Alveolar Microdynamics during Tidal Ventilation in Live Animals Imaged by SPring-8 Synchrotron.

It is self-evident that our chests expand and contract during breathing but, surprisingly, exactly how individual alveoli change shape over the respiratory cycle is still a matter of debate. Some argue that all the alveoli expand and contract rhythmically. Others claim that the lung volume change is due to groups of alveoli collapsing and reopening during ventilation. Although this question might seem to be an insignificant detail for healthy individuals, it might be a matter of life and death for patients with compromised lungs. Past analyses were based on static post-mortem preparations primarily due to technological limitations, and therefore, by definition, incapable of providing dynamic information. In contrast, this study provides the first comprehensive dynamic data on how the shape of the alveoli changes, and, further, provides valuable insights into the optimal lung volume for efficient gas exchange. It is concluded that alveolar micro-dynamics is nonlinear; and at medium lung volume, alveoli expand more than the ducts.

Density physics-informed neural networks reveal sources of cell heterogeneity in signal transduction.

The transduction time between signal initiation and final response provides valuable information on the underlying signaling pathway, including its speed and precision. Furthermore, multi-modality in a transduction-time distribution indicates that the response is regulated by multiple pathways with different transduction speeds. Here, we developed a method called density physics-informed neural networks (Density-PINNs) to infer the transduction-time distribution from measurable final stress response time traces. We applied Density-PINNs to single-cell gene expression data from sixteen promoters regulated by unknown pathways in response to antibiotic stresses. We found that promoters with slower signaling initiation and transduction exhibit larger cell-to-cell heterogeneity in response intensity. However, this heterogeneity was greatly reduced when the response was regulated by slow and fast pathways together. This suggests a strategy for identifying effective signaling pathways for consistent cellular responses to disease treatments. Density-PINNs can also be applied to understand other time delay systems, including infectious diseases.

The monotone traveling wave solution of a bistable three-species competition system via unconstrained neural networks.

In this paper, we approximate traveling wave solutions via artificial neural networks. Finding traveling wave solutions can be interpreted as a forward-inverse problem that solves a differential equation without knowing the exact speed. In general, we require additional restrictions to ensure the uniqueness of traveling wave solutions that satisfy boundary and initial conditions. This paper is based on the theoretical results that the bistable three-species competition system has a unique traveling wave solution on the premise of the monotonicity of the solution. Since the original monotonic neural networks are not smooth functions, they are not suitable for representing solutions of differential equations. We propose a method of approximating a monotone solution via a neural network representing a primitive function of another positive function. In the numerical integration, the operator learning-based neural network resolved the issue of differentiability by replacing the quadrature rule. We also provide theoretical results that a small training loss implies a convergence to a real solution. The set of functions neural networks can represent is dense in the solution space, so the results suggest the convergence of neural networks with appropriate training. We validate that the proposed method works successfully for the cases where the wave speed is identical to zero. Our monotonic neural network achieves a small error, suggesting that an accurate speed and solution can be estimated when the sign of wave speed is known.

Machine Learning-Based COVID-19 Patients Triage Algorithm Using Patient-Generated Health Data from Nationwide Multicenter Database.

INTRODUCTION: A prompt severity assessment model of patients with confirmed infectious diseases could enable efficient diagnosis while alleviating burden on the medical system. This study aims to develop a SARS-CoV-2 severity assessment model and establish a medical system that allows patients to check the severity of their cases and informs them to visit the appropriate clinic center on the basis of past treatment data of other patients with similar severity levels. METHODS: This paper provides the development processes of a severity assessment model using machine learning techniques and its application on SARS-CoV-2-infected patients. The proposed model is trained on a nationwide data set provided by a Korean government agency and only requires patients' basic personal data, allowing them to judge the severity of their own cases. After modeling, the boosting-based decision tree model was selected as the classifier while mortality rate was interpreted as the probability score. The data set was collected from all Korean citizens with confirmed COVID-19 between February 2020 and July 2021 (N = 149,471). RESULTS: The experiments achieved high model performance with an approximate precision of 0.923 and area under the curve of receiver operating characteristic (AUROC) score of 0.950 [95% tolerance interval (TI) 0.940-0.958, 95% confidence interval (CI) 0.949-0.950]. Moreover, our experiments identified the most important variables affecting the severity in the model via sensitivity analysis. CONCLUSION: A prompt severity assessment model for managing infectious people has been attained through using a nationwide data set. It has demonstrated its superior performance by surpassing that of conventional risk assessments. With the model's high performance and easily accessible features, the triage algorithm is expected to be particularly useful when patients monitor their health status by themselves through smartphone applications.

