Modeling motor learning using heteroskedastic functional principal components analysis

Functional data analysis with covariate-dependent mean and covariance structures

Functional data analysis has emerged as a powerful tool in response to the ever-increasing resources and efforts devoted to collecting information about response curves or anything that varies over a continuum. However, limited progress has been made with regard to linking the covariance structures of response curves to external covariates, as most functional models assume a common covariance structure. We propose a new functional regression model with covariate-dependent mean and covariance structures. Particularly, by allowing variances of random scores to be covariate-dependent, we identify eigenfunctions for each individual from the set of eigenfunctions that govern the variation patterns across all individuals, resulting in high interpretability and prediction power. We further propose a new penalized quasi-likelihood procedure that combines regularization and B-spline smoothing for model selection and estimation and establish the convergence rate and asymptotic normality of the proposed estimators. The utility of the developed method is demonstrated via simulations, as well as an analysis of the Avon Longitudinal Study of Parents and Children concerning parental effects on the growth curves of their offspring, which yields biologically interesting results.

Elastic analysis of irregularly or sparsely sampled curves

We provide statistical analysis methods for samples of curves in two or more dimensions, where the image, but not the parameterization of the curves, is of interest and suitable alignment/registration is thus necessary. Examples are handwritten letters, movement paths, or object outlines. We focus in particular on the computation of (smooth) means and distances, allowing, for example, classification or clustering. Existing parameterization invariant analysis methods based on the elastic distance of the curves modulo parameterization, using the square-root-velocity framework, have limitations in common realistic settings where curves are irregularly and potentially sparsely observed. We propose using spline curves to model smooth or polygonal (Fréchet) means of open or closed curves with respect to the elastic distance and show identifiability of the spline model modulo parameterization. We further provide methods and algorithms to approximate the elastic distance for irregularly or sparsely observed curves, via interpreting them as polygons. We illustrate the usefulness of our methods on two datasets. The first application classifies irregularly sampled spirals drawn by Parkinson's patients and healthy controls, based on the elastic distance to a mean spiral curve computed using our approach. The second application clusters sparsely sampled GPS tracks based on the elastic distance and computes smooth cluster means to find new paths on the Tempelhof field in Berlin. All methods are implemented in the R-package "elasdics" and evaluated in simulations.

Assessment of Neurological Impairment and Recovery Using Statistical Models of Neurologically Healthy Behavior

While many areas of medicine have benefited from the development of objective assessment tools and biomarkers, there have been comparatively few improvements in techniques used to assess brain function and dysfunction. Brain functions such as perception, cognition, and motor control are commonly measured using criteria-based, ordinal scales which can be coarse, have floor/ceiling effects, and often lack the precision to detect change. There is growing recognition that kinematic and kinetic-based measures are needed to quantify impairments following neurological injury such as stroke, in particular for clinical research and clinical trials. This paper will first consider the challenges with using criteria-based ordinal scales to quantify impairment and recovery. We then describe how kinematic-based measures can overcome many of these challenges and highlight a statistical approach to quantify kinematic measures of behavior based on performance of neurologically healthy individuals. We illustrate this approach with a visually-guided reaching task to highlight measures of impairment for individuals following stroke. Finally, there has been considerable controversy about the calculation of motor recovery following stroke. Here, we highlight how our statistical-based approach can provide an effective estimate of impairment and recovery.

Covariate-adjusted hybrid principal components analysis for region-referenced functional EEG data

Electroencephalography (EEG) studies produce region-referenced functional data via EEG signals recorded across scalp electrodes. The high-dimensional data can be used to contrast neurodevelopmental trajectories between diagnostic groups, for example between typically developing (TD) children and children with autism spectrum disorder (ASD). Valid inference requires characterization of the complex EEG dependency structure as well as covariate-dependent heteroscedasticity, such as changes in variation over developmental age. In our motivating study, EEG data is collected on TD and ASD children aged two to twelve years old. The peak alpha frequency, a prominent peak in the alpha spectrum, is a biomarker linked to neurodevelopment that shifts as children age. To retain information, we model patterns of alpha spectral variation, rather than just the peak location, regionally across the scalp and chronologically across development. We propose a covariate-adjusted hybrid principal components analysis (CA-HPCA) for EEG data, which utilizes both vector and functional principal components analysis while simultaneously adjusting for covariate-dependent heteroscedasticity. CA-HPCA assumes the covariance process is weakly separable conditional on observed covariates, allowing for covariate-adjustments to be made on the marginal covariances rather than the full covariance leading to stable and computationally efficient estimation. The proposed methodology provides novel insights into neurodevelopmental differences between TD and ASD children.

