Exponential integrators for a Markov chain model of the fast sodium channel of cardiomyocytes

The modern Markov chain models of ionic channels in excitable membranes are numerically stiff. The popular numerical methods for these models require very small time steps to ensure stability. Our objective is to formulate and test two methods addressing this issue, so that the timestep can be chosen based on accuracy rather than stability. Both proposed methods extend Rush-Larsen technique, which was originally developed to Hogdkin-Huxley type gate models. One method, "Matrix Rush-Larsen" (MRL) uses a matrix reformulation of the Rush-Larsen scheme, where the matrix exponentials are calculated using precomputed tables of eigenvalues and eigenvectors. The other, "hybrid operator splitting" (HOS) method exploits asymptotic properties of a particular Markov chain model, allowing explicit analytical expressions for the substeps. We test both methods on the Clancy and Rudy (2002) INa Markov chain model. With precomputed tables for functions of the transmembrane voltage, both methods are comparable to the forward Euler method in accuracy and computational cost, but allow longer time steps without numerical instability. We conclude that both methods are of practical interest. MRL requires more computations than HOS, but is formulated in general terms which can be readily extended to other Markov Chain channel models, whereas the utility of HOS depends on the asymptotic properties of a particular model. The significance of the methods is that they allow a considerable speed-up of large-scale computations of cardiac excitation models by increasing the time step, while maintaining acceptable accuracy and preserving numerical stability.Comment: 9 pages, 5 figures main text + 14 pages, 1 figure appendix, as submitted in final form to IEEE TBME 2014/11/11. Copyright IEEE (2014

Mathematical and Computational Study of Markovian Models of Ion Channels in Cardiac Excitation

This thesis studies numerical methods for integrating the master equations describing Markov chain models of cardiac ion channels. Such models describe the time evolution of the probability that ion channels are in a particular state. Numerical simulations of such models are often computationally demanding because many solvers require relatively small time steps to ensure numerical stability. The aim of this project is to analyse selected Markov chains and develop more efficient and accurate solvers. We separate a Markov chain model into fast and slow time-scales based on the speed of transitions between states. Eliminating the fast transitions, we find an asymptotic reduction of zeroth-order and first-order in a small parameter describing the time-scales separation. We apply the theory to a Markov chain model of the fast sodium channel INa. We consider several variants for classifying some transitions as fast in order to find reduced systems that yield a good accuracy. However, the time step size is still restricted by numerical instabilities. We adapt the Rush-Larsen technique originally developed for gate models. Assuming that a transition matrix can be considered constant during each time step, we solve the Markov chain model analytically. The solution provides a recipe for a stable exponential solver, which we call "Matrix Rush-Larsen" (MRL). Using operator splitting we design an even more flexible "hybrid" method that combines the MRL with other solvers. The resulting improvement in stability allows a large increase in the time step size. In some models, we obtain reasonably accurate results 27 times faster using a hybrid method than with the forward Euler method, even with the maximal time step allowed by the stability constraint. Finally, we extend the cardiac simulation package BeatBox by the developed exponential solvers. We upgrade a format of "ionic" modules which describe a cardiac cell, in order to allow for a specific definition of Markov chain models. We also modify a particular integrator for ionic modules to include the MRL and the hybrid method. To test the functionality of the code, we have converted a number of cellular models into the ionic format. The documented code is available in the official BeatBox package distribution

ADHESION OF BIOCOMPATIBLE TiNb COATING

Preparation of a coating with a high quality requires good adhesion of the film to the substrate. The paper deals with the adhesion of biocompatible TiNb coating with different base materials. Several materials such as titanium CP grade 2, titanium alloys Ti6Al4V and stainless steel AISI 316L were measured. Testing samples were made in the shape of small discs. Those samples were coated with a TiNb layer by using the PVD method (magnetron sputtering). Onto the measured layer of TiNb an assistant cylinder was stuck using a high strength epoxy adhesive E1100S. The sample with the assistant cylinder was fixed into a special fixture and the whole assembly underwent pull-off testing for adhesion. The main result of this experiment was determining the strength needed to peel the layer and morphology and size of the breakaway. As a result, we will be able to determine the best base material and conditions where the coating will be remain intact with the base material

