Guidelines for Mechanistic Modeling and Analysis in Cardiovascular Research.

Computational, or in-silico, models are an effective, non-invasive tool for investigating cardiovascular function. These models can be used in the analysis of experimental and clinical data to identify possible mechanisms of (ab)normal cardiovascular physiology. Recent advances in computing power and data management have led to innovative and complex modeling frameworks that simulate cardiovascular function across multiple scales. While commonly used in multiple disciplines, there is a lack of concise guidelines for the implementation of computer models in cardiovascular research. In line with recent calls for more reproducible research, it is imperative that scientists adhere to credible practices when developing and applying computational models to their research. The goal of this manuscript is to provide a consensus document that identifies best practices for in-silico computational modeling in cardiovascular research. These guidelines provide the necessary methods for mechanistic model development, model analysis, and formal model calibration using fundamentals from statistics. We outline rigorous practices for computational modeling in cardiovascular research and discuss its synergistic value to experimental and clinical data.

Computational framework for the generation of one-dimensional vascular models accounting for uncertainty in networks extracted from medical images.

One-dimensional (1D) cardiovascular models offer a non-invasive method to answer medical questions, including predictions of wave-reflection, shear stress, functional flow reserve, vascular resistance, and compliance. This model type can predict patient-specific outcomes by solving 1D fluid dynamics equations in geometric networks extracted from medical images. However, the inherent uncertainty in in-vivo imaging introduces variability in network size and vessel dimensions, affecting hemodynamic predictions. Understanding the influence of variation in image-derived properties is essential to assess the fidelity of model predictions. Numerous programs exist to render three-dimensional surfaces and construct vessel centerlines. Still, there is no exact way to generate vascular trees from the centerlines while accounting for uncertainty in data. This study introduces an innovative framework employing statistical change point analysis to generate labeled trees that encode vessel dimensions and their associated uncertainty from medical images. To test this framework, we explore the impact of uncertainty in 1D hemodynamic predictions in a systemic and pulmonary arterial network. Simulations explore hemodynamic variations resulting from changes in vessel dimensions and segmentation; the latter is achieved by analyzing multiple segmentations of the same images. Results demonstrate the importance of accurately defining vessel radii and lengths when generating high-fidelity patient-specific hemodynamics models.

Automatic detection of myocardial ischaemia using generalisable spatio-temporal hierarchical Bayesian modelling of DCE-MRI.

Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI) can be used as a non-invasive method for the assessment of myocardial perfusion. The acquired images can be utilised to analyse the spatial extent and severity of myocardial ischaemia (regions with impaired microvascular blood flow). In the present paper, we propose a novel generalisable spatio-temporal hierarchical Bayesian model (GST-HBM) to automate the detection of ischaemic lesions and improve the in silico prediction accuracy by systematically integrating spatio-temporal context information. We present a computational inference procedure with an adequate trade-off between accuracy and computational efficiency, whereby model parameters are sampled from the posterior distribution with Gibbs sampling, while lower-level hyperparameters are selected using model selection strategies based on the Watanabe Akaike information criterion (WAIC). We have assessed our method on both synthetic (in silico) data with known gold-standard and 12 sets of clinical first-pass myocardial perfusion DCE-MRI datasets. We have also carried out a comparative performance evaluation with four established alternative methods: Gaussian mixture model (GMM), opening and closing operations based on Gaussian mixture model (GMMC&Omax), Markov random field constrained Gaussian mixture model (GMM-MRF) and model-based hierarchical Bayesian model (M-HBM). Our results show that the proposed GST-HBM method achieves much higher in silico prediction accuracy than the established alternative methods. Furthermore, this method appears to provide a more robust delineation of ischaemic lesions in datasets affected by spatially variant noise.

LIES of omission: complex observation processes in ecology.

Advances in statistics mean that it is now possible to tackle increasingly sophisticated observation processes. The intricacies and ambitious scale of modern data collection techniques mean that this is now essential. Methodological research to make inference about the biological process while accounting for the observation process has expanded dramatically, but solutions are often presented in field-specific terms, limiting our ability to identify commonalities between methods. We suggest a typology of observation processes that could improve translation between fields and aid methodological synthesis. We propose the LIES framework (defining observation processes in terms of issues of Latency, Identifiability, Effort and Scale) and illustrate its use with both simple examples and more complex case studies.

