Summary We describe a model for the analysis of data distributed over irregularly shaped spatial domains with complex boundaries, strong concavities and interior holes. Adopting an approach that is typical of functional data analysis, we propose a spatial spline regression model that is computationally efficient, allows for spatially distributed covariate information and can impose various conditions over the boundaries of the domain. Accurate surface estimation is achieved by the use of piecewise linear and quadratic finite elements.

The abundance of functional observations in scientific endeavors has led to a significant development in tools for functional data analysis (FDA). This kind of data comes with several challenges: infinite-dimensionality of function spaces, observation noise, and so on. However, there is another interesting phenomena that creates problems in FDA. The functional data often comes with lateral displacements/deformations in curves, a phenomenon which is different from the height or amplitude variability and is termed phase variation. The presence of phase variability artificially often inflates data variance, blurs underlying data structures, and distorts principal components. While the separation and/or removal of phase from amplitude data is desirable, this is a difficult problem. In particular, a commonly used alignment procedure, based on minimizing the $\mathbb{L}^2$ norm between functions, does not provide satisfactory results. In this paper we motivate the importance of dealing with the phase variability and summarize several current ideas for separating phase and amplitude components. These approaches differ in the following: (1) the definition and mathematical representation of phase variability, (2) the objective functions that are used in functional data alignment, and (3) the algorithmic tools for solving estimation/optimization problems. We use simple examples to illustrate various approaches and to provide useful contrast between them.Comment: Published at http://dx.doi.org/10.1214/15-STS524 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

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We propose an innovative method for the accurate estimation of surfaces and spatial fields when a prior knowledge on the phenomenon under study is available. The prior knowledge included in the model derives from physics, physiology or mechanics of the problem at hand, and is formalized in terms of a partial differential equation governing the phenomenon behavior, as well as conditions that the phenomenon

Immune reconstitution plays a crucial role on the outcome of patients given T cell-depleted HLA-haploidentical hematopoietic stem cell transplantation (hHSCT) for hematological malignancies. CD1d-restricted invariant NKT (iNKT) cells are innate-like, lipid-reactive T lymphocytes controlling infections, cancer, and autoimmunity. Adult mature iNKT cells are divided in two functionally distinct CD4+ and CD4− subsets that express the NK receptor CD161 and derive from thymic CD4+CD161− precursors. We investigated iNKT cell reconstitution dynamics in 33 pediatric patients given hHSCT for hematological malignancies, with a follow-up reaching 6 y posttransplantation, and correlated their emergence with disease relapse. iNKT cells fully reconstitute and rapidly convert into IFN-γ–expressing effectors in the 25 patients maintaining remission. CD4+ cells emerge earlier than the CD4− ones, both displaying CD161− immature phenotypes. CD4− cells expand more slowly than CD4+ cells, though they mature with significantly faster kinetics, reaching full maturation by 18 mo post-hHSCT. Between 4 and 6 y post-hHSCT, mature CD4− iNKT cells undergo a substantial expansion burst, resulting in a CD4+<CD4− NKT cell ratio similar to that found in healthy adults. In contrast with patients maintaining remission, iNKT cells failed to reconstitute in all eight patients experiencing disease relapse. These findings define the peripheral dynamics of human iNKT cells and suggest a contribution of these cells to maintain remission, possibly via early IFN-γ provision. Adoptive transfer of donor-derived iNKT cells into HLA-haploidentical patients failing to reconstitute these cells might represent a novel therapeutic option to prevent leukemia recurrence.

Rationale: At the onset of ST-elevation acute myocardial infarction (STEMI), patients can present with very high circulating interleukin-6 (IL-6 + ) levels or very low-IL-6 – levels. Objective: We compared these 2 groups of patients to understand whether it is possible to define specific STEMI phenotypes associated with outcome based on the cytokine response. Methods and Results: We compared 109 patients with STEMI in the top IL-6 level (median, 15.6 pg/mL; IL-6 + STEMI) with 96 in the bottom IL-6 level (median, 1.7 pg/mL; IL-6 − STEMI) and 103 matched controls extracted from the multiethnic First Acute Myocardial Infarction study. We found minimal clinical differences between IL-6 + STEMI and IL-6 − STEMI. We assessed the inflammatory profiles of the 2 STEMI groups and the controls by measuring 18 cytokines in blood samples. We exploited clustering analysis algorithms to infer the functional modules of interacting cytokines. IL-6 + STEMI patients were characterized by the activation of 2 modules of interacting signals comprising IL-10, IL-8, macrophage inflammatory protein-1α, and C-reactive protein, and monocyte chemoattractant protein-1, macrophage inflammatory protein-1β, and monokine induced by interferon-γ. IL-10 was increased both in IL-6 + STEMI and IL-6 − STEMI patients compared with controls. IL-6 + IL-10 + STEMI patients had an increased risk of systolic dysfunction at discharge and an increased risk of death at 6 months in comparison with IL-6 − IL-10 + STEMI patients. We combined IL-10 and monokine induced by interferon-γ (derived from the 2 identified cytokine modules) with IL-6 in a formula yielding a risk index that outperformed any single cytokine in the prediction of systolic dysfunction and death. Conclusions: We have identified a characteristic circulating inflammatory cytokine pattern in STEMI patients, which is not related to the extent of myocardial damage. The simultaneous elevation of IL-6 and IL-10 levels distinguishes STEMI patients with worse clinical outcomes from other STEMI patients. These observations could have potential implications for risk-oriented patient stratification and immune-modulating therapies.

Functional data are data that can be represented by suitable functions, such as curves (potentially multi-dimensional) or surfaces. This paper gives an introduction to some basic but important techniques for the analysis of such data, and we apply the techniques to two datasets from biomedicine. One dataset is about white matter structures in the brain in multiple sclerosis patients; the other dataset is about three-dimensional vascular geometries collected for the study of cerebral aneurysms. The techniques described are smoothing, alignment, principal component analysis, and regression.