Automated Software Metadata Conversion and Publication Based on CodeMeta

Different metadata standards exist for different steps in the research software publication process. The Citation File Format (CFF) became very popular to provide information on how users are supposed to cite the software. For software archiving, DataCite is one of the established standards. The CodeMeta standard is an extension of schema.org specifically tailored to research software. All of these standards serve a purpose and are required for specific phases of the software lifecycle. However, research software developers should ideally not be burdened with maintaining a whole set of metadata files in different formats and largely overlapping content. This poses a risk both to data consistency and to adoption of good software publication practices in the first place. Therefore, we developed Python pipelines that put the developers in a position to only maintain a CodeMeta file. CFF and DataCite files are automatically generated based on the CodeMeta file. The open source pipelines (https://www.openCARP.org/CI) can easily be integrated in continuous integration and deployment environments and are being successfully used for the openCARP project (https://www.openCARP.org). Further aspects of the software lifecycle that are covered by the set of continuous integration scripts are creation of tagged releases including the update of the metadata files, creation of BagIt and BagPack files, deposition of releases in the RADAR research data repository, and the synchronization of documentation files in the repository to the project's webpage. We believe the automated metadata conversion based on CodeMeta can be a useful tool for many research software developers and can facilitate the adoption of good software publication practices by reducing the effort for developers

BeatBox - HPC simulation environment for biophysically and anatomically realistic cardiac electrophysiology

The BeatBox simulation environment combines flexible script language user interface with the robust computational tools, in order to setup cardiac electrophysiology in-silico experiments without re-coding at low-level, so that cell excitation, tissue/anatomy models, stimulation protocols may be included into a BeatBox script, and simulation run either sequentially or in parallel (MPI) without re-compilation. BeatBox is a free software written in C language to be run on a Unix-based platform. It provides the whole spectrum of multi scale tissue modelling from 0-dimensional individual cell simulation, 1-dimensional fibre, 2-dimensional sheet and 3-dimensional slab of tissue, up to anatomically realistic whole heart simulations, with run time measurements including cardiac re-entry tip/filament tracing, ECG, local/global samples of any variables, etc. BeatBox solvers, cell, and tissue/anatomy models repositories are extended via robust and flexible interfaces, thus providing an open framework for new developments in the field. In this paper we give an overview of the BeatBox current state, together with a description of the main computational methods and MPI parallelisation approaches.Comment: 37 pages, 10 figures, last version submitted to PLOS ON

Non-standard Abilities of PostgreSQL

Import 22/07/2015Cílem bakalářské práce je prozkoumat nadstandardní vlastnosti databázového systému PostgreSQL nad rámec standardu SQL, respektive konkurečních databázových systémů a následně pro ně najít situace, ve kterých se dají vhodně uplatnit. V práci jsou nejprve postupně vyčteny možnosti uživatelské rozšířitelnosti PostgreSQL databáze a následně vybrány, zdokumentovány a zdůvodněny právě ty, které jsou jen obtížně nahraditelné vlastnostmi standardu SQL. Další část práce se soustředí na postup vytvoření jednoho praktického uživatelského rozšíření datábaze. Tato část podrobně popisuje, co všechno bylo při implementaci tohoto rozšíření nutno provést. Závěrečná část práce se pak stručně zabývá srovnáním dvou konkurečních SŘBD z hlediska rozšířitelnosti.The goal of this bachelor thesis is to explore non-standard abilities of PostgreSQL database system beyond the SQL standard respectively beyond other competitive database systems and to find situations of practical applications for these non-standard abilities subsenquently. As first there are listed user-defined extensibility options of the PostgreSQL database and then there are picked those that are difficult to replace with abilities of SQL standard. Next part of the thesis is focused on process of creating one practical user-defined extension of the database system. This part in detail describes what was needed for the implementation of that user-defined extension. Final part then briefly compares PostgreSQL database with two other database managements systems from the point of extensibility.460 - Katedra informatikyvelmi dobř

Myeloid antigens in childhood lymphoblastic leukemia:clinical data point to regulation of CD66c distinct from other myeloid antigens