A Bayesian approach to incorporate structural data into the mapping of genotype to antigenic phenotype of influenza A(H3N2) viruses.

Surface antigens of pathogens are commonly targeted by vaccine-elicited antibodies but antigenic variability, notably in RNA viruses such as influenza, HIV and SARS-CoV-2, pose challenges for control by vaccination. For example, influenza A(H3N2) entered the human population in 1968 causing a pandemic and has since been monitored, along with other seasonal influenza viruses, for the emergence of antigenic drift variants through intensive global surveillance and laboratory characterisation. Statistical models of the relationship between genetic differences among viruses and their antigenic similarity provide useful information to inform vaccine development, though accurate identification of causative mutations is complicated by highly correlated genetic signals that arise due to the evolutionary process. Here, using a sparse hierarchical Bayesian analogue of an experimentally validated model for integrating genetic and antigenic data, we identify the genetic changes in influenza A(H3N2) virus that underpin antigenic drift. We show that incorporating protein structural data into variable selection helps resolve ambiguities arising due to correlated signals, with the proportion of variables representing haemagglutinin positions decisively included, or excluded, increased from 59.8% to 72.4%. The accuracy of variable selection judged by proximity to experimentally determined antigenic sites was improved simultaneously. Structure-guided variable selection thus improves confidence in the identification of genetic explanations of antigenic variation and we also show that prioritising the identification of causative mutations is not detrimental to the predictive capability of the analysis. Indeed, incorporating structural information into variable selection resulted in a model that could more accurately predict antigenic assay titres for phenotypically-uncharacterised virus from genetic sequence. Combined, these analyses have the potential to inform choices of reference viruses, the targeting of laboratory assays, and predictions of the evolutionary success of different genotypes, and can therefore be used to inform vaccine selection processes.

Image-based estimation of the left ventricular cavity volume using deep learning and Gaussian process with cardio-mechanical applications.

In this investigation, an image-based method has been developed to estimate the volume of the left ventricular cavity using cardiac magnetic resonance (CMR) imaging data. Deep learning and Gaussian processes have been applied to bring the estimations closer to the cavity volumes manually extracted. CMR data from 339 patients and healthy volunteers have been used to train a stepwise regression model that can estimate the volume of the left ventricular cavity at the beginning and end of diastole. We have decreased the root mean square error (RMSE) of cavity volume estimation approximately from 13 to 8 ml compared to the common practice in the literature. Considering the RMSE of manual measurements is approximately 4 ml on the same dataset, 8 ml of error is notable for a fully automated estimation method, which needs no supervision or user-hours once it has been trained. Additionally, to demonstrate a clinically relevant application of automatically estimated volumes, we inferred the passive material properties of the myocardium given the volume estimates using a well-validated cardiac model. These material properties can be further used for patient treatment planning and diagnosis.

Inferring the interaction rules of complex systems with graph neural networks and approximate Bayesian computation.

Inferring the underlying processes that drive collective behaviour in biological and social systems is a significant statistical and computational challenge. While simulation models have been successful in qualitatively capturing many of the phenomena observed in these systems in a variety of domains, formally fitting these models to data remains intractable. Recently, approximate Bayesian computation (ABC) has been shown to be an effective approach to inference if the likelihood function for a model is unavailable. However, a key difficulty in successfully implementing ABC lies with the design, selection and weighting of appropriate summary statistics, a challenge that is especially acute when modelling high dimensional complex systems. In this work, we combine a Gaussian process accelerated ABC method with the automatic learning of summary statistics via graph neural networks. Our approach bypasses the need to design a model-specific set of summary statistics for inference. Instead, we encode relational inductive biases into a neural network using a graph embedding and then extract summary statistics automatically from simulation data. To evaluate our framework, we use a model of collective animal movement as a test bed and compare our method to a standard summary statistics approach and a linear regression-based algorithm.

Inferring spatially varying animal movement characteristics using a hierarchical continuous-time velocity model.

