Correction: Designing machine learning workflows with an application to topological data analysis.

[This corrects the article DOI: 10.1371/journal.pone.0225577.].

Designing machine learning workflows with an application to topological data analysis.

In this paper we define the concept of the Machine Learning Morphism (MLM) as a fundamental building block to express operations performed in machine learning such as data preprocessing, feature extraction, and model training. Inspired by statistical learning, MLMs are morphisms whose parameters are minimized via a risk function. We explore operations such as composition of MLMs and when sets of MLMs form a vector space. These operations are used to build a machine learning workflow from data preprocessing to final task completion. We examine the Mapper Algorithm from Topological Data Analysis as an MLM, and build several workflows for binary classification incorporating Mapper on Hospital Readmissions and Credit Evaluation datasets. The advantage of this framework lies in the ability to easily build, organize, and compare multiple workflows, and allows joint optimization of parameters across multiple steps in an application.

Electro-Mechanical Ionic Channel Modeling for Uterine Contractions and Oxytocin Effect during Pregnancy.

Uterine contractions during normal pregnancy and preterm birth are an important physiological activity. Although the cause of preterm labor is usually unknown, preterm birth creates very serious health concerns in many cases. Therefore, understanding normal birth and predicting preterm birth can help both newborn babies and their families. In our previous work, we developed a multiscale dynamic electrophysiology model of uterine contractions. In this paper, we mainly focus on the cellular level and use electromyography (EMG) and cell force generation methods to construct a new ionic channel model and a corresponding mechanical force model. Specifically, the ionic channel model takes into consideration the knowledge of individual ionic channels, which include the electrochemical and bioelectrical characteristics of individual myocytes. We develop a new sodium channel and a new potassium channel based on the experimental data from the human myometrium and the average correlations are 0.9946 and 0.9945, respectively. The model is able to generate the single spike, plateau type and bursting type of action potentials. Moreover, we incorporate the effect of oxytocin on changing the properties of the L-type and T-type calcium channels and further influencing the output action potentials. In addition, we develop a mechanical force model based on the new ionic channel model that describes the detailed ionic dynamics. Our model produces cellular mechanical force that propagates to the tissue level. We illustrate the relationship between the cellular mechanical force and the intracellular ionic dynamics and discuss the relationship between the application of oxytocin and the output mechanical force. We also propose a simplified version of the model to enable large scale simulations using sensitivity analysis method. Our results show that the model is able to reproduce the bioelectrical and electromechanical characteristics of uterine contractions during pregnancy.

Estimating uterine source current during contractions using magnetomyography measurements.

Understanding the uterine source of the electrophysiological activity of contractions during pregnancy is of scientific interest and potential clinical applications. In this work, we propose a method to estimate uterine source currents from magnetomyography (MMG) temporal course measurements on the abdominal surface. In particular, we develop a linear forward model, based on the quasistatic Maxwell's equations and a realistic four-compartment volume conductor, relating the magnetic fields to the source currents on the uterine surface through a lead-field matrix. To compute the lead-field matrix, we use a finite element method that considers the anisotropic property of the myometrium. We estimate the source currents by minimizing a constrained least-squares problem to solve the non-uniqueness issue of the inverse problem. Because we lack the ground truth of the source current, we propose to predict the intrauterine pressure from our estimated source currents by using an absolute-value-based method and compare the result with real abdominal deflection recorded during contractile activity. We test the feasibility of the lead-field matrix by displaying the lead fields that are generated by putative source currents at different locations in the myometrium: cervix and fundus, left and right, front and back. We then illustrate our method by using three synthetic MMG data sets, which are generated using our previously developed multiscale model of uterine contractions, and three real MMG data sets, one of which has simultaneous real abdominal deflection measurements. The numerical results demonstrate the ability of our method to capture the local contractile activity of human uterus during pregnancy. Moreover, the predicted intrauterine pressure is in fair agreement with the real abdominal deflection with respect to the timing of uterine contractions.

Modeling Magnetomyograms of Uterine Contractions during Pregnancy Using a Multiscale Forward Electromagnetic Approach.

