Metamodelling of a two-population spiking neural network.

In computational neuroscience, hypotheses are often formulated as bottom-up mechanistic models of the systems in question, consisting of differential equations that can be numerically integrated forward in time. Candidate models can then be validated by comparison against experimental data. The model outputs of neural network models depend on both neuron parameters, connectivity parameters and other model inputs. Successful model fitting requires sufficient exploration of the model parameter space, which can be computationally demanding. Additionally, identifying degeneracy in the parameters, i.e. different combinations of parameter values that produce similar outputs, is of interest, as they define the subset of parameter values consistent with the data. In this computational study, we apply metamodels to a two-population recurrent spiking network of point-neurons, the so-called Brunel network. Metamodels are data-driven approximations to more complex models with more desirable computational properties, which can be run considerably faster than the original model. Specifically, we apply and compare two different metamodelling techniques, masked autoregressive flows (MAF) and deep Gaussian process regression (DGPR), to estimate the power spectra of two different signals; the population spiking activities and the local field potential. We find that the metamodels are able to accurately model the power spectra in the asynchronous irregular regime, and that the DGPR metamodel provides a more accurate representation of the simulator compared to the MAF metamodel. Using the metamodels, we estimate the posterior probability distributions over parameters given observed simulator outputs separately for both LFP and population spiking activities. We find that these distributions correctly identify parameter combinations that give similar model outputs, and that some parameters are significantly more constrained by observing the LFP than by observing the population spiking activities.

The Emerging Role of Cardiac Magnetic Resonance Imaging in the Evaluation of Patients with HFpEF.

PURPOSE OF REVIEW: To give an update on the emerging role of cardiac magnetic resonance imaging in the evaluation of patients with heart failure with preserved ejection fraction (HFpEF). This is important as the diagnosis of HFpEF remains challenging and cardiac imaging is pivotal in establishing the function of the heart and whether there is evidence of structural heart disease or diastolic dysfunction. Echocardiography is widely available, although the gold standard in quantifying heart function is cardiac magnetic resonance (CMR) imaging. RECENT FINDINGS: This review includes the recently updated 2016 European Society of Cardiology guidelines on diagnosing HFpEF that define the central role of imaging in identifying patients with HFpEF. Moreover, it includes the pathophysiology in HFpEF, how CMR works, and details current CMR techniques used to assess structural heart disease and diastolic function. Furthermore, it highlights promising research techniques that over the next few years may become more used in identifying these patients. CMR has an emerging role in establishing the diagnosis of HFpEF by measuring the left ventricular ejection fraction (LVEF) and evidence of structural heart disease and diastolic dysfunction.

Quantifying inter-species differences in contractile function through biophysical modelling.

Animal models and measurements are frequently used to guide and evaluate clinical interventions. In this context, knowledge of inter-species differences in physiology is crucial for understanding the limitations and relevance of animal experimental assays for informing clinical applications. Extensive effort has been put into studying the structure and function of cardiac contractile proteins and how differences in these translate into the functional properties of muscles. However, integrating this knowledge into a quantitative description, formalising and highlighting inter-species differences both in the kinetics and in the regulation of physiological mechanisms, remains challenging. In this study we propose and apply a novel approach for the quantification of inter-species differences between mouse, rat and human. Assuming conservation of the fundamental physiological mechanisms underpinning contraction, biophysically based computational models are fitted to simulate experimentally recorded phenotypes from multiple species. The phenotypic differences between species are then succinctly quantified as differences in the biophysical model parameter values. This provides the potential of quantitatively establishing the human relevance of both animal-based experimental and computational models for application in a clinical context. Our results indicate that the parameters related to the sensitivity and cooperativity of calcium binding to troponin C and the activation and relaxation rates of tropomyosin/crossbridge binding kinetics differ most significantly between mouse, rat and human, while for example the reference tension, as expected, shows only minor differences between the species. Hence, while confirming expected inter-species differences in calcium sensitivity due to large differences in the observed calcium transients, our results also indicate more unexpected differences in the cooperativity mechanism. Specifically, the decrease in the unbinding rate of calcium to troponin C with increasing active tension was much lower for mouse than for rat and human. Our results also predicted crossbridge binding to be slowest in human and fastest in mouse.