Understanding the spatial dynamics of animal movement is an essential component of maintaining ecological connectivity, conserving key habitats, and mitigating the impacts of anthropogenic disturbance. Altered movement and migratory patterns are often an early warning sign of the effects of environmental disturbance, and a precursor to population declines. Here, we present a hierarchical Bayesian framework based on Gaussian processes for analysing the spatial characteristics of animal movement. At the heart of our approach is a novel covariance kernel that links the spatially varying parameters of a continuous-time velocity model with GPS locations from multiple individuals. We demonstrate the effectiveness of our framework by first applying it to a synthetic data set and then by analysing telemetry data from the Serengeti wildebeest migration. Through application of our approach, we are able to identify the key pathways of the wildebeest migration as well as revealing the impacts of environmental features on movement behaviour.

Combining rapid antigen testing and syndromic surveillance improves community-based COVID-19 detection in a low-income country.

Diagnostics for COVID-19 detection are limited in many settings. Syndromic surveillance is often the only means to identify cases but lacks specificity. Rapid antigen testing is inexpensive and easy-to-deploy but can lack sensitivity. We examine how combining these approaches can improve surveillance for guiding interventions in low-income communities in Dhaka, Bangladesh. Rapid-antigen-testing with PCR validation was performed on 1172 symptomatically-identified individuals in their homes. Statistical models were fitted to predict PCR-status using rapid-antigen-test results, syndromic data, and their combination. Under contrasting epidemiological scenarios, the models' predictive and classification performance was evaluated. Models combining rapid-antigen-testing and syndromic data yielded equal-to-better performance to rapid-antigen-test-only models across all scenarios with their best performance in the epidemic growth scenario. These results show that drawing on complementary strengths across rapid diagnostics, improves COVID-19 detection, and reduces false-positive and -negative diagnoses to match local requirements; improvements achievable without additional expense, or changes for patients or practitioners.

Sensitivity analysis and inverse uncertainty quantification for the left ventricular passive mechanics.

Personalized computational cardiac models are considered to be a unique and powerful tool in modern cardiology, integrating the knowledge of physiology, pathology and fundamental laws of mechanics in one framework. They have the potential to improve risk prediction in cardiac patients and assist in the development of new treatments. However, in order to use these models for clinical decision support, it is important that both the impact of model parameter perturbations on the predicted quantities of interest as well as the uncertainty of parameter estimation are properly quantified, where the first task is a priori in nature (meaning independent of any specific clinical data), while the second task is carried out a posteriori (meaning after specific clinical data have been obtained). The present study addresses these challenges for a widely used constitutive law of passive myocardium (the Holzapfel-Ogden model), using global sensitivity analysis (SA) to address the first challenge, and inverse-uncertainty quantification (I-UQ) for the second challenge. The SA is carried out on a range of different input parameters to a left ventricle (LV) model, making use of computationally efficient Gaussian process (GP) surrogate models in place of the numerical forward simulator. The results of the SA are then used to inform a low-order reparametrization of the constitutive law for passive myocardium under consideration. The quality of this parameterization in the context of an inverse problem having observed noisy experimental data is then quantified with an I-UQ study, which again makes use of GP surrogate models. The I-UQ is carried out in a Bayesian manner using Markov Chain Monte Carlo, which allows for full uncertainty quantification of the material parameter estimates. Our study reveals insights into the relation between SA and I-UQ, elucidates the dependence of parameter sensitivity and estimation uncertainty on external factors, like LV cavity pressure, and sheds new light on cardio-mechanic model formulation, with particular focus on the Holzapfel-Ogden myocardial model.

Bayesian optimisation for efficient parameter inference in a cardiac mechanics model of the left ventricle.

We consider parameter inference in cardio-mechanic models of the left ventricle, in particular the one based on the Holtzapfel-Ogden (HO) constitutive law, using clinical in vivo data. The equations underlying these models do not admit closed form solutions and hence need to be solved numerically. These numerical procedures are computationally expensive making computational run times associated with numerical optimisation or sampling excessive for the uptake of the models in the clinical practice. To address this issue, we adopt the framework of Bayesian optimisation (BO), which is an efficient statistical technique of global optimisation. BO seeks the optimum of an unknown black-box function by sequentially training a statistical surrogate-model and using it to select the next query point by leveraging the associated exploration-exploitation trade-off. To guarantee that the estimates based on the in vivo data are realistic also for high-pressures, unobservable in vivo, we include a penalty term based on a previously published empirical law developed using ex vivo data. Two case studies based on real data demonstrate that the proposed BO procedure outperforms the state-of-the-art inference algorithm for the HO constitutive law.

