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Publications (10 of 33) Show all publications
Hanke, M., März, R., Tischendorf, C., Weinmüller, E. & Wurm, S. (2019). Least-Squares Collocation for Higher-Index Linear Differential-Algebraic Equations: Estimating the Instability Threshold. Mathematics of Computation, 88(318), 1647-1683
Open this publication in new window or tab >>Least-Squares Collocation for Higher-Index Linear Differential-Algebraic Equations: Estimating the Instability Threshold
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2019 (English)In: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 88, no 318, p. 1647-1683Article in journal (Refereed) Published
Abstract [en]

Differential-algebraic equations with higher-index give rise to essentially ill-posed problems. The overdetermined least-squares collocation for differential-algebraic equations which has been proposed recently is not much more computationally expensive than standard collocation methods for ordinary differential equations. This approach has displayed impressive convergence properties in numerical experiments, however, theoretically, till now convergence could be established merely for regular linear differential-algebraic equations with constant coefficients. We present now an estimate of the instability threshold which serves as the basic key for proving convergence for general regular linear differential-algebraic equations.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2019
Keywords
Differential-algebraic equation, higher-index, essentially ill-posed problem, collocation, boundary value problem, initial value problem
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-248306 (URN)10.1090/mcom/3393 (DOI)000461927500006 ()2-s2.0-85007586422 (Scopus ID)
Note

QC 20190409

Available from: 2019-04-09 Created: 2019-04-09 Last updated: 2019-06-24Bibliographically approved
Brocke, E., Djurfeldt, M., Bhalla, U. S., Hellgren Kotaleski, J. & Hanke, M. (2017). Multirate method for co-simulation of electrical-chemical systems in multiscale modeling. Journal of Computational Neuroscience, 42(3), 245-256
Open this publication in new window or tab >>Multirate method for co-simulation of electrical-chemical systems in multiscale modeling
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2017 (English)In: Journal of Computational Neuroscience, ISSN 0929-5313, E-ISSN 1573-6873, Vol. 42, no 3, p. 245-256Article in journal (Refereed) Published
Abstract [en]

Multiscale modeling by means of co-simulation is a powerful tool to address many vital questions in neuroscience. It can for example be applied in the study of the process of learning and memory formation in the brain. At the same time the co-simulation technique makes it possible to take advantage of interoperability between existing tools and multi-physics models as well as distributed computing. However, the theoretical basis for multiscale modeling is not sufficiently understood. There is, for example, a need of efficient and accurate numerical methods for time integration. When time constants of model components are different by several orders of magnitude, individual dynamics and mathematical definitions of each component all together impose stability, accuracy and efficiency challenges for the time integrator. Following our numerical investigations in Brocke et al. (Frontiers in Computational Neuroscience, 10, 97, 2016), we present a new multirate algorithm that allows us to handle each component of a large system with a step size appropriate to its time scale. We take care of error estimates in a recursive manner allowing individual components to follow their discretization time course while keeping numerical error within acceptable bounds. The method is developed with an ultimate goal of minimizing the communication between the components. Thus it is especially suitable for co-simulations. Our preliminary results support our confidence that the multirate approach can be used in the class of problems we are interested in. We show that the dynamics ofa communication signal as well as an appropriate choice of the discretization order between system components may have a significant impact on the accuracy of the coupled simulation. Although, the ideas presented in the paper have only been tested on a single model, it is likely that they can be applied to other problems without loss of generality. We believe that this work may significantly contribute to the establishment of a firm theoretical basis and to the development of an efficient computational framework for multiscale modeling and simulations.

