Age and sex-dependent sensitivity analysis of a common carotid artery model

The common carotid artery (CCA) is an accessible and informative site for assessing cardiovascular function which makes it a prime candidate for clinically relevant computational modelling. The interpretation of supplemental information possible through modelling is encumbered by measurement uncertainty and population variability in model parameters. The distribution of model parameters likely depends on the specific sub-population of interest and delineation based on sex, age or health status may correspond to distinct ranges of typical parameter values. To assess this impact in a 1D-CCA-model, we delineated specific sub-populations based on age, sex and health status and carried out uncertainty quantification and sensitivity analysis for each sub-population. We performed a structured literature review to characterize sub-population-specific variabilities for eight model parameters without consideration of health status; variations for a healthy sub-populations were based on previously established references values. The variabilities of diameter and distensibility found in the literature review differed from those previously established in a healthy population. Model diameter change and pulse pressure were most sensitive to variations in distensibility, while pressure was most sensitive to resistance in the Windkessel model for all groups. Uncertainties were lower when variabilities were based on a healthy sub-population; however, the qualitative distribution of sensitivity indices was largely similar between the healthy and general population. Average sensitivity of the pressure waveform showed a moderate dependence on age with decreasing sensitivity to distal resistance and increasing sensitivity to distensibility and diameter. The female population was less sensitive to variations in diameter but more sensitive to distensibility coefficient than the male population. Overall, as hypothesized input variabilities differed between sub-populations and resulted in distinct uncertainties and sensitivities of the 1D-CCA-model outputs, particularly over age for the pressure waveform and between males and females for pulse pressure.

Uncertainty quantification of the lattice Boltzmann method focussing on studies of human-scale vascular blood flow

Uncertainty quantification is becoming a key tool to ensure that numerical models can be sufficiently trusted to be used in domains such as medical device design. Demonstration of how input parameters impact the quantities of interest generated by any numerical model is essential to understanding the limits of its reliability. With the lattice Boltzmann method now a widely used approach for computational fluid dynamics, building greater understanding of its numerical uncertainty characteristics will support its further use in science and industry. In this study we apply an in-depth uncertainty quantification study of the lattice Boltzmann method in a canonical bifurcating geometry that is representative of the vascular junctions present in arterial and venous domains. These campaigns examine how quantities of interest-pressure and velocity along the central axes of the bifurcation-are influenced by the algorithmic parameters of the lattice Boltzmann method and the parameters controlling the values imposed at inlet velocity and outlet pressure boundary conditions. We also conduct a similar campaign on a set of personalised vessels to further illustrate the application of these techniques. Our work provides insights into how input parameters and boundary conditions impact the velocity and pressure distributions calculated in a simulation and can guide the choices of such values when applied to vascular studies of patient specific geometries. We observe that, from an algorithmic perspective, the number of time steps and the size of the grid spacing are the most influential parameters. When considering the influence of boundary conditions, we note that the magnitude of the inlet velocity and the mean pressure applied within sinusoidal pressure outlets have the greatest impact on output quantities of interest. We also observe that, when comparing the magnitude of variation imposed in the input parameters with that observed in the output quantities, this variability is particularly magnified when the input velocity is altered. This study also demonstrates how open-source toolkits for validation, verification and uncertainty quantification can be applied to numerical models deployed on high-performance computers without the need for modifying the simulation code itself. Such an ability is key to the more widespread adoption of the analysis of uncertainty in numerical models by significantly reducing the complexity of their execution and analysis.

Quantifying uncertainty: Air quality forecasting based on dynamic spatial-temporal denoising diffusion probabilistic model

Air pollution constitutes a substantial peril to human health, thereby catalyzing the evolution of an array of air quality prediction models. These models span from mechanistic and statistical strategies to machine learning methodologies. The burgeoning field of deep learning has given rise to a plethora of advanced models, which have demonstrated commendable performance. However, previous investigations have overlooked the salience of quantifying prediction uncertainties and potential future interconnections among air monitoring stations. Moreover, prior research typically utilized static predetermined spatial relationships, neglecting dynamic dependencies. To address these limitations, we propose a model named Dynamic Spatial-Temporal Denoising Diffusion Probabilistic Model (DST-DDPM) for air quality prediction. Our model is underpinned by the renowned denoising diffusion model, aiding us in discerning indeterminacy. In order to encapsulate dynamic patterns, we design a dynamic context encoder to generate dynamic adjacency matrices, whilst maintaining static spatial information. Furthermore, we incorporate a spatial-temporal denoising model to concurrently learn both spatial and temporal dependencies. Authenticating our model's performance using a real-world dataset collected in Beijing, the outcomes indicate that our model eclipses other baseline models in terms of both short-term and long-term predictions by 1.36% and 11.62% respectively. Finally, we conduct a case study to exhibit our model's capacity to quantify uncertainties.

Multielement simultaneous quantitative analysis of trace elements in stainless steel via full spectrum laser-induced breakdown spectroscopy

Laser-Induced Breakdown Spectroscopy (LIBS) instruments are increasingly recognized as valuable tools for detecting trace metal elements due to their simplicity, rapid detection, and ability to perform simultaneous multi-element analysis. Traditional LIBS modeling often relies on empirical or machine learning-based feature band selection to establish quantitative models. In this study, we introduce a novel approach-simultaneous multi-element quantitative analysis based on the entire spectrum, which enhances model establishment efficiency and leverages the advantages of LIBS. By logarithmically processing the spectra and quantifying the cognitive uncertainty of the model, we achieved remarkable predictive performance (R2) for trace elements Mn, Mo, Cr, and Cu (0.9876, 0.9879, 0.9891, and 0.9841, respectively) in stainless steel. Our multi-element model shares features and parameters during the learning process, effectively mitigating the impact of matrix effects and self-absorption. Additionally, we introduce a cognitive error term to quantify the cognitive uncertainty of the model. The results suggest that our approach has significant potential in the quantitative analysis of trace elements, providing a reliable data processing method for efficient and accurate multi-task analysis in LIBS. This methodology holds promising applications in the field of LIBS quantitative analysis.

Uncertainty quantification in multivariable regression for material property prediction with Bayesian neural networks

With the increased use of data-driven approaches and machine learning-based methods in material science, the importance of reliable uncertainty quantification (UQ) of the predicted variables for informed decision-making cannot be overstated. UQ in material property prediction poses unique challenges, including multi-scale and multi-physics nature of materials, intricate interactions between numerous factors, limited availability of large curated datasets, etc. In this work, we introduce a physics-informed Bayesian Neural Networks (BNNs) approach for UQ, which integrates knowledge from governing laws in materials to guide the models toward physically consistent predictions. To evaluate the approach, we present case studies for predicting the creep rupture life of steel alloys. Experimental validation with three datasets of creep tests demonstrates that this method produces point predictions and uncertainty estimations that are competitive or exceed the performance of conventional UQ methods such as Gaussian Process Regression. Additionally, we evaluate the suitability of employing UQ in an active learning scenario and report competitive performance. The most promising framework for creep life prediction is BNNs based on Markov Chain Monte Carlo approximation of the posterior distribution of network parameters, as it provided more reliable results in comparison to BNNs based on variational inference approximation or related NNs with probabilistic outputs.

Modelling lower-limb peripheral arterial disease using clinically available datasets: impact of inflow boundary conditions on hemodynamic indices for restenosis prediction

BACKGROUND AND OBJECTIVES

The integration of hemodynamic markers as risk factors in restenosis prediction models for lower-limb peripheral arteries is hindered by fragmented clinical datasets. Computed tomography (CT) scans enable vessel geometry reconstruction and can be obtained at different times than the Doppler ultrasound (DUS) images, which provide information on blood flow velocity. Computational fluid dynamics (CFD) simulations allow the computation of near-wall hemodynamic indices, whose accuracy depends on the prescribed inlet boundary condition (BC), derived from the DUS images. This study aims to: (i) investigate the impact of different DUS-derived velocity waveforms on CFD results; (ii) test whether the same vessel areas, subjected to altered hemodynamics, can be detected independently of the applied inlet BC; (iii) suggest suitable DUS images to obtain reliable CFD results.

METHODS

CFD simulations were conducted on three patients treated with bypass surgery, using patient-specific DUS-derived inlet BCs recorded at either the same or different time points than the CT scan. The impact of the chosen inflow condition on bypass hemodynamics was assessed in terms of wall shear stress (WSS)-derived quantities. Patient-specific critical thresholds for the hemodynamic indices were applied to identify critical luminal areas and compare the results with a reference obtained with a DUS image acquired in close temporal proximity to the CT scan.

RESULTS

The main findings indicate that: (i) DUS-derived inlet velocity waveforms acquired at different time points than the CT scan led to statistically significantly different CFD results (p<0.001); (ii) the same luminal surface areas, exposed to low time-averaged WSS, could be identified independently of the applied inlet BCs; (iii) similar outcomes were observed for the other hemodynamic indices if the prescribed inlet velocity waveform had the same shape and comparable systolic acceleration time to the one recorded in close temporal proximity to the CT scan.