Neural network-based left ventricle geometry prediction from CMR images with application in biomechanics.

Combining biomechanical modelling of left ventricular (LV) function and dysfunction with cardiac magnetic resonance (CMR) imaging has the potential to improve the prognosis of patient-specific cardiovascular disease risks. Biomechanical studies of LV function in three dimensions usually rely on a computerized representation of the LV geometry based on finite element discretization, which is essential for numerically simulating in vivo cardiac dynamics. Detailed knowledge of the LV geometry is also relevant for various other clinical applications, such as assessing the LV cavity volume and wall thickness. Accurately and automatically reconstructing personalized LV geometries from conventional CMR images with minimal manual intervention is still a challenging task, which is a pre-requisite for any subsequent automated biomechanical analysis. We propose a deep learning-based automatic pipeline for predicting the three-dimensional LV geometry directly from routinely-available CMR cine images, without the need to manually annotate the ventricular wall. Our framework takes advantage of a low-dimensional representation of the high-dimensional LV geometry based on principal component analysis. We analyze how the inference of myocardial passive stiffness is affected by using our automatically generated LV geometries instead of manually generated ones. These insights will inform the development of statistical emulators of LV dynamics to avoid computationally expensive biomechanical simulations. Our proposed framework enables accurate LV geometry reconstruction, outperforming previous approaches by delivering a reconstruction error 50% lower than reported in the literature. We further demonstrate that for a nonlinear cardiac mechanics model, using our reconstructed LV geometries instead of manually extracted ones only moderately affects the inference of passive myocardial stiffness described by an anisotropic hyperelastic constitutive law. The developed methodological framework has the potential to make an important step towards personalized medicine by eliminating the need for time consuming and costly manual operations. In addition, our method automatically maps the CMR scan into a low-dimensional representation of the LV geometry, which constitutes an important stepping stone towards the development of an LV geometry-heterogeneous emulator.

A hierarchical machine learning framework for the analysis of large scale animal movement data.

BACKGROUND: In recent years the field of movement ecology has been revolutionized by our ability to collect high-accuracy, fine scale telemetry data from individual animals and groups. This growth in our data collection capacity has led to the development of statistical techniques that integrate telemetry data with random walk models to infer key parameters of the movement dynamics. While much progress has been made in the use of these models, several challenges remain. Notably robust and scalable methods are required for quantifying parameter uncertainty, coping with intermittent location fixes, and analysing the very large volumes of data being generated. METHODS: In this work we implement a novel approach to movement modelling through the use of multilevel Gaussian processes. The hierarchical structure of the method enables the inference of continuous latent behavioural states underlying movement processes. For efficient inference on large data sets, we approximate the full likelihood using trajectory segmentation and sample from posterior distributions using gradient-based Markov chain Monte Carlo methods. RESULTS: While formally equivalent to many continuous-time movement models, our Gaussian process approach provides flexible, powerful models that can detect multiscale patterns and trends in movement trajectory data. We illustrate a further advantage to our approach in that inference can be performed using highly efficient, GPU-accelerated machine learning libraries. CONCLUSIONS: Multilevel Gaussian process models offer efficient inference for large-volume movement data sets, along with the fitting of complex flexible models. Applications of this approach include inferring the mean location of a migration route and quantifying significant changes, detecting diurnal activity patterns, or identifying the onset of directed persistent movements.

Markov chain Monte Carlo with Gaussian processes for fast parameter estimation and uncertainty quantification in a 1D fluid-dynamics model of the pulmonary circulation.

The past few decades have witnessed an explosive synergy between physics and the life sciences. In particular, physical modelling in medicine and physiology is a topical research area. The present work focuses on parameter inference and uncertainty quantification in a 1D fluid-dynamics model for quantitative physiology: the pulmonary blood circulation. The practical challenge is the estimation of the patient-specific biophysical model parameters, which cannot be measured directly. In principle this can be achieved based on a comparison between measured and predicted data. However, predicting data requires solving a system of partial differential equations (PDEs), which usually have no closed-form solution, and repeated numerical integrations as part of an adaptive estimation procedure are computationally expensive. In the present article, we demonstrate how fast parameter estimation combined with sound uncertainty quantification can be achieved by a combination of statistical emulation and Markov chain Monte Carlo (MCMC) sampling. We compare a range of state-of-the-art MCMC algorithms and emulation strategies, and assess their performance in terms of their accuracy and computational efficiency. The long-term goal is to develop a method for reliable disease prognostication in real time, and our work is an important step towards an automatic clinical decision support system.

