Differential Responders to a Mixed Meal Tolerance Test Associated with Type 2 Diabetes Risk Factors and Gut Microbiota-Data from the MEDGI-Carb Randomized Controlled Trial.

The global prevalence of type 2 diabetes mellitus (T2DM) has surged in recent decades, and the identification of differential glycemic responders can aid tailored treatment for the prevention of prediabetes and T2DM. A mixed meal tolerance test (MMTT) based on regular foods offers the potential to uncover differential responders in dynamical postprandial events. We aimed to fit a simple mathematical model on dynamic postprandial glucose data from repeated MMTTs among participants with elevated T2DM risk to identify response clusters and investigate their association with T2DM risk factors and gut microbiota. Data were used from a 12-week multi-center dietary intervention trial involving high-risk T2DM adults, comparing high- versus low-glycemic index foods within a Mediterranean diet context (MEDGICarb). Model-based analysis of MMTTs from 155 participants (81 females and 74 males) revealed two distinct plasma glucose response clusters that were associated with baseline gut microbiota. Cluster A, inversely associated with HbA1c and waist circumference and directly with insulin sensitivity, exhibited a contrasting profile to cluster B. Findings imply that a standardized breakfast MMTT using regular foods could effectively distinguish non-diabetic individuals at varying risk levels for T2DM using a simple mechanistic model.

Model-based estimation of AV-nodal refractory period and conduction delay trends from ECG.

Introduction: Atrial fibrillation (AF) is the most common arrhythmia, associated with significant burdens to patients and the healthcare system. The atrioventricular (AV) node plays a vital role in regulating heart rate during AF by filtering electrical impulses from the atria. However, it is often insufficient in regards to maintaining a healthy heart rate, thus the AV node properties are modified using rate-control drugs. Moreover, treatment selection during permanent AF is currently done empirically. Quantifying individual differences in diurnal and short-term variability of AV-nodal function could aid in personalized treatment selection. Methods: This study presents a novel methodology for estimating the refractory period (RP) and conduction delay (CD) trends, and their uncertainty in the two pathways of the AV node during 24 h using non-invasive data. This was achieved by utilizing a network model together with a problem-specific genetic algorithm and an approximate Bayesian computation algorithm. Diurnal variability in the estimated RP and CD was quantified by the difference between the daytime and nighttime estimates, and short-term variability was quantified by the Kolmogorov-Smirnov distance between adjacent 10-min segments in the 24-h trends. Additionally, the predictive value of the derived parameter trends regarding drug outcome was investigated using several machine learning tools. Results: Holter electrocardiograms from 51 patients with permanent AF during baseline were analyzed, and the predictive power of variations in RP and CD on the resulting heart rate reduction after treatment with four rate control drugs was investigated. Diurnal variability yielded no correlation to treatment outcome, and no prediction of drug outcome was possible using the machine learning tools. However, a correlation between the short-term variability for the RP and CD in the fast pathway and resulting heart rate reduction during treatment with metoprolol (ρ = 0.48, p < 0.005 in RP, ρ = 0.35, p < 0.05 in CD) were found. Discussion: The proposed methodology enables non-invasive estimation of the AV node properties during 24 h, which-indicated by the correlation between the short-term variability and heart rate reduction-may have the potential to assist in treatment selection.

Data-driven analysis and prediction of dynamic postprandial metabolic response to multiple dietary challenges using dynamic mode decomposition.