Understanding the mechanisms of uterine contractions during pregnancy is especially important in predicting the onset of labor and thus in forecasting preterm deliveries. Preterm birth can cause serious health problems in newborns, as well as large financial burdens to society. Various techniques such as electromyography (EMG) and magnetomyography (MMG) have been developed to quantify uterine contractions. However, no widely accepted method to predict labor based on electromagnetic measurement is available. Therefore, developing a biophysical model of EMG and MMG could help better understand uterine contractions, interpret real measurements, and detect labor. In this work, we propose a multiscale realistic model of uterine contractions during pregnancy. At the cellular level, building on bifurcation theory, we apply generalized FitzHugh-Nagumo (FHN) equations that produces both plateau-type and bursting-type action potentials. At the tissue level, we introduce a random fiber orientation model applicable to an arbitrary uterine shape. We also develop an analytical expression for the propagation speed of transmembrane potential. At the organ level, a realistic volume conductor geometry model is provided based on magnetic resonance images of a pregnant woman. To simulate the measurements from the SQUID Array for Reproductive Assessment (SARA) device, we propose a sensor array model. Our model is able to reproduce the characteristics of action potentials. Additionally, we investigate the sensitivity of MMG to model configuration aspects such as volume geometry, fiber orientation, and pacemaker location. Our numerical results show that fiber orientation and pacemaker location are the key aspects that greatly affect the MMG as measured by the SARA device. We conclude that sphere is appropriate as an approximation of the volume geometry. The initial step towards validating the model against real MMG measurement is also presented. Our results show that the model is flexible to mimic the limited-propagation magnetic signature during the emergence and decay of a uterine contraction.

Gibbs distribution for statistical analysis of graphical data with a sample application to fcMRI brain images.

This paper develops object-oriented data analysis (OODA) statistical methods that are novel and complementary to existing methods of analysis of human brain scan connectomes, defined as graphs representing brain anatomical or functional connectivity. OODA is an emerging field where classical statistical approaches (e.g., hypothesis testing, regression, estimation, and confidence intervals) are applied to data objects such as graphs or functions. By analyzing data objects directly we avoid loss of information that occurs when data objects are transformed into numerical summary statistics. By providing statistical tools that analyze sets of connectomes without loss of information, new insights into neurology and medicine may be achieved. In this paper we derive the formula for statistical model fitting, regression, and mixture models; test their performance in simulation experiments; and apply them to connectomes from fMRI brain scans collected during a serial reaction time task study. Software for fitting graphical object-oriented data analysis is provided.

Patterned progression of bacterial populations in the premature infant gut.

In the weeks after birth, the gut acquires a nascent microbiome, and starts its transition to bacterial population equilibrium. This early-in-life microbial population quite likely influences later-in-life host biology. However, we know little about the governance of community development: does the gut serve as a passive incubator where the first organisms randomly encountered gain entry and predominate, or is there an orderly progression of members joining the community of bacteria? We used fine interval enumeration of microbes in stools from multiple subjects to answer this question. We demonstrate via 16S rRNA gene pyrosequencing of 922 specimens from 58 subjects that the gut microbiota of premature infants residing in a tightly controlled microbial environment progresses through a choreographed succession of bacterial classes from Bacilli to Gammaproteobacteria to Clostridia, interrupted by abrupt population changes. As infants approach 33-36 wk postconceptional age (corresponding to the third to the twelfth weeks of life depending on gestational age at birth), the gut is well colonized by anaerobes. Antibiotics, vaginal vs. Caesarian birth, diet, and age of the infants when sampled influence the pace, but not the sequence, of progression. Our results suggest that in infants in a microbiologically constrained ecosphere of a neonatal intensive care unit, gut bacterial communities have an overall nonrandom assembly that is punctuated by microbial population abruptions. The possibility that the pace of this assembly depends more on host biology (chiefly gestational age at birth) than identifiable exogenous factors warrants further consideration.

Exploration of bacterial community classes in major human habitats.

BACKGROUND: Determining bacterial abundance variation is the first step in understanding bacterial similarity between individuals. Categorization of bacterial communities into groups or community classes is the subsequent step in describing microbial distribution based on abundance patterns. Here, we present an analysis of the groupings of bacterial communities in stool, nasal, skin, vaginal and oral habitats in a healthy cohort of 236 subjects from the Human Microbiome Project. RESULTS: We identify distinct community group patterns in the anterior nares, four skin sites, and vagina at the genus level. We also confirm three enterotypes previously identified in stools. We identify two clusters with low silhouette values in most oral sites, in which bacterial communities are more homogeneous. Subjects sharing a community class in one habitat do not necessarily share a community class in another, except in the three vaginal sites and the symmetric habitats of the left and right retroauricular creases. Demographic factors, including gender, age, and ethnicity, significantly influence community composition in several habitats. Community classes in the vagina, retroauricular crease and stool are stable over approximately 200 days. CONCLUSION: The community composition, association of demographic factors with community classes, and demonstration of community stability deepen our understanding of the variability and dynamics of human microbiomes. This also has significant implications for experimental designs that seek microbial correlations with clinical phenotypes.

