Use of consumer wearables to monitor and predict pain in patients with sickle cell disease.

Background: In sickle cell disease (SCD), unpredictable episodes of acute severe pain, known as vaso-occlusive crises (VOC), disrupt school, work activities and family life and ultimately lead to multiple hospitalizations. The ability to predict VOCs would allow a timely and adequate intervention. The first step towards this ultimate goal is to use patient-friendly and accessible technology to collect relevant data that helps infer a patient's pain experience during VOC. This study aims to: (1) determine the feasibility of remotely monitoring with a consumer wearable during hospitalization for VOC and up to 30 days after discharge, and (2) evaluate the accuracy of pain prediction using machine learning models based on physiological parameters measured by a consumer wearable. Methods: Patients with SCD (≥18 years) who were admitted for a vaso-occlusive crisis were enrolled at a single academic center. Participants were instructed to report daily pain scores (0-10) in a mobile app (Nanbar) and to continuously wear an Apple Watch up to 30 days after discharge. Data included heart rate (in rest, average and variability) and step count. Demographics, SCD genotype, and details of hospitalization including pain scores reported to nurses, were extracted from electronic medical records. Physiological data from the wearable were associated with pain scores to fit 3 different machine learning classification models. The performance of the machine learning models was evaluated using: accuracy, F1, root-mean-square error and area under the receiver-operating curve. Results: Between April and June 2022, 19 patients (74% HbSS genotype) were included in this study and followed for a median time of 28 days [IQR 22-34], yielding a dataset of 2,395 pain data points. Ten participants were enrolled while hospitalized for VOC. The metrics of the best performing model, the random forest model, were micro-averaged accuracy of 92%, micro-averaged F1-score of 0.63, root-mean-square error of 1.1, and area under the receiving operating characteristic curve of 0.9. Conclusion: Our random forest model accurately predicts high pain scores during admission for VOC and after discharge. The Apple Watch was a feasible method to collect physiologic data and provided accuracy in prediction of pain scores.

Improving Pain Assessment Using Vital Signs and Pain Medication for Patients With Sickle Cell Disease: Retrospective Study.

BACKGROUND: Sickle cell disease (SCD) is the most common inherited blood disorder affecting millions of people worldwide. Most patients with SCD experience repeated, unpredictable episodes of severe pain. These pain episodes are the leading cause of emergency department visits among patients with SCD and may last for several weeks. Arguably, the most challenging aspect of treating pain episodes in SCD is assessing and interpreting a patient's pain intensity level. OBJECTIVE: This study aims to learn deep feature representations of subjective pain trajectories using objective physiological signals collected from electronic health records. METHODS: This study used electronic health record data collected from 496 Duke University Medical Center participants over 5 consecutive years. Each record contained measures for 6 vital signs and the patient's self-reported pain score, with an ordinal range from 0 (no pain) to 10 (severe and unbearable pain). We also extracted 3 features related to medication: medication type, medication status (given or applied, or missed or removed or due), and total medication dosage (mg/mL). We used variational autoencoders for representation learning and designed machine learning classification algorithms to build pain prediction models. We evaluated our results using an accuracy and confusion matrix and visualized the qualitative data representations. RESULTS: We designed a classification model using raw data and deep representational learning to predict subjective pain scores with average accuracies of 82.8%, 70.6%, 49.3%, and 47.4% for 2-point, 4-point, 6-point, and 11-point pain ratings, respectively. We observed that random forest classification models trained on deep represented features outperformed models trained on unrepresented data for all pain rating scales. We observed that at varying Likert scales, our models performed better when provided with medication data along with vital signs data. We visualized the data representations to understand the underlying latent representations, indicating neighboring representations for similar pain scores with a higher resolution of pain ratings. CONCLUSIONS: Our results demonstrate that medication information (the type of medication, total medication dosage, and whether the medication was given or missed) can significantly improve subjective pain prediction modeling compared with modeling with only vital signs. This study shows promise in data-driven estimated pain scores that will help clinicians with additional information about the patient's condition, in addition to the patient's self-reported pain scores.

Pain Intensity Assessment in Sickle Cell Disease Patients Using Vital Signs During Hospital Visits.