Motivation: In the field of precision nutrition, predicting metabolic response to diet and identifying groups of differential responders are two highly desirable steps toward developing tailored dietary strategies. However, data analysis tools are currently lacking, especially for complex settings such as crossover studies with repeated measures.Current methods of analysis often rely on matrix or tensor decompositions, which are well suited for identifying differential responders but lacking in predictive power, or on dynamical systems modeling, which may be used for prediction but typically requires detailed mechanistic knowledge of the system under study. To remedy these shortcomings, we explored dynamic mode decomposition (DMD), which is a recent, data-driven method for deriving low-rank linear dynamical systems from high dimensional data.Combining the two recent developments "parametric DMD" (pDMD) and "DMD with control" (DMDc) enabled us to (i) integrate multiple dietary challenges, (ii) predict the dynamic response in all measured metabolites to new diets from only the metabolite baseline and dietary input, and (iii) identify inter-individual metabolic differences, i.e., metabotypes. To our knowledge, this is the first time DMD has been applied to analyze time-resolved metabolomics data. Results: We demonstrate the potential of pDMDc in a crossover study setting. We could predict the metabolite response to unseen dietary exposures on both measured (R2 = 0.40) and simulated data of increasing size (Rmax2= 0.65), as well as recover clusters of dynamic metabolite responses. We conclude that this method has potential for applications in personalized nutrition and could be useful in guiding metabolite response to target levels. Availability and implementation: The measured data analyzed in this study can be provided upon reasonable request. The simulated data along with a MATLAB implementation of pDMDc is available at https://github.com/FraunhoferChalmersCentre/pDMDc.

ECG based assessment of circadian variation in AV-nodal conduction during AF-Influence of rate control drugs.

The heart rate during atrial fibrillation (AF) is highly dependent on the conduction properties of the atrioventricular (AV) node. These properties can be affected using ß-blockers or calcium channel blockers, mainly chosen empirically. Characterization of individual AV-nodal conduction could assist in personalized treatment selection during AF. Individual AV nodal refractory periods and conduction delays were characterized based on 24-hour ambulatory ECGs from 60 patients with permanent AF. This was done by estimating model parameters from a previously created mathematical network model of the AV node using a problem-specific genetic algorithm. Based on the estimated model parameters, the circadian variation and its drug-dependent difference between treatment with two ß-blockers and two calcium channel blockers were quantified on a population level by means of cosinor analysis using a linear mixed-effect approach. The mixed-effects analysis indicated increased refractoriness relative to baseline for all drugs. An additional decrease in circadian variation for parameters representing conduction delay was observed for the ß-blockers. This indicates that the two drug types have quantifiable differences in their effects on AV-nodal conduction properties. These differences could be important in treatment outcome, and thus quantifying them could assist in treatment selection.

An atrioventricular node model incorporating autonomic tone.

The response to atrial fibrillation (AF) treatment is differing widely among patients, and a better understanding of the factors that contribute to these differences is needed. One important factor may be differences in the autonomic nervous system (ANS) activity. The atrioventricular (AV) node plays an important role during AF in modulating heart rate. To study the effect of the ANS-induced activity on the AV nodal function in AF, mathematical modelling is a valuable tool. In this study, we present an extended AV node model that incorporates changes in autonomic tone. The extension was guided by a distribution-based sensitivity analysis and incorporates the ANS-induced changes in the refractoriness and conduction delay. Simulated RR series from the extended model driven by atrial impulse series obtained from clinical tilt test data were qualitatively evaluated against clinical RR series in terms of heart rate, RR series variability and RR series irregularity. The changes to the RR series characteristics during head-down tilt were replicated by a 10% decrease in conduction delay, while the changes during head-up tilt were replicated by a 5% decrease in the refractory period and a 10% decrease in the conduction delay. We demonstrate that the model extension is needed to replicate ANS-induced changes during tilt, indicating that the changes in RR series characteristics could not be explained by changes in atrial activity alone.

An integrative pharmacokinetic-cardiovascular physiology modelling approach based on in vivo dog studies including five reference compounds.