CONCLUSIONS

Despite a lack of standardised data collection for diseased lower-limb peripheral arteries, an accurate estimation of luminal areas subjected to altered near-wall hemodynamics is possible independently of the applied inlet BC. This holds if the applied inlet waveform shares some characteristics - derivable from the DUS report - as one matching the acquisition time of the CT scan.

Multilevel Monte Carlo Methods for Stochastic Convection-Diffusion Eigenvalue Problems

We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection-diffusion operator with random coefficients. The MLMC method is based on a sequence of finite element (FE) discretizations of the eigenvalue problem on a hierarchy of increasingly finer meshes. For the discretized, algebraic eigenproblems we use both the Rayleigh quotient (RQ) iteration and implicitly restarted Arnoldi (IRA), providing an analysis of the cost in each case. By studying the variance on each level and adapting classical FE error bounds to the stochastic setting, we are able to bound the total error of our MLMC estimator and provide a complexity analysis. As expected, the complexity bound for our MLMC estimator is superior to plain Monte Carlo. To improve the efficiency of the MLMC further, we exploit the hierarchy of meshes and use coarser approximations as starting values for the eigensolvers on finer ones. To improve the stability of the MLMC method for convection-dominated problems, we employ two additional strategies. First, we consider the streamline upwind Petrov-Galerkin formulation of the discrete eigenvalue problem, which allows us to start the MLMC method on coarser meshes than is possible with standard FEs. Second, we apply a homotopy method to add stability to the eigensolver for each sample. Finally, we present a multilevel quasi-Monte Carlo method that replaces Monte Carlo with a quasi-Monte Carlo (QMC) rule on each level. Due to the faster convergence of QMC, this improves the overall complexity. We provide detailed numerical results comparing our different strategies to demonstrate the practical feasibility of the MLMC method in different use cases. The results support our complexity analysis and further demonstrate the superiority over plain Monte Carlo in all cases.

Establishing finite element model credibility of a pedicle screw system under compression-bending: An end-to-end example of the ASME V&V 40 standard

Computational modeling and simulation (CM&S) is a key tool in medical device design, development, and regulatory approval. For example, finite element analysis (FEA) is widely used to understand the mechanical integrity and durability of orthopaedic implants. The ASME V&V 40 standard and supporting FDA guidance provide a framework for establishing model credibility, enabling deeper reliance on CM&S throughout the total product lifecycle. Examples of how to apply the principles outlined in the ASME V&V 40 standard are important to facilitating greater adoption by the medical device community, but few published examples are available that demonstrate best practices. Therefore, this paper outlines an end-to-end (E2E) example of the ASME V&V 40 standard applied to an orthopaedic implant. The objective of this study was to illustrate how to establish the credibility of a computational model intended for use as part of regulatory evaluation. In particular, this study focused on whether a design change to a spinal pedicle screw construct (specifically, the addition of a cannulation to an existing non-cannulated pedicle screw) would compromise the rod-screw construct mechanical performance. This question of interest (?OI) was addressed by establishing model credibility requirements according to the ASME V&V 40 standard. Experimental testing to support model validation was performed using spinal rods and non-cannulated pedicle screw constructs made with medical grade titanium (Ti-6Al-4V ELI). FEA replicating the experimental tests was performed by three independent modelers and validated through comparisons of common mechanical properties such as stiffness and yield force. The validated model was then used to simulate F1717 compression-bending testing on the new cannulated pedicle screw design to answer the ?OI, without performing any additional experimental testing. This E2E example provides a realistic scenario for the application of the ASME V&V 40 standard to orthopedic medical device applications.

Photometric stereo data for the validation of a structural health monitoring test rig

Photometric stereo uses images of objects illuminated from various directions to calculate surface normals which can be used to generate 3D meshes of the object. Such meshes can be used by engineers to estimate damage of a concrete surface, or track damage progression over time to inform maintenance decisions. This dataset [1] was collected to quantify the uncertainty in a photometric stereo test rig through both the comparison with a well characterised method (coordinate measurement machine) and experiment virtualisation. Data was collected for 9 real objects using both the test rig and the coordinate measurement machine. These objects range from clay statues to damaged concrete slabs. Furthermore, synthetic data for 12 objects was created via virtual renders generated using Blender (3D software) [2]. The two methods of data generation allowed the decoupling of the physical rig (used to light and photograph objects) and the photometric stereo algorithm (used to convert images and lighting information into 3D meshes). This data can allow users to: test their own photometric stereo algorithms, with specialised data created for structural health monitoring applications; provide an industrially relevant case study to develop and test uncertainty quantification methods on test rigs for structural health monitoring of concrete; or develop data processing methodologies for the alignment of scaled, translated, and rotated data.

Uncertainty-aware image classification on 3D CT lung

Early detection is crucial for lung cancer to prolong the patient's survival. Existing model architectures used in such systems have shown promising results. However, they lack reliability and robustness in their predictions and the models are typically evaluated on a single dataset, making them overconfident when a new class is present. With the existence of uncertainty, uncertain images can be referred to medical experts for a second opinion. Thus, we propose an uncertainty-aware framework that includes three phases: data preprocessing and model selection and evaluation, uncertainty quantification (UQ), and uncertainty measurement and data referral for the classification of benign and malignant nodules using 3D CT images. To quantify the uncertainty, we employed three approaches; Monte Carlo Dropout (MCD), Deep Ensemble (DE), and Ensemble Monte Carlo Dropout (EMCD). We evaluated eight different deep learning models consisting of ResNet, DenseNet, and the Inception network family, all of which achieved average F1 scores above 0.832, and the highest average value of 0.845 was obtained using InceptionResNetV2. Furthermore, incorporating the UQ demonstrated significant improvement in the overall model performance. Upon evaluation of the uncertainty estimate, MCD outperforms the other UQ models except for the metric, URecall, where DE and EMCD excel, implying that they are better at identifying incorrect predictions with higher uncertainty levels, which is vital in the medical field. Finally, we show that using a threshold for data referral can greatly improve the performance further, increasing the accuracy up to 0.959.

Neural orientation distribution fields for estimation and uncertainty quantification in diffusion MRI

Inferring brain connectivity and structure in-vivo requires accurate estimation of the orientation distribution function (ODF), which encodes key local tissue properties. However, estimating the ODF from diffusion MRI (dMRI) signals is a challenging inverse problem due to obstacles such as significant noise, high-dimensional parameter spaces, and sparse angular measurements. In this paper, we address these challenges by proposing a novel deep-learning based methodology for continuous estimation and uncertainty quantification of the spatially varying ODF field. We use a neural field (NF) to parameterize a random series representation of the latent ODFs, implicitly modeling the often ignored but valuable spatial correlation structures in the data, and thereby improving efficiency in sparse and noisy regimes. An analytic approximation to the posterior predictive distribution is derived which can be used to quantify the uncertainty in the ODF estimate at any spatial location, avoiding the need for expensive resampling-based approaches that are typically employed for this purpose. We present empirical evaluations on both synthetic and real in-vivo diffusion data, demonstrating the advantages of our method over existing approaches.

Modeling county level COVID-19 transmission in the greater St. Louis area: Challenges of uncertainty and identifiability when fitting mechanistic models to time-varying processes

We use a compartmental model with a time-varying transmission parameter to describe county level COVID-19 transmission in the greater St. Louis area of Missouri and investigate the challenges in fitting such a model to time-varying processes. We fit this model to synthetic and real confirmed case and hospital discharge data from May to December 2020 and calculate uncertainties in the resulting parameter estimates. We also explore non-identifiability within the estimated parameter set. We find that the death rate of infectious non-hospitalized individuals, the testing parameter and the initial number of exposed individuals are not identifiable based on an investigation of correlation coefficients between pairs of parameter estimates. We also explore how this non-identifiability ties back into uncertainties in the estimated parameters and find that it inflates uncertainty in the estimates of our time-varying transmission parameter. However, we do find that R0 is not highly affected by non-identifiability of its constituent components and the uncertainties associated with the quantity are smaller than those of the estimated parameters. Parameter values estimated from data will always be associated with some uncertainty and our work highlights the importance of conducting these analyses when fitting such models to real data. Exploring identifiability and uncertainty is crucial in revealing how much we can trust the parameter estimates.