Pain in sickle cell disease (SCD) is often associated with increased morbidity, mortality, and high healthcare costs. The standard method for predicting the absence, presence, and intensity of pain has long been self-report. However, medical providers struggle to manage patients based on subjective pain reports correctly and pain medications often lead to further difficulties in patient communication as they may cause sedation and sleepiness. Recent studies have shown that objective physiological measures can predict subjective self-reported pain scores for inpatient visits using machine learning (ML) techniques. In this study, we evaluate the generalizability of ML techniques to data collected from 50 patients over an extended period across three types of hospital visits (i.e., inpatient, outpatient and outpatient evaluation). We compare five classification algorithms for various pain intensity levels at both intra-individual (within each patient) and inter-individual (between patients) level. While all the tested classifiers perform much better than chance, a Decision Tree (DT) model performs best at predicting pain on an 11-point severity scale (from 0-10) with an accuracy of 0.728 at an inter-individual level and 0.653 at an intra-individual level. The accuracy of DT significantly improves to 0.941 on a 2-point rating scale (i.e., no/mild pain: 0-5, severe pain: 6-10) at an inter-individual level. Our experimental results demonstrate that ML techniques can provide an objective and quantitative evaluation of pain intensity levels for all three types of hospital visits.

A dynamical model for the origin of anisogamy.

The vast majority of multi-cellular organisms are anisogamous, meaning that male and female sex cells differ in size. It remains an open question how this asymmetric state evolved, presumably from the symmetric isogamous state where all gametes are roughly the same size (drawn from the same distribution). Here, we use tools from the study of nonlinear dynamical systems to develop a simple mathematical model for this phenomenon. Unlike some prior work, we do not assume the existence of mating types. We also model frequency dependent selection via "mean-field coupling," whereby the likelihood that a gamete survives is an increasing function of its size relative to the population's mean gamete size. Using theoretical analysis and numerical simulation, we demonstrate that this mean-referenced competition will almost inevitably result in a stable anisogamous equilibrium, and thus isogamy may naturally lead to anisogamy.

Can subjective pain be inferred from objective physiological data? Evidence from patients with sickle cell disease.

Patients with sickle cell disease (SCD) experience lifelong struggles with both chronic and acute pain, often requiring medical interventMaion. Pain can be managed with medications, but dosages must balance the goal of pain mitigation against the risks of tolerance, addiction and other adverse effects. Setting appropriate dosages requires knowledge of a patient's subjective pain, but collecting pain reports from patients can be difficult for clinicians and disruptive for patients, and is only possible when patients are awake and communicative. Here we investigate methods for estimating SCD patients' pain levels indirectly using vital signs that are routinely collected and documented in medical records. Using machine learning, we develop both sequential and non-sequential probabilistic models that can be used to infer pain levels or changes in pain from sequences of these physiological measures. We demonstrate that these models outperform null models and that objective physiological data can be used to inform estimates for subjective pain.

Modeling the origin of urban-output scaling laws.

Urban outputs often scale superlinearly with city population. A difficulty in understanding the mechanism of this phenomenon is that different outputs differ considerably in their scaling behaviors. Here, we formulate a physics-based model for the origin of superlinear scaling in urban outputs by treating human interaction as a random process. Our model suggests that the increased likelihood of finding required collaborations in a larger population can explain this superlinear scaling, which our model predicts to be non-power-law. Moreover, the extent of superlinearity should be greater for activities that require more collaborators. We test this model using a novel dataset for seven crime types and find strong support.

Continuous Pain Assessment Using Ensemble Feature Selection from Wearable Sensor Data.

Sickle cell disease (SCD) is a red blood cell disorder complicated by lifelong issues with pain. Management of SCD related pain is particularly challenging due to its subjective nature. Hence, the development of an objective automatic pain assessment method is critical to pain management in SCD. In this work, we developed a continuous pain assessment model using physiological and body movement sensor signals collected from a wearable wrist-worn device. Specifically, we implemented ensemble feature selection methods to select robust and stable features extracted from wearable data for better understanding of pain. Our experiments showed that the stability of feature selection methods could be substantially increased by using the ensemble approach. Since different ensemble feature selection methods prefer varying feature subsets for pain estimation, we further utilized stacked generalization to maximize the information usage contained in the selected features from different methods. Using this approach, our best performing model obtained the root-mean-square error of 1.526 and the Pearson correlation of 0.618 for continuous pain assessment. This indicates that subjective pain scores can be estimated using objective wearable sensor data with high precision.

The tipping point: A mathematical model for the profit-driven abandonment of restaurant tipping.

The custom of voluntarily tipping for services rendered has gone in and out of fashion in America since its introduction in the 19th century. Restaurant owners that ban tipping in their establishments often claim that social justice drives their decisions, but we show that rational profit-maximization may also justify the decisions. Here, we propose a conceptual model of restaurant competition for staff and customers, and we show that there exists a critical conventional tip rate at which restaurant owners should eliminate tipping to maximize profits. Because the conventional tip rate has been increasing steadily for the last several decades, our model suggests that restaurant owners may abandon tipping en masse when that critical tip rate is reached.

The statistical mechanics of human weight change.

Over the past 35 years there has been a near doubling in the worldwide prevalence of obesity. Body Mass Index (BMI) distributions in high-income societies have increasingly shifted rightwards, corresponding to increases in average BMI that are due to well-studied changes in the socioeconomic environment. However, in addition to this shift, BMI distributions have also shown marked changes in their particular shape over time, exhibiting an ongoing right-skewed broadening that is not well understood. Here, we compile and analyze the largest data set so far of year-over-year BMI changes. The data confirm that, on average, heavy individuals become lighter while light individuals become heavier year-over-year, and also show that year-over-year BMI evolution is characterized by fluctuations with a magnitude that is linearly proportional to BMI. We find that the distribution of human BMIs is intrinsically dynamic-due to the short-term variability of human weight-and its shape is determined by a balance between deterministic drift towards a natural set point and diffusion resulting from random fluctuations in, e.g., diet and physical activity. We formulate a stochastic mathematical model for BMI dynamics, deriving a theoretical shape for the BMI distribution and offering a mechanism that may explain the right-skewed broadening of BMI distributions over time. An extension of the base model investigates the hypothesis that peer-to-peer social influence plays a role in BMI dynamics. While including this effect improves the fit with the data, indicating that correlations in the behavior of individuals with similar BMI may be important for BMI dynamics, testing social transmission against other plausible unmodeled effects and interpretations remains the subject of future work. Implications of our findings on the dynamics of BMI distributions for public health interventions are discussed.

Hybrid Statistical and Mechanistic Mathematical Model Guides Mobile Health Intervention for Chronic Pain.

Nearly a quarter of visits to the emergency department are for conditions that could have been managed via outpatient treatment; improvements that allow patients to quickly recognize and receive appropriate treatment are crucial. The growing popularity of mobile technology creates new opportunities for real-time adaptive medical intervention, and the simultaneous growth of "big data" sources allows for preparation of personalized recommendations. Here we focus on the reduction of chronic suffering in the sickle cell disease (SCD) community. SCD is a chronic blood disorder in which pain is the most frequent complication. There currently is no standard algorithm or analytical method for real-time adaptive treatment recommendations for pain. Furthermore, current state-of-the-art methods have difficulty in handling continuous-time decision optimization using big data. Facing these challenges, in this study, we aim to develop new mathematical tools for incorporating mobile technology into personalized treatment plans for pain. We present a new hybrid model for the dynamics of subjective pain that consists of a dynamical systems approach using differential equations to predict future pain levels, as well as a statistical approach tying system parameters to patient data (both personal characteristics and medication response history). Pilot testing of our approach suggests that it has significant potential to well predict pain dynamics, given patients reported pain levels and medication usages. With more abundant data, our hybrid approach should allow physicians to make personalized, data-driven recommendations for treating chronic pain.

Connecting the Kuramoto Model and the Chimera State.

Since its discovery in 2002, the chimera state has frequently been described as a counterintuitive, puzzling phenomenon. The Kuramoto model, in contrast, has become a celebrated paradigm useful for understanding a range of phenomena related to phase transitions, synchronization, and network effects. Here we show that the chimera state can be understood as emerging naturally through a symmetry-breaking bifurcation from the Kuramoto model's partially synchronized state. Our analysis sheds light on recent observations of chimera states in laser arrays, chemical oscillators, and mechanical pendula.

Handicap principle implies emergence of dimorphic ornaments.

Species spanning the animal kingdom have evolved extravagant and costly ornaments to attract mating partners. Zahavi's handicap principle offers an elegant explanation for this: ornaments signal individual quality, and must be costly to ensure honest signalling, making mate selection more efficient. Here, we incorporate the assumptions of the handicap principle into a mathematical model and show that they are sufficient to explain the heretofore puzzling observation of bimodally distributed ornament sizes in a variety of species.

Introduction to focus issue: Patterns of network synchronization.

The study of synchronization of coupled systems is currently undergoing a major surge fueled by recent discoveries of new forms of collective dynamics and the development of techniques to characterize a myriad of new patterns of network synchronization. This includes chimera states, phenomena determined by symmetry, remote synchronization, and asymmetry-induced synchronization. This Focus Issue presents a selection of contributions at the forefront of these developments, to which this introduction is intended to offer an up-to-date foundation.

Symmetry-broken states on networks of coupled oscillators.

When identical oscillators are coupled together in a network, dynamical steady states are often assumed to reflect network symmetries. Here, we show that alternative persistent states may also exist that break the symmetries of the underlying coupling network. We further show that these symmetry-broken coexistent states are analogous to those dubbed "chimera states," which can occur when identical oscillators are coupled to one another in identical ways.

Chimera states in networks of phase oscillators: The case of two small populations.

Chimera states are dynamical patterns in networks of coupled oscillators in which regions of synchronous and asynchronous oscillation coexist. Although these states are typically observed in large ensembles of oscillators and analyzed in the continuum limit, chimeras may also occur in systems with finite (and small) numbers of oscillators. Focusing on networks of 2N phase oscillators that are organized in two groups, we find that chimera states, corresponding to attracting periodic orbits, appear with as few as two oscillators per group and demonstrate that for N>2 the bifurcations that create them are analogous to those observed in the continuum limit. These findings suggest that chimeras, which bear striking similarities to dynamical patterns in nature, are observable and robust in small networks that are relevant to a variety of real-world systems.

The influence of societal individualism on a century of tobacco use: modelling the prevalence of smoking.

BACKGROUND: Smoking of tobacco is estimated to have caused approximately six million deaths worldwide in 2014. Responding effectively to this epidemic requires a thorough understanding of how smoking behaviour is transmitted and modified. METHODS: We present a new mathematical model of the social dynamics that cause cigarette smoking to spread in a population, incorporating aspects of individual and social utility. Model predictions are tested against two independent data sets spanning 25 countries: a newly compiled century-long composite data set on smoking prevalence, and Hofstede's individualism/collectivism measure (IDV). RESULTS: The general model prediction that more individualistic societies will show faster adoption and cessation of smoking is supported by the full 25 country smoking prevalence data set. Calibration of the model to the available smoking prevalence data is possible in a subset of 7 countries. Consistency of fitted model parameters with an additional, independent, data set further supports our model: the fitted value of the country-specific model parameter that determines the relative importance of social and individual factors in the decision of whether or not to smoke, is found to be significantly correlated with Hofstede's IDV for the 25 countries in our data set. CONCLUSIONS: Our model in conjunction with extensive data on smoking prevalence provides evidence for the hypothesis that individualism/collectivism may have an important influence on the dynamics of smoking prevalence at the aggregate, population level. Significant implications for public health interventions are discussed.

Chimera states on the surface of a sphere.

A chimera state is a spatiotemporal pattern in which a network of identical coupled oscillators exhibits coexisting regions of asynchronous and synchronous oscillation. Two distinct classes of chimera states have been shown to exist: "spots" and "spirals." Here we study coupled oscillators on the surface of a sphere, a single system in which both spot and spiral chimera states appear. We present an analysis of the birth and death of spiral chimera states and show that although they coexist with spot chimeras, they are stable in disjoint regions of parameter space.

Nonlinear oscillations and bifurcations in silicon photonic microresonators.

Silicon microdisks are optical resonators that can exhibit surprising nonlinear behavior. We present a new analysis of the dynamics of these resonators elucidating the mathematical origin of spontaneous oscillations and deriving predictions for observed phenomena such as a frequency comb spectrum with MHz-scale repetition rate. We test predictions through laboratory experiment and numerical simulation.

Symmetry breaking in optimal timing of traffic signals on an idealized two-way street.

Simple physical models based on fluid mechanics have long been used to understand the flow of vehicular traffic on freeways; analytically tractable models of flow on an urban grid, however, have not been as extensively explored. In an ideal world, traffic signals would be timed such that consecutive lights turned green just as vehicles arrived, eliminating the need to stop at each block. Unfortunately, this "green-wave" scenario is generally unworkable due to frustration imposed by competing demands of traffic moving in different directions. Until now this has typically been resolved by numerical simulation and optimization. Here, we develop a theory for the flow in an idealized system consisting of a long two-way road with periodic intersections. We show that optimal signal timing can be understood analytically and that there are counterintuitive asymmetric solutions to this signal coordination problem. We further explore how these theoretical solutions degrade as traffic conditions vary and automotive density increases.