Abstract Mathematical modelling is essential for understanding how complex biological systems respond to genetic, physiological, and environmental changes. Existing approaches, however, often require trade-offs between mechanistic detail, model size, parameter uncertainty, and interpretability. Ordinary differential equation (ODE) models capture biochemical processes with quantitative precision but can demand extensive parameterisation. In contrast, large statistical and machine-learning models rely on substantial datasets and frequently lack mechanistic transparency. Qualitative approaches such as Boolean networks improve scalability but may oversimplify biological behaviour. To address some of these limitations, we present PSoup, an R package that automatically converts knowledge graphs into transparent, parameter-free, qualitative models. PSoup uses algebraic update rules designed around a fixed, biologically interpretable baseline, enabling predictions of relative change across diverse perturbations without requiring kinetic parameters. This design allows PSoup to integrate information across biological scales and from heterogeneous experimental sources. We evaluated PSoup using the well-studied shoot branching network of Bertheloot et al. (2019), which incorporates hormonal (auxin, strigolactone, cytokinin) and metabolic (sucrose) regulation. Across 78 experimental conditions, PSoup correctly predicted 88.5%of perturbation outcomes, including 89.5%accuracy for unique, biologically consistent comparisons. We further demonstrate how PSoup can distinguish among alternative plausible network topologies, revealing how structural differences influence emergent system behaviour. PSoup offers an intuitive, accessible, and mathematically transparent framework for exploring biological networks. Its capacity to integrate diverse knowledge and test alternative hypotheses positions it as a powerful tool for biological discovery and a valuable complement to existing modelling approaches.

Mechanistic models in systems biology enable biophysically-backed testing of hypothesised mechanisms. However, determination of their parameter values is highly challenging, and the data available for calibration is frequently qualitative in nature. Acknowledging this, many approaches abandon mechanistic description, avoiding parameterisation and simulating biological network behaviours in a qualitative fashion. Appealing are the methods that capture some of the best of both types of approach, maintaining a qualitative perspective while using mechanistic models that naturally generalise to quantitative data and carry biochemical implications. Here, using a pea branching network model as an exemplar, we demonstrate the conversion of biological hypotheses into simplified, parameter-free mathematical models, elucidating the biophysical assumptions implicitly made by this approach and analysing the exemplar model's behaviour. Using likelihood-free Bayesian calibration, we compare the parameter-free model to the set of plausible calibrations of its parameterised analog, hence demonstrating that almost all of the qualitative conclusions given data - including both suitability of a hypothesised network structure, and sensitivity analysis - are obtained by the parameter-free paradigm. Altogether, our findings highlight the usefulness of parameter-free treatments of quantitative models, and also deepen understanding of branching network function across mutant and grafted plants.

Plants are essential for life on Earth, serving as a major source of food supply and contributing to the planet's carbon balance. Mathematical modelling is an important mechanism for predicting and optimising plant growth in agriculture, and Thornley's mathematical model (Thornley, 1997) is one of the most widely used models describing carbon and nitrogen allocation in plants. However, a formal mathematical analysis of the model's behaviour has not been performed. Our analysis of the model provides new insights into how and why the model can be inappropriate. By varying the values of some model parameters, we identify non-physical and even quite chaotic behaviour. In response, we modify Thornley's model by including additional litter terms, resulting in the elimination of these non-physical behaviours.

Multiple myeloma (MM) is a plasma cell cancer that occurs in the bone marrow. A leading treatment for MM is the monoclonal antibody Daratumumab, targeting the CD38 receptor, which is highly overexpressed in myeloma cells. In this work we model drug resistance via loss of CD38 expression, which is a proposed mechanism of resistance to Daratumumab treatment. We develop an ODE model that includes drug resistance via two mechanisms: a direct effect in which CD38 expression is lost without cell death in response to Daratumumab, and an indirect effect in which CD38 expression switches on and off in the cancer cells; myeloma cells that do not express CD38 have lower fitness but are shielded from the drug action. The model also incorporates competition with healthy cells, death of healthy cells due to off-target drug effects, and a Michaelis-Menten type immune response. Using optimal control theory, we study the effect of the drug resistance mechanisms and the off-target drug effect on the optimal treatment regime. We identify a general increase in the duration and costs of optimal treatment, as a result of these added mechanisms. Several distinct optimal treatment regimes are identified within the parameter space.