Prediction and recommendation by machine learning through repetitive internal validation for hepatic veno-occlusive disease/sinusoidal obstruction syndrome and early death after allogeneic hematopoietic cell transplantation.

Using traditional statistical methods, we previously analyzed the risk factors and treatment outcomes of veno-occlusive disease/sinusoidal obstruction syndrome (VOD/SOS) after allogeneic hematopoietic cell transplantation. Within the same cohort, we applied machine learning to create prediction and recommendation models. We analyzed 2572 transplants using eXtreme Gradient Boosting (XGBoost) to predict post-transplant VOD/SOS and early death. Using the XGBoost and SHapley Additive exPlanations (SHAP), we found influential factors and devised recommendation models, which were internally verified by repetitive ten-fold cross-validation. SHAP values suggested that gender, busulfan dosage, age, forced expiratory volume, and Disease Risk Index were significant factors for VOD/SOS. The areas under the receiver operating characteristic curves and the areas under the precision-recall curve of the models were 0.740, 0.144 for all VOD/SOS, 0.793, 0.793 for severe to very severe VOD/SOS, and 0.746, 0.304 for early death. According to our single feature recommendation, following the busulfan dosage was the most effective for preventing VOD/SOS. The recommendation method for six adjustable feature sets was also validated, and a subgroup corresponding to five to six features showed significant preventive power for VOD/SOS and early death. Our personalized treatment set recommendation showed reproducibility in repetitive internal validation, but large external cohorts should prospectively validate our model.

Local Stability of Wasserstein GANs With Abstract Gradient Penalty.

The convergence of generative adversarial networks (GANs) has been studied substantially in various aspects to achieve successful generative tasks. Ever since it is first proposed, the idea has achieved many theoretical improvements by injecting an instance noise, choosing different divergences, penalizing the discriminator, and so on. In essence, these efforts are to approximate a real-world measure with an idle measure through a learning procedure. In this article, we provide an analysis of GANs in the most general setting to reveal what, in essence, should be satisfied to achieve successful convergence. This work is not trivial since handling a converging sequence of an abstract measure requires a lot more sophisticated concepts. In doing so, we find an interesting fact that the discriminator can be penalized in a more general setting than what has been implemented. Furthermore, our experiment results substantiate our theoretical argument on various generative tasks.

Neural network approach to data-driven estimation of chemotactic sensitivity in the Keller-Segel model.

We consider the mathematical model of chemotaxis introduced by Patlak, Keller, and Segel. Aggregation and progression waves are present everywhere in the population dynamics of chemotactic cells. Aggregation originates from the chemotaxis of mobile cells, where cells are attracted to migrate to higher concentrations of the chemical signal region produced by themselves. The neural net can be used to find the approximate solution of the PDE. We proved that the error, the difference between the actual value and the predicted value, is bound to a constant multiple of the loss we are learning. Also, the Neural Net approximation can be easily applied to the inverse problem. It was confirmed that even when the coefficient of the PDE equation was unknown, prediction with high accuracy was achieved.

Mechanism Design of Health Care Blockchain System Token Economy: Development Study Based on Simulated Real-World Scenarios.

BACKGROUND: Despite the fact that the adoption rate of electronic health records has increased dramatically among high-income nations, it is still difficult to properly disseminate personal health records. Token economy, through blockchain smart contracts, can better distribute personal health records by providing incentives to patients. However, there have been very few studies regarding the particular factors that should be considered when designing incentive mechanisms in blockchain. OBJECTIVE: The aim of this paper is to provide 2 new mathematical models of token economy in real-world scenarios on health care blockchain platforms. METHODS: First, roles were set for the health care blockchain platform and its token flow. Second, 2 scenarios were introduced: collecting life-log data for an incentive program at a life insurance company to motivate customers to exercise more and recruiting participants for clinical trials of anticancer drugs. In our 2 scenarios, we assumed that there were 3 stakeholders: participants, data recipients (companies), and data providers (health care organizations). We also assumed that the incentives are initially paid out to participants by data recipients, who are focused on minimizing economic and time costs by adapting mechanism design. This concept can be seen as a part of game theory, since the willingness-to-pay of data recipients is important in maintaining the blockchain token economy. In both scenarios, the recruiting company can change the expected recruitment time and number of participants. Suppose a company considers the recruitment time to be more important than the number of participants and rewards. In that case, the company can increase the time weight and adjust cost. When the reward parameter is fixed, the corresponding expected recruitment time can be obtained. Among the reward and time pairs, the pair that minimizes the company's cost was chosen. Finally, the optimized results were compared with the simulations and analyzed accordingly. RESULTS: To minimize the company's costs, reward-time pairs were first collected. It was observed that the expected recruitment time decreased as rewards grew, while the rewards decreased as time cost grew. Therefore, the cost was represented by a convex curve, which made it possible to obtain a minimum-an optimal point-for both scenarios. Through sensitivity analysis, we observed that, as the time weight increased, the optimized reward increased, while the optimized time decreased. Moreover, as the number of participants increased, the optimization reward and time also increased. CONCLUSIONS: In this study, we were able to model the incentive mechanism of blockchain based on a mechanism design that recruits participants through a health care blockchain platform. This study presents a basic approach to incentive modeling in personal health records, demonstrating how health care organizations and funding companies can motivate one another to join the platform.

Patient-Level Cancer Prediction Models From a Nationwide Patient Cohort: Model Development and Validation.

BACKGROUND: Nationwide population-based cohorts provide a new opportunity to build automated risk prediction models at the patient level, and claim data are one of the more useful resources to this end. To avoid unnecessary diagnostic intervention after cancer screening tests, patient-level prediction models should be developed. OBJECTIVE: We aimed to develop cancer prediction models using nationwide claim databases with machine learning algorithms, which are explainable and easily applicable in real-world environments. METHODS: As source data, we used the Korean National Insurance System Database. Every Korean in ≥40 years old undergoes a national health checkup every 2 years. We gathered all variables from the database including demographic information, basic laboratory values, anthropometric values, and previous medical history. We applied conventional logistic regression methods, light gradient boosting methods, neural networks, survival analysis, and one-class embedding classifier methods to effectively analyze high dimension data based on deep learning-based anomaly detection. Performance was measured with area under the curve and area under precision recall curve. We validated our models externally with a health checkup database from a tertiary hospital. RESULTS: The one-class embedding classifier model received the highest area under the curve scores with values of 0.868, 0.849, 0.798, 0.746, 0.800, 0.749, and 0.790 for liver, lung, colorectal, pancreatic, gastric, breast, and cervical cancers, respectively. For area under precision recall curve, the light gradient boosting models had the highest score with values of 0.383, 0.401, 0.387, 0.300, 0.385, 0.357, and 0.296 for liver, lung, colorectal, pancreatic, gastric, breast, and cervical cancers, respectively. CONCLUSIONS: Our results show that it is possible to easily develop applicable cancer prediction models with nationwide claim data using machine learning. The 7 models showed acceptable performances and explainability, and thus can be distributed easily in real-world environments.

Automated cortical thickness measurement of the mandibular condyle head on CBCT images using a deep learning method.

This study proposes a deep learning model for cortical bone segmentation in the mandibular condyle head using cone-beam computed tomography (CBCT) and an automated method for measuring cortical thickness with a color display based on the segmentation results. In total, 12,800 CBCT images from 25 normal subjects, manually labeled by an oral radiologist, served as the gold-standard. The segmentation model combined a modified U-Net and a convolutional neural network for target region classification. Model performance was evaluated using intersection over union (IoU) and the Hausdorff distance in comparison with the gold standard. The second automated model measured the cortical thickness based on a three-dimensional (3D) model rendered from the segmentation results and presented a color visualization of the measurements. The IoU and Hausdorff distance showed high accuracy (0.870 and 0.928 for marrow bone and 0.734 and 1.247 for cortical bone, respectively). A visual comparison of the 3D color maps showed a similar trend to the gold standard. This algorithm for automatic segmentation of the mandibular condyle head and visualization of the measured cortical thickness as a 3D-rendered model with a color map may contribute to the automated quantification of bone thickness changes of the temporomandibular joint complex on CBCT.

Real-World Implications of a Rapidly Responsive COVID-19 Spread Model with Time-Dependent Parameters via Deep Learning: Model Development and Validation.

BACKGROUND: The COVID-19 pandemic has caused major disruptions worldwide since March 2020. The experience of the 1918 influenza pandemic demonstrated that decreases in the infection rates of COVID-19 do not guarantee continuity of the trend. OBJECTIVE: The aim of this study was to develop a precise spread model of COVID-19 with time-dependent parameters via deep learning to respond promptly to the dynamic situation of the outbreak and proactively minimize damage. METHODS: In this study, we investigated a mathematical model with time-dependent parameters via deep learning based on forward-inverse problems. We used data from the Korea Centers for Disease Control and Prevention (KCDC) and the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University for Korea and the other countries, respectively. Because the data consist of confirmed, recovered, and deceased cases, we selected the susceptible-infected-recovered (SIR) model and found approximated solutions as well as model parameters. Specifically, we applied fully connected neural networks to the solutions and parameters and designed suitable loss functions. RESULTS: We developed an entirely new SIR model with time-dependent parameters via deep learning methods. Furthermore, we validated the model with the conventional Runge-Kutta fourth order model to confirm its convergent nature. In addition, we evaluated our model based on the real-world situation reported from the KCDC, the Korean government, and news media. We also crossvalidated our model using data from the CSSE for Italy, Sweden, and the United States. CONCLUSIONS: The methodology and new model of this study could be employed for short-term prediction of COVID-19, which could help the government prepare for a new outbreak. In addition, from the perspective of measuring medical resources, our model has powerful strength because it assumes all the parameters as time-dependent, which reflects the exact status of viral spread.

Global well-posedness and pattern formations of the immune system induced by chemotaxis.

This paper studies a reaction-diffusion-advection system describing a directed movement of immune cells toward chemokines during the immune process. We investigate the global solvability of the model based on the bootstrap argument for minimal chemotaxis models. We also examine the stability of nonconstant steady states and the existence of periodic orbits from theoretical aspects of bifurcation analysis. Through numerical simulations, we observe the occurrence of steady or time-periodic pattern formations.

Trend to equilibrium for the kinetic Fokker-Planck equation via the neural network approach.

The issue of the relaxation to equilibrium has been at the core of the kinetic theory of rarefied gas dynamics. In the paper, we introduce the Deep Neural Network (DNN) approximated solutions to the kinetic Fokker-Planck equation in a bounded interval and study the large-time asymptotic behavior of the solutions and other physically relevant macroscopic quantities. We impose the varied types of boundary conditions including the inflow-type and the reflection-type boundaries as well as the varied diffusion and friction coefficients and study the boundary effects on the asymptotic behaviors. These include the predictions on the large-time behaviors of the pointwise values of the particle distribution and the macroscopic physical quantities including the total kinetic energy, the entropy, and the free energy. We also provide the theoretical supports for the pointwise convergence of the neural network solutions to the a priori analytic solutions. We use the library PyTorch, the activation function tanh between layers, and the Adam optimizer for the Deep Learning algorithm.

Mathematical modeling and its analysis for instability of the immune system induced by chemotaxis.

In this paper, we study how chemotaxis affects the immune system by proposing a minimal mathematical model, a reaction-diffusion-advection system, describing a cross-talk between antigens and immune cells via chemokines. We analyze the stability and instability arising in our chemotaxis model and find their conditions for different chemotactic strengths by using energy estimates, spectral analysis, and bootstrap argument. Numerical simulations are also performed to the model, by using the finite volume method in order to deal with the chemotaxis term, and the fractional step methods are used to solve the whole system. From the analytical and numerical results for our model, we explain not only the effective attraction of immune cells toward the site of infection but also hypersensitivity when chemotactic strength is greater than some threshold.

Structural design of a double-layered porous hydrogel for effective mass transport.

Mass transport in porous materials is universal in nature, and its worth attracts great attention in many engineering applications. Plant leaves, which work as natural hydraulic pumps for water uptake, have evolved to have the morphological structure for fast water transport to compensate large water loss by leaf transpiration. In this study, we tried to deduce the advantageous structural features of plant leaves for practical applications. Inspired by the tissue organization of the hydraulic pathways in plant leaves, analogous double-layered porous models were fabricated using agarose hydrogel. Solute transport through the hydrogel models with different thickness ratios of the two layers was experimentally observed. In addition, numerical simulation and theoretical analysis were carried out with varying porosity and thickness ratio to investigate the effect of structural factors on mass transport ability. A simple parametric study was also conducted to examine unveiled relations between structural factors. As a result, the porosity and thickness ratio of the two layers are found to govern the mass transport ability in double-layered porous materials. The hydrogel models with widely dispersed pores at a fixed porosity, i.e., close to a homogeneously porous structure, are mostly turned out to exhibit fast mass transport. The present results would provide a new framework for fundamental design of various porous structures for effective mass transport.

Nonlinear oscillations of a sessile drop on a hydrophobic surface induced by ac electrowetting.

We examine the nature of ac electrowetting (EW)-driven axisymmetric oscillations of a sessile water drop on a dielectric substrate. In ac EW, small-amplitude oscillations of a drop differ from the Rayleigh linear modes of freely oscillating drops. In this paper, we demonstrate that changes in the time-averaged contact angle of the sessile drop attributed to the presence of an electric field and a solid substrate mainly caused this discrepancy. We combine the domain perturbation method with the Lindsted-Poincaré method to derive an asymptotic formula for resonant frequency. Theoretical analysis shows that the resonant frequency is a function of the time-averaged contact angle. Each mode of the resonance frequency is a linear function of ɛ(1), which is the magnitude of the cosine of the time-averaged contact angle. The most dominant mode in this study, that is, the fundamental mode n=2, decreases linearly with ɛ(1). The results of the theoretical model are compared with those of both the experiments and numerical simulations. The average resonant frequency deviation between the perturbation solutions and numerical simulations is 4.3%, whereas that between the perturbation solutions and the experiments is 1.8%.

Modeling the role of TGF-ß in regulation of the Th17 phenotype in the LPS-driven immune system.

Airway exposure levels of lipopolysaccharide (LPS) are known to determine type I versus type II helper T cell induced experimental asthma. While low doses of LPS derive Th2 inflammatory responses, high (and/or intermediate) LPS levels induce Th1- or Th17-dominant responses. The present paper develops a mathematical model of the phenotypic switches among three Th phenotypes (Th1, Th2, and Th17) in response to various LPS levels. In the present work, we simplify the complex network of the interactions between cells and regulatory molecules. The model describes the nonlinear cross-talks between the IL-4/Th2 activities and a key regulatory molecule, transforming growth factor ß (TGF-ß), in response to high, intermediate, and low levels of LPS. The model characterizes development of three phenotypes (Th1, Th2, and Th17) and predicts the onset of a new phenotype, Th17, under the tight control of TGF-ß. Analysis of the model illustrates the mono-, bi-, and oneway-switches in the key regulatory parameter sets in the absence or presence of time delays. The model also predicts coexistence of those phenotypes and Th1- or Th2-dominant immune responses in a spatial domain under various biochemical and bio-mechanical conditions in the microenvironment.

Regulation of Th1/Th2 cells in asthma development: a mathematical model.

Airway exposure levels of lipopolysaccharide (LPS) determine type I versus type II helper T cell induced experimental asthma. While high LPS levels induce Th1-dominant responses, low LPS levels derive Th2 cell induced asthma. The present paper develops a mathematical model of asthma development which focuses on the relative balance of Th1 and Th2 cell induced asthma. In the present work we represent the complex network of interactions between cells and molecules by a mathematical model. The model describes the behaviors of cells (Th0, Th1, Th2 and macrophages) and regulatory molecules (IFN- γ, IL-4, IL-12, TNF-α) in response to high, intermediate, and low levels of LPS. The simulations show how variations in the levels of injected LPS affect the development of Th1 or Th2 cell responses through differential cytokine induction. The model also predicts the coexistence of these two types of response under certain biochemical and biomechanical conditions in the microenvironment.

Travelling waves in hyperbolic chemotaxis equations.

Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s (Keller and Segel, J. Theor. Biol. 30:235-248, 1971). The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this paper, we formulate a model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We prove the global existence of solutions and then show the existence of travelling wave solutions both numerically and analytically.