Relationship between prediction accuracy and uncertainty in compound potency prediction using deep neural networks and control models

The assessment of prediction variance or uncertainty contributes to the evaluation of machine learning models. In molecular machine learning, uncertainty quantification is an evolving area of research where currently no standard approaches or general guidelines are available. We have carried out a detailed analysis of deep neural network variants and simple control models for compound potency prediction to study relationships between prediction accuracy and uncertainty. For comparably accurate predictions obtained with models of different complexity, highly variable prediction uncertainties were detected using different metrics. Furthermore, a strong dependence of prediction characteristics and uncertainties on potency levels of test compounds was observed, often leading to over- or under-confident model decisions with respect to the expected variance of predictions. Moreover, neural network models responded very differently to training set modifications. Taken together, our findings indicate that there is only little, if any correlation between compound potency prediction accuracy and uncertainty, especially for deep neural network models, when predictions are assessed on the basis of currently used metrics for uncertainty quantification.

Cryo-forum: A framework for orientation recovery with uncertainty measure with the application in cryo-EM image analysis

In single-particle cryo-electron microscopy (cryo-EM), efficient determination of orientation parameters for particle images poses a significant challenge yet is crucial for reconstructing 3D structures. This task is complicated by the high noise levels in the datasets, which often include outliers, necessitating several time-consuming 2D clean-up processes. Recently, solutions based on deep learning have emerged, offering a more streamlined approach to the traditionally laborious task of orientation estimation. These solutions employ amortized inference, eliminating the need to estimate parameters individually for each image. However, these methods frequently overlook the presence of outliers and may not adequately concentrate on the components used within the network. This paper introduces a novel method using a 10-dimensional feature vector for orientation representation, extracting orientations as unit quaternions with an accompanying uncertainty metric. Furthermore, we propose a unique loss function that considers the pairwise distances between orientations, thereby enhancing the accuracy of our method. Finally, we also comprehensively evaluate the design choices in constructing the encoder network, a topic that has not received sufficient attention in the literature. Our numerical analysis demonstrates that our methodology effectively recovers orientations from 2D cryo-EM images in an end-to-end manner. Notably, the inclusion of uncertainty quantification allows for direct clean-up of the dataset at the 3D level. Lastly, we package our proposed methods into a user-friendly software suite named cryo-forum, designed for easy access by developers.

Uncertainty-based saltwater intrusion prediction using integrated Bayesian machine learning modeling (IBMLM) in a deep aquifer

Data-driven machine learning approaches are promising to substitute physically based groundwater numerical models and capture input-output relationships for reducing computational burden. But the performance and reliability are strongly influenced by different sources of uncertainty. Conventional researches generally rely on a stand-alone machine learning surrogate approach and fail to account for errors in model outputs resulting from structural deficiencies. To overcome this issue, this study proposes a flexible integrated Bayesian machine learning modeling (IBMLM) method to explicitly quantify uncertainties originating from structures and parameters of machine learning surrogate models. An Expectation-Maximization (EM) algorithm is combined with Bayesian model averaging (BMA) to find out maximum likelihood and construct posterior predictive distribution. Three machine learning approaches representing different model complexity are incorporated in the framework, including artificial neural network (ANN), support vector machine (SVM) and random forest (RF). The proposed IBMLM method is demonstrated in a field-scale real-world "1500-foot" sand aquifer, Baton Rouge, USA, where overexploitation caused serious saltwater intrusion (SWI) issues. This study adds to the understanding of how chloride concentration transport responds to multi-dimensional extraction-injection remediation strategies in a sophisticated saltwater intrusion model. Results show that most IBMLM exhibit r values above 0.98 and NSE values above 0.93, both slightly higher than individual machine learning, confirming that the IBMLM is well established to provide better model predictions than individual machine learning models, while maintaining the advantage of high computing efficiency. The IBMLM is found useful to predict saltwater intrusion without running the physically based numerical simulation model. We conclude that an explicit consideration of machine learning model structure uncertainty along with parameters improves accuracy and reliability of predictions, and also corrects uncertainty bounds. The applicability of the IBMLM framework can be extended in regions where a physical hydrogeologic model is difficult to build due to lack of subsurface information.

Uncertainty quantification of the wall thickness and stiffness in an idealized dissected aorta

Personalized treatment informed by computational models has the potential to markedly improve the outcome for patients with a type B aortic dissection. However, existing computational models of dissected walls significantly simplify the characteristic false lumen, tears and/or material behavior. Moreover, the patient-specific wall thickness and stiffness cannot be accurately captured non-invasively in clinical practice, which inevitably leads to assumptions in these wall models. It is important to evaluate the impact of the corresponding uncertainty on the predicted wall deformations and stress, which are both key outcome indicators for treatment optimization. Therefore, a physiology-inspired finite element framework was proposed to model the wall deformation and stress of a type B aortic dissection at diastolic and systolic pressure. Based on this framework, 300 finite element analyses, sampled with a Latin hypercube, were performed to assess the global uncertainty, introduced by 4 uncertain wall thickness and stiffness input parameters, on 4 displacement and stress output parameters. The specific impact of each input parameter was estimated using Gaussian process regression, as surrogate model of the finite element framework, and a δ moment-independent analysis. The global uncertainty analysis indicated minor differences between the uncertainty at diastolic and systolic pressure. For all output parameters, the 4th quartile contained the major fraction of the uncertainty. The parameter-specific uncertainty analysis elucidated that the material stiffness and relative thickness of the dissected membrane were the respective main determinants of the wall deformation and stress. The uncertainty analysis provides insight into the effect of uncertain wall thickness and stiffness parameters on the predicted deformation and stress. Moreover, it emphasizes the need for probabilistic rather than deterministic predictions for clinical decision making in aortic dissections.

Model-based dimensionality reduction for single-cell RNA-seq using generalized bilinear models

Dimensionality reduction is a critical step in the analysis of single-cell RNA-seq (scRNA-seq) data. The standard approach is to apply a transformation to the count matrix followed by principal components analysis (PCA). However, this approach can induce spurious heterogeneity and mask true biological variability. An alternative approach is to directly model the counts, but existing methods tend to be computationally intractable on large datasets and do not quantify uncertainty in the low-dimensional representation. To address these problems, we develop scGBM, a novel method for model-based dimensionality reduction of scRNA-seq data using a Poisson bilinear model. We introduce a fast estimation algorithm to fit the model using iteratively reweighted singular value decompositions, enabling the method to scale to datasets with millions of cells. Furthermore, scGBM quantifies the uncertainty in each cell's latent position and leverages these uncertainties to assess the confidence associated with a given cell clustering. On real and simulated single-cell data, we find that scGBM produces low-dimensional embeddings that better capture relevant biological information while removing unwanted variation.

Intrinsic and extrinsic techniques for quantification uncertainty of an interpretable GRU deep learning model used to predict atmospheric total suspended particulates (TSP) in Zabol, Iran during the dusty period of 120-days wind

Total suspended particulates (TSP), as a key pollutant, is a serious threat for air quality, climate, ecosystems and human health. Therefore, measurements, prediction and forecasting of TSP concentrations are necessary to mitigate their negative effects. This study applies the gated recurrent unit (GRU) deep learning model to predict TSP concentrations in Zabol, Iran, during the dust period of the 120-day wind (3 June - 4 October 2014). Three uncertainty quantification (UQ) techniques consisting of the blackbox metamodel, heteroscedastic regression and infinitesimal jackknife were applied to quantify the uncertainty associated with GRU model. Permutation feature importance measure (PFIM), based on the game theory, was employed for the interpretability of the predictive model's outputs. A total of 80 TSP samples were collected and were randomly divided as training (70%) and validation (30%) datasets, while eight variables were used in the TSP prediction model. Our findings showed that GRU performed very well for TSP prediction (with r and Nash Sutcliffe coefficient (NSC) values above 0.99 for both datasets, and RMSE of 57 μg m-3 and 73 μg m-3 for training and validation datasets, respectively). Among the three UQ techniques, the infinitesimal jackknife was the most accurate one, while all the observed and predicted TSP values fell within the continence limitation estimated by the model. PFIM plots showed that wind speed and air humidity were the most and least important variables, respectively, impacting the predictive model's outputs. This is the first attempt of using an interpretable DL model for TSP prediction modelling, recommending that future research should involve aspects of uncertainty and interpretability of the predictive models. Overall, UQ and interpretability techniques have a key role in reducing the impact of uncertainties during optimization and decision making, resulting in better understanding of sophisticated mechanisms related to the predictive model.

Experimental vibration dataset collected of a beam reinforced with masses under different health conditions

Vibration signals extracted from structures across diverse health conditions have become indispensable for monitoring structural integrity. These datasets represent a resource for real-time condition monitoring, enabling the precise detection and diagnosis of system anomalies. This paper aims to enrich the scientific community's database on structural dynamics and experimental methodologies pertinent to system modelling. Leveraging experimental measurements obtained from mass-reinforced beams, these datasets validate numerical models, refine identification techniques, quantify uncertainties, and continuously foster machine learning algorithms' evolution to monitor structural integrity. Furthermore, the beam dataset is data-driven and can be used to develop and test innovative structural health monitoring strategies, specifically identifying damages and anomalies within intricate structural frameworks. Supplemental datasets like Mass-position and damage index introduce parametric uncertainty into experimental and damage identification metrics. Thereby offering valuable insights to elevate the efficacy of monitoring and control techniques. These comprehensive tests also encapsulate paramedic uncertainty, providing robust support for applications in uncertainty quantification, stochastic modelling, and supervised and unsupervised machine learning methodologies.