Place, publisher, year, edition, pages
Springer-Verlag New York, 2017
Keywords
Adaptive time step integration, Backward differentiation formula, Co-simulation, Coupled integration, Coupled system, Multirate integration, Multiscale modeling, Multiscale simulation, Parallel numerical integration
National Category
Computer and Information Sciences
Identifiers
urn:nbn:se:kth:diva-207312 (URN)10.1007/s10827-017-0639-7 (DOI)000400077500003 ()2-s2.0-85017136818 (Scopus ID)
Funder
EU, FP7, Seventh Framework Programme, 604102EU, Horizon 2020, 720270Swedish Research CouncilSwedish e‐Science Research CenterScience for Life Laboratory - a national resource center for high-throughput molecular bioscience
Note

QC 20170609

Available from: 2017-06-09 Created: 2017-06-09 Last updated: 2018-01-13Bibliographically approved
Brocke, E., Bhalla, U. S., Djurfeldt, M., Hällgren Kotaleski, J. & Hanke, M. (2016). Efficient Integration of Coupled Electrical-Chemical Systems in Multiscale Neuronal Simulations. Frontiers in Computational Neuroscience, 10, Article ID 97.
Open this publication in new window or tab >>Efficient Integration of Coupled Electrical-Chemical Systems in Multiscale Neuronal Simulations
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2016 (English)In: Frontiers in Computational Neuroscience, ISSN 1662-5188, E-ISSN 1662-5188, Vol. 10, article id 97Article in journal (Refereed) Published
Abstract [en]

Multiscale modeling and simulations in neuroscience is gaining scientific attention due to its growing importance and unexplored capabilities. For instance, it can help to acquire better understanding of biological phenomena that have important features at multiple scales of time and space. This includes synaptic plasticity, memory formation and modulation, homeostasis. There are several ways to organize multiscale simulations depending on the scientific problem and the system to be modeled. One of the possibilities is to simulate different components of a multiscale system simultaneously and exchange data when required. The latter may become a challenging task for several reasons. First, the components of a multiscale system usually span different spatial and temporal scales, such that rigorous analysis of possible coupling solutions is required. Then, the components can be defined by different mathematical formalisms. For certain classes of problems a number of coupling mechanisms have been proposed and successfully used. However, a strict mathematical theory is missing in many cases. Recent work in the field has not so far investigated artifacts that may arise during coupled integration of different approximation methods. Moreover, in neuroscience, the coupling of widely used numerical fixed step size solvers may lead to unexpected inefficiency. In this paper we address the question of possible numerical artifacts that can arise during the integration of a coupled system. We develop an efficient strategy to couple the components comprising a multiscale test problem in neuroscience. We introduce an efficient coupling method based on the second-order backward differentiation formula (BDF2) numerical approximation. The method uses an adaptive step size integration with an error estimation proposed by Skelboe (2000). The method shows a significant advantage over conventional fixed step size solvers used in neuroscience for similar problems. We explore different coupling strategies that define the organization of computations between system components. We study the importance of an appropriate approximation of exchanged variables during the simulation. The analysis shows a substantial impact of these aspects on the solution accuracy in the application to our multiscale neuroscientific test problem. We believe that the ideas presented in the paper may essentially contribute to the development of a robust and efficient framework for multiscale brain modeling and simulations in neuroscience.

Place, publisher, year, edition, pages
FRONTIERS MEDIA SA, 2016
Keywords
multiscale modeling, multiscale simulation, co-simulation, coupled system, adaptive time step integration, backward differentiation formula, parallel numerical integration, coupled integration
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-193806 (URN)10.3389/fncom.2016.00097 (DOI)000383015600001 ()27672364 (PubMedID)2-s2.0-84989336945 (Scopus ID)
Funder
EU, FP7, Seventh Framework Programme, 604102Swedish Research CouncilSwedish e‐Science Research Center
Note

QC 20161024

Available from: 2016-10-24 Created: 2016-10-11 Last updated: 2017-11-29Bibliographically approved
Hast, A., Hanke, M. & Karlsson, H. O. (2015). Swedish eScience education: A graduate school in eScience. In: Proceedings - 11th IEEE International Conference on eScience, eScience 2015: . Paper presented at 11th IEEE International Conference on eScience, eScience 2015; Munich; German (pp. 31-35). IEEE
Open this publication in new window or tab >>Swedish eScience education: A graduate school in eScience
2015 (English)In: Proceedings - 11th IEEE International Conference on eScience, eScience 2015, IEEE , 2015, p. 31-35Conference paper, Published paper (Refereed)
Abstract [en]

Swedish eScience Education (SeSE) is a national graduate school in eScience in Sweden. It comes from the collaboration between two major research initiatives in eScience and the school has turned out to be very successful. It has made it possible for students at different universities to get access to education that is not normally available at their home universities. With SeSE they get access to education by the top experts within their respective field. We argue why such graduate school is important and how it is different from training offered by many HPC centres in Europe. Furthermore, examples of courses and their structure is discussed as well as lessons learned from SeSE and its two predecessors in Sweden.

Place, publisher, year, edition, pages
IEEE, 2015
National Category
Learning
Identifiers
urn:nbn:se:kth:diva-186718 (URN)10.1109/eScience.2015.19 (DOI)000380433500004 ()2-s2.0-84959048171 (Scopus ID)978-146739325-6 (ISBN)
External cooperation:
Conference
11th IEEE International Conference on eScience, eScience 2015; Munich; German
Note

QC 20160516

Available from: 2016-05-16 Created: 2016-05-13 Last updated: 2016-09-05Bibliographically approved
Chaudhry, Q. A., Hanke, M., Morgenstern, R. & Dreij, K. (2014). Surface reactions on the cytoplasmatic membranes - Mathematical modeling of reaction and diffusion systems in a cell. Paper presented at 13th Seminar Numerical Solution of Differential and Differential-Algebraic Equations (NUMDIFF), Martin Luther Univ Halle Wittenberg, Halle, Germany. Journal of Computational and Applied Mathematics, 262, 244-260
Open this publication in new window or tab >>Surface reactions on the cytoplasmatic membranes - Mathematical modeling of reaction and diffusion systems in a cell
2014 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 262, p. 244-260Article in journal (Refereed) Published
Abstract [en]

A human cell consists schematically of an outer cellular membrane, a cytoplasm containing a large number of organelles (mitochondria, endoplasmatic reticulum etc.), a nuclear membrane and finally the cellular nucleus containing DNA. The organelles create a complex and dense system of membranes or sub-domains throughout the cytoplasm. The mathematical description leads to a system of reaction-diffusion equations in a complex geometrical domain, dominated by thin membranous structures with similar physical and chemical properties. In a previous model, we considered only spatially distributed reaction and diffusion processes. However, from experiments it is known that membrane bound proteins play an important role in the metabolism of certain substances. In the present paper we develop a homogenization strategy which includes both volume and surface reactions. The homogenized system is a reaction-diffusion system in the cytoplasm which is coupled to the surrounding cell components by correspondingly modified transfer conditions. The approach is verified by application to a system modeling the cellular uptake and intracellular dynamics of carcinogenic polycyclic aromatic hydrocarbons.

Keywords
Effective equations, Homogenization, Reaction-diffusion equations, Surface diffusion, Surface reaction
National Category
Bioinformatics (Computational Biology)
Identifiers
urn:nbn:se:kth:diva-142299 (URN)10.1016/j.cam.2013.09.026 (DOI)000332050200022 ()2-s2.0-84893782671 (Scopus ID)
Conference
13th Seminar Numerical Solution of Differential and Differential-Algebraic Equations (NUMDIFF), Martin Luther Univ Halle Wittenberg, Halle, Germany
Note

QC 20140305

Available from: 2014-03-05 Created: 2014-02-28 Last updated: 2018-01-11Bibliographically approved
Chaudhry, Q. A. & Hanke, M. (2013). Study of intracellular reaction and diffusion mechanism of carcinogenic PAHs: Using non-standard compartment modeling approach. Paper presented at 49th Congress of the European-Societies-of-Toxicology (EUROTOX), SEP 01-04, 2013, Interlaken, Switzerland. Toxicology Letters, 221, S182-S182
Open this publication in new window or tab >>Study of intracellular reaction and diffusion mechanism of carcinogenic PAHs: Using non-standard compartment modeling approach
2013 (English)In: Toxicology Letters, ISSN 0378-4274, E-ISSN 1879-3169, Vol. 221, p. S182-S182Article in journal, Meeting abstract (Other academic) Published
National Category
Pharmacology and Toxicology
Identifiers
urn:nbn:se:kth:diva-129454 (URN)10.1016/j.toxlet.2013.05.409 (DOI)000323865800560 ()
Conference
49th Congress of the European-Societies-of-Toxicology (EUROTOX), SEP 01-04, 2013, Interlaken, Switzerland
Note

QC 20131002

Available from: 2013-10-02 Created: 2013-09-30 Last updated: 2018-01-11Bibliographically approved
Dreij, K., Chaudhry, Q. A., Jernström, B., Hanke, M. & Morgenstern, R. (2012). In silico Modeling of Intracellular Diffusion and Reaction of Benzo[a]pyrene Diol Epoxide. KTH Royal Institute of Technology
Open this publication in new window or tab >>In silico Modeling of Intracellular Diffusion and Reaction of Benzo[a]pyrene Diol Epoxide
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2012 (English)Report (Other academic)
Abstract [en]

Several studies has suggested that glutathione conjugation of polycyclicaromatic hydrocarbons (PAHs) catalyzed by glutathione transferases (GSTs)are important factors in protecting cells against toxicity and DNA damagederived from these compounds. To further characterize the intracellular dynamicsof PAH DEs and the role of GSTs in protection against DNA damage,we recently developed a PDE model using techniques for mathematicalhomogenization (Dreij K et al. PLoS One 6(8), 2011). In this study, wewanted to further develop our model by benchmarking against results fromfour V79 cell lines; control cells and cells overexpressing human GSTs A1-1, M1-1 and P1-1. We used an approach of global optimization of the parametersdescribing the diffusion and reaction of the ultimate carcinogenic PAHmetabolite benzo[a]pyrene diol epoxide to fit measured values from the fourV79 cell lines. Numerical results concerning the formation of glutathioneconjugates and hydrolysis were in good agreement with results from measurementsin V79 cell culture. Cellular results showed significant protectionby GST expression against formation of DNA adducts with more than 10-fold reduced levels compared to control cells. Results from the model usingglobally optimized parameters showed that the model cannot predict theprotective effects of GSTs. Extending the model to also include effects fromprotein interactions and GST localization showed the same discrepancy. Insummary, the results show that we have an incomplete understanding of theintracellular dynamics of the interaction between BPDE and GST that warrantsfurther investigation and development of the model.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2012. p. 28
Series
TRITA-NA ; 2012:3
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-93464 (URN)
Funder
Swedish e‐Science Research Center
Note

QC 20120418

Available from: 2012-04-17 Created: 2012-04-17 Last updated: 2013-04-09Bibliographically approved
Dreij, K., Chaudhry, Q. A., Zhang, J., Sundberg, K., Jernström, B., Hanke, M. & Morgenstern, R. (2012). In silico modeling of the intracellular dynamics of polycyclic aromatic hydrocarbons. Paper presented at 48th Congress of the European-Societies-of-Toxicology (EUROTOX), JUN 17-20, 2012, Stockholm, Sweden. Toxicology Letters, 211, S60-S61
Open this publication in new window or tab >>In silico modeling of the intracellular dynamics of polycyclic aromatic hydrocarbons
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2012 (English)In: Toxicology Letters, ISSN 0378-4274, E-ISSN 1879-3169, Vol. 211, p. S60-S61Article in journal, Meeting abstract (Other academic) Published
National Category
Pharmacology and Toxicology
Identifiers
urn:nbn:se:kth:diva-98926 (URN)10.1016/j.toxlet.2012.03.238 (DOI)000305173900195 ()
Conference
48th Congress of the European-Societies-of-Toxicology (EUROTOX), JUN 17-20, 2012, Stockholm, Sweden
Note

QC 20120712

Available from: 2012-07-12 Created: 2012-07-05 Last updated: 2018-01-12Bibliographically approved
Chaudhry, Q. A., Morgenstern, R., Hanke, M. & Dreij, K. (2012). Influence of Biological Cell Geometry on Reaction and Diffusion Simulation. KTH Royal Institute of Technology
Open this publication in new window or tab >>Influence of Biological Cell Geometry on Reaction and Diffusion Simulation
2012 (English)Report (Other academic)
Abstract [en]

Mathematical modeling of reaction-diffusion system in a biological cellis an important and difficult task, especially when the chemical compoundsare lipophilic. The difficulty level increases, when we take into account theheterogeneity of the cell, and the variation of cellular architecture. Mathematicalmodeling of reaction-diffusion systems in spherical cell geometryhas earlier been performed by us. In the present paper, we have workedwith non-spherical cell geometry, because the cellular geometry can play animportant role for drug diffusion in the cell. Homogenization techniques,which were earlier applied in the case of a spherical cell model, have beenused for the numerical treatment of the model. This technique considerablyreduces the complexity of the model. To further reduce the complexity ofthe model, a simplified model was also developed. The key idea of this simplifiedmodel has been advocated in Virtual Cell, where PDEs are used forthe extracellular domain, cytoplasm and nucleus, whereas the plasma andnuclear membranes have been taken away, and replaced by membrane flux,using Fick’s Law of diffusion. The numerical results of the non-sphericalcell model have been compared with the results of the spherical cell model,where the numerical results of spherical cell model have already been validatedagainst in vitro cell experimental results. From the numerical results,we conclude that the plasma and nuclear membranes can be protective reservoirsof significance. The numerical results of the simplified model werecompared against the numerical results of our detailed model, revealing theimportance of detailed modeling of membranes in our model.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2012. p. 28
Series
TRITA-NA ; 2012:2
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-93462 (URN)
Funder
Swedish e‐Science Research Center
Note

QC 20120418

Available from: 2012-04-17 Created: 2012-04-17 Last updated: 2013-04-09
Chaudhry, Q. A., Hanke, M., Dreij, K. & Morgenstern, R. (2012). Mathematical Modeling of Reaction and Diffusion Systems in a Cell Including Surface Reactions on the Cytoplasmic Membranes. KTH Royal Institute of Technology
Open this publication in new window or tab >>Mathematical Modeling of Reaction and Diffusion Systems in a Cell Including Surface Reactions on the Cytoplasmic Membranes
2012 (English)Report (Other academic)
Abstract [en]

Benzo[a]pyrene (BP) is a toxic polycyclic aromatic hydrocarbon (PAH) whichis found in our environment. These BPs are metabolized to benzo[a]pyrene diol(BPD) by enzymes bound to the cytoplasmic membranes e.g. members of thecytochrome P450 protein family and epoxide hydrolyses. BPDs are further metabolizedto two stereochemical variants of Benzo[a]pyrene diol expoxide (BPDE) bythe cytochrome P450 family of proteins. These are the two steps of metabolismcategorized as Phase I. In Phase II, BPDEs are further metabolized by soluble enzymesin the cytoplasm e.g. members of the glutathione transferase protein familyto GSH conjugates. BPDE can also diffuse into the cellular nucleus and reactwith DNA forming mutagenic DNA adducts. The formation of GSH conjugatesand DNA adducts, was earlier studied by us by developing a mathematical modeldescribing the intracellular reaction and diffusion of lipophilic PAHs taking intoaccount the partitioning phenomenon (Dreij K et al. PLoS One 6(8), 2011). In thispaper part of Phase I metabolism i.e formation of BPDE metabolites, will be addedto the model, thus enhancing the previous model. These cytochrome P450 reactionstake place on the intracellular membranes, and are modeled as a membranesurface reaction within the cytoplasm using the standard process of adsorption anddesorption. The effective equations are derived using iterative homogenization forthe numerical treatment of the cytoplasm including surface effects. The numericalresults of some of the species have been qualitatively verified against in vitroresults found in the literature.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2012. p. 24
Series
TRITA-NA ; 2012:4
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-93465 (URN)
Funder
Swedish e‐Science Research Center
Note

QC 20120418

Available from: 2012-04-17 Created: 2012-04-17 Last updated: 2014-01-29Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-4950-6646

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