Multivariate functional additive mixed models

Multivariate functional data can be intrinsically multivariate like movement trajectories in 2D or complementary such as precipitation, temperature and wind speeds over time at a given weather station. We propose a multivariate functional additive mixed model (multiFAMM) and show its application to both data situations using examples from sports science (movement trajectories of snooker players) and phonetic science (acoustic signals and articulation of consonants). The approach includes linear and nonlinear covariate effects and models the dependency structure between the dimensions of the responses using multivariate functional principal component analysis. Multivariate functional random intercepts capture both the auto-correlation within a given function and cross-correlations between the multivariate functional dimensions. They also allow us to model between-function correlations as induced by, for example, repeated measurements or crossed study designs. Modelling the dependency structure between the dimensions can generate additional insight into the properties of the multivariate functional process, improves the estimation of random effects, and yields corrected confidence bands for covariate effects. Extensive simulation studies indicate that a multivariate modelling approach is more parsimonious than fitting independent univariate models to the data while maintaining or improving model fit.

JOINT AND INDIVIDUAL ANALYSIS OF BREAST CANCER HISTOLOGIC IMAGES AND GENOMIC COVARIATES

The two main approaches in the study of breast cancer are histopathology (analyzing visual characteristics of tumors) and genomics. While both histopathology and genomics are fundamental to cancer research, the connections between these fields have been relatively superficial. We bridge this gap by investigating the Carolina Breast Cancer Study through the development of an integrative, exploratory analysis framework. Our analysis gives insights - some known, some novel - that are engaging to both pathologists and geneticists. Our analysis framework is based on Angle-based Joint and Individual Variation Explained (AJIVE) for statistical data integration and exploits Convolutional Neural Networks (CNNs) as a powerful, automatic method for image feature extraction. CNNs raise interpretability issues that we address by developing novel methods to explore visual modes of variation captured by statistical algorithms (e.g. PCA or AJIVE) applied to CNN features.

Smoothness metric during reach-to-grasp after stroke: part 2. longitudinal association with motor impairment

BACKGROUND

The cause of smoothness deficits as a proxy for quality of movement post stroke is currently unclear. Previous simulation analyses showed that spectral arc length (SPARC) is a valid metric for investigating smoothness during a multi-joint goal-directed reaching task. The goal of this observational study was to investigate how SPARC values change over time, and whether SPARC is longitudinally associated with the recovery from motor impairments reflected by the Fugl-Meyer motor assessment of the upper extremity (FM-UE) in the first 6 months after stroke.

METHODS

Forty patients who suffered a first-ever unilateral ischemic stroke (22 males, aged 58.6 ± 12.5 years) with upper extremity paresis underwent kinematic and clinical measurements in weeks 1, 2, 3, 4, 5, 8, 12, and 26 post stroke. Clinical measures included amongst others FM-UE. SPARC was obtained by three-dimensional kinematic measurements using an electromagnetic motion tracking system during a reach-to-grasp movement. Kinematic assessments of 12 healthy, age-matched individuals served as reference. Longitudinal linear mixed model analyses were performed to determine SPARC change over time, compare smoothness in patients with reference values of healthy individuals, and establish the longitudinal association between SPARC and FM-UE scores.

RESULTS

SPARC showed a significant positive longitudinal association with FM-UE (B: 31.73, 95%-CI: [27.27 36.20], P < 0.001), which encompassed significant within- and between-subject effects (B: 30.85, 95%-CI: [26.28 35.41], P < 0.001 and B: 50.59, 95%-CI: [29.97 71.21], P < 0.001, respectively). Until 5 weeks post stroke, progress of time contributed significantly to the increase in SPARC and FM-UE scores (P < 0.05), whereafter they levelled off. At group level, smoothness was lower in patients who suffered a stroke compared to healthy subjects at all time points (P < 0.05).

CONCLUSIONS

The present findings show that, after stroke, recovery of smoothness in a multi-joint reaching task and recovery from motor impairments are longitudinally associated and follow a similar time course. This suggests that the reduction of smoothness deficits quantified by SPARC is a proper objective reflection of recovery from motor impairment, as reflected by FM-UE, probably driven by a common underlying process of spontaneous neurological recovery early post stroke.

Machine Learning for 3D Kinematic Analysis of Movements in Neurorehabilitation

PURPOSE OF REVIEW

Recent advances in the machine learning field, especially in deep learning, provide the opportunity for automated, detailed, and unbiased analysis of motor behavior. Although there has not yet been wide use of these techniques in the motor rehabilitation field, they have great potential. In this review, I describe how the current state of machine learning can be applied to 3D kinematic analysis, and how this will have an impact on neurorehabilitation.

RECENT FINDINGS

Applications of deep learning methods, in the form of convolutional neural networks, have been revolutionary for image analysis such as face recognition and object detection in images, exceeding human level performance. Recent studies have shown applicability of these deep learning approaches to human posture and movement classification. It is to be expected that portable stereo-camera systems will bring 3D pose estimation into the clinical setting and allow the assessment of movement quality in response to interventions. Advances in machine learning can help automate the process of obtaining 3D kinematics of human movements and to identify/classify patterns of movement.