Cardiovascular (CV) effects represent a major safety issue during drug development. Typically, this risk is mitigated by preclinical in vivo CV studies, based on which measured CV readouts are analyzed independently. Here, we apply a regression approach to simultaneously integrate CV readouts, i.e., heart rate (HR), mean arterial pressure (MAP) and QT from five dog telemetry studies. These CV studies comprise data on verapamil, captopril, dofetilide, pimobendan, and formoterol, and are combined with the respective dog pharmacokinetic (PK) profiles. A published PK/CV model structure for rats is extended by a semi-mechanistic parameterization of the interaction between HR and QT specific to dogs. This semi-mechanistic modelling approach allows differentiation between compound-independent system-specific parameters (e.g., HR baseline) and compound-specific parameters (e.g., EC50). Compared to previous results in rodents, estimated parameters for dogs indicate stronger dependency of stroke volume on HR, slower HR response, faster QT response and steeper concentration-response relationships. In addition, we illustrate how to practically apply the PK/CV model to derive concentration-response relationships for CV readouts. This approach allows a more detailed quantitative evaluation based on the maximum effect on CV effects (Emax), the EC50, and the steepness of this relation (Hill coefficient) especially for HR-independent effects on QT interval duration (QTc) while taking the systemic feedback into account. This approach also allows to derive plasma concentrations associated with relevant CV effects ("threshold concentration"; CTHRESH). The presented modelling analysis highlights the potential of an integrative evaluation of CV data and provides a framework for obtaining quantitative insights from safety pharmacology evaluations.

Non-invasive Characterization of Human AV-Nodal Conduction Delay and Refractory Period During Atrial Fibrillation.

During atrial fibrillation (AF), the heart relies heavily on the atrio-ventricular (AV) node to regulate the heart rate. Thus, characterization of AV-nodal properties may provide valuable information for patient monitoring and prediction of rate control drug effects. In this work we present a network model consisting of the AV node, the bundle of His, and the Purkinje fibers, together with an associated workflow, for robust estimation of the model parameters from ECG. The model consists of two pathways, referred to as the slow and the fast pathway, interconnected at one end. Both pathways are composed of interacting nodes, with separate refractory periods and conduction delays determined by the stimulation history of each node. Together with this model, a fitness function based on the Poincaré plot accounting for dynamics in RR interval series and a problem specific genetic algorithm, are also presented. The robustness of the parameter estimates is evaluated using simulated data, based on clinical measurements from five AF patients. Results show that the proposed model and workflow could estimate the slow pathway parameters for the refractory period, R m i n S P and ΔR SP , with an error (mean ± std) of 10.3 ± 22 and -12.6 ± 26 ms, respectively, and the parameters for the conduction delay, D m i n , t o t S P and Δ D t o t S P , with an error of 7 ± 35 and 4 ± 36 ms. Corresponding results for the fast pathway were 31.7 ± 65, -0.3 ± 77, 17 ± 29, and 43 ± 109 ms. These results suggest that both conduction delay and refractory period can be robustly estimated from non-invasive data with the proposed methodology. Furthermore, as an application example, the methodology was used to analyze ECG data from one patient at baseline and during treatment with Diltiazem, illustrating its potential to assess the effect of rate control drugs.

An Integrative Approach for Improved Assessment of Cardiovascular Safety Data.

Cardiovascular adverse effects in drug development are a major source of compound attrition. Characterization of blood pressure (BP), heart rate (HR), stroke volume (SV), and QT-interval prolongation are therefore necessary in early discovery. It is, however, common practice to analyze these effects independently of each other. High-resolution time courses are collected via telemetric techniques, but only low-resolution data are analyzed and reported. This ignores codependencies among responses (HR, BP, SV, and QT-interval) and separation of system (turnover properties) and drug-specific properties (potencies, efficacies). An analysis of drug exposure-time and high-resolution response-time data of HR and mean arterial blood pressure was performed after acute oral dosing of ivabradine, sildenafil, dofetilide, and pimobendan in Han-Wistar rats. All data were modeled jointly, including different compounds and exposure and response time courses, using a nonlinear mixed-effects approach. Estimated fractional turnover rates [h-1, relative standard error (%RSE) within parentheses] were 9.45 (15), 30.7 (7.8), 3.8 (13), and 0.115 (1.7) for QT, HR, total peripheral resistance, and SV, respectively. Potencies (nM, %RSE within parentheses) were IC 50 = 475 (11), IC 50 = 4.01 (5.4), EC 50 = 50.6 (93), and IC 50 = 47.8 (16), and efficacies (%RSE within parentheses) were I max = 0.944 (1.7), Imax = 1.00 (1.3), E max = 0.195 (9.9), and Imax = 0.745 (4.6) for ivabradine, sildenafil, dofetilide, and pimobendan. Hill parameters were estimated with good precision and below unity, indicating a shallow concentration-response relationship. An equilibrium concentration-biomarker response relationship was predicted and displayed graphically. This analysis demonstrates the utility of a model-based approach integrating data from different studies and compounds for refined preclinical safety margin assessment. SIGNIFICANCE STATEMENT: A model-based approach was proposed utilizing biomarker data on heart rate, blood pressure, and QT-interval. A pharmacodynamic model was developed to improve assessment of high-resolution telemetric cardiovascular safety data driven by different drugs (ivabradine, sildenafil, dofetilide, and pimobondan), wherein system- (turnover rates) and drug-specific parameters (e.g., potencies and efficacies) were sought. The model-predicted equilibrium concentration-biomarker response relationships and was used for safety assessment (predictions of 20% effective concentration, for example) of heart rate, blood pressure, and QT-interval.