Increased interpretation of deep learning models using hierarchical cluster-based modelling.

Linear prediction models based on data with large inhomogeneity or abrupt non-linearities often perform poorly because relationships between groups in the data dominate the model. Given that the data is locally linear, this can be overcome by splitting the data into smaller clusters and creating a local model within each cluster. In this study, the previously published Hierarchical Cluster-based Partial Least Squares Regression (HC-PLSR) procedure was extended to deep learning, in order to increase the interpretability of the deep learning models through local modelling. Hierarchical Cluster-based Convolutional Neural Networks (HC-CNNs), Hierarchical Cluster-based Recurrent Neural Networks (HC-RNNs) and Hierarchical Cluster-based Support Vector Regression models (HC-SVRs) were implemented and tested on spectroscopic data consisting of Fourier Transform Infrared (FT-IR) measurements of raw material dry films, for prediction of average molecular weight during hydrolysis and a simulated data set constructed to contain three clusters of observations with different non-linear relationships between the independent variables and the response. HC-CNN, HC-RNN and HC-SVR outperformed HC-PLSR for the simulated data set, showing the disadvantage of PLSR for highly non-linear data, but for the FT-IR data set there was little to gain in prediction ability from using more complex models than HC-PLSR. Local modelling can ease the interpretation of deep learning models through highlighting differences in feature importance between different regions of the input or output space. Our results showed clear differences between the feature importance for the various local models, which demonstrate the advantages of a local modelling approach with regards to interpretation of deep learning models.

Crude Oil Density Prediction Improved by Multiblock Analysis of Fourier Transform Ion Cyclotron Resonance Mass Spectrometry, Fourier Transform Infrared, and Near-Infrared Spectroscopy Data.

Crude oils are among the world's most complex organic mixtures containing a large number of unique components and many analytical techniques lack resolving power to characterize. Fourier transform ion cyclotron resonance mass spectrometry offers a high mass accuracy, making a detailed analysis of crude oils possible. Infrared (IR) spectroscopic methods such as Fourier transform IR spectroscopy (FT-IR) and near-IR, can also be used for crude oil characterization. The three methods measure different properties of the samples, and different data sources can often be combined to improve the prediction accuracy of models. In this study, partial least squares regression (PLSR) models for each of the three methods (single-block PLSR) were compared to multiblock PLSR and sequential and orthogonalized PLSR (SO-PLSR), with the aim of predicting the density of crude oils. Variable importance in projection was used to identify the important variables for each method, as spectroscopic data often contain irrelevant variation. The variables were interpreted to evaluate their underlying chemistry and to check whether consistency could be found between the variables selected from the spectroscopic data for the single-block and multiblock methods. Combining the different blocks of data increased the prediction abilities of the models both before and after variable selection, and SO-PLSR using a reduced data set resulted in the best-performing prediction model.

Using machine learning-based variable selection to identify hydrate related components from FT-ICR MS spectra.

The blockages of pipelines caused by agglomeration of gas hydrates is a major flow assurance issue in the oil and gas industry. Some crude oils form gas hydrates that remain as transportable particles in a slurry. It is commonly believed that naturally occurring components in those crude oils alter the surface properties of gas hydrate particles when formed. The exact structure of the crude oil components responsible for this surface modification remains unknown. In this study, a successive accumulation and spiking of hydrate-active crude oil fractions was performed to increase the concentration of hydrate related compounds. Fourier Transform Ion Cyclotron Resonance Mass Spectrometry (FT-ICR MS) was then utilised to analyse extracted oil samples for each spiking generation. Machine learning-based variable selection was used on the FT-ICR MS spectra to identify the components related to hydrate formation. Among six different methods, Partial Least Squares Discriminant Analysis (PLS-DA) was selected as the best performing model and the 23 most important variables were determined. The FT-ICR MS mass spectra for each spiking level was compared to samples extracted before the successive accumulation, to identify changes in the composition. Principal Component Analysis (PCA) exhibited differences between the oils and spiking levels, indicating an accumulation of hydrate active components. Molecular formulas, double bond equivalents (DBE) and hydrogen-carbon (H/C) ratios were determined for each of the selected variables and evaluated. Some variables were identified as possibly asphaltenes and naphthenic acids which could be related to the positive wetting index (WI) for the oils.