Biogeography of the ecosystems of the healthy human body.

BACKGROUND: Characterizing the biogeography of the microbiome of healthy humans is essential for understanding microbial associated diseases. Previous studies mainly focused on a single body habitat from a limited set of subjects. Here, we analyzed one of the largest microbiome datasets to date and generated a biogeographical map that annotates the biodiversity, spatial relationships, and temporal stability of 22 habitats from 279 healthy humans. RESULTS: We identified 929 genera from more than 24 million 16S rRNA gene sequences of 22 habitats, and we provide a baseline of inter-subject variation for healthy adults. The oral habitat has the most stable microbiota with the highest alpha diversity, while the skin and vaginal microbiota are less stable and show lower alpha diversity. The level of biodiversity in one habitat is independent of the biodiversity of other habitats in the same individual. The abundances of a given genus at a body site in which it dominates do not correlate with the abundances at body sites where it is not dominant. Additionally, we observed the human microbiota exhibit both cosmopolitan and endemic features. Finally, comparing datasets of different projects revealed a project-based clustering pattern, emphasizing the significance of standardization of metagenomic studies. CONCLUSIONS: The data presented here extend the definition of the human microbiome by providing a more complete and accurate picture of human microbiome biogeography, addressing questions best answered by a large dataset of subjects and body sites that are deeply sampled by sequencing.

Multiscale forward electromagnetic model of uterine contractions during pregnancy.

BACKGROUND: Analyzing and monitoring uterine contractions during pregnancy is relevant to the field of reproductive health assessment. Its clinical importance is grounded in the need to reliably predict the onset of labor at term and pre-term. Preterm births can cause health problems or even be fatal for the fetus. Currently, there are no objective methods for consistently predicting the onset of labor based on sensing of the mechanical or electrophysiological aspects of uterine contractions. Therefore, modeling uterine contractions could help to better interpret such measurements and to develop more accurate methods for predicting labor. In this work, we develop a multiscale forward electromagnetic model of myometrial contractions during pregnancy. In particular, we introduce a model of myometrial current source densities and compute its magnetic field and action potential at the abdominal surface, using Maxwell's equations and a four-compartment volume conductor geometry. To model the current source density at the myometrium we use a bidomain approach. We consider a modified version of the Fitzhugh-Nagumo (FHN) equation for modeling ionic currents in each myocyte, assuming a plateau-type transmembrane potential, and we incorporate the anisotropic nature of the uterus by designing conductivity-tensor fields. RESULTS: We illustrate our modeling approach considering a spherical uterus and one pacemaker located in the fundus. We obtained a travelling transmembrane potential depolarizing from -56 mV to -16 mV and an average potential in the plateau area of -25 mV with a duration, before hyperpolarization, of 35 s, which is a good approximation with respect to the average recorded transmembrane potentials at term reported in the technical literature. Similarly, the percentage of myometrial cells contracting as a function of time had the same symmetric properties and duration as the intrauterine pressure waveforms of a pregnant human myometrium at term. CONCLUSIONS: We introduced a multiscale modeling approach of uterine contractions which allows for incorporating electrophysiological and anatomical knowledge of the myometrium jointly. Our results are in good agreement with the values reported in the experimental technical literature, and these are potentially important as a tool for helping in the characterization of contractions and for predicting labor using magnetomyography (MMG) and electromyography (EMG).

Statistical object data analysis of taxonomic trees from human microbiome data.

Human microbiome research characterizes the microbial content of samples from human habitats to learn how interactions between bacteria and their host might impact human health. In this work a novel parametric statistical inference method based on object-oriented data analysis (OODA) for analyzing HMP data is proposed. OODA is an emerging area of statistical inference where the goal is to apply statistical methods to objects such as functions, images, and graphs or trees. The data objects that pertain to this work are taxonomic trees of bacteria built from analysis of 16S rRNA gene sequences (e.g. using RDP); there is one such object for each biological sample analyzed. Our goal is to model and formally compare a set of trees. The contribution of our work is threefold: first, a weighted tree structure to analyze RDP data is introduced; second, using a probability measure to model a set of taxonomic trees, we introduce an approximate MLE procedure for estimating model parameters and we derive LRT statistics for comparing the distributions of two metagenomic populations; and third the Jumpstart HMP data is analyzed using the proposed model providing novel insights and future directions of analysis.