Cardiac digital twins are computational tools capturing key functional and anatomical characteristics of patient hearts for investigating disease phenotypes and predicting responses to therapy. When paired with large-scale computational resources and large clinical datasets, digital twin technology can enable virtual clinical trials on virtual cohorts to fast-track therapy development. Here, we present an automated pipeline for personalising ventricular anatomy and electrophysiological function based on routinely acquired cardiac magnetic resonance (CMR) imaging data and the standard 12-lead electrocardiogram (ECG). Using CMR-based anatomical models, a sequential Monte-Carlo approximate Bayesian computational inference method is extended to infer electrical activation and repolarisation characteristics from the ECG. Fast simulations are conducted with a reaction-Eikonal model, including the Purkinje network and biophysically-detailed subcellular ionic current dynamics for repolarisation. For each patient, parameter uncertainty is represented by inferring a population of ventricular models rather than a single one, which means that parameter uncertainty can be propagated to therapy evaluation. Furthermore, we have developed techniques for translating from reaction-Eikonal to monodomain simulations, which allows more realistic simulations of cardiac electrophysiology. The pipeline is demonstrated in a healthy female subject, where our inferred reaction-Eikonal models reproduced the patient's ECG with a Pearson's correlation coefficient of 0.93, and the translated monodomain simulations have a correlation coefficient of 0.89. We then apply the effect of Dofetilide to the monodomain population of models for this subject and show dose-dependent QT and T-peak to T-end prolongations that are in keeping with large population drug response data.

Cardiac in silico clinical trials can virtually assess the safety and efficacy of therapies using human-based modelling and simulation. These technologies can provide mechanistic explanations for clinically observed pathological behaviour. Designing virtual cohorts for in silico trials requires exploiting clinical data to capture the physiological variability in the human population. The clinical characterisation of ventricular activation and the Purkinje network is challenging, especially non-invasively. Our study aims to present a novel digital twinning pipeline that can efficiently generate and integrate Purkinje networks into human multiscale biventricular models based on subject-specific clinical 12-lead electrocardiogram and magnetic resonance recordings. Essential novel features of the pipeline are the human-based Purkinje network generation method, personalisation considering ECG R wave progression as well as QRS morphology, and translation from reduced-order Eikonal models to equivalent biophysically-detailed monodomain ones. We demonstrate ECG simulations in line with clinical data with clinical image-based multiscale models with Purkinje in four control subjects and two hypertrophic cardiomyopathy patients (simulated and clinical QRS complexes with Pearson's correlation coefficients > 0.7). Our methods also considered possible differences in the density of Purkinje myocardial junctions in the Eikonal-based inference as regional conduction velocities. These differences translated into regional coupling effects between Purkinje and myocardial models in the monodomain formulation. In summary, we demonstrate a digital twin pipeline enabling simulations yielding clinically-consistent ECGs with clinical CMR image-based biventricular multiscale models, including personalised Purkinje in healthy and cardiac disease conditions.

Cardiac digital twins represent the required functional mechanisms of patient hearts to evaluate therapies and inform clinical decision-making virtually. A scalable generation of cardiac digital twins can enable virtual clinical trials on virtual cohorts to fast-track therapy development. Here, we present an open-source digital twinning framework for personalising electrophysiological function based on routinely acquired magnetic resonance imaging (MRI) data and the standard 12-lead electrocardiogram (ECG). We extended a Bayesian-based inference framework to infer electrical repolarisation characteristics. Fast simulations are conducted with a decoupled reaction-Eikonal model, including the Purkinje network and biophysically-detailed subcellular ionic current dynamics. Parameter uncertainty is represented by inferring a population of ventricular models rather than a single one, which means that parameter uncertainty can be propagated to virtual therapy evaluations. The framework is demonstrated in a healthy female subject, where our inferred reaction-Eikonal models reproduced the patient’s ECG with a Pearson’s correlation coefficient of 0.93. The methodologies for cardiac digital twinning presented here are a step towards personalised virtual therapy testing. The tools developed for this study are open-source, ensuring accessibility, inclusivity, and reproducibility, this is available on GitHub.