Assessing model mismatch and model selection in a Bayesian uncertainty quantification analysis of a fluid-dynamics model of pulmonary blood circulation.

This study uses Bayesian inference to quantify the uncertainty of model parameters and haemodynamic predictions in a one-dimensional pulmonary circulation model based on an integration of mouse haemodynamic and micro-computed tomography imaging data. We emphasize an often neglected, though important source of uncertainty: in the mathematical model form due to the discrepancy between the model and the reality, and in the measurements due to the wrong noise model (jointly called 'model mismatch'). We demonstrate that minimizing the mean squared error between the measured and the predicted data (the conventional method) in the presence of model mismatch leads to biased and overly confident parameter estimates and haemodynamic predictions. We show that our proposed method allowing for model mismatch, which we represent with Gaussian processes, corrects the bias. Additionally, we compare a linear and a nonlinear wall model, as well as models with different vessel stiffness relations. We use formal model selection analysis based on the Watanabe Akaike information criterion to select the model that best predicts the pulmonary haemodynamics. Results show that the nonlinear pressure-area relationship with stiffness dependent on the unstressed radius predicts best the data measured in a control mouse.

Rationale and design of the Medical Research Council's Precision Medicine with Zibotentan in Microvascular Angina (PRIZE) trial.

Microvascular angina is caused by cardiac small vessel disease, and dysregulation of the endothelin system is implicated. The minor G allele of the non-coding single nucleotide polymorphism (SNP) rs9349379 enhances expression of the endothelin 1 gene in human vascular cells, increasing circulating concentrations of ET-1. The prevalence of this allele is higher in patients with ischemic heart disease. Zibotentan is a potent, selective inhibitor of the ETA receptor. We have identified zibotentan as a potential disease-modifying therapy for patients with microvascular angina. METHODS: We will assess the efficacy and safety of adjunctive treatment with oral zibotentan (10 mg daily) in patients with microvascular angina and assess whether rs9349379 (minor G allele; population prevalence ~36%) acts as a theragnostic biomarker of the response to treatment with zibotentan. The PRIZE trial is a prospective, randomized, double-blind, placebo-controlled, sequential cross-over trial. The study population will be enriched to ensure a G-allele frequency of 50% for the rs9349379 SNP. The participants will receive a single-blind placebo run-in followed by treatment with either 10 mg of zibotentan daily for 12 weeks then placebo for 12 weeks, or vice versa, in random order. The primary outcome is treadmill exercise duration using the Bruce protocol. The primary analysis will assess the within-subject difference in exercise duration following treatment with zibotentan versus placebo. CONCLUSION: PRIZE invokes precision medicine in microvascular angina. Should our hypotheses be confirmed, this developmental trial will inform the rationale and design for undertaking a larger multicenter trial.

Analysis of Cardiac Amyloidosis Progression Using Model-Based Markers.

Deposition of amyloid in the heart can lead to cardiac dilation and impair its pumping ability. This ultimately leads to heart failure with worsening symptoms of breathlessness and fatigue due to the progressive loss of elasticity of the myocardium. Biomarkers linked to the clinical deterioration can be crucial in developing effective treatments. However, to date the progression of cardiac amyloidosis is poorly characterized. There is an urgent need to identify key predictors for disease progression and cardiac tissue function. In this proof of concept study, we estimate a group of new markers based on mathematical models of the left ventricle derived from routine clinical magnetic resonance imaging and follow-up scans from the National Amyloidosis Center at the Royal Free in London. Using mechanical modeling and statistical classification, we show that it is possible to predict disease progression. Our predictions agree with clinical assessments in a double-blind test in six out of the seven sample cases studied. Importantly, we find that multiple factors need to be used in the classification, which includes mechanical, geometrical and shape features. No single marker can yield reliable prediction given the complexity of the growth and remodeling process of diseased hearts undergoing high-dimensional shape changes. Our approach is promising in terms of clinical translation but the results presented should be interpreted with caution due to the small sample size.

COVID-19 - exploring the implications of long-term condition type and extent of multimorbidity on years of life lost: a modelling study.

Background: COVID-19 is responsible for increasing deaths globally. As most people dying with COVID-19 are older with underlying long-term conditions (LTCs), some speculate that YLL are low. We aim to estimate YLL attributable to COVID-19, before and after adjustment for number/type of LTCs, using the limited data available early in the pandemic. Methods: We first estimated YLL from COVID-19 using WHO life tables, based on published age/sex data from COVID-19 deaths in Italy. We then used aggregate data on number/type of LTCs in a Bayesian model to estimate likely combinations of LTCs among people dying with COVID-19. We used routine UK healthcare data from Scotland and Wales to estimate life expectancy based on age/sex/these combinations of LTCs using Gompertz models from which we then estimate YLL. Results: Using the standard WHO life tables, YLL per COVID-19 death was 14 for men and 12 for women. After adjustment for number and type of LTCs, the mean YLL was slightly lower, but remained high (11.6 and 9.4 years for men and women, respectively). The number and type of LTCs led to wide variability in the estimated YLL at a given age (e.g. at ≥80 years, YLL was >10 years for people with 0 LTCs, and <3 years for people with ≥6). Conclusions: Deaths from COVID-19 represent a substantial burden in terms of per-person YLL, more than a decade, even after adjusting for the typical number and type of LTCs found in people dying of COVID-19. The extent of multimorbidity heavily influences the estimated YLL at a given age. More comprehensive and standardised collection of data (including LTC type, severity, and potential confounders such as socioeconomic-deprivation and care-home status) is needed to optimise YLL estimates for specific populations, and to understand the global burden of COVID-19, and guide policy-making and interventions.

Fast parameter inference in a biomechanical model of the left ventricle by using statistical emulation.

A central problem in biomechanical studies of personalized human left ventricular modelling is estimating the material properties and biophysical parameters from in vivo clinical measurements in a timeframe that is suitable for use within a clinic. Understanding these properties can provide insight into heart function or dysfunction and help to inform personalized medicine. However, finding a solution to the differential equations which mathematically describe the kinematics and dynamics of the myocardium through numerical integration can be computationally expensive. To circumvent this issue, we use the concept of emulation to infer the myocardial properties of a healthy volunteer in a viable clinical timeframe by using in vivo magnetic resonance image data. Emulation methods avoid computationally expensive simulations from the left ventricular model by replacing the biomechanical model, which is defined in terms of explicit partial differential equations, with a surrogate model inferred from simulations generated before the arrival of a patient, vastly improving computational efficiency at the clinic. We compare and contrast two emulation strategies: emulation of the computational model outputs and emulation of the loss between the observed patient data and the computational model outputs. These strategies are tested with two interpolation methods, as well as two loss functions. The best combination of methods is found by comparing the accuracy of parameter inference on simulated data for each combination. This combination, using the output emulation method, with local Gaussian process interpolation and the Euclidean loss function, provides accurate parameter inference in both simulated and clinical data, with a reduction in the computational cost of about three orders of magnitude compared with numerical integration of the differential equations by using finite element discretization techniques.

Influence of image segmentation on one-dimensional fluid dynamics predictions in the mouse pulmonary arteries.

Computational fluid dynamics (CFD) models are emerging tools for assisting in diagnostic assessment of cardiovascular disease. Recent advances in image segmentation have made subject-specific modelling of the cardiovascular system a feasible task, which is particularly important in the case of pulmonary hypertension, requiring a combination of invasive and non-invasive procedures for diagnosis. Uncertainty in image segmentation propagates to CFD model predictions, making the quantification of segmentation-induced uncertainty crucial for subject-specific models. This study quantifies the variability of one-dimensional CFD predictions by propagating the uncertainty of network geometry and connectivity to blood pressure and flow predictions. We analyse multiple segmentations of a single, excised mouse lung using different pre-segmentation parameters. A custom algorithm extracts vessel length, vessel radii and network connectivity for each segmented pulmonary network. Probability density functions are computed for vessel radius and length and then sampled to propagate uncertainties to haemodynamic predictions in a fixed network. In addition, we compute the uncertainty of model predictions to changes in network size and connectivity. Results show that variation in network connectivity is a larger contributor to haemodynamic uncertainty than vessel radius and length.