Over the last 15 years, basic thresholding techniques in combination with standard statistical correlation-based data analysis tools have been widely used to investigate different aspects of evolution of acute or subacute to late stage ischemic stroke in both human and animal data. Yet, a wave of biology-dependent and imaging-dependent issues is still untackled pointing towards the key question: "how does an ischemic stroke evolve?" Paving the way for potential answers to this question, both magnetic resonance (MRI) and CT (computed tomography) images have been used to visualize the lesion extent, either with or without spatial distinction between dead and salvageable tissue. Combining diffusion and perfusion imaging modalities may provide the possibility of predicting further tissue recovery or eventual necrosis. Going beyond these basic thresholding techniques, in this critical appraisal, we explore different semi-automatic or fully automatic 2D/3D medical image analysis methods and mathematical models applied to human, animal (rats/rodents) and/or synthetic ischemic stroke to tackle one of the following three problems: (1) segmentation of infarcted and/or salvageable (also called penumbral) tissue, (2) prediction of final ischemic tissue fate (death or recovery) and (3) dynamic simulation of the lesion core and/or penumbra evolution. To highlight the key features in the reviewed segmentation and prediction methods, we propose a common categorization pattern. We also emphasize some key aspects of the methods such as the imaging modalities required to build and test the presented approach, the number of patients/animals or synthetic samples, the use of external user interaction and the methods of assessment (clinical or imaging-based). Furthermore, we investigate how any key difficulties, posed by the evolution of stroke such as swelling or reperfusion, were detected (or not) by each method. In the absence of any imaging-based macroscopic dynamic model applied to ischemic stroke, we have insights into relevant microscopic dynamic models simulating the evolution of brain ischemia in the hope to further promising and challenging 4D imaging-based dynamic models. By depicting the major pitfalls and the advanced aspects of the different reviewed methods, we present an overall critique of their performances and concluded our discussion by suggesting some recommendations for future research work focusing on one or more of the three addressed problems.

Mixed-effects models provide a rich theoretical framework for the analysis of longitudinal data. However, when used to analyze or predict the progression of a neurodegenerative disease such as Alzheimer’s disease, these models usually do not take into account the fact that subjects may be at different stages of disease progression and the interpretation of the model may depend on some implicit reference time. In this paper, we propose a generative statistical model for longitudinal data, described in a univariate Riemannian manifold setting, which estimates an average disease progression model, subject-specific time shifts and acceleration factors. The time shifts account for variability in age at disease-onset time. The acceleration factors account for variability in speed of disease progression. For a given individual, the estimated time shift and acceleration factor define an affine reparametrization of the average disease progression model. This statistical model has been used to analyze neuropsychological assessments scores and cortical thickness measurements from the Alzheimer’s Disease Neuroimaging Initiative database. The numerical results showed that we can distinguish between slow versus fast progressing and early versus late-onset individuals.

We extend the image-to-image metamorphosis into constrained longitudinal metamorphosis. We apply it to estimate an evolution scenario, in patients with acute ischemic stroke, of both scattered and solitary ischemic lesions visible on serial MR perfusion weighted imaging from acute to subacute stages. We then estimate a patient-specific residual map that enables us to capture the most relevant shape and intensity changes, continuously, as the lesion evolves from acute through subacute to chronic timepoints until merging into the final image. We detect areas with high residuals (i.e., high dynamics) and identify areas that became part of the final T2-w lesion obtained at ≥ 1 month after stroke. This allows the investigation of the dynamic influence of perfusion values on the final lesion outcome as seen on T2-w imaging. The model provides detailed insights into stroke lesion dynamic evolution in space and time that will help identify factors that determine final outcome and identify targets for interventions to improve outcome.

Network analysis provides a rich framework to model complex phenomena, such as human brain connectivity. It has proven efficient to understand their natural properties and design predictive models. In this paper, we study the variability within groups of networks, i.e., the structure of connection similarities and differences across a set of networks. We propose a statistical framework to model these variations based on manifold-valued latent factors. Each network adjacency matrix is decomposed as a weighted sum of matrix patterns with rank one. Each pattern is described as a random perturbation of a dictionary element. As a hierarchical statistical model, it enables the analysis of heterogeneous populations of adjacency matrices using mixtures. Our framework can also be used to infer the weight of missing edges. We estimate the parameters of the model using an Expectation-Maximization-based algorithm. Experimenting on synthetic data, we show that the algorithm is able to accurately estimate the latent structure in both low and high dimensions. We apply our model on a large data set of functional brain connectivity matrices from the UK Biobank. Our results suggest that the proposed model accurately describes the complex variability in the data set with a small number of degrees of freedom.

The Expectation Maximisation (EM) algorithm is widely used to optimise non-convex likelihood functions with latent variables. Many authors modified its simple design to fit more specific situations. For instance, the Expectation (E) step has been replaced by Monte Carlo (MC), Markov Chain Monte Carlo or tempered approximations, etc. Most of the well-studied approximations belong to the stochastic class. By comparison, the literature is lacking when it comes to deterministic approximations. In this paper, we introduce a theoretical framework, with state-of-the-art convergence guarantees, for any deterministic approximation of the E step. We analyse theoretically and empirically several approximations that fit into this framework. First, for intractable E-steps, we introduce a deterministic version of MC-EM using Riemann sums. A straightforward method, not requiring any hyper-parameter fine-tuning, useful when the low dimensionality does not warrant a MC-EM. Then, we consider the tempered approximation, borrowed from the Simulated Annealing literature and used to escape local extrema. We prove that the tempered EM verifies the convergence guarantees for a wider range of temperature profiles than previously considered. We showcase empirically how new non-trivial profiles can more successfully escape adversarial initialisations. Finally, we combine the Riemann and tempered approximations into a method that accomplishes both their purposes.

Gaussian Graphical Models (GGM) are often used to describe the conditional correlations between the components of a random vector. In this article, we compare two families of GGM inference methods: nodewise edge selection and penalised likelihood maximisation. We demonstrate on synthetic data that, when the sample size is small, the two methods produce graphs with either too few or too many edges when compared to the real one. As a result, we propose a composite procedure that explores a family of graphs with an nodewise numerical scheme and selects a candidate among them with an overall likelihood criterion. We demonstrate that, when the number of observations is small, this selection method yields graphs closer to the truth and corresponding to distributions with better KL divergence with regards to the real distribution than the other two. Finally, we show the interest of our algorithm on two concrete cases: first on brain imaging data, then on biological nephrology data. In both cases our results are more in line with current knowledge in each field.