American society of anesthesiologists physical status classification significantly affects the performances of machine learning models in intraoperative hypotension inference

STUDY OBJECTIVE

To explore how American Society of Anesthesiologists (ASA) physical status classification affects different machine learning models in hypotension prediction and whether the prediction uncertainty could be quantified.

DESIGN

Observational Studies SETTING: UofL health hospital PATIENTS: This study involved 562 hysterectomy surgeries performed on patients (≥ 18 years) between June 2020 and July 2021.

INTERVENTIONS

None MEASUREMENTS: Preoperative and intraoperative data is collected. Three parametric machine learning models, including Bayesian generalized linear model (BGLM), Bayesian neural network (BNN), a newly proposed BNN with multivariate mixed responses (BNNMR), and one nonparametric model, Gaussian Process (GP), were explored to predict patients' diastolic and systolic blood pressures (continuous responses) and patients' hypotensive event (binary response) for the next five minutes. Data was separated into American Society of Anesthesiologists (ASA) physical status class 1- 4 before being read in by four machine learning models. Statistical analysis and models' constructions are performed in Python. Sensitivity, specificity, and the confidence/credible intervals were used to evaluate the prediction performance of each model for each ASA physical status class.

MAIN RESULTS

ASA physical status classes require distinct models to accurately predict intraoperative blood pressures and hypotensive events. Overall, high sensitivity (above 0.85) and low uncertainty can be achieved by all models for ASA class 4 patients. In contrast, models trained without controlling ASA classes yielded lower sensitivity (below 0.5) and larger uncertainty. Particularly, in terms of predicting binary hypotensive event, for ASA physical status class 1, BNNMR yields the highest sensitivity of 1. For classes 2 and 3, BNN has the highest sensitivity of 0.429 and 0.415, respectively. For class 4, BNNMR and GP are tied with the highest sensitivity of 0.857. On the other hand, the sensitivity is just 0.031, 0.429, 0.165 and 0.305 for BNNMR, BNN, GBLM and GP models respectively, when training data is not divided by ASA physical status classes. In terms of predicting systolic blood pressure, the GP regression yields the lowest root mean squared errors (RMSE) of 2.072, 7.539, 9.214 and 0.295 for ASA physical status classes 1, 2, 3 and 4, respectively, but a RMSE of 126.894 if model is trained without controlling the ASA physical status class. The RMSEs for other models are far higher. RMSEs are 2.175, 13.861, 17.560 and 22.426 for classes 1, 2, 3 and 4 respectively for the BGLM. In terms of predicting diastolic blood pressure, the GP regression yields the lowest RMSEs of 2.152, 6.573, 5.371 and 0.831 for ASA physical status classes 1, 2, 3 and 4, respectively; RMSE of 8.084 if model is trained without controlling the ASA physical status class. The RMSEs for other models are far higher. Finally, in terms of the width of the 95% confidence interval of the mean prediction for systolic and diastolic blood pressures, GP regression gives narrower confidence interval with much smaller margin of error across all four ASA physical status classes.

CONCLUSIONS

Different ASA physical status classes present different data distributions, and thus calls for distinct machine learning models to improve prediction accuracy and reduce predictive uncertainty. Uncertainty quantification enabled by Bayesian inference provides valuable information for clinicians as an additional metric to evaluate performance of machine learning models for medical decision making.

Enhancing subsurface contamination assessment via ensemble prediction of ground electrical property: A Colorado AMD-impacted wetland case study

Acid mine drainage (AMD) is recognized as a major environmental challenge in the Western United States, particularly in Colorado, leading to extreme subsurface contamination issue. Given Colorado's arid climate and dependence on groundwater, an accurate assessment of AMD-induced contamination is deemed crucial. While in past, machine learning (ML)-based inversion algorithms were used to reconstruct ground electrical properties (GEP) such as relative dielectric permittivity (RDP) from ground penetrating radar (GPR) data for contamination assessment, their inherent non-linear nature can introduce significant uncertainty and non-uniqueness into the reconstructed models. This is a challenge that traditional ML methods are not explicitly designed to address. In this study, a probabilistic hybrid technique has been introduced that combines the DeepLabv3+ architecture-based deep convolutional neural network (DCNN) with an ensemble prediction-based Monte Carlo (MC) dropout method. Different MC dropout rates (1%, 5%, and 10%) were initially evaluated using 1D and 2D synthetic GPR data for accurate and reliable RDP model prediction. The optimal rate was chosen based on minimal prediction uncertainty and the closest alignment of the mean or median model with the true RDP model. Notably, with the optimal MC dropout rate, prediction accuracy of over 95% for the 1D and 2D cases was achieved. Motivated by these results, the hybrid technique was applied to field GPR data collected over an AMD-impacted wetland near Silverton, Colorado. The field results underscored the hybrid technique's ability to predict an accurate subsurface RDP distribution for estimating the spatial extent of AMD-induced contamination. Notably, this technique not only provides a precise assessment of subsurface contamination but also ensures consistent interpretations of subsurface condition by different environmentalists examining the same GPR data. In conclusion, the hybrid technique presents a promising avenue for future environmental studies in regions affected by AMD or other contaminants that alter the natural distribution of GEP.

Leveraging Bayesian deep learning and ensemble methods for uncertainty quantification in image classification: A ranking-based approach

Bayesian deep learning (BDL) has emerged as a powerful technique for quantifying uncertainty in classification tasks, surpassing the effectiveness of traditional models by aligning with the probabilistic nature of real-world data. This alignment allows for informed decision-making by not only identifying the most likely outcome but also quantifying the surrounding uncertainty. Such capabilities hold great significance in fields like medical diagnoses and autonomous driving, where the consequences of misclassification are substantial. To further improve uncertainty quantification, the research community has introduced Bayesian model ensembles, which combines multiple Bayesian models to enhance predictive accuracy and uncertainty quantification. These ensembles have exhibited superior performance compared to individual Bayesian models and even non-Bayesian counterparts. In this study, we propose a novel approach that leverages the power of Bayesian ensembles for enhanced uncertainty quantification. The proposed method exploits the disparity between predicted positive and negative classes and employes it as a ranking metric for model selection. For each instance or sample, the ensemble's output for each class is determined by selecting the top 'k' models based on this ranking. Experimental results on different medical image classifications demonstrate that the proposed method consistently outperforms or achieves comparable performance to conventional Bayesian ensemble. This investigation highlights the practical application of Bayesian ensemble techniques in refining predictive performance and enhancing uncertainty evaluation in image classification tasks.

DM-CNN: Dynamic Multi-scale Convolutional Neural Network with uncertainty quantification for medical image classification

Convolutional neural network (CNN) has promoted the development of diagnosis technology of medical images. However, the performance of CNN is limited by insufficient feature information and inaccurate attention weight. Previous works have improved the accuracy and speed of CNN but ignored the uncertainty of the prediction, that is to say, uncertainty of CNN has not received enough attention. Therefore, it is still a great challenge for extracting effective features and uncertainty quantification of medical deep learning models In order to solve the above problems, this paper proposes a novel convolutional neural network model named DM-CNN, which mainly contains the four proposed sub-modules : dynamic multi-scale feature fusion module (DMFF), hierarchical dynamic uncertainty quantifies attention (HDUQ-Attention) and multi-scale fusion pooling method (MF Pooling) and multi-objective loss (MO loss). DMFF select different convolution kernels according to the feature maps at different levels, extract different-scale feature information, and make the feature information of each layer have stronger representation ability for information fusion HDUQ-Attention includes a tuning block that adjust the attention weight according to the different information of each layer, and a Monte-Carlo (MC) dropout structure for quantifying uncertainty MF Pooling is a pooling method designed for multi-scale models, which can speed up the calculation and prevent overfitting while retaining the main important information Because the number of parameters in the backbone part of DM-CNN is different from other modules, MO loss is proposed, which has a fast optimization speed and good classification effect DM-CNN conducts experiments on publicly available datasets in four areas of medicine (Dermatology, Histopathology, Respirology, Ophthalmology), achieving state-of-the-art classification performance on all datasets. DM-CNN can not only maintain excellent performance, but also solve the problem of quantification of uncertainty, which is a very important task for the medical field. The code is available: https://github.com/QIANXIN22/DM-CNN.

A calibration and uncertainty quantification analysis of classical, fractional and multiscale logistic models of tumour growth

BACKGROUND AND OBJECTIVE

The validation of mathematical models of tumour growth is frequently hampered by the lack of sufficient experimental data, resulting in qualitative rather than quantitative studies. Recent approaches to this problem have attempted to extract information about tumour growth by integrating multiscale experimental measurements, such as longitudinal cell counts and gene expression data. In the present study, we investigated the performance of several mathematical models of tumour growth, including classical logistic, fractional and novel multiscale models, in terms of quantifying in-vitro tumour growth in the presence and absence of therapy. We further examined the effect of genes associated with changes in chemosensitivity in cell death rates.

METHODS

The multiscale expansion of logistic growth models was performed by coupling gene expression profiles to the cell death rates. State-of-the-art Bayesian inference, likelihood maximisation and uncertainty quantification techniques allowed a thorough evaluation of model performance.

RESULTS

The results suggest that the classical single-cell population model (SCPM) was the best fit for the untreated and low-dose treatment conditions, while the multiscale model with a cell death rate symmetric with the expression profile of OCT4 (Sym-SCPM) yielded the best fit for the high-dose treatment data. Further identifiability analysis showed that the multiscale model was both structurally and practically identifiable under the condition of known OCT4 expression profiles.

CONCLUSIONS

Overall, the present study demonstrates that model performance can be improved by incorporating multiscale measurements of tumour growth when high-dose treatment is involved.

Machine learning modeling of lung mechanics: Assessing the variability and propagation of uncertainty in respiratory-system compliance and airway resistance

BACKGROUND AND OBJECTIVE

Traditional assessment of patient response in mechanical ventilation relies on respiratory-system compliance and airway resistance. Clinical evidence has shown high variability in these parameters, highlighting the difficulty of predicting them before the start of ventilation therapy. This motivates the creation of computational models that can connect structural and tissue features with lung mechanics. In this work, we leverage machine learning (ML) techniques to construct predictive lung function models informed by non-linear finite element simulations, and use them to investigate the propagation of uncertainty in the lung mechanical response.

METHODS

We revisit a continuum poromechanical formulation of the lungs suitable for determining patient response. Based on this framework, we create high-fidelity finite element models of human lungs from medical images. We also develop a low-fidelity model based on an idealized sphere geometry. We then use these models to train and validate three ML architectures: single-fidelity and multi-fidelity Gaussian process regression, and artificial neural networks. We use the best predictive ML model to further study the sensitivity of lung response to variations in tissue structural parameters and boundary conditions via sensitivity analysis and forward uncertainty quantification. Codes are available for download at https://github.com/comp-medicine-uc/ML-lung-mechanics-UQ RESULTS: The low-fidelity model delivers a lung response very close to that predicted by high-fidelity simulations and at a fraction of the computational time. Regarding the trained ML models, the multi-fidelity GP model consistently delivers better accuracy than the single-fidelity GP and neural network models in estimating respiratory-system compliance and resistance (R2∼0.99). In terms of computational efficiency, our ML model delivers a massive speed-up of ∼970,000× with respect to high-fidelity simulations. Regarding lung function, we observed an almost matched and non-linear behavior between specific structural parameters and chest wall stiffness with compliance. Also, we observed a strong modulation of airways resistance with tissue permeability.

CONCLUSIONS

Our findings unveil the relevance of specific lung tissue parameters and boundary conditions in the respiratory-system response. Furthermore, we highlight the advantages of adopting a multi-fidelity ML approach that combines data from different levels to yield accurate and efficient estimates of clinical mechanical markers. We envision that the methods presented here can open the way to the development of predictive ML models of the lung response that can inform clinical decisions.

Deep learning uncertainty quantification for clinical text classification

INTRODUCTION

Machine learning algorithms are expected to work side-by-side with humans in decision-making pipelines. Thus, the ability of classifiers to make reliable decisions is of paramount importance. Deep neural networks (DNNs) represent the state-of-the-art models to address real-world classification. Although the strength of activation in DNNs is often correlated with the network's confidence, in-depth analyses are needed to establish whether they are well calibrated.

METHOD

In this paper, we demonstrate the use of DNN-based classification tools to benefit cancer registries by automating information extraction of disease at diagnosis and at surgery from electronic text pathology reports from the US National Cancer Institute (NCI) Surveillance, Epidemiology, and End Results (SEER) population-based cancer registries. In particular, we introduce multiple methods for selective classification to achieve a target level of accuracy on multiple classification tasks while minimizing the rejection amount-that is, the number of electronic pathology reports for which the model's predictions are unreliable. We evaluate the proposed methods by comparing our approach with the current in-house deep learning-based abstaining classifier.

RESULTS

Overall, all the proposed selective classification methods effectively allow for achieving the targeted level of accuracy or higher in a trade-off analysis aimed to minimize the rejection rate. On in-distribution validation and holdout test data, with all the proposed methods, we achieve on all tasks the required target level of accuracy with a lower rejection rate than the deep abstaining classifier (DAC). Interpreting the results for the out-of-distribution test data is more complex; nevertheless, in this case as well, the rejection rate from the best among the proposed methods achieving 97% accuracy or higher is lower than the rejection rate based on the DAC.

CONCLUSIONS

We show that although both approaches can flag those samples that should be manually reviewed and labeled by human annotators, the newly proposed methods retain a larger fraction and do so without retraining-thus offering a reduced computational cost compared with the in-house deep learning-based abstaining classifier.

Empirical Quantification of Predictive Uncertainty Due to Model Discrepancy by Training with an Ensemble of Experimental Designs: An Application to Ion Channel Kinetics

When using mathematical models to make quantitative predictions for clinical or industrial use, it is important that predictions come with a reliable estimate of their accuracy (uncertainty quantification). Because models of complex biological systems are always large simplifications, model discrepancy arises-models fail to perfectly recapitulate the true data generating process. This presents a particular challenge for making accurate predictions, and especially for accurately quantifying uncertainty in these predictions. Experimentalists and modellers must choose which experimental procedures (protocols) are used to produce data used to train models. We propose to characterise uncertainty owing to model discrepancy with an ensemble of parameter sets, each of which results from training to data from a different protocol. The variability in predictions from this ensemble provides an empirical estimate of predictive uncertainty owing to model discrepancy, even for unseen protocols. We use the example of electrophysiology experiments that investigate the properties of hERG potassium channels. Here, 'information-rich' protocols allow mathematical models to be trained using numerous short experiments performed on the same cell. In this case, we simulate data with one model and fit it with a different (discrepant) one. For any individual experimental protocol, parameter estimates vary little under repeated samples from the assumed additive independent Gaussian noise model. Yet parameter sets arising from the same model applied to different experiments conflict-highlighting model discrepancy. Our methods will help select more suitable ion channel models for future studies, and will be widely applicable to a range of biological modelling problems.

Evaluating uncertainty-based active learning for accelerating the generalization of molecular property prediction

Deep learning models have proven to be a powerful tool for the prediction of molecular properties for applications including drug design and the development of energy storage materials. However, in order to learn accurate and robust structure-property mappings, these models require large amounts of data which can be a challenge to collect given the time and resource-intensive nature of experimental material characterization efforts. Additionally, such models fail to generalize to new types of molecular structures that were not included in the model training data. The acceleration of material development through uncertainty-guided experimental design has the promise to significantly reduce the data requirements and enable faster generalization to new types of materials. To evaluate the potential of such approaches for electrolyte design applications, we perform comprehensive evaluation of existing uncertainty quantification methods on the prediction of two relevant molecular properties - aqueous solubility and redox potential. We develop novel evaluation methods to probe the utility of the uncertainty estimates for both in-domain and out-of-domain data sets. Finally, we leverage selected uncertainty estimation methods for active learning to evaluate their capacity to support experimental design.

Sensitivity of hostile hemodynamics to aneurysm geometry via unsupervised shape interpolation

BACKGROUND AND OBJECTIVE

Vessel geometry and hemodynamics are intrinsically linked, whereby geometry determines hemodynamics, and hemodynamics influence vascular remodeling. Both have been used for testing clinical outcomes, but geometry/morphology generally has less uncertainty than hemodynamics derived from medical image-based computational fluid dynamics (CFD). To provide clinical utility, CFD-based hemodynamic parameters must be robust to modeling errors and/or uncertainties, but must also provide useful information not more-easily extracted from shape alone. The objective of this study was to methodically assess the response of hemodynamic parameters to gradual changes in shape created using an unsupervised 3D shape interpolation method.

METHODS

We trained the neural network NeuroMorph on 3 patient-derived intracranial aneurysm surfaces (labelled A, B, C), and then generated 3 distinct morph sequences (A→B, B→C, C→A) each containing 10 interpolated surfaces. From high-fidelity CFD simulation of these, we calculated a variety of common reduced hemodynamic parameters, including many previously associated with aneurysm rupture, and analyzed their responses to changes in shape, and their correlations.

