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Edited by: Qingming Luo, Huazhong University of Science and Technology-Wuhan National Laboratory for Optoelectronics, China

Reviewed by: Jussi Tohka, Universidad Carlos III de Madrid, Spain; Anan Li, Huazhong University of Science and Technology, China

*Correspondence: Pedro Rosa-Neto

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

In healthy individuals, behavioral outcomes are highly associated with the variability on brain regional structure or neurochemical phenotypes. Similarly, in the context of neurodegenerative conditions, neuroimaging reveals that cognitive decline is linked to the magnitude of atrophy, neurochemical declines, or concentrations of abnormal protein aggregates across brain regions. However, modeling the effects of multiple regional abnormalities as determinants of cognitive decline at the voxel level remains largely unexplored by multimodal imaging research, given the high computational cost of estimating regression models for every single voxel from various imaging modalities. VoxelStats is a voxel-wise computational framework to overcome these computational limitations and to perform statistical operations on multiple scalar variables and imaging modalities at the voxel level. VoxelStats package has been developed in Matlab^{®} and supports imaging formats such as Nifti-1, ANALYZE, and MINC v2. Prebuilt functions in VoxelStats enable the user to perform voxel-wise general and generalized linear models and mixed effect models with multiple volumetric covariates. Importantly, VoxelStats can recognize scalar values or image volumes as response variables and can accommodate volumetric statistical covariates as well as their interaction effects with other variables. Furthermore, this package includes built-in functionality to perform voxel-wise receiver operating characteristic analysis and paired and unpaired group contrast analysis. Validation of VoxelStats was conducted by comparing the linear regression functionality with existing toolboxes such as glim_image and RMINC. The validation results were identical to existing methods and the additional functionality was demonstrated by generating feature case assessments (t-statistics, odds ratio, and true positive rate maps). In summary, VoxelStats expands the current methods for multimodal imaging analysis by allowing the estimation of advanced regional association metrics at the voxel level.

Research studies based on multiple neuroimaging modalities in the same individual (multimodal acquisition) is becoming increasingly popular due to the widespread availability of imaging techniques such as Magnetic Resonance Imaging (MRI) and Positron Emission Tomography (PET). The availability of ample computational resources permits the widespread use of analytical algorithms performing voxel-wise statistical operations where each voxel is treated as a Region-of-Interest (ROI; Friston,

Multiparametric imaging research brings the hope of a comprehensive understanding of the dynamic neurodegenerative processes in the human brain. Imaging has the power to provide longitudinal information regarding the accumulation of toxic proteins in the brain as well as the degeneration associated with disease processes. This information is virtually absent in postmortem evaluations given its intrinsic cross sectional nature. Furthermore, it has been shown that clinical symptoms of neurodegenerative diseases such as Alzheimer's (AD) or Parkinson's disease (PD) constitute a late event on the progression of the disease process given the amount of brain damage present in symptomatic individuals. In the context of longitudinal studies, multiparametric imaging analysis would serve to identify signatures of imminent clinical progression and determine the optimal scenario for a disease modifying intervention. Such information is crucial for designing clinical trials. For instance, the widely accepted pathophysiological model of AD involves a cascade of events initialized by the accumulation of a protein called amyloid (measured by PET ligands such as [^{11}C]Pittsburgh Compound B ([^{11}C]PIB), [^{18}F]Florbetapir) and subsequent neurodegenerative events involving hypo-metabolism [measured by PET ligands such as [^{18}F] Fludeoxyglucose ([^{18}F]FDG)], atrophy, accumulation of neurofibrillary tangles, neuro-inflammation, and many other neurochemical changes (Jack et al., ^{18}F]Florbetapir PET and [^{18}F]FDG PET images in patients in multiple stages of dementia (Engler et al.,

In this article we present an approach to multimodal integrative image analyses using VoxelStats statistical framework. This framework facilitates the investigation of neuroimaging data using information from other functional or structural imaging modalities. Furthermore, VoxelStats framework allows probing the interactive and mediating effects between imaging modalities and performing sophisticated mathematical operations at the voxel level. The application of the methods facilitated by VoxelStats provides a powerful tool for studies which require multimodal information including, but not limited to, studies for neurodegenerative disorders as mentioned above, neuropsychiatric disorders, and brain injury.