Characterisation of human AV-nodal properties using a network model.

Characterisation of the AV-node is an important step in determining the optimal form of treatment for supraventricular tachycardias. To integrate and analyse patient-specific measurements, mathematical modelling has emerged as a valuable tool. Here we present a model of the human AV-node, consisting of a series of interacting nodes, each with separate dynamics in refractory time and conduction delay. The model is evaluated in several scenarios, including atrial fibrillation (AF) and clinical pacing, using simulated and measured data. The model is able to replicate signals derived from clinical ECG data as well as from invasive measurements, both under AF and pacing. To quantify the uncertainty in parameter estimation, 1000 parameter sets were sampled, showing that model output similar to data corresponds to limited regions in the model parameter space. The model is the first human AV-node model to capture both spatial and temporal dynamics while being efficient enough to allow interactive use on clinical timescales, as well as parameter estimation and uncertainty quantification. As such, it fills a new niche in the current set of published models and forms a valuable tool for both understanding and clinical research.

Investigating a Novel Activation-Repolarisation Time Metric to Predict Localised Vulnerability to Reentry Using Computational Modelling.

Exit sites associated with scar-related reentrant arrhythmias represent important targets for catheter ablation therapy. However, their accurate location in a safe and robust manner remains a significant clinical challenge. We recently proposed a novel quantitative metric (termed the Reentry Vulnerability Index, RVI) to determine the difference between activation and repolarisation intervals measured from pairs of spatial locations during premature stimulation to accurately locate the critical site of reentry formation. In the clinic, the method showed potential to identify regions of low RVI corresponding to areas vulnerable to reentry, subsequently identified as ventricular tachycardia (VT) circuit exit sites. Here, we perform an in silico investigation of the RVI metric in order to aid the acquisition and interpretation of RVI maps and optimise its future usage within the clinic. Within idealised 2D sheet models we show that the RVI produces lower values under correspondingly more arrhythmogenic conditions, with even low resolution (8 mm electrode separation) recordings still able to locate vulnerable regions. When applied to models of infarct scars, the surface RVI maps successfully identified exit sites of the reentrant circuit, even in scenarios where the scar was wholly intramural. Within highly complex infarct scar anatomies with multiple reentrant pathways, the identified exit sites were dependent upon the specific pacing location used to compute the endocardial RVI maps. However, simulated ablation of these sites successfully prevented the reentry re-initiation. We conclude that endocardial surface RVI maps are able to successfully locate regions vulnerable to reentry corresponding to critical exit sites during sustained scar-related VT. The method is robust against highly complex and intramural scar anatomies and low resolution clinical data acquisition. Optimal location of all relevant sites requires RVI maps to be computed from multiple pacing locations.

Human-based approaches to pharmacology and cardiology: an interdisciplinary and intersectorial workshop.