RESULTS

The interpolated surfaces demonstrate complex, gradual changes in branch angles, vessel diameters, and aneurysm morphology. CFD simulation showed gradual changes in aneurysm jetting characteristics and wall-shear stress (WSS) patterns, but demonstrated a range of responses from the reduced hemodynamic parameters. Spatially and temporally averaged parameters including time-averaged WSS, time-averaged velocity, and low-shear area (LSA) showed low variation across all morph sequences, while parameters of flow complexity such as oscillatory shear, spectral broadening, and spectral bandedness indices showed high variation between slightly-altered neighboring surfaces. Correlation analysis revealed a great deal of mutual information with easier-to-measure shape-based parameters.

CONCLUSIONS

In the absence of large clinical datasets, unsupervised shape interpolation provides an ideal laboratory for exploring the delicate balance between robustness and sensitivity of nominal hemodynamic predictors of aneurysm rupture. Parameters like time-averaged WSS and LSA that are highly "robust" may, as a result, be effectively redundant to morphological predictors, whereas more sensitive parameters may be too uncertain for practical clinical use. Understanding these sensitivities may help identify parameters that are capable of providing added value to rupture risk assessment.

Quantification of forest carbon flux and stock uncertainties under climate change and their use in regionally explicit decision making: Case study in Finland

Uncertainties are essential, yet often neglected, information for evaluating the reliability in forest carbon balance projections used in national and regional policy planning. We analysed uncertainties in the forest net biome exchange (NBE) and carbon stocks under multiple management and climate scenarios with a process-based ecosystem model. Sampled forest initial state values, model parameters, harvest levels and global climate models (GCMs) served as inputs in Monte Carlo simulations, which covered forests of the 18 regions of mainland Finland over the period 2015-2050. Under individual scenarios, the results revealed time- and region-dependent variability in the magnitude of uncertainty and mean values of the NBE projections. The main sources of uncertainty varied with time, by region and by the amount of harvested wood. Combinations of uncertainties in the representative concentration pathways scenarios, GCMs, forest initial values and model parameters were the main sources of uncertainty at the beginning, while the harvest scenarios dominated by the end of the simulation period, combined with GCMs and climate scenarios especially in the north. Our regionally explicit uncertainty analysis was found a useful approach to reveal the variability in the regional potentials to reach a policy related, future target level of NBE, which is important information when planning realistic and regionally fair national policy actions.

Computation of a probabilistic uranium concentration map of Norway: A digital expert elicitation approach employing random forests and artificial neural networks

We compute the first probabilistic uranium concentration map of Norway. Such a map can support mineral exploration, geochemical mapping, or the assessment of the health risk to the human population. We employ multiple non-linear regression to fill the information gaps in sparse airborne and ground-borne uranium data sets. We mimic an expert elicitation by employing Random Forests and Multi-layer Perceptrons as digital agents equally qualified to find regression models. In addition to the regression, we use supervised classification to produce conservative and alarmistic classified maps outlining regions with different potential for the local occurrence of uranium concentration extremes. Embedding the introduced digital expert elicitation in a Monte Carlo approach we compute an ensemble of plausible uranium concentrations maps of Norway discretely quantifying the uncertainty resulting from the choice of the regression algorithm and the chosen parametrization of the used regression algorithms. We introduce digitated glyphs to visually integrate all computed maps and their associated uncertainties in a loss-free manner to fully communicate our probabilistic results to map perceivers. A strong correlation between mapped geology and uranium concentration is found, which could be used to optimize future sparse uranium concentration sampling to lower extrapolation components in future map updates.

Probabilistic assessment of failure of infiltration structures under model and parametric uncertainty

We focus on the quantification of the probability of failure (PF) of an infiltration structure, of the kind that is typically employed for the implementation of low impact development strategies in urban settings. Our approach embeds various sources of uncertainty. These include (a) the mathematical models rendering key hydrological traits of the system and the ensuing model parametrization as well as (b) design variables related to the drainage structure. As such, we leverage on a rigorous multi-model Global Sensitivity Analysis framework. We consider a collection of commonly used alternative models to represent our knowledge about the conceptualization of the system functioning. Each model is characterized by a set of uncertain parameters. As an original aspect, the sensitivity metrics we consider are related to a single- and a multi-model context. The former provides information about the relative importance that model parameters conditional to the choice of a given model can have on PF. The latter yields the importance that the selection of a given model has on PF and enables one to consider at the same time all of the alternative models analyzed. We demonstrate our approach through an exemplary application focused on the preliminary design phase of infiltration structures serving a region in the northern part of Italy. Results stemming from a multi-model context suggest that the contribution arising from the adoption of a given model is key to the quantification of the degree of importance associated with each uncertain parameter.

A Bayesian method with nonlinear noise model to calibrate constitutive parameters of soft tissue

The measured mechanical responses of soft tissue exhibit large variability and errors, especially for the softest brain tissue, while calibrating its constitutive parameters in a deterministic way remains a common practice. Here we implement a Bayesian method considering the nonlinear noise model to calibrate constitutive parameters of brain tissue. A probability model is first developed based on the measured experimental data, likelihood function, and prior function, from which the posterior distributions of model parameters are formulated. The likelihood function considers the nonlinear behaviors of the constitutive response and noise distribution of the experimentally measured data. Meanwhile, the prior predictive distribution is computed to check the probability model preliminarily. Secondly, the Markov Chain Monte Carlo (MCMC) method is used to compute the posterior distributions of model parameters, enabling assessment of parameter uncertainty, correlation, and model calibration error. Finally, the posterior predictive distributions of the overall response, constitutive response, and noise response are computed to validate the probabilistic model, all of which are consistent with the corresponding data. Furthermore, the effect of the prior distribution, experimental data, and noise model on posterior distribution is studied. Our study provides a general approach to calibrating constitutive parameters of soft tissue despite errors and large variability in experimental data.

Uncertainty quantification of microcirculatory characteristic parameters for recognition of cardiovascular diseases

BACKGROUND

Cardiovascular disease is one of the leading causes of death worldwide. However, according to studies, 90% of cardiovascular diseases can be prevented. Cardiovascular function parameters are an important basis for the diagnosis of cardiovascular diseases. The pulse wave also contains a wealth of physiological and pathological information, which can reflect the trend of cardiac function parameters at an early stage, so the measurement and analysis of the pulse wave signal becomes more and more important. The wearable pulse signal acquisition device has gradually become a new trend. In the mobile health scenario, convenient use is the prerequisite for long-term and rapid health monitoring. The data containing diverse pulse wave signals is the basis for obtaining more comprehensive and accurate human physiopathological information. Accurate data analysis and processing is the key to realizing the important goal of cardiovascular health monitoring.

OBJECTIVE

Based on the concept of mobile health care, wearable devices are developed to obtain physiological signals. The zero-dimensional model and the optimization algorithm are combined to complete the uncertainty quantification of the microcirculation parameters. Then, a feature set containing the cardiovasvular parameters can be constructed. The machine learning algorithm can be used to build a model that can accurately realize cardiovascular disease identification.

METHODS

This paper adopts laboratory-developed equipment to acquire the wrist pulse wave and fingertip volume pulse wave. A total of 323 samples were collected from healthy populations, hypertensive patients and patients with coronary heart disease (CHD). The pulse blood flow model in fingertip microcirculation is established, and the uncertainty quantification of model parameters is completed based on slime mold algorithm (SMA). After comparing and analyzing the performance of four algorithms on pulse wave classification, the identification model of cardiovascular diseases is established based on the microcirculatory characteristic parameter set and random forest algorithm (RF).

RESULTS

RF showed good classification performance among the four classification algorithms. The identification accuracy of the model built on the microcirculatory characteristic parameter set and RF algorithm all reached more than 88%. The highest recognition accuracy was 95.51% for coronary heart disease samples, 92.11% for healthy samples, and 88.55% for hypertensive samples. It can be seen that the model based on RF algorithm has a good ability to distinguish the characteristic parameters in different cardiovascular health states.

CONCLUSIONS

The wearable device designed in this paper can facilitate the daily health monitoring of cardiovascular disease. By using the combination of the physical model and machine learning model, the uncertainty quantification of microcirculation parameters and the identification of cardiovascular disease was finally completed. The recognition model based on machine learning provides a new idea and method for the research of cardiovascular health monitoring through pulse waves.

Impact of the Spatial Velocity Inlet Distribution on the Hemodynamics of the Thoracic Aorta

The impact of the distribution in space of the inlet velocity in the numerical simulations of the hemodynamics in the thoracic aorta is systematically investigated. A real healthy aorta geometry, for which in-vivo measurements are available, is considered. The distribution is modeled through a truncated cone shape, which is a suitable approximation of the real one downstream of a trileaflet aortic valve during the systolic part of the cardiac cycle. The ratio between the upper and the lower base of the truncated cone and the position of the center of the upper base are selected as uncertain parameters. A stochastic approach is chosen, based on the generalized Polynomial Chaos expansion, to obtain accurate response surfaces of the quantities of interest in the parameter space. The selected parameters influence the velocity distribution in the ascending aorta. Consequently, effects on the wall shear stress are observed, confirming the need to use patient-specific inlet conditions if interested in the hemodynamics of this region. The surface base ratio is globally the most important parameter. Conversely, the impact on the velocity and wall shear stress in the aortic arch and descending aorta is almost negligible.