Fibrosis, a pathological increase in extracellular matrix proteins, is a significant health issue that hinders the function of many organs in the body, in some cases fatally. In the heart, fibrosis impacts on electrical propagation in a complex and poorly predictable fashion, potentially serving as a substrate for dangerous arrhythmias. Individual risk depends on the spatial manifestation of fibrotic tissue, and learning the spatial arrangement on the fine scale in order to predict these impacts still relies upon invasive ex vivo procedures. As a result, the effects of spatial variability on the symptomatic impact of cardiac fibrosis remain poorly understood. In this work, we address the issue of availability of such imaging data via a computational methodology for generating new realisations of cardiac fibrosis microstructure. Using the Perlin noise technique from computer graphics, together with an automated calibration process that requires only a single training image, we demonstrate successful capture of collagen texturing in four types of fibrosis microstructure observed in histological sections. We then use this generator to quantitatively analyse the conductive properties of these different types of cardiac fibrosis, as well as produce three-dimensional realisations of histologically-observed patterning. Owing to the generator’s flexibility and automated calibration process, we also anticipate that it might be useful in producing additional realisations of other physiological structures.

Cardiac digital twins are computational tools capturing key functional and anatomical characteristics of patient hearts for investigating disease phenotypes and predicting responses to therapy. When paired with large-scale computational resources and large clinical datasets, digital twin technology can enable virtual clinical trials on virtual cohorts to fast-track therapy development. Here, we present an open-source automated pipeline for personalising ventricular electrophysiological function based on routinely acquired magnetic resonance imaging (MRI) data and the standard 12-lead electrocardiogram (ECG).Using MRI-based anatomical models, a sequential Monte-Carlo approximate Bayesian computational inference method is extended to infer electrical activation and repolarisation characteristics from the ECG. Fast simulations are conducted with a reaction-Eikonal model, including the Purkinje network and biophysically-detailed subcellular ionic current dynamics for repolarisation. For each patient, parameter uncertainty is represented by inferring an envelope of plausible ventricular models rather than a single one, which means that parameter uncertainty can be propagated to therapy evaluation. Furthermore, we have developed techniques for translating from reaction-Eikonal to monodomain simulations, which allows more realistic simulations of cardiac electrophysiology. The pipeline is demonstrated in three healthy subjects, where our inferred pseudo-diffusion reaction-Eikonal models reproduced the patient's ECG with a median Pearson's correlation coefficient of 0.9, and then translated to monodomain simulations with a median correlation coefficient of 0.84 across all subjects. We then demonstrate our digital twins for virtual evaluation of Dofetilide with uncertainty quantification. These evaluations using our cardiac digital twins reproduced dose-dependent QTc and T peak to T end prolongations that are in keeping with large population drug response data.The methodologies for cardiac digital twinning presented here are a step towards personalised virtual therapy testing and can be scaled to generate virtual populations for clinical trials to fast-track therapy evaluation. The tools developed for this paper are open-source, documented, and made publicly available.

Choosing the Fisher information as the metric tensor for a Riemannian manifold provides a powerful yet fundamental way to understand statistical distribution families. Distances along this manifold become a compelling measure of statistical distance, and paths of shorter distance improve sampling techniques that leverage a sequence of distributions in their operation. Unfortunately, even for a distribution as generally tractable as the multivariate normal distribution, this information geometry proves unwieldy enough that closed-form solutions for shortest-distance paths or their lengths remain unavailable outside of limited special cases. In this review we present for general statisticians the most practical aspects of the Fisher geometry for this fundamental distribution family. Rather than a differential geometric treatment, we use an intuitive understanding of the covariance-induced curvature of this manifold to unify the special cases with known closed-form solution and review approximate solutions for the general case. We also use the multivariate normal information geometry to better understand the paths or distances commonly used in statistics (annealing, Wasserstein). Given the unavailability of a general solution, we also discuss the methods used for numerically obtaining geodesics in the space of multivariate normals, identifying remaining challenges and suggesting methodological improvements.

This paper uses recurrence quantification analysis (RQA) combined with entropy measures and organization indices to characterize arrhythmic patterns and dynamics in computer simulations of cardiac tissue. We performed different simulations of cardiac tissues of sizes comparable to the human heart atrium. In these simulations, we observed four classic arrhythmic patterns: a spiral wave anchored to a highly fibrotic region resulting in sustained re-entry, a meandering spiral wave, fibrillation, and a spiral wave anchored to a scar region that breaks up into wavelets away from the main rotor. A detailed analysis revealed that, within the same simulation, maps of RQA metrics could differentiate regions with regular AP propagation from ones with chaotic activity. In particular, the combination of two RQA metrics, the length of the longest diagonal string of recurrence points and the mean length of diagonal lines, was able to identify the location of rotor tips, which are the active elements that maintain spiral waves and fibrillation. By proposing low-dimensional models based on the mean value and spatial correlation of metrics calculated from membrane potential time series, we identify RQA-based metrics that successfully separate the four different types of cardiac arrhythmia into distinct regions of the feature space, and thus might be used for automatic classification, in particular distinguishing between fibrillation driven by self-sustaining chaos and that created by a persistent rotor and wavebreak. We also discuss the practical applicability of such an approach.