Deep learning-enabled Inference of 3D molecular absorption distribution of biological cells from IR spectra.

Infrared spectroscopy delivers abundant information about the chemical composition, as well as the structural and optical properties of intact samples in a non-destructive manner. We present a deep convolutional neural network which exploits all of this information and solves full-wave inverse scattering problems and thereby obtains the 3D optical, structural and chemical properties from infrared spectroscopic measurements of intact micro-samples. The proposed model encodes scatter-distorted infrared spectra and infers the distribution of the complex refractive index function of concentrically spherical samples, such as many biological cells. The approach delivers simultaneously the molecular absorption, sample morphology and effective refractive index in both the cell wall and interior from a single measured spectrum. The model is trained on simulated scatter-distorted spectra, where absorption in the distinct layers is simulated and the scatter-distorted spectra are estimated by analytic solutions of Maxwell's equations for samples of different sizes. This allows for essentially real-time deep learning-enabled infrared diffraction micro-tomography, for a large subset of biological cells.

Morphological Heterogeneity in Pancreatic Cancer Reflects Structural and Functional Divergence.

Inter- and intratumor heterogeneity is an important cause of treatment failure. In human pancreatic cancer (PC), heterogeneity has been investigated almost exclusively at the genomic and transcriptional level. Morphological heterogeneity, though prominent and potentially easily assessable in clinical practice, remains unexplored. This proof-of-concept study aims at demonstrating that morphological heterogeneity reflects structural and functional divergence. From the wide morphological spectrum of conventional PC, four common and distinctive patterns were investigated in 233 foci from 39 surgical specimens. Twenty-six features involved in key biological processes in PC were analyzed (immuno-)histochemically and morphometrically: cancer cell proliferation (Ki67) and migration (collagen fiber alignment, MMP14), cancer stem cells (CD44, CD133, ALDH1), amount, composition and spatial arrangement of extracellular matrix (epithelial proximity, total collagen, collagen I and III, fibronectin, hyaluronan), cancer-associated fibroblasts (density, αSMA), and cancer-stroma interactions (integrins α2, α5, α1; caveolin-1). All features differed significantly between at least two of the patterns. Stromal and cancer-cell-related features co-varied with morphology and allowed prediction of the morphological pattern. In conclusion, morphological heterogeneity in the cancer-cell and stromal compartments of PC correlates with structural and functional diversity. As such, histopathology has the potential to inform on the operationality of key biological processes in individual tumors.

Grayscale representation of infrared microscopy images by extended multiplicative signal correction for registration with histological images.

Fourier-transform infrared (FTIR) microspectroscopy is rounding the corner to become a label-free routine method for cancer diagnosis. In order to build infrared-spectral based classifiers, infrared images need to be registered with Hematoxylin and Eosin (H&E) stained histological images. While FTIR images have a deep spectral domain with thousands of channels carrying chemical and scatter information, the H&E images have only three color channels for each pixel and carry mainly morphological information. Therefore, image representations of infrared images are needed that match the morphological information in H&E images. In this paper, we propose a novel approach for representation of FTIR images based on extended multiplicative signal correction highlighting morphological features that showed to correlate well with morphological information in H&E images. Based on the obtained representations, we developed a strategy for global-to-local image registration for FTIR images and H&E stained histological images of parallel tissue sections.

Deep convolutional neural network recovers pure absorbance spectra from highly scatter-distorted spectra of cells.