Uncertainty quantification and attention-aware fusion guided multi-modal MR brain tumor segmentation

Brain tumor is one of the most aggressive cancers in the world, accurate brain tumor segmentation plays a critical role in clinical diagnosis and treatment planning. Although deep learning models have presented remarkable success in medical segmentation, they can only obtain the segmentation map without capturing the segmentation uncertainty. To achieve accurate and safe clinical results, it is necessary to produce extra uncertainty maps to assist the subsequent segmentation revision. To this end, we propose to exploit the uncertainty quantification in the deep learning model and apply it to multi-modal brain tumor segmentation. In addition, we develop an effective attention-aware multi-modal fusion method to learn the complimentary feature information from the multiple MR modalities. First, a multi-encoder-based 3D U-Net is proposed to obtain the initial segmentation results. Then, an estimated Bayesian model is presented to measure the uncertainty of the initial segmentation results. Finally, the obtained uncertainty maps are integrated into a deep learning-based segmentation network, serving as an additional constraint information to further refine the segmentation results. The proposed network is evaluated on publicly available BraTS 2018 and BraTS 2019 datasets. The experimental results demonstrate that the proposed method outperforms the previous state-of-the-art methods on Dice score, Hausdorff distance and Sensitivity metrics. Furthermore, the proposed components could be easily applied to other network architectures and other computer vision fields.

Calibrating ensembles for scalable uncertainty quantification in deep learning-based medical image segmentation

Uncertainty quantification in automated image analysis is highly desired in many applications. Typically, machine learning models in classification or segmentation are only developed to provide binary answers; however, quantifying the uncertainty of the models can play a critical role for example in active learning or machine human interaction. Uncertainty quantification is especially difficult when using deep learning-based models, which are the state-of-the-art in many imaging applications. The current uncertainty quantification approaches do not scale well in high-dimensional real-world problems. Scalable solutions often rely on classical techniques, such as dropout, during inference or training ensembles of identical models with different random seeds to obtain a posterior distribution. In this paper, we present the following contributions. First, we show that the classical approaches fail to approximate the classification probability. Second, we propose a scalable and intuitive framework for uncertainty quantification in medical image segmentation that yields measurements that approximate the classification probability. Third, we suggest the usage of k-fold cross-validation to overcome the need for held out calibration data. Lastly, we motivate the adoption of our method in active learning, creating pseudo-labels to learn from unlabeled images and human-machine collaboration.

Reducing Bias and Quantifying Uncertainty in Fluorescence Produced by PCR

We present a new approach for relating nucleic-acid content to fluorescence in a real-time Polymerase Chain Reaction (PCR) assay. By coupling a two-type branching process for PCR with a fluorescence analog of Beer's Law, the approach reduces bias and quantifies uncertainty in fluorescence. As the two-type branching process distinguishes between complementary strands of DNA, it allows for a stoichiometric description of reactions between fluorescent probes and DNA and can capture the initial conditions encountered in assays targeting RNA. Analysis of the expected copy-number identifies additional dynamics that occur at short times (or, equivalently, low cycle numbers), while investigation of the variance reveals the contributions from liquid volume transfer, imperfect amplification, and strand-specific amplification (i.e., if one strand is synthesized more efficiently than its complement). Linking the branching process to fluorescence by the Beer's Law analog allows for an a priori description of background fluorescence. It also enables uncertainty quantification (UQ) in fluorescence which, in turn, leads to analytical relationships between amplification efficiency (probability) and limit of detection. This work sets the stage for UQ-PCR, where both the input copy-number and its uncertainty are quantified from fluorescence kinetics.

A data-driven approach for modelling Karst spring discharge using transfer function noise models

Karst aquifers are important sources of fresh water on a global scale. The hydrological modelling of karst spring discharge, however, still poses a challenge. In this study we apply a transfer function noise (TFN) model in combination with a bucket-type recharge model to simulate karst spring discharge. The application of the noise model for the residual series has the advantage that it is more consistent with assumptions for optimization such as homoscedasticity and independence. In an earlier hydrological modeling study, named Karst Modeling Challenge (KMC; Jeannin et al., J Hydrol 600:126-508, 2021), several modelling approaches were compared for the Milandre Karst System in Switzerland. This serves as a benchmark and we apply the TFN model to KMC data, subsequently comparing the results to other models. Using different data-model-combinations, the most promising data-model-combination is identified in a three-step least-squares calibration. To quantify uncertainty, the Bayesian approach of Markov-chain Monte Carlo (MCMC) sampling is subsequently used with uniform priors for the previously identified best data-model combination. The MCMC maximum likelihood solution is used to simulate spring discharge for a previously unseen testing period, indicating a superior performance compared to all other models in the KMC. It is found that the model gives a physically feasible representation of the system, which is supported by field measurements. While the TFN model simulated rising limbs and flood recession especially well, medium and baseflow conditions were not represented as accurately. The TFN approach poses a well-performing data-driven alternative to other approaches that should be considered in future studies.

Uncertainty quantification of CO2 emissions from China's civil aviation industry to 2050

To mitigate aviation's carbon emissions of the aviation industry, the following steps are vital: accurately quantifying the carbon emission path by considering uncertainty factors, including transportation demand in the post-COVID-19 pandemic period; identifying gaps between this path and emission reduction targets; and providing mitigation measures. Some mitigation measures that can be employed by China's civil aviation industry include the gradual realization of large-scale production of sustainable aviation fuels and transition to 100% sustainable and low-carbon sources of energy. This study identified the key driving factors of carbon emissions by using the Delphi Method and set scenarios that consider uncertainty, such as aviation development and emission reduction policies. A backpropagation neural network and Monte Carlo simulation were used to quantify the carbon emission path. The study results show that China's civil aviation industry can effectively help the country achieve its carbon peak and carbon neutrality goals. However, to achieve the net-zero carbon emissions goal of global aviation, China needs to reduce its emissions by approximately 82%-91% based on the optimal emission scenario. Thus, under the international net-zero target, China's civil aviation industry will face significant pressure to reduce its emissions. The use of sustainable aviation fuels is the best way to reduce aviation emissions by 2050. Moreover, in addition to the application of sustainable aviation fuel, it will be necessary to develop a new generation of aircraft introducing new materials and upgrading technology, implement additional carbon absorption measures, and make use of carbon trading markets to facilitate China's civil aviation industry's contribution to reduce climate change.

Evaluating point-prediction uncertainties in neural networks for protein-ligand binding prediction

Neural Network (NN) models provide potential to speed up the drug discovery process and reduce its failure rates. The success of NN models requires uncertainty quantification (UQ) as drug discovery explores chemical space beyond the training data distribution. Standard NN models do not provide uncertainty information. Some methods require changing the NN architecture or training procedure, limiting the selection of NN models. Moreover, predictive uncertainty can come from different sources. It is important to have the ability to separately model different types of predictive uncertainty, as the model can take assorted actions depending on the source of uncertainty. In this paper, we examine UQ methods that estimate different sources of predictive uncertainty for NN models aiming at protein-ligand binding prediction. We use our prior knowledge on chemical compounds to design the experiments. By utilizing a visualization method we create non-overlapping and chemically diverse partitions from a collection of chemical compounds. These partitions are used as training and test set splits to explore NN model uncertainty. We demonstrate how the uncertainties estimated by the selected methods describe different sources of uncertainty under different partitions and featurization schemes and the relationship to prediction error.

Conservation of forest biomass and forest-dependent wildlife population: Uncertainty quantification of the model parameters

The ecosystem is confronted with numerous challenges as a consequence of the escalating human population and its corresponding activities. Among these challenges lies the degradation of forest biomass, which directly contributes to a reduction in forested areas and poses a significant threat to the survival of wildlife species through the intensification of intraspecific competition. In this paper, a non-linear mathematical model to study the conservation of forest and wildlife species that are reliant on forest ecosystem within the framework of human population dynamics and its related activities is developed and analysed. The study assessed the impacts of economic measures in the form of incentives on reducing population pressure on forest resources as well as the potential benefits of technological efforts to accelerate the rate of reforestation. Qualitative and quantitative analyses reveals that economic and technological factors have the potential to contribute to resource conservation efforts. However, these efforts can only be used to a limited extent, and contrary to that, the system will be destabilised. Sensitivity analysis identified the parameters pertaining to human population, human activities, economic measures, and technological efforts as the most influential factors in the model.

