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Empirical Quantification of Predictive Uncertainty Due to Model Discrepancy by Training with an Ensemble of Experimental Designs: An Application to Ion Channel Kinetics (2023)
Journal Article
Shuttleworth, J. G., Lei, C. L., Whittaker, D. G., Windley, M. J., Hill, A. P., Preston, S. P., & Mirams, G. R. (2024). Empirical Quantification of Predictive Uncertainty Due to Model Discrepancy by Training with an Ensemble of Experimental Designs: An Application to Ion Channel Kinetics. Bulletin of Mathematical Biology, 86(1), Article 2. https://doi.org/10.1007/s11538-023-01224-6

When using mathematical models to make quantitative predictions for clinical or industrial use, it is important that predictions come with a reliable estimate of their accuracy (uncertainty quantification). Because models of complex biological system... Read More about Empirical Quantification of Predictive Uncertainty Due to Model Discrepancy by Training with an Ensemble of Experimental Designs: An Application to Ion Channel Kinetics.

The impact of uncertainty in hERG binding mechanism on in silico predictions of drug-induced proarrhythmic risk (2023)
Journal Article
Lei, C. L., Whittaker, D. G., & Mirams, G. R. (2024). The impact of uncertainty in hERG binding mechanism on in silico predictions of drug-induced proarrhythmic risk. British Journal of Pharmacology, 181(7), 987-1004. https://doi.org/10.1111/bph.16250

Background and Purpose Drug-induced reduction of the rapid delayed rectifier potassium current carried by the human Ether-à-go-go-Related Gene (hERG) channel is associated with increased risk of arrhythmias. Recent updates to drug safety regulatory... Read More about The impact of uncertainty in hERG binding mechanism on in silico predictions of drug-induced proarrhythmic risk.

Computational Cardiac Safety Testing (2023)
Book Chapter
Mirams, G. R. (2023). Computational Cardiac Safety Testing. In F. J. Hock, M. R. Gralinski, & M. K. Pugsley (Eds.), Drug Discovery and Evaluation: Safety and Pharmacokinetic Assays (1-33). Springer. https://doi.org/10.1007/978-3-030-73317-9_137-1

In recent years, computational cardiac electrophysiology simulations using mathematical models have begun to be used in industrial and regulatory assessment of the proarrhythmic risk of candidate drug compounds. The aim of this chapter is to equip th... Read More about Computational Cardiac Safety Testing.

Dynamical Survival Analysis for Epidemic Modeling (2023)
Book Chapter
Rempała, G. A., & KhudaBukhsh, W. R. (2023). Dynamical Survival Analysis for Epidemic Modeling. In Handbook of Visual, Experimental and Computational Mathematics: Bridges through Data (1-17). Springer. https://doi.org/10.1007/978-3-030-93954-0_31-1

This chapter describes the dynamical survival analysis (DSA) method for modeling infectious diseases. This method provides a powerful framework for analyzing compartmental models of large epidemics, such as the popular susceptible-infected-recovered... Read More about Dynamical Survival Analysis for Epidemic Modeling.

Ion channel model reduction using manifold boundaries (2022)
Journal Article
Whittaker, D. G., Wang, J., Shuttleworth, J., Venkateshappa, R., Kemp, J. M., Claydon, T. W., & Mirams, G. R. (2022). Ion channel model reduction using manifold boundaries. Journal of the Royal Society, Interface, 19(193), Article 20220193. https://doi.org/10.1098/rsif.2022.0193

Mathematical models of voltage-gated ion channels are used in basic research, industrial and clinical settings. These models range in complexity, but typically contain numerous variables representing the proportion of channels in a given state, and p... Read More about Ion channel model reduction using manifold boundaries.

A Parameter Representing Missing Charge Should Be Considered when Calibrating Action Potential Models (2022)
Journal Article
Barral, Y. H. M., Shuttleworth, J., Clerx, M., Whittaker, D. G., Wang, K., Polonchuk, L., …Mirams, G. R. (2022). A Parameter Representing Missing Charge Should Be Considered when Calibrating Action Potential Models. Frontiers in Physiology, 13, Article 879035. https://doi.org/10.3389/fphys.2022.879035

Computational models of the electrical potential across a cell membrane are longstanding and vital tools in electrophysiology research and applications. These models describe how ionic currents, internal fluxes, and buffering interact to determine me... Read More about A Parameter Representing Missing Charge Should Be Considered when Calibrating Action Potential Models.