Both biomedical research and clinical practice rely on complex datasets for the physiological and genetic characterization of human hearts in health and disease. Given the complexity and variety of approaches and recordings, there is now growing recognition of the need to embed computational methods in cardiovascular medicine and science for analysis, integration and prediction. This paper describes a Workshop on Computational Cardiovascular Science that created an international, interdisciplinary and inter-sectorial forum to define the next steps for a human-based approach to disease supported by computational methodologies. The main ideas highlighted were (i) a shift towards human-based methodologies, spurred by advances in new in silico, in vivo, in vitro, and ex vivo techniques and the increasing acknowledgement of the limitations of animal models. (ii) Computational approaches complement, expand, bridge, and integrate in vitro, in vivo, and ex vivo experimental and clinical data and methods, and as such they are an integral part of human-based methodologies in pharmacology and medicine. (iii) The effective implementation of multi- and interdisciplinary approaches, teams, and training combining and integrating computational methods with experimental and clinical approaches across academia, industry, and healthcare settings is a priority. (iv) The human-based cross-disciplinary approach requires experts in specific methodologies and domains, who also have the capacity to communicate and collaborate across disciplines and cross-sector environments. (v) This new translational domain for human-based cardiology and pharmacology requires new partnerships supported financially and institutionally across sectors. Institutional, organizational, and social barriers must be identified, understood and overcome in each specific setting.

Computational methods to reduce uncertainty in the estimation of cardiac conduction properties from electroanatomical recordings.

Cardiac imaging is routinely used to evaluate cardiac tissue properties prior to therapy. By integrating the structural information with electrophysiological data from e.g. electroanatomical mapping systems, knowledge of the properties of the cardiac tissue can be further refined. However, as in other clinical modalities, electrophysiological data are often sparse and noisy, and this results in high levels of uncertainty in the estimated quantities. In this study, we develop a methodology based on Bayesian inference, coupled with a computationally efficient model of electrical propagation to achieve two main aims: (1) to quantify values and associated uncertainty for different tissue conduction properties inferred from electroanatomical data, and (2) to design strategies to optimize the location and number of measurements required to maximize information and reduce uncertainty. The methodology is validated in an in silico study performed using simulated data obtained from a human image-based ventricular model, including realistic fibre orientation and a transmural scar. We demonstrate that the method provides a simultaneous description of clinically-relevant electrophysiological conduction properties and their associated uncertainty for various levels of noise. By using the developed methodology to investigate how the uncertainty decreases in response to added measurements, we then derive an a priori index for placing electrophysiological measurements in order to optimize the information content of the collected data. Results show that the derived index has a clear benefit in minimizing the uncertainty of inferred conduction properties compared to a random distribution of measurements, reducing the number of required measurements by over 50% in several of the investigated settings. This suggests that the methodology presented in this work provides an important step towards improving the quality of the spatiotemporal information obtained using electroanatomical mapping.

A comparative study of graph-based, eikonal, and monodomain simulations for the estimation of cardiac activation times.

The bidomain and monodomain equations are well established as the standard set of equations for the simulation of cardiac electrophysiological behavior. However, the computational cost of detailed bidomain/monodomain simulations limits their applicability in scenarios where a large number of simulations needs to be performed (e.g., parameter estimation). In this study, we present a graph-based method, which relies on point-to-point path finding to estimate activation times for single points in cardiac tissue with minimal computational costs. To validate our approach, activation times are compared to monodomain simulation results for an anatomically based rabbit ventricular model, incorporating realistic fiber orientation and conduction heterogeneities. Differences in activation times between the graph-based method and monodomain results are less than 10% of the total activation time, and computational performance is orders of magnitude faster with the proposed method when calculating activation times at single points. These results suggest that the graph-based method is well suited for estimating activation times when the need for fast performance justifies a limited loss of accuracy.

Shock-induced arrhythmogenesis in the human heart: A computational modelling study.