N-Map: High-resolution groundwater N-retention mapping and modelling by integration of geophysical, geological, geochemical, and hydrological data

A key aspect of protecting aquatic ecosystems from agricultural nitrogen (N) is to locate (i) farmlands where nitrate leaches from the bottom of the root zone and (ii) denitrifying zones in the aquifers where nitrate is removed before entering the surface water (N-retention). N-retention affects the choice of field mitigation measures to reduce delivered N to surface water. Farmland parcels associated with high N-retention gives the lowest impact of the targeted field measures and vice versa. In Denmark, a targeted N-regulation approach is currently implemented on small catchment scale (approx. 15 km²). Although this regulatory scale is much more detailed than what has been used previously, it is still so large that regulation for most individual fields will be either over- or under-regulated due to large spatial variation in the N-retention. The potential cost reduction for farmers is of up to 20-30% from detailed retention mapping at the field scale compared to the current small catchment scale. In this study, we present a mapping framework (N-Map) for differentiating farmland according to their N-retention, which can be used for improving the effectiveness of targeted N-regulation. The framework currently only includes N-retention in the groundwater. The framework benefits from the incorporation of innovative geophysics in hydrogeological and geochemical mapping and modelling. To capture and describe relevant uncertainties a large number of equally probable realizations are created through Multiple Point Statistical (MPS) methods. This allows relevant descriptions of uncertainties of parts of the model structure and includes other relevant uncertainty measures that affects the obtained N-retention. The output is data-driven high-resolution groundwater N-retention maps, to be used by the individual farmers to manage their cropping systems due to the given regulatory boundary conditions. The detailed mapping allows farmers to use this information in the farm planning in order to optimize the use of field measures to reduce delivered agricultural N to the surface water and thereby lower the costs of the field measures. From farmer interviews, however, it is clear that not all farms will have an economic gain from the detailed mapping as the mapping costs will exceed the potential economic gains for the farmers. The costs of N-Map is here estimated to 5-7 €/ha/year plus implementation costs at the farm. At the society level, the N-retention maps allow authorities to point out opportunities for a more targeted implementation of field measures to efficiently reduce the delivered N-load to surface waters.

Large-scale evaluation of k-fold cross-validation ensembles for uncertainty estimation

It is insightful to report an estimator that describes how certain a model is in a prediction, additionally to the prediction alone. For regression tasks, most approaches implement a variation of the ensemble method, apart from few exceptions. Instead of a single estimator, a group of estimators yields several predictions for an input. The uncertainty can then be quantified by measuring the disagreement between the predictions, for example by the standard deviation. In theory, ensembles should not only provide uncertainties, they also boost the predictive performance by reducing errors arising from variance. Despite the development of novel methods, they are still considered the "golden-standard" to quantify the uncertainty of regression models. Subsampling-based methods to obtain ensembles can be applied to all models, regardless whether they are related to deep learning or traditional machine learning. However, little attention has been given to the question whether the ensemble method is applicable to virtually all scenarios occurring in the field of cheminformatics. In a widespread and diversified attempt, ensembles are evaluated for 32 datasets of different sizes and modeling difficulty, ranging from physicochemical properties to biological activities. For increasing ensemble sizes with up to 200 members, the predictive performance as well as the applicability as uncertainty estimator are shown for all combinations of five modeling techniques and four molecular featurizations. Useful recommendations were derived for practitioners regarding the success and minimum size of ensembles, depending on whether predictive performance or uncertainty quantification is of more importance for the task at hand.

Tropical altitudinal gradient soil organic carbon and nitrogen estimation using Specim IQ portable imaging spectrometer

The largest actively cycling terrestrial carbon pool, soil, has been disturbed during latest centuries by human actions through reduction of woody land cover. Soil organic carbon (SOC) content can reliably be estimated in laboratory conditions, but more cost-efficient and mobile techniques are needed for large-scale monitoring of SOC e.g. in remote areas. We demonstrate the capability of a mobile hyperspectral camera operating in the visible-near infrared wavelength range for practical estimation of soil organic carbon (SOC) and nitrogen content, to support efficient monitoring of soil properties. The 191 soil samples were collected in Taita Taveta County, Kenya representing an altitudinal gradient comprising five typical land use types: agroforestry, cropland, forest, shrubland and sisal estate. The soil samples were imaged using a Specim IQ hyperspectral camera under controlled laboratory conditions, and their carbon and nitrogen content was determined with a combustion analyzer. We use machine learning for estimating SOC and N content based on the spectral images, studying also automatic selection of informative wavelengths and quantification of prediction uncertainty. Five alternative methods were all found to perform well with a cross-validated R² of approximately 0.8 and an RMSE of one percentage point, demonstrating feasibility of the proposed imaging setup and computational pipeline.

A comparison of numerical approaches for statistical inference with stochastic models

Due to our limited knowledge about complex environmental systems, our predictions of their behavior under different scenarios or decision alternatives are subject to considerable uncertainty. As this uncertainty can often be relevant for societal decisions, the consideration, quantification and communication of it is very important. Due to internal stochasticity, often poorly known influence factors, and only partly known mechanisms, in many cases, a stochastic model is needed to get an adequate description of uncertainty. As this implies the need to infer constant parameters, as well as the time-course of stochastic model states, a very high-dimensional inference problem for model calibration has to be solved. This is very challenging from a methodological and a numerical perspective. To illustrate aspects of this problem and show options to successfully tackle it, we compare three numerical approaches: Hamiltonian Monte Carlo, Particle Markov Chain Monte Carlo, and Conditional Ornstein-Uhlenbeck Sampling. As a case study, we select the analysis of hydrological data with a stochastic hydrological model. We conclude that the performance of the investigated techniques is comparable for the analyzed system, and that also generality and practical considerations may be taken into account to guide the choice of which technique is more appropriate for a particular application.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00477-023-02434-z.

Improving Bayesian radiological profiling of waste drums using Dirichlet priors, Gaussian process priors, and hierarchical modeling

We present three methodological improvements of our recently proposed approach for Bayesian inference of the radionuclide inventory in radioactive waste drums, from radiological measurements. First we resort to the Dirichlet distribution for the prior distribution of the isotopic vector. The Dirichlet distribution possesses the attractive property that the elements of its vector samples sum up to 1. Second, we demonstrate that such Dirichlet priors can be incorporated within an hierarchical modeling of the prior uncertainty in the isotopic vector, when prior information about isotopic composition is available. Our used Bayesian hierarchical modeling framework makes use of this available information but also acknowledges its uncertainty by letting to a controlled extent the information content of the indirect measurement data (i.e., gamma and neutron counts) shape the actual prior distribution of the isotopic vector. Third, we propose to regularize the Bayesian inversion by using Gaussian process (GP) prior modeling when inferring 1D spatially-distributed mass or, equivalently, activity distributions. As of uncertainty in the efficiencies, we keep using the same stylized drum modeling approach as proposed in our previous work to account for the source distribution uncertainty across the vertical direction of the drum. A series of synthetic tests followed by application to a real waste drum show that combining hierarchical modeling of the prior isotopic composition uncertainty together with GP prior modeling of the vertical Pu profile across the drum works well. We also find that our GP prior can handles both cases with and without spatial correlation. Of course, our GP prior modeling framework only makes sense in the context of spatial inference. Furthermore, the computational times involved by our approach are on the order of a few hours, say about 2, to provide uncertainty estimates for all variables of interest in the considered inverse problem. This warrants further investigations to speed up the inference.

Optimizing autoinjector devices using physics-based simulations and Gaussian processes

Autoinjectors are becoming a primary drug delivery option to the subcutaneous space. These devices need to work robustly and autonomously to maximize drug bio-availability. However, current designs ignore the coupling between autoinjector dynamics and tissue biomechanics. Here we present a Bayesian framework for optimization of autoinjector devices that can account for the coupled autoinjector-tissue biomechanics and uncertainty in tissue mechanical behavior. The framework relies on replacing the high fidelity model of tissue insertion with a Gaussian process (GP). The GP model is accurate yet computationally affordable, enabling a thorough sensitivity analysis that identified tissue properties, which are not part of the autoinjector design space, as important variables for the injection process. Higher fracture toughness decreases the crack depth, while tissue shear modulus has the opposite effect. The sensitivity analysis also shows that drug viscosity and spring force, which are part of the design space, affect the location and timing of drug delivery. Low viscosity could lead to premature delivery, but can be prevented with smaller spring forces, while higher viscosity could prevent premature delivery while demanding larger spring forces and increasing the time of injection. Increasing the spring force guarantees penetration to the desired depth, but it can result in undesirably high accelerations. The Bayesian optimization framework tackles the challenge of designing devices with performance metrics coupled to uncertain tissue properties. This work is important for the design of other medical devices for which optimization in the presence of material behavior uncertainty is needed.