Analysis of individual-level data from 2018–2020 Ebola outbreak in Democratic Republic of the Congo (2022)
Journal Article
Vossler, H., Akilimali, P., Pan, Y., KhudaBukhsh, W. R., Kenah, E., & Rempała, G. A. (2022). Analysis of individual-level data from 2018–2020 Ebola outbreak in Democratic Republic of the Congo. Scientific Reports, 12, Article 5534. https://doi.org/10.1038/s41598-022-09564-4

The 2018–2020 Ebola virus disease epidemic in Democratic Republic of the Congo (DRC) resulted in 3481 cases (probable and confirmed) and 2299 deaths. In this paper, we use a novel statistical method to analyze the individual-level incidence and hospi... Read More about Analysis of individual-level data from 2018–2020 Ebola outbreak in Democratic Republic of the Congo.

Some computable quasiconvex multiwell models in linear subspaces without rank-one matrices (2022)
Journal Article
Zhang, K., & Yin, K. (2022). Some computable quasiconvex multiwell models in linear subspaces without rank-one matrices. Electronic Research Archive, 30(5), 1632-1652. https://doi.org/10.3934/era.2022082

In this paper we apply a smoothing technique for the maximum function, based on the compensated convex transforms, originally proposed by Zhang in [1] to construct some computable multiwell non-negative quasiconvex functions in the calculus of variat... Read More about Some computable quasiconvex multiwell models in linear subspaces without rank-one matrices.

chaste codegen: automatic CellML to C++ code generation with fixes for singularities and automatically generated Jacobians (2022)
Journal Article
Hendrix, M., Clerx, M., Tamuri, A. U., Keating, S. M., Johnstone, R. H., Cooper, J., & Mirams, G. R. (2022). chaste codegen: automatic CellML to C++ code generation with fixes for singularities and automatically generated Jacobians. Wellcome Open Research, 6, Article 261. https://doi.org/10.12688/wellcomeopenres.17206.1

Hundreds of different mathematical models have been proposed for describing electrophysiology of various cell types. These models are quite complex (nonlinear systems of typically tens of ODEs and sometimes hundreds of parameters) and software packag... Read More about chaste codegen: automatic CellML to C++ code generation with fixes for singularities and automatically generated Jacobians.

Neural Network Differential Equations For Ion Channel Modelling (2021)
Journal Article
Lei, C. L., & Mirams, G. R. (2021). Neural Network Differential Equations For Ion Channel Modelling. Frontiers in Physiology, 12, Article 708944. https://doi.org/10.3389/fphys.2021.708944

Mathematical models of cardiac ion channels have been widely used to study and predict the behaviour of ion currents. Typically models are built using biophysically-based mechanistic principles such as Hodgkin-Huxley or Markov state transitions. Thes... Read More about Neural Network Differential Equations For Ion Channel Modelling.

Cardiac TdP risk stratification modelling of anti-infective compounds including chloroquine and hydroxychloroquine (2021)
Journal Article
Whittaker, D. G., Capel, R. A., Hendrix, M., Chan, X. H. S., Herring, N., White, N. J., …Burton, R. A. B. (2021). Cardiac TdP risk stratification modelling of anti-infective compounds including chloroquine and hydroxychloroquine. Royal Society Open Science, 8(4), https://doi.org/10.1098/rsos.210235

Hydroxychloroquine (HCQ), the hydroxyl derivative of chloroquine (CQ), is widely used in the treatment of rheumatological conditions (systemic lupus erythematosus, rheumatoid arthritis) and is being studied for the treatment and prevention of COVID-1... Read More about Cardiac TdP risk stratification modelling of anti-infective compounds including chloroquine and hydroxychloroquine.

Hausdorff Stability and Error Estimates for Compensated Convexity Based Methods for Approximation and Interpolation for Functions in Rn (2020)
Journal Article
Alatawi, M., & Zhang, K. (2020). Hausdorff Stability and Error Estimates for Compensated Convexity Based Methods for Approximation and Interpolation for Functions in Rn. Journal of Convex Analysis, 27(4),

We establish error estimates and Hausdorff stability for approximations and interpolations for sampled functions in Rn by using compensated convex transforms introduced previously by K. Zhang [Compensated convexity and its applications, Ann. l’Instit... Read More about Hausdorff Stability and Error Estimates for Compensated Convexity Based Methods for Approximation and Interpolation for Functions in Rn.

Pseudo?Waveform?Selective Metasurfaces and their Limited Performance (2020)
Journal Article
Nakasha, T., Phang, S., & Wakatsuchi, H. (2021). Pseudo?Waveform?Selective Metasurfaces and their Limited Performance. Advanced Theory and Simulations, 4(1), Article 2000187. https://doi.org/10.1002/adts.202000187

Abstract In recent years, metasurfaces composed of lumped circuit components, including nonlinear Schottky diodes, have been reported to be capable of sensing particular electromagnetic waves even at the same frequency depending on their waveforms, o... Read More about Pseudo?Waveform?Selective Metasurfaces and their Limited Performance.

