables future applications of OCT where precise removal of all depth-dependent effects on OCT images is critical.

Basis function compression for field probe monitoring

PURPOSE

Field monitoring using field probes allows for accurate measurement of magnetic field perturbations, such as from eddy currents, during MRI scanning. However, errors may result when the spatial variation of the fields is not well-described by the conventionally used spherical harmonics model that has the maximum order constrained by the number of probes. The objective of this work was to develop and validate a field monitoring approach that compresses higher order spherical harmonics into a smaller set of new basis functions that can be characterized using fewer probes.

METHODS

Field monitoring of acquisitions was repeated with probes in different locations. High-order field dynamics were computed from this "calibration" data assembled from provided scans, from which compression matrices could be devised using principal component analysis. Compression matrices were then used to fit field dynamics using "compressed" basis functions with data from 16 probes, which were then used in image reconstruction. Performance was evaluated by assessing the accuracy of computed field dynamics as well as in vivo image quality. Technique generalizability was also assessed by using various acquisition and diffusion encoding strategies in the calibration.

RESULTS

Qualitative and quantitative improvements in accuracy were observed when using the proposed fitting method compared to the conventional approach. However, compression effectiveness was influenced by the probe quantity and arrangement, and the specific acquisition data included in the calibration.

CONCLUSION

The ability to tailor basis functions to more compactly describe the spatial variation of field perturbations enables improved characterization of fields with rapid spatial variations.

PM2.5 Concentrations Variability in North China Explored with a Multi-Scale Spatial Random Effect Model

Compiling fine-resolution geospatial PM_2.5 concentrations data is essential for precisely assessing the health risks of PM_2.5 pollution exposure as well as for evaluating environmental policy effectiveness. In most previous studies, global and local spatial heterogeneity of PM_2.5 is captured by the inclusion of multi-scale covariate effects, while the modelling of genuine scale-dependent variabilities pertaining to the spatial random process of PM_2.5 has not yet been much studied. Consequently, this work proposed a multi-scale spatial random effect model (MSSREM), based a recently developed fixed-rank Kriging method, to capture both the scale-dependent variabilities and the spatial dependence effect simultaneously. Furthermore, a small-scale Monte Carlo simulation experiment was conducted to assess the performance of MSSREM against classic geospatial Kriging models. The key results indicated that when the multiple-scale property of local spatial variabilities were exhibited, the MSSREM had greater ability to recover local- or fine-scale variations hidden in a real spatial process. The methodology was applied to the PM_2.5 concentrations modelling in North China, a region with the worst air quality in the country. The MSSREM provided high prediction accuracy, 0.917 R-squared, and 3.777 root mean square error (RMSE). In addition, the spatial correlations in PM_2.5 concentrations were properly captured by the model as indicated by a statistically insignificant Moran's I statistic (a value of 0.136 with p-value > 0.2). Overall, this study offers another spatial statistical model for investigating and predicting PM_2.5 concentration, which would be beneficial for precise health risk assessment of PM_2.5 pollution exposure.