VoxelStats is a statistical framework for voxel-wise operations written in Matlab with existing support for Nifti-1 (Cox et al.,

The primary objective of VoxelStats is to serve as a framework to facilitate image based statistical modeling at a voxel level. Its users can utilize the supplied utility functions to perform trivial tasks such as file input/output, artificial parcellation of data for parallel computation, etc. while the main computational task will be carried out by a built in Matlab function. This architectural design has enabled VoxelStats toolbox to be computationally accurate and highly scalable as a framework to support a vast array of functionality, and would allow for seamless integration into existing Matlab pipelines.

The primary challenges encountered when performing voxel-wise mathematical operations are the computational time and the memory requirement. These challenges have been addressed in existing voxel-wise statistical toolkits by implementing specialized regression algorithms for multi-dimensional analyses. With the architectural design to utilize Matlab's built-in methods to perform the primary operation, VoxelStats has increased the scalability of the framework to support sophisticated statistical operations. However, it has increased the time and memory requirement for the statistical operation.

To overcome the computational time limitation, VoxelStats utilizes data parallelism techniques through the Matlab parallel computing toolbox and the Matlab distributed computing server, with artificial parcellation of data to reduce the memory and network footprint. The artificial parcellation step splits and transforms the masked volumetric data from image space to a process space, which contains a predefined number of parcellations and a uniform number of voxels in each parcellation (Figure

^{−1}).

The number of artificial parcellations has been set to 200 and has been calculated based on the performance of the framework on the development setup; a Matlab computing cluster with 5 nodes/32 workers and volumetric images resampled to the MNI 152 (Fonov et al.,

Prebuilt statistical operations in VoxelStats use the utility functions to perform trivial operations including reading and writing volumetric data and mask information while the computational operations are performed using Matlab's own implementations. Although the manner in which the framework can be utilized is conditional on the analysis performed, the prebuilt functions follow a similar procedural structure differing only to allow function-specific operations.

Two prebuilt functions are available to perform voxel-wise statistical group differences; one for unpaired

Both statistical group difference procedures use this string argument to refine the input samples which will be included in the analysis. This step is followed by the evaluation of the volume information from the provided mask file, which will be used in multiple steps of the analysis including extracting volumetric data from subject files and performing voxel-wise statistical analysis. Subsequently, grouping information is evaluated and the volumetric data is read based on the mask information provided. Unpaired

Four prebuilt functions are available to perform voxel-wise linear regression analysis, generalized linear regression analysis, and general/generalized mixed effects regression analysis with support for voxel-wise predictor and covariate effects. Analogous to statistical difference procedures, these functions follow the filtering string argument to refine the sample set. This step is followed by parsing the statistical model string to identify the variables used in the mathematical model. Subsequently, the mask information is read, and the volumetric data from the subject files are read based on the variable information and the mask information provided. This step is followed by performing any operation (arithmetic operations such as negation, inverse, scalar addition, or multiplication) specified by the user on the subject data extracted. Subsequently a sample regression (single voxel) is performed to identify the output parameters such as the number of output variables and their names.

Following this step, the extracted voxel data are artificially parcellated, and the voxel-wise statistical operation is performed using Matlab's “fitlm,” “fitlme,” “fitglm,” and “fitglme” functions for linear regression analysis, mixed effects regression analysis, generalized linear regression analysis, and generalized mixed effects regression analysis, respectively, utilizing the Matlab parallel computing toolbox and Matlab distributed computing server.

The function that performs voxel-wise ROC analysis follows the steps adapted from the regression functions by evaluating the sample filtering string argument mentioned earlier, followed by extracting the mask information and corresponding subject volumetric data. Subsequently, grouping information is evaluated and the extracted volumetric data are artificially parcellated similar to the regression function. Matlab's “perfcurve” method is utilized to carry out the ROC analysis.