Efficient Statistical Model for Predicting Electromagnetic Wave Distribution in Coupled Enclosures (2020)
Journal Article
Ma, S., Phang, S., Drikas, Z., Addissie, B., Hong, R., Blakaj, V., …Anlage, S. M. (2020). Efficient Statistical Model for Predicting Electromagnetic Wave Distribution in Coupled Enclosures. Physical Review Applied, 14(1), Article 014022. https://doi.org/10.1103/PhysRevApplied.14.014022

The random coupling model (RCM) has been successfully applied to predicting the statistics of currents and voltages at ports in complex electromagnetic (EM) enclosures operating in the short-wavelength limit. Recent studies have extended the RCM to s... Read More about Efficient Statistical Model for Predicting Electromagnetic Wave Distribution in Coupled Enclosures.

Accounting for variability in ion current recordings using a mathematical model of artefacts in voltage-clamp experiments (2020)
Journal Article
Clerx, M., Lei, C. L., Whittaker, D. G., Gavaghan, D. J., de Boer, T. P., & Mirams, G. R. (2020). Accounting for variability in ion current recordings using a mathematical model of artefacts in voltage-clamp experiments. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 378(2173), Article 20190348. https://doi.org/10.1098/rsta.2019.0348

Mathematical models of ion channels, which constitute indispensable components of action potential models, are commonly constructed by fitting to whole-cell patch-clamp data. In a previous study, we fitted cell-specific models to hERG1a (Kv11.1) reco... Read More about Accounting for variability in ion current recordings using a mathematical model of artefacts in voltage-clamp experiments.

Rapid characterisation of hERG channel kinetics II: temperature dependence (2019)
Journal Article
Lei, C. L., Clerx, M., Beattie, K. A., Melgari, D., Hancox, J. C., Gavaghan, D. J., …Mirams, G. R. (2019). Rapid characterisation of hERG channel kinetics II: temperature dependence. Biophysical Journal, 117(12), 2455-2470. https://doi.org/10.1101/609719

Ion channel behavior can depend strongly on temperature, with faster kinetics at physiological temperatures leading to considerable changes in currents relative to room temperature. These temperature-dependent changes in voltage-dependent ion channel... Read More about Rapid characterisation of hERG channel kinetics II: temperature dependence.

General Principles for the Validation of Proarrhythmia Risk Prediction Models: An Extension of the CiPA In Silico Strategy (2019)
Journal Article
Li, Z., Mirams, G. R., Yoshinaga, T., Ridder, B. J., Han, X., Chen, J. E., …Strauss, D. G. (2020). General Principles for the Validation of Proarrhythmia Risk Prediction Models: An Extension of the CiPA In Silico Strategy. Clinical Pharmacology and Therapeutics, 107(1), 102-111. https://doi.org/10.1002/cpt.1647

This white paper presents principles for validating proarrhythmia risk prediction models for regulatory use as discussed at the In Silico Breakout Session of a Cardiac Safety Research Consortium/Health and Environmental Sciences Institute/US Food and... Read More about General Principles for the Validation of Proarrhythmia Risk Prediction Models: An Extension of the CiPA In Silico Strategy.

Four Ways to Fit an Ion Channel Model (2019)
Journal Article
Clerx, M., Beattie, K., Gavaghan, D., & Mirams, G. (2019). Four Ways to Fit an Ion Channel Model. Biophysical Journal, 117(12), 2420-2437. https://doi.org/10.1016/j.bpj.2019.08.001

© 2019 Biophysical Society Mathematical models of ionic currents are used to study the electrophysiology of the heart, brain, gut, and several other organs. Increasingly, these models are being used predictively in the clinic, for example, to predict... Read More about Four Ways to Fit an Ion Channel Model.

Rapid Characterization of hERG Channel Kinetics I: Using an Automated High-Throughput System (2019)
Journal Article
Lei, C. L., Clerx, M., Gavaghan, D. J., Polonchuk, L., Mirams, G. R., & Wang, K. (2019). Rapid Characterization of hERG Channel Kinetics I: Using an Automated High-Throughput System. Biophysical Journal, 117(12), 2438-2454. https://doi.org/10.1016/j.bpj.2019.07.029

Predicting how pharmaceuticals may affect heart rhythm is a crucial step in drug-development, and requires a deep understanding of a compound’s action on ion channels. In vitro hERG-channel current recordings are an important step in evaluating the p... Read More about Rapid Characterization of hERG Channel Kinetics I: Using an Automated High-Throughput System.