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.

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.

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.

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.

ShinyKGode: an interactive application for ODE parameter inference using gradient matching.

Motivation: Mathematical modelling based on ordinary differential equations (ODEs) is widely used to describe the dynamics of biological systems, particularly in systems and pathway biology. Often the kinetic parameters of these ODE systems are unknown and have to be inferred from the data. Approximate parameter inference methods based on gradient matching (which do not require performing computationally expensive numerical integration of the ODEs) have been getting popular in recent years, but many implementations are difficult to run without expert knowledge. Here, we introduce ShinyKGode, an interactive web application to perform fast parameter inference on ODEs using gradient matching. Results: ShinyKGode can be used to infer ODE parameters on simulated and observed data using gradient matching. Users can easily load their own models in Systems Biology Markup Language format, and a set of pre-defined ODE benchmark models are provided in the application. Inferred parameters are visualized alongside diagnostic plots to assess convergence. Availability and implementation: The R package for ShinyKGode can be installed through the Comprehensive R Archive Network (CRAN). Installation instructions, as well as tutorial videos and source code are available at https://joewandy.github.io/shinyKGode. Supplementary information: Supplementary data are available at Bioinformatics online.

Statistical inference in mechanistic models: time warping for improved gradient matching.

Inference in mechanistic models of non-linear differential equations is a challenging problem in current computational statistics. Due to the high computational costs of numerically solving the differential equations in every step of an iterative parameter adaptation scheme, approximate methods based on gradient matching have become popular. However, these methods critically depend on the smoothing scheme for function interpolation. The present article adapts an idea from manifold learning and demonstrates that a time warping approach aiming to homogenize intrinsic length scales can lead to a significant improvement in parameter estimation accuracy. We demonstrate the effectiveness of this scheme on noisy data from two dynamical systems with periodic limit cycle, a biopathway, and an application from soft-tissue mechanics. Our study also provides a comparative evaluation on a wide range of signal-to-noise ratios.

Targeting Bayes factors with direct-path non-equilibrium thermodynamic integration.

Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly stems from the prior regime. When comparing complex models with differences in a comparatively small number of parameters, intrinsic errors from sampling fluctuations may outweigh the differences in the log marginal likelihood estimates. In the present article, we propose a TI scheme that directly targets the log Bayes factor. The method is based on a modified annealing path between the posterior distributions of the two models compared, which systematically avoids the high variance prior regime. We combine this scheme with the concept of non-equilibrium TI to minimise discretisation errors from numerical integration. Results obtained on Bayesian regression models applied to standard benchmark data, and a complex hierarchical model applied to biopathway inference, demonstrate a significant reduction in estimator variance over state-of-the-art TI methods.

Inferring bi-directional interactions between circadian clock genes and metabolism with model ensembles.

There has been much interest in reconstructing bi-directional regulatory networks linking the circadian clock to metabolism in plants. A variety of reverse engineering methods from machine learning and computational statistics have been proposed and evaluated. The emphasis of the present paper is on combining models in a model ensemble to boost the network reconstruction accuracy, and to explore various model combination strategies to maximize the improvement. Our results demonstrate that a rich ensemble of predictors outperforms the best individual model, even if the ensemble includes poor predictors with inferior individual reconstruction accuracy. For our application to metabolomic and transcriptomic time series from various mutagenesis plants grown in different light-dark cycles we also show how to determine the optimal time lag between interactions, and we identify significant interactions with a randomization test. Our study predicts new statistically significant interactions between circadian clock genes and metabolites in Arabidopsis thaliana, and thus provides independent statistical evidence that the regulation of metabolism by the circadian clock is not uni-directional, but that there is a statistically significant feedback mechanism aiming from metabolism back to the circadian clock.

Approximate parameter inference in systems biology using gradient matching: a comparative evaluation.

BACKGROUND: A challenging problem in current systems biology is that of parameter inference in biological pathways expressed as coupled ordinary differential equations (ODEs). Conventional methods that repeatedly numerically solve the ODEs have large associated computational costs. Aimed at reducing this cost, new concepts using gradient matching have been proposed, which bypass the need for numerical integration. This paper presents a recently established adaptive gradient matching approach, using Gaussian processes (GPs), combined with a parallel tempering scheme, and conducts a comparative evaluation with current state-of-the-art methods used for parameter inference in ODEs. Among these contemporary methods is a technique based on reproducing kernel Hilbert spaces (RKHS). This has previously shown promising results for parameter estimation, but under lax experimental settings. We look at a range of scenarios to test the robustness of this method. We also change the approach of inferring the penalty parameter from AIC to cross validation to improve the stability of the method. METHODS: Methodology for the recently proposed adaptive gradient matching method using GPs, upon which we build our new method, is provided. Details of a competing method using RKHS are also described here. RESULTS: We conduct a comparative analysis for the methods described in this paper, using two benchmark ODE systems. The analyses are repeated under different experimental settings, to observe the sensitivity of the techniques. CONCLUSIONS: Our study reveals that for known noise variance, our proposed method based on GPs and parallel tempering achieves overall the best performance. When the noise variance is unknown, the RKHS method proves to be more robust.

Statistical inference of regulatory networks for circadian regulation.

We assess the accuracy of various state-of-the-art statistics and machine learning methods for reconstructing gene and protein regulatory networks in the context of circadian regulation. Our study draws on the increasing availability of gene expression and protein concentration time series for key circadian clock components in Arabidopsis thaliana. In addition, gene expression and protein concentration time series are simulated from a recently published regulatory network of the circadian clock in A. thaliana, in which protein and gene interactions are described by a Markov jump process based on Michaelis-Menten kinetics. We closely follow recent experimental protocols, including the entrainment of seedlings to different light-dark cycles and the knock-out of various key regulatory genes. Our study provides relative network reconstruction accuracy scores for a critical comparative performance evaluation, and sheds light on a series of highly relevant questions: it quantifies the influence of systematically missing values related to unknown protein concentrations and mRNA transcription rates, it investigates the dependence of the performance on the network topology and the degree of recurrency, it provides deeper insight into when and why non-linear methods fail to outperform linear ones, it offers improved guidelines on parameter settings in different inference procedures, and it suggests new hypotheses about the structure of the central circadian gene regulatory network in A. thaliana.

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.

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.

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.

A Bayesian approach for parameter estimation in the extended clock gene circuit of Arabidopsis thaliana.

The circadian clock is an important molecular mechanism that enables many organisms to anticipate and adapt to environmental change. Pokhilko et al. recently built a deterministic ODE mathematical model of the plant circadian clock in order to understand the behaviour, mechanisms and properties of the system. The model comprises 30 molecular species (genes, mRNAs and proteins) and over 100 parameters. The parameters have been fitted heuristically to available gene expression time series data and the calibrated model has been shown to reproduce the behaviour of the clock components. Ongoing work is extending the clock model to cover downstream effects, in particular metabolism, necessitating further parameter estimation and model selection. This work investigates the challenges facing a full Bayesian treatment of parameter estimation. Using an efficient adaptive MCMC proposed by Haario et al. and working in a high performance computing setting, we quantify the posterior distribution around the proposed parameter values and explore the basin of attraction. We investigate if Bayesian inference is feasible in this high dimensional setting and thoroughly assess convergence and mixing with different statistical diagnostics, to prevent apparent convergence in some domains masking poor mixing in others.

A non-homogeneous dynamic Bayesian network with sequentially coupled interaction parameters for applications in systems and synthetic biology.

An important and challenging problem in systems biology is the inference of gene regulatory networks from short non-stationary time series of transcriptional profiles. A popular approach that has been widely applied to this end is based on dynamic Bayesian networks (DBNs), although traditional homogeneous DBNs fail to model the non-stationarity and time-varying nature of the gene regulatory processes. Various authors have therefore recently proposed combining DBNs with multiple changepoint processes to obtain time varying dynamic Bayesian networks (TV-DBNs). However, TV-DBNs are not without problems. Gene expression time series are typically short, which leaves the model over-flexible, leading to over-fitting or inflated inference uncertainty. In the present paper, we introduce a Bayesian regularization scheme that addresses this difficulty. Our approach is based on the rationale that changes in gene regulatory processes appear gradually during an organism's life cycle or in response to a changing environment, and we have integrated this notion in the prior distribution of the TV-DBN parameters. We have extensively tested our regularized TV-DBN model on synthetic data, in which we have simulated short non-homogeneous time series produced from a system subject to gradual change. We have then applied our method to real-world gene expression time series, measured during the life cycle of Drosophila melanogaster, under artificially generated constant light condition in Arabidopsis thaliana, and from a synthetically designed strain of Saccharomyces cerevisiae exposed to a changing environment.

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.

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.

Improvements in the reconstruction of time-varying gene regulatory networks: dynamic programming and regularization by information sharing among genes.

METHOD: Dynamic Bayesian networks (DBNs) have been applied widely to reconstruct the structure of regulatory processes from time series data, and they have established themselves as a standard modelling tool in computational systems biology. The conventional approach is based on the assumption of a homogeneous Markov chain, and many recent research efforts have focused on relaxing this restriction. An approach that enjoys particular popularity is based on a combination of a DBN with a multiple changepoint process, and the application of a Bayesian inference scheme via reversible jump Markov chain Monte Carlo (RJMCMC). In the present article, we expand this approach in two ways. First, we show that a dynamic programming scheme allows the changepoints to be sampled from the correct conditional distribution, which results in improved convergence over RJMCMC. Second, we introduce a novel Bayesian clustering and information sharing scheme among nodes, which provides a mechanism for automatic model complexity tuning. RESULTS: We evaluate the dynamic programming scheme on expression time series for Arabidopsis thaliana genes involved in circadian regulation. In a simulation study we demonstrate that the regularization scheme improves the network reconstruction accuracy over that obtained with recently proposed inhomogeneous DBNs. For gene expression profiles from a synthetically designed Saccharomyces cerevisiae strain under switching carbon metabolism we show that the combination of both: dynamic programming and regularization yields an inference procedure that outperforms two alternative established network reconstruction methods from the biology literature. AVAILABILITY AND IMPLEMENTATION: A MATLAB implementation of the algorithm and a supplementary paper with algorithmic details and further results for the Arabidopsis data can be downloaded from: http://www.statistik.tu-dortmund.de/bio2010.html.

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.

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.