Estimating electrical conductivity tensors of biological tissues using microelectrode arrays.

Finding the electrical conductivity of tissue is highly important for understanding the tissue's structure and functioning. However, the inverse problem of inferring spatial conductivity from data is highly ill-posed and computationally intensive. In this paper, we propose a novel method to solve the inverse problem of inferring tissue conductivity from a set of transmembrane potential and stimuli measurements made by microelectrode arrays (MEA). We first formalize the discrete forward model of transmembrane potential propagation, based on a reaction-diffusion model with an anisotropic inhomogeneous electrical conductivity-tensor field. Then, we propose a novel parallel optimization algorithm for solving the complex inverse problem of estimating the electrical conductivity-tensor field. Specifically, we propose a single-step approximation with a parallel block-relaxation optimization routine that simplifies the joint tensor field estimation problem into a set of computationally tractable subproblems, allowing the use of efficient standard optimization tools. Finally, using numerical examples of several electrical conductivity field topologies and noise levels, we analyze the performance of our algorithm, and discuss its application to real measurements obtained from smooth-muscle cardiac tissue, using data collected with a high-resolution MEA system.

Estimating electrical conductivity tensors of biological tissues using microelectrode arrays.

Finding the electrical conductivity of tissue is important for understanding the tissue's structure and functioning. However, the inverse problem of inferring spatial conductivity from data is highly ill-posed and computationally intensive. In this paper, we propose a novel method to solve the inverse problem of inferring tissue conductivity from a set of transmembrane potential and stimuli measurements made by microelectrode arrays (MEA). We propose a parallel optimization algorithm based on a single-step approximation with a parallel alternating optimization routine. This algorithm simplifies the joint tensor field estimation problem into a set of computationally tractable subproblems, allowing the use of efficient standard optimization tools.

Hypothesis testing and power calculations for taxonomic-based human microbiome data.

This paper presents new biostatistical methods for the analysis of microbiome data based on a fully parametric approach using all the data. The Dirichlet-multinomial distribution allows the analyst to calculate power and sample sizes for experimental design, perform tests of hypotheses (e.g., compare microbiomes across groups), and to estimate parameters describing microbiome properties. The use of a fully parametric model for these data has the benefit over alternative non-parametric approaches such as bootstrapping and permutation testing, in that this model is able to retain more information contained in the data. This paper details the statistical approaches for several tests of hypothesis and power/sample size calculations, and applies them for illustration to taxonomic abundance distribution and rank abundance distribution data using HMP Jumpstart data on 24 subjects for saliva, subgingival, and supragingival samples. Software for running these analyses is available.

Detection of uterine MMG contractions using a multiple change point estimator and the K-means cluster algorithm.

We propose a single channel two-stage time-segment discriminator of uterine magnetomyogram (MMG) contractions during pregnancy. We assume that the preprocessed signals are piecewise stationary having distribution in a common family with a fixed number of parameters. Therefore, at the first stage, we propose a model-based segmentation procedure, which detects multiple change-points in the parameters of a piecewise constant time-varying autoregressive model using a robust formulation of the Schwarz information criterion (SIC) and a binary search approach. In particular, we propose a test statistic that depends on the SIC, derive its asymptotic distribution, and obtain closed-form optimal detection thresholds in the sense of the Neyman-Pearson criterion; therefore, we control the probability of false alarm and maximize the probability of change-point detection in each stage of the binary search algorithm. We compute and evaluate the relative energy variation [root mean squares (RMS)] and the dominant frequency component [first order zero crossing (FOZC)] in discriminating between time segments with and without contractions. The former consistently detects a time segment with contractions. Thus, at the second stage, we apply a nonsupervised K-means cluster algorithm to classify the detected time segments using the RMS values. We apply our detection algorithm to real MMG records obtained from ten patients admitted to the hospital for contractions with gestational ages between 31 and 40 weeks. We evaluate the performance of our detection algorithm in computing the detection and false alarm rate, respectively, using as a reference the patients' feedback. We also analyze the fusion of the decision signals from all the sensors as in the parallel distributed detection approach.