Electrical defibrillation by application of a strong shock to the heart is the only effective treatment against lethal cardiac arrhythmias such as ventricular fibrillation. A large body of experimental and computational research has been devoted to understanding shock-induced effects on the heart in an attempt to improve defibrillation efficacy. However, most of the research has been performed in small animal hearts, and in particular rabbits. The difference in size between rabbits and humans might limit the extrapolation of the results to the clinical setting. In this paper, we present, for the first time, computer simulations of shock-induced effects on a human ventricular model with realistic ion channel dynamics and fibre architecture. Bidomain simulations using the human ventricular model were performed using the Chaste open source simulation package. The parallel performance of the software package was highly improved in order to meet the computational requirements of these kind of studies.

Modeling the effect of Kv1.5 block on the canine action potential.

A wide range of ion channels have been considered as potential targets for pharmacological treatment of atrial fibrillation. The Kv1.5 channel, carrying the I(Kur) current, has received special attention because it contributes to repolarization in the atria but is absent or weakly expressed in ventricular tissue. The dog serves as an important animal model for electrophysiological studies of the heart and mathematical models of the canine atrial action potential (CAAP) have been developed to study the interplay between ionic currents. To enable more-realistic studies on the effects of Kv1.5 blockers on the CAAP in silico, two continuous-time Markov models of the guarded receptor type were formulated for Kv1.5 and subsequently inserted into the Ramirez-Nattel-Courtemanche model of the CAAP. The main findings were: 1), time- and state-dependent Markov models of open-channel Kv1.5 block gave significantly different results compared to a time- and state-independent model with a downscaled conductance; 2), the outcome of Kv1.5 block on the macroscopic system variable APD(90) was dependent on the precise mechanism of block; and 3), open-channel block produced a reverse use-dependent prolongation of APD(90). This study suggests that more-complex ion-channel models are a prerequisite for quantitative modeling of drug effects.

Improving Bayesian credibility intervals for classifier error rates using maximum entropy empirical priors.

OBJECTIVE: Successful use of classifiers that learn to make decisions from a set of patient examples require robust methods for performance estimation. Recently many promising approaches for determination of an upper bound for the error rate of a single classifier have been reported but the Bayesian credibility interval (CI) obtained from a conventional holdout test still delivers one of the tightest bounds. The conventional Bayesian CI becomes unacceptably large in real world applications where the test set sizes are less than a few hundred. The source of this problem is that fact that the CI is determined exclusively by the result on the test examples. In other words, there is no information at all provided by the uniform prior density distribution employed which reflects complete lack of prior knowledge about the unknown error rate. Therefore, the aim of the study reported here was to study a maximum entropy (ME) based approach to improved prior knowledge and Bayesian CIs, demonstrating its relevance for biomedical research and clinical practice. METHOD AND MATERIAL: It is demonstrated how a refined non-uniform prior density distribution can be obtained by means of the ME principle using empirical results from a few designs and tests using non-overlapping sets of examples. RESULTS: Experimental results show that ME based priors improve the CIs when employed to four quite different simulated and two real world data sets. CONCLUSIONS: An empirically derived ME prior seems promising for improving the Bayesian CI for the unknown error rate of a designed classifier.

External cross-validation for unbiased evaluation of protein family detectors: application to allergens.

Key issues in protein science and computational biology are design and evaluation of algorithms aimed at detection of proteins that belong to a specific family, as defined by structural, evolutionary, or functional criteria. In this context, several validation techniques are often used to compare different parameter settings of the detector, and to subsequently select the setting that yields the smallest error rate estimate. A frequently overlooked problem associated with this approach is that this smallest error rate estimate may have a large optimistic bias. Based on computer simulations, we show that a detector's error rate estimate can be overly optimistic and propose a method to obtain unbiased performance estimates of a detector design procedure. The method is founded on an external 10-fold cross-validation (CV) loop that embeds an internal validation procedure used for parameter selection in detector design. The designed detector generated in each of the 10 iterations are evaluated on held-out examples exclusively available in the external CV iterations. Notably, the average of these 10 performance estimates is not associated with a final detector, but rather with the average performance of the design procedure used. We apply the external CV loop to the particular problem of detecting potentially allergenic proteins, using a previously reported design procedure. Unbiased performance estimates of the allergen detector design procedure are presented together with information about which algorithms and parameter settings that are most frequently selected.