BACKGROUND: Aberrant expression of myeloid antigens (MyAgs) on acute lymphoblastic leukemia (ALL) cells is a well-documented phenomenon, although its regulating mechanisms are unclear. MyAgs in ALL are interpreted e.g. as hallmarks of early differentiation stage and/or lineage indecisiveness. Granulocytic marker CD66c – Carcinoembryonic antigen-related cell adhesion molecule 6 (CEACAM6) is aberrantly expressed on ALL with strong correlation to genotype (negative in TEL/AML1 and MLL/AF4, positive in BCR/ABL and hyperdiploid cases). METHODS: In a cohort of 365 consecutively diagnosed Czech B-precursor ALL patients, we analyze distribution of MyAg+ cases and mutual relationship among CD13, CD15, CD33, CD65 and CD66c. The most frequent MyAg (CD66c) is studied further regarding its stability from diagnosis to relapse, prognostic significance and regulation of surface expression. For the latter, flow cytometry, Western blot and quantitative RT-PCR on sorted cells is used. RESULTS: We show CD66c is expressed in 43% patients, which is more frequent than other MyAgs studied. In addition, CD66c expression negatively correlates with CD13 (p < 0.0001), CD33 (p = 0.002) and/or CD65 (p = 0.029). Our data show that different myeloid antigens often differ in biological importance, which may be obscured by combining them into "MyAg positive ALL". We show that unlike other MyAgs, CD66c expression is not shifted from the onset of ALL to relapse (n = 39, time to relapse 0.3–5.3 years). Although opposite has previously been suggested, we show that CEACAM6 transcription is invariably followed by surface expression (by quantitative RT-PCR on sorted cells) and that malignant cells containing CD66c in cytoplasm without surface expression are not found by flow cytometry nor by Western blot in vivo. We report no prognostic significance of CD66c, globally or separately in genotype subsets of B-precursor ALL, nor an association with known risk factors (n = 254). CONCLUSION: In contrast to general notion we show that different MyAgs in lymphoblastic leukemia represent different biological circumstances. We chose the most frequent and tightly genotype-associated MyAg CD66c to show its stabile expression in patients from diagnosis to relapse, which differs from what is known on the other MyAgs. Surface expression of CD66c is regulated at the gene transcription level, in contrast to previous reports

Mitochondrial physiology

As the knowledge base and importance of mitochondrial physiology to evolution, health and disease expands, the necessity for harmonizing the terminology concerning mitochondrial respiratory states and rates has become increasingly apparent. The chemiosmotic theory establishes the mechanism of energy transformation and coupling in oxidative phosphorylation. The unifying concept of the protonmotive force provides the framework for developing a consistent theoretical foundation of mitochondrial physiology and bioenergetics. We follow the latest SI guidelines and those of the International Union of Pure and Applied Chemistry (IUPAC) on terminology in physical chemistry, extended by considerations of open systems and thermodynamics of irreversible processes. The concept-driven constructive terminology incorporates the meaning of each quantity and aligns concepts and symbols with the nomenclature of classical bioenergetics. We endeavour to provide a balanced view of mitochondrial respiratory control and a critical discussion on reporting data of mitochondrial respiration in terms of metabolic flows and fluxes. Uniform standards for evaluation of respiratory states and rates will ultimately contribute to reproducibility between laboratories and thus support the development of data repositories of mitochondrial respiratory function in species, tissues, and cells. Clarity of concept and consistency of nomenclature facilitate effective transdisciplinary communication, education, and ultimately further discovery

Mitochondrial physiology

As the knowledge base and importance of mitochondrial physiology to evolution, health and disease expands, the necessity for harmonizing the terminology concerning mitochondrial respiratory states and rates has become increasingly apparent. The chemiosmotic theory establishes the mechanism of energy transformation and coupling in oxidative phosphorylation. The unifying concept of the protonmotive force provides the framework for developing a consistent theoretical foundation of mitochondrial physiology and bioenergetics. We follow the latest SI guidelines and those of the International Union of Pure and Applied Chemistry (IUPAC) on terminology in physical chemistry, extended by considerations of open systems and thermodynamics of irreversible processes. The concept-driven constructive terminology incorporates the meaning of each quantity and aligns concepts and symbols with the nomenclature of classical bioenergetics. We endeavour to provide a balanced view of mitochondrial respiratory control and a critical discussion on reporting data of mitochondrial respiration in terms of metabolic flows and fluxes. Uniform standards for evaluation of respiratory states and rates will ultimately contribute to reproducibility between laboratories and thus support the development of data repositories of mitochondrial respiratory function in species, tissues, and cells. Clarity of concept and consistency of nomenclature facilitate effective transdisciplinary communication, education, and ultimately further discovery