Computational models in cardiac electrophysiology are notorious for long runtimes, restricting the numbers of nodes and mesh elements in the numerical discretisations used for their solution. This makes it particularly challenging to incorporate structural heterogeneities on small spatial scales, preventing a full understanding of the critical arrhythmogenic effects of conditions such as cardiac fibrosis. In this work, we explore the technique of homogenisation by volume averaging for the inclusion of non-conductive micro-structures into larger-scale cardiac meshes with minor computational overhead. Importantly, our approach is not restricted to periodic patterns, enabling homogenised models to represent, for example, the intricate patterns of collagen deposition present in different types of fibrosis. We first highlight the importance of appropriate boundary condition choice for the closure problems that define the parameters of homogenised models. Then, we demonstrate the technique's ability to correctly upscale the effects of fibrotic patterns with a spatial resolution of 10µm into much larger numerical mesh sizes of 100-250µm. The homogenised models using these coarser meshes correctly predict critical pro-arrhythmic effects of fibrosis, including slowed conduction, source/sink mismatch, and stabilisation of re-entrant activation patterns. As such, this approach to homogenisation represents a significant step towards whole organ simulations that unravel the effects of microscopic cardiac tissue heterogeneities.

This work introduces a comprehensive approach to assess the sensitivity of model outputs to changes in parameter values, constrained by the combination of prior beliefs and data. This approach identifies stiff parameter combinations strongly affecting the quality of the model-data fit while simultaneously revealing which of these key parameter combinations are informed primarily by the data or are also substantively influenced by the priors. We focus on the very common context in complex systems where the amount and quality of data are low compared to the number of model parameters to be collectively estimated, and showcase the benefits of this technique for applications in biochemistry, ecology, and cardiac electrophysiology. We also show how stiff parameter combinations, once identified, uncover controlling mechanisms underlying the system being modeled and inform which of the model parameters need to be prioritized in future experiments for improved parameter inference from collective model-data fitting.

The Purkinje network plays a determinant role in the electrical activation sequence of the human heart. However, Purkinje properties cannot be clinically measured directly. Recent studies have successfully demonstrated cardiac digital twins without Purkinje networks, using inference methods integrating cardiac magnetic resonance (CMR) imaging and electrocardiogram (ECG) data. A sophisticated strategy to recover a patient's plausible Purkinje structure would enable these cardiac digital twins to augment clinical data and inform Purkinje-based risk stratification. This study presents and evaluates new computational techniques to infer physiological Purkinje terminal locations, timings, and cardiac conduction properties from clinical CMR and ECG using Eikonal simulations. Our extended sequential Monte Carlo approximate Bayesian computation-based inference method shows an improved match in simulated QRS complexes to Q-wave morphologies in clinical 12-lead ECGs with Pearson's correlation coefficients of 0.89.

In this paper we develop a likelihood-free approach for population calibration, which involves finding distributions of model parameters when fed through the model produces a set of outputs that matches available population data. Unlike most other approaches to population calibration, our method produces uncertainty quantification on the estimated distribution. Furthermore, the method can be applied to any population calibration problem, regardless of whether the model of interest is deterministic or stochastic, or whether the population data is observed with or without measurement error. We demonstrate the method on several examples, including one with real data. We also discuss the computational limitations of the approach. Immediate applications for the methodology developed here exist in many areas of medical research including cancer, COVID-19, drug development and cardiology.

Fibrosis, the excess of extracellular matrix, can affect, and even block, propagation of action potential in cardiac tissue. This can result in deleterious effects on heart function, but the nature and severity of these effects depend strongly on the localisation of fibrosis and its by-products in cardiac tissue, such as collagen scar formation. Computer simulation is an important means of understanding the complex effects of fibrosis on activation patterns in the heart, but concerns of computational cost place restrictions on the spatial resolution of these simulations. In this work, we present a novel numerical homogenisation technique that uses both Eikonal and graph approaches to allow fine-scale heterogeneities in conductivity to be incorporated into a coarser mesh. Homogenisation achieves this by deriving effective conductivity tensors so that a coarser mesh can then be used for numerical simulation. By taking a graph-based approach, our homogenisation technique functions naturally on irregular grids and does not rely upon any assumptions of periodicity, even implicitly. We present results of action potential propagation through fibrotic tissue in two dimensions that show the graph-based homogenisation technique is an accurate and effective way to capture fine-scale domain information on coarser meshes in the context of sharp-fronted travelling waves of activation. As test problems, we consider excitation propagation in tissue with diffuse fibrosis and through a tunnel-like structure designed to test homogenisation, interaction of an excitation wave with a scar region, and functional re-entry.

In this paper, we forecast cumulative production for stimulated gas wells using a combination of fast-to-implement modeling methodologies, including polynomial chaos expansion (PCE) and Gaussian processes (GP) proxy models coupled with populations of phenomenological models (POMs). These modeling techniques allow for a reduction in forecast uncertainty and are shown to be effective techniques for extrapolating early time data for stimulated well production from a field of wells in the Surat Basin, Queensland, Australia. The proposed techniques strategically capture and capitalize on production trends across an entire gas field, even in the presence of early production transients. We demonstrate that learning cycles can be shortened, leading to reasonable forecasts, as well as meaningful and actionable insights.

The integration of cardiac magnetic resonance (CMR) imaging and electrocardiogram (ECG) data through advanced computational methods could enable the development of the cardiac 'digital twin', a comprehensive virtual tool that mechanistically reveals a patient's heart condition from clinical data and simulates treatment outcomes. The adoption of cardiac digital twins requires the non-invasive efficient personalisation of the electrophysiological properties in cardiac models. This study develops and evaluates new computational techniques to estimate key ventricular activation properties for individual subjects by exploiting the synergy between CMR, ECG, and modelling and simulation. We present an efficient sequential Monte Carlo approximate Bayesian computation-based inference method, integrated with Eikonal simulations and torso-biventricular models constructed based on clinical CMR imaging to recover conduction speeds and earliest activation sites from 12-lead ECGs. We demonstrate successful results of our inference method on a cohort of twenty virtual subjects with cardiac ventricular myocardial-mass volumes ranging from 74 cm 3 to 171 cm 3 .

Cardiac fibrosis and other scarring of the heart, arising from conditions ranging from myocardial infarction to ageing, promotes dangerous arrhythmias by blocking the healthy propagation of cardiac excitation. Owing to the complexity of the dynamics of electrical signalling in the heart, however, the connection between different arrangements of blockage and various arrhythmic consequences remains poorly understood. Where a mechanism defies traditional understanding, machine learning can be invaluable for enabling accurate prediction of quantities of interest (measures of arrhythmic risk) in terms of predictor variables (such as the arrangement or pattern of obstructive scarring). In this study, we simulate the propagation of the action potential (AP) in tissue affected by fibrotic changes and hence detect sites that initiate re-entrant activation patterns. By separately considering multiple different stimulus regimes, we directly observe and quantify the sensitivity of re-entry formation to activation sequence in the fibrotic region. Then, by extracting the fibrotic structures around locations that both do and do not initiate re-entries, we use neural networks to determine to what extent re-entry initiation is predictable, and over what spatial scale conduction heterogeneities appear to act to produce this effect. We find that structural information within about 0.5 mm of a given point is sufficient to predict structures that initiate re-entry with more than 90% accuracy.

Electrophysiological (and electromechanical) simulations are infamous for their computational runtimes, and this remains a significant barrier to a full understanding of the electrical signalling process in the heart. These computational challenges are particularly impactful when it comes to understanding the important effects of small-scale heterogeneities, for example due to cardiac fibrosis, as refinement of cardiac meshes to even finer spatial resolutions incurs an insurmountable increase in simulation time. Therefore, methods that are able to appropriately upscale these micro-scale heterogeneities, representing their effects on conduction in a coarser mesh, are of critical importance to understanding when and how conditions such as cardiac fibrosis act to promote dangerous arrhythmia. In this work, we combine our recent ideas for upscaling using homogenisation via volume averaging and a unique graph-based approach to demonstrate a powerful tool for capturing some of the subtler and localisation-dependent effects of cardiac fibrosis with only minor impact on simulation runtimes.