Covariate-Adjusted Hybrid Principal Components Analysis

Electroencephalography (EEG) studies produce region-referenced functional data in the form of EEG signals recorded across electrodes on the scalp. The high-dimensional data capture underlying neural dynamics and it is of clinical interest to model differences in neurodevelopmental trajectories between diagnostic groups, for example typically developing (TD) children and children with autism spectrum disorder (ASD). In such cases, valid group-level inference requires characterization of the complex EEG dependency structure as well as covariate-dependent heteroscedasticity, such as changes in variation over developmental age. In our motivating study, resting state EEG is collected on both TD and ASD children aged two to twelve years old. The peak alpha frequency (PAF), defined as the location of a prominent peak in the alpha frequency band of the spectral density, is an important biomarker linked to neurodevelopment and is known to shift from lower to higher frequencies as children age. To retain the most amount of information from the data, we model patterns of alpha spectral variation, rather than just the peak location, regionally across the scalp and chronologically across development for both the TD and ASD diagnostic groups. We propose a covariate-adjusted hybrid principal components analysis (CA-HPCA) for region-referenced functional EEG data, which utilizes both vector and functional principal components analysis while simultaneously adjusting for covariate-dependent heteroscedasticity. CA-HPCA assumes the covariance process is weakly separable conditional on observed covariates, allowing for covariate-adjustments to be made on the marginal covariances rather than the full covariance leading to stable and computationally efficient estimation. A mixed effects framework is proposed to estimate the model components coupled with a bootstrap test for group-level inference. The proposed methodology provides novel insights into neurodevelopmental differences between TD and ASD children.

Standardized Measurement of Quality of Upper Limb Movement After Stroke: Consensus-Based Core Recommendations From the Second Stroke Recovery and Rehabilitation Roundtable

The second Stroke Recovery and Rehabilitation Roundtable "metrics" task force developed consensus around the recognized need to add kinematic and kinetic movement quantification to its core recommendations for standardized measurements of sensorimotor recovery in stroke trials. Specifically, we focused on measurement of the quality of upper limb movement. We agreed that the recommended protocols for measurement should be conceptually rigorous, reliable, valid and responsive to change. The recommended measurement protocols include four performance assays (i.e. 2D planar reaching, finger individuation, grip strength, and precision grip at body function level) and one functional task (3D drinking task at activity level) that address body function and activity respectively. This document describes the criteria for assessment and makes recommendations about the type of technology that should be used for reliable and valid movement capture. Standardization of kinematic measurement protocols will allow pooling of participant data across sites, thereby increasing sample size aiding meta-analyses of published trials, more detailed exploration of recovery profiles, the generation of new research questions with testable hypotheses, and development of new treatment approaches focused on impairment. We urge the clinical and research community to consider adopting these recommendations.

Standardized measurement of quality of upper limb movement after stroke: Consensus-based core recommendations from the Second Stroke Recovery and Rehabilitation Roundtable

The second Stroke Recovery and Rehabilitation Roundtable “metrics” task force developed consensus around the recognized need to add kinematic and kinetic movement quantification to its core recommendations for standardized measurements of sensorimotor recovery in stroke trials. Specifically, we focused on measurement of the quality of upper limb movement. We agreed that the recommended protocols for measurement should be conceptually rigorous, reliable, valid and responsive to change. The recommended measurement protocols include four performance assays (i.e. 2D planar reaching, finger individuation, grip strength, and precision grip at body function level) and one functional task (3D drinking task at activity level) that address body function and activity respectively. This document describes the criteria for assessment and makes recommendations about the type of technology that should be used for reliable and valid movement capture. Standardization of kinematic measurement protocols will allow pooling of participant data across sites, thereby increasing sample size aiding meta-analyses of published trials, more detailed exploration of recovery profiles, the generation of new research questions with testable hypotheses, and development of new treatment approaches focused on impairment. We urge the clinical and research community to consider adopting these recommendations.

Multivariate functional response regression, with application to fluorescence spectroscopy in a cervical pre-cancer study

Many scientific studies measure different types of high-dimensional signals or images from the same subject, producing multivariate functional data. These functional measurements carry different types of information about the scientific process, and a joint analysis that integrates information across them may provide new insights into the underlying mechanism for the phenomenon under study. Motivated by fluorescence spectroscopy data in a cervical pre-cancer study, a multivariate functional response regression model is proposed, which treats multivariate functional observations as responses and a common set of covariates as predictors. This novel modeling framework simultaneously accounts for correlations between functional variables and potential multi-level structures in data that are induced by experimental design. The model is fitted by performing a two-stage linear transformation-a basis expansion to each functional variable followed by principal component analysis for the concatenated basis coefficients. This transformation effectively reduces the intra-and inter-function correlations and facilitates fast and convenient calculation. A fully Bayesian approach is adopted to sample the model parameters in the transformed space, and posterior inference is performed after inverse-transforming the regression coefficients back to the original data domain. The proposed approach produces functional tests that flag local regions on the functional effects, while controlling the overall experiment-wise error rate or false discovery rate. It also enables functional discriminant analysis through posterior predictive calculation. Analysis of the fluorescence spectroscopy data reveals local regions with differential expressions across the pre-cancer and normal samples. These regions may serve as biomarkers for prognosis and disease assessment.