Statistical inference based on the results from any massively univariate analysis resulting in voxel wise hypothesis testing must be preceded by multiple comparison correction to reduce the family wise error (FWE). VoxelStats framework provides functionality to perform cluster based multiple comparisons correction based on Random Field Theory (RFT; Worsley et al.,

Commands to perform statistical operations in VoxelStats are designed to be intuitive and convenient to increase the ease of accessibility and user-friendliness. This reduces the complexity of the functions in VoxelStats, allowing rapid prototyping of statistical hypotheses with minimal programming fluency. In addition, VoxelStats includes a graphical user interface (GUI; Figure

At present, inputs to VoxelStats must be 3D volumetric images with the same image resolution (in voxels). This includes any volumetric response variables, predictor variables, covariates, and the image mask. Furthermore, it is expected that all the images are spatially normalized to a common image space and appropriately smoothed. Example input image modalities include, but not limited to, Fractional anisotropy (FA) images, Mean Diffusivity (MD) images, Voxel, or Deformation based morphometric images (DBM or VBM), PET Binding Potential (BP), or Standardized Uptake Value Ratio (SUVR) images, PET, or Single-photon emission computed tomography (SPECT) volume of distribution images and cerebral blood flow images.

To compare VoxelStats with other available toolboxes, neuroimaging data ([^{18}F]Florbetapir PET, [^{18}F]FDG PET, T1-MRI) were acquired for 273 individuals from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Demographic (clinical classification, age, gender) and neurophysiological assessments [mini–mental state examination (MMSE), Clinical Dementia Rating Scale Sum of Boxes scores (CDR-SOB)] were also obtained for the same individuals to be included in the regression models. ADNI was launched in 2003 as a public-private partnership, led by Principal Investigator Michael W. Weiner, MD. The primary goal of ADNI has been to test whether serial MRI, PET, other biological markers, and clinical and neuropsychological assessment can be combined to measure the progression of mild cognitive impairment (MCI) and early Alzheimer's disease (AD).

T1 neuroimaging data were processed using the CIVET image processing pipeline (Zijdenbos et al.,

Linear regression with volumetric dependent variable | 273 | |

Linear regression with volumetric independent and dependent variables | 219 | |

Logistic regression with volumetric independent variable (binary dependent variable) | 273 | |

Linear regression with continuous dependent variable and the interaction two volumetric variables | 219 | |

Voxel-wise ROC analysis | Decision Variable |
273 |

Evaluating the computational accuracy of VoxelStats was performed using a linear regression analysis with 273 samples, using volumetric data as the dependent variable. The regression model contained one predictor scalar variable, one continuous scalar covariate and one factor covariate. The result was then compared with other toolboxes available for MINC v2 volumes; glim_image and RMINC. Two parallelization configurations [one to utilize 12 processing cores in a single computational node and the other to utilize 32 processing cores in 5 different computational nodes in a network (see Supplementary Materials)] for VoxelStats have been compared with the aforementioned toolboxes.

T-statistic image from VoxelStats for the statistical significance of the model parameter (β_{1}) for the variable MMSE score is shown in Figure

Results from the additional feature case analysis of VoxelStats are shown in Figure ^{18}F]Florbetapir PET using generalized linear regression with a volumetric independent variable model, statistical significance of the model parameter for the interaction of [^{18}F]Florbetapir PET and [^{18}F]FDG PET using linear regression with interaction of volumetric variables model, and the true positive rate based on [^{18}F]Florbetapir PET for development of dementia using the volumetric ROC analysis. It is important to mention that the parameters of the statistical models are calculated by comparing the same voxel in the dependent and the independent volumetric variables. Although not demonstrated, the utility of the general and generalized regression features can be further expanded with mixed effect modeling to incorporate longitudinal study designs. Statistical maps in Figures

^{18}F]FDG PET. ^{18}F] Florbetapir PET SUVR. ^{18}F]Florbetapir PET and [^{18}F] FDG PET for the association with CDR-SOB. ^{18}F] Florbetapir PET SUVR in classifying individual developing dementia in 24 months.