Infrared spectroscopy of cells and tissues is prone to Mie scattering distortions, which grossly obscure the relevant chemical signals. The state-of-the-art Mie extinction extended multiplicative signal correction (ME-EMSC) algorithm is a powerful tool for the recovery of pure absorbance spectra from highly scatter-distorted spectra. However, the algorithm is computationally expensive and the correction of large infrared imaging datasets requires weeks of computations. In this paper, we present a deep convolutional descattering autoencoder (DSAE) which was trained on a set of ME-EMSC corrected infrared spectra and which can massively reduce the computation time for scatter correction. Since the raw spectra showed large variability in chemical features, different reference spectra matching the chemical signals of the spectra were used to initialize the ME-EMSC algorithm, which is beneficial for the quality of the correction and the speed of the algorithm. One DSAE was trained on the spectra, which were corrected with different reference spectra and validated on independent test data. The DSAE outperformed the ME-EMSC correction in terms of speed, robustness, and noise levels. We confirm that the same chemical information is contained in the DSAE corrected spectra as in the spectra corrected with ME-EMSC.

A comparison of early redo surgery rates in Mosaic porcine and Perimount bovine pericardial valves.

OBJECTIVES: The objective of this study was to compare rates of redo surgery for the Medtronic Mosaic 305 A Porcine Prosthesis and the Carpentier-Edwards Perimount Pericardial Aortic Bioprosthesis 2900. METHODS: This was a single-centre retrospective observational study. We included all 1018 patients who underwent aortic valve replacement with a Mosaic (n = 216) or Perimount (n = 809) bioprosthesis between October 2000 and August 2008. The total follow-up was 1508 patient-years for the Mosaic valve and 5813 for the Perimount valve. The maximal follow-up and interquartile range were 14.8 and 7.0 years for the Mosaic valve and 15.1 and 5.6 years for the Perimount valve, respectively. A propensity score-weighted version of the Cox model, Kaplan-Meier analysis and multivariate regression model was used. RESULTS: Despite no statistical difference in the number of non-structural valve deterioration cases between valves, redo surgery occurred earlier in 10 (4.6%) Mosaic than for 17 (2.1%) Perimount valves (P = 0.02) and was required for structural valve deterioration in 5 (2.3%) Mosaic valves when compared with 7 (0.9%; P = 0.04) Perimount valves. Four of 5 Mosaic failures occurred before 5 years, whereas all Perimount failures occurred after 5 years. Redo surgery for non-structural valve deterioration occurred in 3 patients with Mosaic valves (1.4%) and no patients with Perimount valves. Surgery for the remaining patients with Perimount valves was due to infection or aortic disease. CONCLUSIONS: Early redo surgery for structural valve degeneration was uncommon but occurred earlier for the Mosaic porcine than the Perimount bovine pericardial replacement aortic valve.

Cardiac Motion Evolution Model for Analysis of Functional Changes Using Tensor Decomposition and Cross-Sectional Data.

Cardiac disease can reduce the ability of the ventricles to function well enough to sustain long-term pumping efficiency. Recent advances in cardiac motion tracking have led to improvements in the analysis of cardiac function. We propose a method to study cohort effects related to age with respect to cardiac function. The proposed approach makes use of a recent method for describing cardiac motion of a given subject using a polyaffine model, which gives a compact parameterization that reliably and accurately describes the cardiac motion across populations. Using this method, a data tensor of motion parameters is extracted for a given population. The partial least squares method for higher order arrays is used to build a model to describe the motion parameters with respect to age, from which a model of motion given age is derived. Based on the cross-sectional statistical analysis with the data tensor of each subject treated as an observation along time, the left ventricular motion over time of Tetralogy of Fallot patients is analysed to understand the temporal evolution of functional abnormalities in this population compared to healthy motion dynamics.

Is heart failure with mid range ejection fraction (HFmrEF) a distinct clinical entity or an overlap group?

BACKGROUND: The new category of heart failure (HF), Heart Failure with mid range Ejection Fraction (HFmrEF) has recently been proposed with recent publications reporting that HFmrEF represents a transitional phase. The aim of this study was to determine the prevalence and clinical characteristics of patients with HFmrEF and to establish what proportion of patients transitioned to other types of HF, and how this affected clinical outcomes. METHODS AND RESULTS: Patients were diagnosed with HF according to the 2016 ESC guidelines. Clinical outcomes and variables were recorded for all consecutive in-patients referred to the heart failure service. In total, 677 patients with new HF were identified; 25.6% with HFpEF, 21% with HFmrEF and 53.5% with HFrEF. While clinical characteristics and prognostic factors of HFmrEF were intermediate between HFrEF and HFpEF, HFmrEF patients had the best outcome, with higher mortality in the HFrEF population (p 0.02) and higher HF rehospitalisation rates in the HFpEF population (p < 0.01).38.7% of the HFmrEF patients transitioned (56.4% to HFpEF and 43.6% to HFrEF) with fewest deaths in the patients that transitioned to HFpEF (p 0.04), and fewest HF readmissions in the patients that remained as HFmrEF (<0.01). CONCLUSION: HFmrEF patients had the best outcomes, compared to high rates of mortality seen in patients with HFrEF and high rates of HF readmissions seen in patients with HFpEF. Only 1/3 of HFmrEF patients transitioned during follow up, with the lowest mortality seen in patients transitioning to HFpEF.

Characterizing the optimal flux space of genome-scale metabolic reconstructions through modified latin-hypercube sampling.

Genome-Scale Metabolic Reconstructions (GSMRs), along with optimization-based methods, predominantly Flux Balance Analysis (FBA) and its derivatives, are widely applied for assessing and predicting the behavior of metabolic networks upon perturbation, thereby enabling identification of potential novel drug targets and biotechnologically relevant pathways. The abundance of alternate flux profiles has led to the evolution of methods to explore the complete solution space aiming to increase the accuracy of predictions. Herein we present a novel, generic algorithm to characterize the entire flux space of GSMR upon application of FBA, leading to the optimal value of the objective (the optimal flux space). Our method employs Modified Latin-Hypercube Sampling (LHS) to effectively border the optimal space, followed by Principal Component Analysis (PCA) to identify and explain the major sources of variability within it. The approach was validated with the elementary mode analysis of a smaller network of Saccharomyces cerevisiae and applied to the GSMR of Pseudomonas aeruginosa PAO1 (iMO1086). It is shown to surpass the commonly used Monte Carlo Sampling (MCS) in providing a more uniform coverage for a much larger network in less number of samples. Results show that although many fluxes are identified as variable upon fixing the objective value, majority of the variability can be reduced to several main patterns arising from a few alternative pathways. In iMO1086, initial variability of 211 reactions could almost entirely be explained by 7 alternative pathway groups. These findings imply that the possibilities to reroute greater portions of flux may be limited within metabolic networks of bacteria. Furthermore, the optimal flux space is subject to change with environmental conditions. Our method may be a useful device to validate the predictions made by FBA-based tools, by describing the optimal flux space associated with these predictions, thus to improve them.

Homology-based modelling of targets for rational drug design.

The current status in rational drug design using homology-based models is discussed, with focus on template selection, model building, model verification and strategies for drug design based on model structures. A novel approach for identification of unique binding site features from homology-based models, Protein Alpha Shape Similarity Analysis (PASSA) is described.

Insight into model mechanisms through automatic parameter fitting: a new methodological framework for model development.

BACKGROUND: Striking a balance between the degree of model complexity and parameter identifiability, while still producing biologically feasible simulations using modelling is a major challenge in computational biology. While these two elements of model development are closely coupled, parameter fitting from measured data and analysis of model mechanisms have traditionally been performed separately and sequentially. This process produces potential mismatches between model and data complexities that can compromise the ability of computational frameworks to reveal mechanistic insights or predict new behaviour. In this study we address this issue by presenting a generic framework for combined model parameterisation, comparison of model alternatives and analysis of model mechanisms. RESULTS: The presented methodology is based on a combination of multivariate metamodelling (statistical approximation of the input-output relationships of deterministic models) and a systematic zooming into biologically feasible regions of the parameter space by iterative generation of new experimental designs and look-up of simulations in the proximity of the measured data. The parameter fitting pipeline includes an implicit sensitivity analysis and analysis of parameter identifiability, making it suitable for testing hypotheses for model reduction. Using this approach, under-constrained model parameters, as well as the coupling between parameters within the model are identified. The methodology is demonstrated by refitting the parameters of a published model of cardiac cellular mechanics using a combination of measured data and synthetic data from an alternative model of the same system. Using this approach, reduced models with simplified expressions for the tropomyosin/crossbridge kinetics were found by identification of model components that can be omitted without affecting the fit to the parameterising data. Our analysis revealed that model parameters could be constrained to a standard deviation of on average 15% of the mean values over the succeeding parameter sets. CONCLUSIONS: Our results indicate that the presented approach is effective for comparing model alternatives and reducing models to the minimum complexity replicating measured data. We therefore believe that this approach has significant potential for reparameterising existing frameworks, for identification of redundant model components of large biophysical models and to increase their predictive capacity.

A computational pipeline for quantification of mouse myocardial stiffness parameters.

The mouse is an important model for theoretical-experimental cardiac research, and biophysically based whole organ models of the mouse heart are now within reach. However, the passive material properties of mouse myocardium have not been much studied. We present an experimental setup and associated computational pipeline to quantify these stiffness properties. A mouse heart was excised and the left ventricle experimentally inflated from 0 to 1.44kPa in eleven steps, and the resulting deformation was estimated by echocardiography and speckle tracking. An in silico counterpart to this experiment was built using finite element methods and data on ventricular tissue microstructure from diffusion tensor MRI. This model assumed a hyperelastic, transversely isotropic material law to describe the force-deformation relationship, and was simulated for many parameter scenarios, covering the relevant range of parameter space. To identify well-fitting parameter scenarios, we compared experimental and simulated outcomes across the whole range of pressures, based partly on gross phenotypes (volume, elastic energy, and short- and long-axis diameter), and partly on node positions in the geometrical mesh. This identified a narrow region of experimentally compatible values of the material parameters. Estimation turned out to be more precise when based on changes in gross phenotypes, compared to the prevailing practice of using displacements of the material points. We conclude that the presented experimental setup and computational pipeline is a viable method that deserves wider application.

Multi-way metamodelling facilitates insight into the complex input-output maps of nonlinear dynamic models.

BACKGROUND: Statistical approaches to describing the behaviour, including the complex relationships between input parameters and model outputs, of nonlinear dynamic models (referred to as metamodelling) are gaining more and more acceptance as a means for sensitivity analysis and to reduce computational demand. Understanding such input-output maps is necessary for efficient model construction and validation. Multi-way metamodelling provides the opportunity to retain the block-wise structure of the temporal data typically generated by dynamic models throughout the analysis. Furthermore, a cluster-based approach to regional metamodelling allows description of highly nonlinear input-output relationships, revealing additional patterns of covariation. RESULTS: By presenting the N-way Hierarchical Cluster-based Partial Least Squares Regression (N-way HC-PLSR) method, we here combine multi-way analysis with regional cluster-based metamodelling, together making a powerful methodology for extensive exploration of the input-output maps of complex dynamic models. We illustrate the potential of the N-way HC-PLSR by applying it both to predict model outputs as functions of the input parameters, and in the inverse direction (predicting input parameters from the model outputs), to analyse the behaviour of a dynamic model of the mammalian circadian clock. Our results display a more complete cartography of how variation in input parameters is reflected in the temporal behaviour of multiple model outputs than has been previously reported. CONCLUSIONS: Our results indicated that the N-way HC-PLSR metamodelling provides a gain in insight into which parameters that are related to a specific model output behaviour, as well as variations in the model sensitivity to certain input parameters across the model output space. Moreover, the N-way approach allows a more transparent and detailed exploration of the temporal dimension of complex dynamic models, compared to alternative 2-way methods.

Hierarchical cluster-based partial least squares regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models.

BACKGROUND: Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. RESULTS: Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. CONCLUSIONS: HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems.