Myocardial material parameter estimation

The passive material properties of myocardium play a major role in diastolic performance of the heart. In particular, the shear behaviour is thought to play an important mechanical role due to the laminar architecture of myocardium. We have previously compared a number of myocardial constitutive relations with the aim to extract their suitability for inverse material parameter estimation. The previous study assumed a homogeneous deformation. In the present study we relaxed the homogeneous assumption by implementing these laws into a finite element environment in order to obtain more realistic measures for the suitability of these laws in both their ability to fit a given set of experimental data, as well as their stability in the finite element environment. In particular, we examined five constitutive laws and compare them on the basis of (i) "goodness of fit": how well they fit a set of six shear deformation tests, (ii) "determinability": how well determined the objective function is at the optimal parameter fit, and (iii) "variability": how well determined the material parameters are over the range of experiments. Furthermore, we compared the FE results with those from the previous study.It was found that the same material law as in the previous study, the orthotropic Fung-type "Costa-Law", was the most suitable for inverse material parameter estimation for myocardium in simple shear.     

A hybrid approach for efficient and robust parameter estimation in biochemical pathways

Developing suitable dynamic models of biochemical pathways is a key issue in Systems Biology. Predictive models for cells or whole organisms could ultimately lead to model-based predictive and/or preventive medicine. Parameter estimation (i.e. model calibration) in these dynamic models is therefore a critical problem. In a recent contribution [Moles, C.G., Mendes, P., Banga, J.R., 2003b. Parameter estimation in biochemical pathways: a comparison of global optimisation methods. Genome Res. 13, 2467-2474], the challenging nature of such inverse problems was highlighted considering a benchmark problem, and concluding that only a certain type of stochastic global optimisation method, Evolution Strategies (ES), was able to solve it successfully, although at a rather large computational cost. In this new contribution, we present a new integrated optimisation methodology with a number of very significant improvements: (i) computation time is reduced by one order of magnitude by means of a hybrid method which increases efficiency while guaranteeing robustness, (ii) measurement noise (errors) and partial observations are handled adequately, (iii) automatic testing of identifiability of the model (both local and practical) is included and (iv) the information content of the experiments is evaluated via the Fisher information matrix, with subsequent application to design of new optimal experiments through dynamic optimisation.     

A modified particle swarm optimization algorithm for parameter estimation of a biological system

Background

Mathematical modeling has achieved a broad interest in the field of biology. These models represent the associations among the metabolism of the biological phenomenon with some mathematical equations such that the observed time course profile of the biological data fits the model. However, the estimation of the unknown parameters of the model is a challenging task. Many algorithms have been developed for parameter estimation, but none of them is entirely capable of finding the best solution. The purpose of this paper is to develop a method for precise estimation of parameters of a biological model.

Methods

In this paper, a novel particle swarm optimization algorithm based on a decomposition technique is developed. Then, its root mean square error is compared with simple particle swarm optimization, Iterative Unscented Kalman Filter and Simulated Annealing algorithms for two different simulation scenarios and a real data set related to the metabolism of CAD system.

Results

Our proposed algorithm results in 54.39% and 26.72% average reduction in root mean square error when applied to the simulation and experimental data, respectively.

Conclusion

The results show that the metaheuristic approaches such as the proposed method are very wise choices for finding the solution of nonlinear problems with many unknown parameters.

     

A computationally efficient algorithm for genomic prediction using a Bayesian model

Background

Genomic prediction of breeding values from dense single nucleotide polymorphisms (SNP) genotypes is used for livestock and crop breeding, and can also be used to predict disease risk in humans. For some traits, the most accurate genomic predictions are achieved with non-linear estimates of SNP effects from Bayesian methods that treat SNP effects as random effects from a heavy tailed prior distribution. These Bayesian methods are usually implemented via Markov chain Monte Carlo (MCMC) schemes to sample from the posterior distribution of SNP effects, which is computationally expensive. Our aim was to develop an efficient expectation–maximisation algorithm (emBayesR) that gives similar estimates of SNP effects and accuracies of genomic prediction than the MCMC implementation of BayesR (a Bayesian method for genomic prediction), but with greatly reduced computation time.

Methods

emBayesR is an approximate EM algorithm that retains the BayesR model assumption with SNP effects sampled from a mixture of normal distributions with increasing variance. emBayesR differs from other proposed non-MCMC implementations of Bayesian methods for genomic prediction in that it estimates the effect of each SNP while allowing for the error associated with estimation of all other SNP effects. emBayesR was compared to BayesR using simulated data, and real dairy cattle data with 632 003 SNPs genotyped, to determine if the MCMC and the expectation-maximisation approaches give similar accuracies of genomic prediction.

Results

We were able to demonstrate that allowing for the error associated with estimation of other SNP effects when estimating the effect of each SNP in emBayesR improved the accuracy of genomic prediction over emBayesR without including this error correction, with both simulated and real data. When averaged over nine dairy traits, the accuracy of genomic prediction with emBayesR was only 0.5% lower than that from BayesR. However, emBayesR reduced computing time up to 8-fold compared to BayesR.

Conclusions

The emBayesR algorithm described here achieved similar accuracies of genomic prediction to BayesR for a range of simulated and real 630 K dairy SNP data. emBayesR needs less computing time than BayesR, which will allow it to be applied to larger datasets.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-014-0082-4) contains supplementary material, which is available to authorized users.     

A computationally efficient electrophysiological model of human ventricular cells

Recent experimental and theoretical results have stressed the importance of modeling studies of reentrant arrhythmias in cardiac tissue and at the whole heart level. We introduce a six-variable model obtained by a reformulation of the Priebe-Beuckelmann model of a single human ventricular cell. The reformulated model is 4.9 times faster for numerical computations and it is more stable than the original model. It retains the action potential shape at various frequencies, restitution of action potential duration, and restitution of conduction velocity. We were able to reproduce the main properties of epicardial, endocardial, and M cells by modifying selected ionic currents. We performed a simulation study of spiral wave behavior in a two-dimensional sheet of human ventricular tissue and showed that spiral waves have a frequency of 3.3 Hz and a linear core of approximately 50-mm diameter that rotates with an average frequency of 0.62 rad/s. Simulation results agreed with experimental data. In conclusion, the proposed model is suitable for efficient and accurate studies of reentrant phenomena in human ventricular tissue.     

A general method for biological parameter estimation

Summary A general observer-based estimator method is developed and applied for process modelling and monitoring. This parameter estimation technique was successfully applied to a L-lysine fermentation process. It was a useful tool to detect the effect of major culture conditions on cell growth and product synthesis. It can also be used for the development of adaptive optimal control schemes.     

A computationally efficient method for evaluating the gradient of 2D NOESY intensities

Summary A computationally efficient method for calculating the derivative of NOE intensities with respect to any parameter is presented. This method is based on an integral expression representing the gradient. We will derive this expression from first principles using standard perturbation expansion techniques, and show it to be equivalent to an analytical expression [Yip, P. and Case, D.A. (1989) J. Magn. Reson., 83, 643] Implementation of this method in a refinement scheme (NOE-MD) is also briefly mentioned.     

Hamiltonian Monte Carlo methods for efficient parameter estimation in steady state dynamical systems

Background

Parameter estimation for differential equation models of intracellular processes is a highly relevant bu challenging task. The available experimental data do not usually contain enough information to identify all parameters uniquely, resulting in ill-posed estimation problems with often highly correlated parameters. Sampling-based Bayesian statistical approaches are appropriate for tackling this problem. The samples are typically generated via Markov chain Monte Carlo, however such methods are computationally expensive and their convergence may be slow, especially if there are strong correlations between parameters. Monte Carlo methods based on Euclidean or Riemannian Hamiltonian dynamics have been shown to outperform other samplers by making proposal moves that take the local sensitivities of the system’s states into account and accepting these moves with high probability. However, the high computational cost involved with calculating the Hamiltonian trajectories prevents their widespread use for all but the smallest differential equation models. The further development of efficient sampling algorithms is therefore an important step towards improving the statistical analysis of predictive models of intracellular processes.

Results

We show how state of the art Hamiltonian Monte Carlo methods may be significantly improved for steady state dynamical models. We present a novel approach for efficiently calculating the required geometric quantities by tracking steady states across the Hamiltonian trajectories using a Newton-Raphson method and employing local sensitivity information. Using our approach, we compare both Euclidean and Riemannian versions of Hamiltonian Monte Carlo on three models for intracellular processes with real data and demonstrate at least an order of magnitude improvement in the effective sampling speed. We further demonstrate the wider applicability of our approach to other gradient based MCMC methods, such as those based on Langevin diffusions.

Conclusion

Our approach is strictly benefitial in all test cases. The Matlab sources implementing our MCMC methodology is available from https://github.com/a-kramer/ode_rmhmc.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-253) contains supplementary material, which is available to authorized users.     

A methodology for parameter estimation in seaweed productivity modelling

This paper presents a combined approach for parameter estimation in models of primary production. The focus is on gross primary production and nutrient assimilation by seaweeds.A database of productivity determinations, biomass and mortality measurements and nutrient uptake rates obtained over one year for Gelidium sesquipedale in the Atlantic Ocean off Portugal has been used. Annual productivity was estimated by harvesting methods, and empirical relationships using mortality/wave energy and respiration rates have been derived to correct for losses and to convert the estimates to gross production. In situ determinations of productivity have been combined with data on the light climate (radiation periods, intensity, mean turbidity) to give daily and annual productivity estimates. The theoretical nutrient uptake calculated using a Redfield ratio approach and determinations of in situ N and P consumption by the algae during incubation periods have also been compared.The results of the biomass difference and incubation approaches are discussed in order to assess the utility of coefficients determined in situ for parameter estimation in seaweed production models.     

A Bayesian framework for parameter estimation in dynamical models

Mathematical models in biology are powerful tools for the study and exploration of complex dynamics. Nevertheless, bringing theoretical results to an agreement with experimental observations involves acknowledging a great deal of uncertainty intrinsic to our theoretical representation of a real system. Proper handling of such uncertainties is key to the successful usage of models to predict experimental or field observations. This problem has been addressed over the years by many tools for model calibration and parameter estimation. In this article we present a general framework for uncertainty analysis and parameter estimation that is designed to handle uncertainties associated with the modeling of dynamic biological systems while remaining agnostic as to the type of model used. We apply the framework to fit an SIR-like influenza transmission model to 7 years of incidence data in three European countries: Belgium, the Netherlands and Portugal.     

Method and apparatus for soft tissue material parameter estimation using tissue tagged Magnetic Resonance Imaging

We describe an experimental method and apparatus for the estimation of constitutive parameters of soft tissue using Magnetic Resonance Imaging (MRI), in particular for the estimation of passive myocardial material properties. MRI tissue tagged images were acquired with simultaneous pressure recordings, while the tissue was cyclically deformed using a custom built reciprocating pump actuator A continuous three-dimensional (3D) displacement field was reconstructed from the imaged tag motion. Cavity volume changes and local tissue microstructure were determined from phase contrast velocity and diffusion tensor MR images, respectively. The Finite Element Method (FEM) was used to solve the finite elasticity problem and obtain the displacement field that satisfied the applied boundary conditions and a given set of material parameters. The material parameters which best fit the FEM predicted displacements to the displacements reconstructed from the tagged images were found by nonlinear optimization. The equipment and method were validated using inflation of a deformable silicon gel phantom in the shape of a cylindrical annulus. The silicon gel was well described by a neo-Hookian material law with a single material parameter C1=8.71+/-0.06kPa, estimated independently using a rotational shear apparatus. The MRI derived parameter was allowed to vary regionally and was estimated as C1 =8.80+/-0.86kPa across the model. Preliminary results from the passive inflation of an isolated arrested pig heart are also presented, demonstrating the feasibility of the apparatus and method for isolated heart preparations. FEM based models can therefore estimate constitutive parameters accurately and reliably from MRI tagging data.     

A robust methodology for kinetic model parameter estimation for biocatalytic reactions

Effective estimation of parameters in biocatalytic reaction kinetic expressions are very important when building process models to enable evaluation of process technology options and alternative biocatalysts. The kinetic models used to describe enzyme‐catalyzed reactions generally include several parameters, which are strongly correlated with each other. State‐of‐the‐art methodologies such as nonlinear regression (using progress curves) or graphical analysis (using initial rate data, for example, the Lineweaver‐Burke plot, Hanes plot or Dixon plot) often incorporate errors in the estimates and rarely lead to globally optimized parameter values. In this article, a robust methodology to estimate parameters for biocatalytic reaction kinetic expressions is proposed. The methodology determines the parameters in a systematic manner by exploiting the best features of several of the current approaches. The parameter estimation problem is decomposed into five hierarchical steps, where the solution of each of the steps becomes the input for the subsequent step to achieve the final model with the corresponding regressed parameters. The model is further used for validating its performance and determining the correlation of the parameters. The final model with the fitted parameters is able to describe both initial rate and dynamic experiments. Application of the methodology is illustrated with a case study using the ω‐transaminase catalyzed synthesis of 1‐phenylethylamine from acetophenone and 2‐propylamine. © 2012 American Institute of Chemical Engineers Biotechnol. Prog., 2012     

A comparison of the parameter estimating procedures for the Michaelis-Menten model

The performance of four parameter estimating procedures for the estimation of the adjustable parameters in the Michaelis-Menten model, the maximum initial rate Vmax, and the Michaelis-Menten constant Km, including Lineweaver & Burk transformation (L-B), Eadie & Hofstee transformation (E-H), Eisenthal & Cornish-Bowden transformation (ECB), and Hsu & Tseng random search (H-T) is compared. The analysis of the simulated data reveals the followings: (i) Vmax can be estimated more precisely than Km. (ii) The sum of square errors, from the smallest to the largest, follows the sequence H-T, E-H, ECB, L-B. (iii) Considering the sum of square errors, relative error, and computing time, the overall performance follows the sequence H-T, L-B, E-H, ECB, from the best to the worst. (iv) The performance of E-H and ECB are on the same level. (v) L-B and E-H are appropriate for pricesly measured data. H-T should be adopted for data whose error level are high. (vi) Increasing the number of data points has a positive effect on the performance of H-T, and a negative effect on the performance of L-B, E-H, and ECB.