Figure ^{18}F]FDG PET. Based on the images, it can be concluded that the glucose metabolism is associated with the gray-matter density of the particular region. Figure ^{18}F]Florbetapir PET and [^{18}F]FDG PET is evaluated, while including Age, Gender, and the main effects of both [^{18}F]Florbetapir PET and [^{18}F]FDG PET in the statistical model. It should be noted that the [^{18}F]FDG PET measures have been negated using VoxelStats variable operations prior to the statistical modeling to increase the interpretability of the interaction analysis, as the expected relationship of the CDR-SOB and [^{18}F]FDG PET is inversed. The resultant images highlight that the interaction of [^{18}F]Florbetapir PET and [^{18}F]FDG PET in brain regions such as the posterior cingulate cortex (PCC) has a positive association with the CDR-SOB test score. Another important feature of VoxelStats is the ability to perform generalized linear modeling with multiple volumetric covariates. This functionality enables the user to perform a vast array of sophisticated association studies using neuroimaging data. Similar to the general linear modeling, these prebuilt functions support any type of dependent variable (voxel-wise or subject wise) and the interaction among any independent variables. Figure ^{18}F]Florbetapir PET images. Based on the results, the regions such as the the Precuneus, PCC, parts of the temporal lobe and frontal cortex have the highest odds ratios of developing dementia with the increase of [^{18}F]Florbetapir PET SUVR. The ability to perform generalized linear regression enables the user to perform a vast array of association studies using neuroimaging data involving response variables derived from distributions such as Binomial, Poisson, Gamma, or Inverse Gaussian. Another important feature in VoxelStats is the ability to perform voxel-wise ROC analyses to identify the brain regions that have the highest differentiation between two classes based on the classifying performance of an imaging measurement. Figure ^{18}F]Florbetapir PET images to classify individuals who develop dementia within 24 months. Based on the result, [^{18}F]Florbetapir PET measurements from brain regions such as the Precuneus, cingulate, medial frontal, and temporal cortices have the highest classification ability.

VoxelStats is a statistical framework that enables sophisticated voxel-wise operations using multispectral neuroimaging datasets that can be used to answer a multitude of research questions. At present, VoxelStats includes prebuilt functions to perform common statistical operations including general and generalized linear modeling with mixed effects, which can lead to new insights in the analysis of longitudinal neuroimaging data. Its ability to work as an independent Matlab toolbox and the support for Nifti-1, ANALYZE, and MINC v2 format volumes will make VoxelStats immediately useful in the neuroimaging community.

Although ROI-based correction for imaging variables can be considered viable for correcting regional differences, tools similar to VoxelStats will ensure that imaging matrices from one brain region is corrected only for the behavior within the same region. This method also enables voxel-wise independent statistical modeling to assess the relationship between multiple imaging modalities as well as non-imaging measurements such as fluid biomarkers, neurophysiological assessments, and clinical outcomes.

The aforementioned existing toolboxes have limited functionality to perform sophisticated voxel-wise statistical operations, particularly generalized linear modeling and the support for volumetric covariates and their interactions. In Oakes et al. (

The example used in this article to evaluate the accuracy of VoxelStats is a typical use case in a voxel-wise statistical analysis where a volumetric dependent variable is regressed against one other independent measurement from each individual to identify the brain regions that are associated with the independent measurement. Although the results from VoxelStats are identical to the results from existing toolboxes, it falls behind in time required, due to the architectural design to incorporate built-in Matlab procedures. However, this architectural design has enabled VoxelStats toolbox to be computationally accurate and scalable as a framework to support a vast array of functionalities. The average memory usage of VoxelStats across all the computational nodes during all the analyses was less than 8 GB.

VoxelStats toolbox has many potential uses and while it would not be possible to demonstrate all of the use cases, it is worthwhile to mention the principle feature cases for which VoxelStats can be used (Table

General linear model | ✓ | ✓ | ✓ | ✓ |

Generalized linear models | ✓ | |||

Voxel-wise independent variables | ✓ | ^{a} |
||

Interactions of voxel-wise variables | ||||

Scalar response variables | ||||

User friendly commands/interface | ✓ | ✓^{b} |
✓ | |

Multiple comparison correction | ✓ | ✓ | ✓ | |

Results visualization | ✓ | ✓ | ✓ | |

Nifti file format support | ✓ | ✓ | ||

ANALYZE file format support | ✓ | ✓ | ||

MINC file format support | ✓ | ✓ | ✓ |

The voxel-wise ROC analysis based on amyloid-β deposition and the clinical progression can be considered as an example to identify region specific [^{18}F]Florbetapir PET thresholds which will be valuable in enrichment of study populations in clinical trials (Carbonell et al.,

Due to the amount of statistical computations performed, one of the biggest challenges in VoxelStats is the computational time of the analysis. Although the time required to complete an analysis is acceptable as recorded, it can be further reduced by utilizing the modern grid/cluster computing environments. Other toolboxes developed for neuroimage processing and analysis such as NIAK (web:

One other challenge that needs to be mentioned is the accuracy of the co-registration required between different imaging modalities. As each of the voxel-wise calculation assumes that the information is originated from the same region of the brain, inaccurate or suboptimal image registration will reduce the accuracy of the result. This challenge has been effectively addressed by the advanced image registration algorithms such as DARTEL (Ashburner,

At present, VoxelStats framework supports 3-dimensional volumetric images, therefore analysis using higher dimensional neuroimaging data [functional MRI, dynamic PET, diffusion tensor imaging (DTI)] cannot be performed. However, the support for multidimensional volumetric images are expected to be included in a future release of VoxelStats. VoxelStats also requires the image variables and the image mask used in a single analysis to have the same resolution (in voxels). Users can download the VoxelStats framework as a freely available Matlab library from

VoxelStats framework expands the current multimodal neuroimaging analysis possibilities by enabling the testing of sophisticated image-based hypotheses incorporating multiple imaging modalities simultaneously and response variables from normal, binomial, poisson, gamma, or inverse gaussian distributions. To this extent, VoxelStats framework bests the functional specific or modal specific limitations of existing neuroimaging analysis software.

Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at:

SM, TP, SG, and PR were responsible for the tool concept and design. SM and SW were responsible for the implementation of the tool. SM, MS, AB, MK, TB, VF, and PR were responsible for preparing the imaging data used in the article. SM, AL, and PR were responsible for validating the functionality of the tool. SM drafted the manuscript and all authors reviewed and approved the final version of the manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The handling Editor declared a shared affiliation, though no other collaboration, with one of the reviewers AL and states that the process nevertheless met the standards of a fair and objective review.

The authors would like to thank Dr. Jason Lerch for the discussions during the preparation of this manuscript. This work was supported by the Canadian Institutes of Health Research (CIHR) [MOP-11-51-31], Canadian Consortium of Neurodegeneration and Aging (CCNA), the Alan Tiffin Foundation, the Alzheimer's Association [NIRG-12-92090, NIRP-12-259245], the Fonds de Recherche du Québec – Santé (P-RN), and the Centre for Studies on Prevention of Alzheimer's Disease (Prevent-AD Centre). Data collection and sharing for this project was funded by the ADNI (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense award number W81XWH-12-2-0012). ADNI is funded by the National Institute on Aging, the National Institute of Biomedical Imaging and Bioengineering, and through generous contributions from the following: AbbVie, Alzheimer's Association; Alzheimer's Drug Discovery Foundation; Araclon Biotech; BioClinica, Inc.; Biogen; Bristol-Myers Squibb Company; CereSpir, Inc.; Eisai Inc.; Elan Pharmaceuticals, Inc.; Eli Lilly and Company; EuroImmun; F. Hoffmann-La Roche Ltd and its affiliated company Genentech, Inc.; Fujirebio; GE Healthcare; IXICO Ltd.; Janssen Alzheimer Immunotherapy Research and Development, LLC.; Johnson & Johnson Pharmaceutical Research & Development LLC.; Lumosity; Lundbeck; Merck & Co., Inc.; Meso Scale Diagnostics, LLC.; NeuroRx Research; Neurotrack Technologies; Novartis Pharmaceuticals Corporation; Pfizer Inc.; Piramal Imaging; Servier; Takeda Pharmaceutical Company; and Transition Therapeutics. The Canadian Institutes of Health Research also provides funds to support ADNI clinical sites in Canada. Private sector contributions are facilitated by the Foundation for the National Institutes of Health (

The Supplementary Material for this article can be found online at: