In this note, we combined pediatric sarcoma data from Columbia University with adult sarcoma data collected from TCGA, in order to see if one can automatically discern a unique pediatric cluster in the combined data set. Using a novel clustering pipeline based on optimal transport theory, this turned out to be the case. The overall methodology may find uses for the classification of data from other biological networking problems.
Yongxin Chen, Tryphon Georgiou, Michele Pavon, and Allen Tannenbaum. 2017. “Robust Transport over Networks”. IEEE Trans Automat Contr, 62, 9, Pp. 4675-82.
We consider transportation over a strongly connected, directed graph. The scheduling amounts to selecting transition probabilities for a discrete-time Markov evolution which is designed to be consistent with initial and final marginal constraints on mass transport. We address the situation where initially the mass is concentrated on certain nodes and needs to be transported in a certain time period to another set of nodes, possibly disjoint from the first. The random evolution is selected to be closest to a prior measure on paths in the relative entropy sense-such a construction is known as a Schrödinger bridge between the two given marginals. It may be viewed as an atypical stochastic control problem where the control consists in suitably modifying the prior transition mechanism. The prior can be chosen to incorporate constraints and costs for traversing specific edges of the graph, but it can also be selected to allocate equal probability to all paths of equal length connecting any two nodes (i.e., a uniform distribution on paths). This latter choice for prior transitions relies on the so-called Ruelle-Bowen random walker and gives rise to scheduling that tends to utilize all paths as uniformly as the topology allows. Thus, this Ruelle-Bowen law ([["fid":3628056,"view_mode":"default","type":"media","attributes":"style":"width: 22px; height: 12px;","alt":"Ruelle-Bowen Law","class":"media-element file-default "]]) taken as prior, leads to a transportation plan that tends to lessen congestion and ensures a level of robustness. We also show that the distribution [["fid":3628056,"view_mode":"default","type":"media","attributes":"style":"width: 22px; height: 12px;","alt":"Ruelle-Bowen Law","class":"media-element file-default"]] on paths, which attains the maximum entropy rate for the random walker given by the topological entropy, can itself be obtained as the time-homogeneous solution of a maximum entropy problem for measures on paths (also a Schrödinger bridge problem, albeit with prior that is not a probability measure). Finally we show that the paradigm of Schrödinger bridges as a mechanism for scheduling transport on networks can be adapted to graphs that are not strongly connected, as well as to weighted graphs. In the latter case, our approach may be used to design a transportation plan which effectively compromises between robustness and other criteria such as cost. Indeed, we explicitly provide a robust transportation plan which assigns maximum probability to minimum cost paths and therefore compares favourably with Optimal Mass Transportation strategies.
Diffusion tensor imaging (DTI) studies in chronic schizophrenia have found widespread but often inconsistent patterns of white matter abnormalities. These studies have typically used the conventional measure of fractional anisotropy, which can be contaminated by extracellular free-water. A recent free-water imaging study reported reduced free-water corrected fractional anisotropy (FAT) in chronic schizophrenia across several brain regions, but limited changes in the extracellular volume. The present study set out to validate these findings in a substantially larger sample. Tract-based spatial statistics (TBSS) was performed in 188 healthy controls and 281 chronic schizophrenia patients. Forty-two regions of interest (ROIs), as well as average whole-brain FAT and FW were extracted from free-water corrected diffusion tensor maps. Compared to healthy controls, reduced FAT was found in the chronic schizophrenia group in the anterior limb of the internal capsule bilaterally, the posterior thalamic radiation bilaterally, as well as the genu and body of the corpus callosum. While a significant main effect of group was observed for FW, none of the follow-up contrasts survived correction for multiple comparisons. The observed FAT reductions in the absence of extracellular FW changes, in a large, multi-site sample of chronic schizophrenia patients, validate the pattern of findings reported by a previous, smaller free-water imaging study of a similar sample. The limited number of regions in which FAT was reduced in the schizophrenia group suggests that actual white matter tissue degeneration in chronic schizophrenia, independent of extracellular FW, might be more localized than suggested previously.
BACKGROUND: Imaging markers that are sensitive to parkinsonism across multiple sites are critically needed for clinical trials. The objective of this study was to evaluate changes in the substantia nigra using single- and bi-tensor models of diffusion magnetic resonance imaging in PD, MSA, and PSP. METHODS: The study cohort (n = 425) included 107 healthy controls and 184 PD, 63 MSA, and 71 PSP patients from 3 movement disorder centers. Bi-tensor free water, free-water-corrected fractional anisotropy, free-water-corrected mean diffusivity, single-tensor fractional anisotropy, and single-tensor mean diffusivity were computed for the anterior and posterior substantia nigra. Correlations were computed between diffusion MRI measures and clinical measures. RESULTS: In the posterior substantia nigra, free water was greater for PSP than MSA and PD patients and controls. PD and MSA both had greater free water than controls. Free-water-corrected fractional anisotropy values were greater for PSP patents than for controls and PD patients. PSP and MSA patient single-tensor mean diffusivity values were greater than controls, and single-tensor fractional anisotropy values were lower for PSP patients than for healthy controls. The parkinsonism effect size for free water was 0.145 in the posterior substantia nigra and 0.072 for single-tensor mean diffusivity. The direction of correlations between single-tensor mean diffusivity and free-water values and clinical scores was similar at each site. CONCLUSIONS: Free-water values in the posterior substantia nigra provide a consistent pattern of findings across patients with PD, MSA, and PSP in a large cohort across 3 sites. Free water in the posterior substantia nigra relates to clinical measures of motor and cognitive symptoms in a large cohort of parkinsonism. 2017 International Parkinson and Movement Disorder Society.
This paper presents an efficient algorithm for large deformation diffeomorphic metric mapping (LDDMM) with geodesic shooting for image registration. We introduce a novel finite dimensional Fourier representation of diffeomorphic deformations based on the key fact that the high frequency components of a diffeomorphism remain stationary throughout the integration process when computing the deformation associated with smooth velocity fields. We show that manipulating high dimensional diffeomorphisms can be carried out entirely in the bandlimited space by integrating the nonstationary low frequency components of the displacement field. This insight substantially reduces the computational cost of the registration problem. Experimental results show that our method is significantly faster than the state-of-the-art diffeomorphic image registration methods while producing equally accurate alignment. We demonstrate our algorithm in two different applications of image registration: neuroimaging and in-utero imaging.
In schizophrenia, abnormalities in structural connectivity between brain regions known to contain mirror neurons and their relationship to negative symptoms related to a domain of social cognition are not well understood. Diffusion tensor imaging (DTI) scans were acquired in 16 patients with first episode schizophrenia and 16 matched healthy controls. FA and Trace of the tracts interconnecting regions known to be rich in mirror neurons, i.e., anterior cingulate cortex (ACC), inferior parietal lobe (IPL) and premotor cortex (PMC) were evaluated. A significant group effect for Trace was observed in IPL-PMC white matter fiber tract (F (1, 28) = 7.13, p = .012), as well as in the PMC-ACC white matter fiber tract (F (1, 28) = 4.64, p = .040). There were no group differences in FA. In addition, patients with schizophrenia showed a significant positive correlation between the Trace of the left IPL-PMC white matter fiber tract, and the Ability to Feel Intimacy and Closeness score (rho = .57, p = 0.034), and a negative correlation between the Trace of the left PMC-ACC and the Relationships with Friends and Peers score (rho = remove -.54, p = 0.049). We have demonstrated disrupted white mater microstructure within the white matter tracts subserving brain regions containing mirror neurons. We further showed that such structural disruptions might impact negative symptoms and, more specifically, contribute to the inability to feel intimacy (a measure conceptually related to theory of mind) in first episode schizophrenia. Further studies are needed to understand the potential of our results for diagnosis, prognosis and therapeutic interventions.
Hypoplastic left heart syndrome (HLHS) is a single-ventricle congenital heart disease that is fatal if left unpalliated. In HLHS patients, the tricuspid valve is the only functioning atrioventricular valve, and its competence is therefore critical. This work demonstrates the first automated strategy for segmentation, modeling, and morphometry of the tricuspid valve in transthoracic 3D echocardiographic (3DE) images of pediatric patients with HLHS. After initial landmark placement, the automated segmentation step uses multi-atlas label fusion and the modeling approach uses deformable modeling with medial axis representation to produce patient-specific models of the tricuspid valve that can be comprehensively and quantitatively assessed. In a group of 16 pediatric patients, valve segmentation and modeling attains an accuracy (mean boundary displacement) of 0.8 ± 0.2 mm relative to manual tracing and shows consistency in annular and leaflet measurements. In the future, such image-based tools have the potential to improve understanding and evaluation of tricuspid valve morphology in HLHS and guide strategies for patient care.