Mathematical Algorithmic Optimization - Otto-von-Guericke-University Magdeburg

 
 
 
 
 
 
 
 

Systems Biology and Medicine

Our research in this area is funded by the European Research Council, compare this page.

Mathematical Optimization has been developing into a mature research area within Mathematics, often driven by applications in, e.g., mechanics, chemical engineering, or economics. Many dynamic processes in construction, separation, or transport are analyzed and controled in an efficient way making use of mathematical algorithms. More recently also biological and medical processes are being investigated. On the one hand, they pose a bunch of additional challenges, such as the nonavailability of mathematical models, uncertainties, and often low quality measurement data. On the other hand there is an obvious large potential for more efficiency and a huge amount of available patient-specific data. Our research comprehends several interdisciplinary projects. Two prototypical ones are described below.

Prediction of Earliest Activation of Focal Cardiac Arrhythmias

We investigate premature beats which are a common finding in patients suffering from structural heart disease, but they can also be present in healthy individuals. Catheter ablation represents a suitable therapeutic approach. However, the exact localization of the origin can be challenging, especially in cases of low PB burden during the procedure.

The algorithm is based on iterative regression analyses. When acquiring local activation times (LATs) within a 3-dimensional anatomic map of the corresponding heart chamber, this algorithm is able to identify that position where a next LAT measurement adds maximum information about the predicted site of origin. Furthermore, on the basis of the acquired LAT measurements, the algorithm is able to predict earliest activation with high accuracy.

A systematic retrospective analysis of the mapping performance comparing the operator with simulated search processes by the algorithm within 17 electroanatomic maps of focal spreading arrhythmias revealed a highly significant reduction of necessary LAT measurements from 55 to 10.

Chemotherapy Treatment

We want to mathematically analyze chemotherapy treatments with the long term goal to obtain individual decision support for dosage and treatment scheduling.

An optimally controlled therapy can make the difference between a growing and a diminishing tumor.
An optimally controlled therapy can make the difference between a growing and a diminishing tumor.

We are specifically interested in the modulation of circadian rhythms and in chemotherapy treatment of cancer. Being well aware that practical application in a model-predictive control context is still far away, we focus on general properties of dynamical systems and on an improvement of numerical methods. As a first result we can give indications on how much potential there is in the exact timing of a chemotherapeutical treatment. Ongoing research is a cooperation with the Department of Hematology and Oncology at OvGU.

Comparison between optimal, worst and no treatment
Comparison between optimal, worst and no treatment for a prototypical mathematical model.

Discrimination between Atrial Fibrillation and Atrial Flutter

We use mathematical optimization to discriminate atrial fibrillation from atypical atrial flutter, based on ECG data. We have been developing phenomenological mathematical models for multi-level blocks of signals in the AV node and optimization problems on top of them. The optimal objective function value gives an indication on whether an atypical atrial flutter may be the cause for the irregular signal in the ventricular chambers. We have also been developing tailored optimization algorithms to solve the arising mixed-integer nonlinear optimization problems efficiently. The resulting diagnosis tool has been evaluated in a large clinical study involving 100 patients with excellent results, as described in the Heart Rhythm article of Scholz et al. from 2014. The ongoing research is a cooperation with the Work Group Ion Channel Cardiomyopathies of Eberhard Scholz in Heidelberg.

Decision support in Cardiac Resynchronization Therapy

The modern multimodal therapy of chronic heart disease with optimization of medication and device therapy improves the prognosis and quality of life. Pathophysiologically, cardiac decompensation is mediated and accompanied by severe neurohumoral dysregulations with consecutive further cardiac and renal irreversible damage. A decisive goal is the prevention of imminent decompensation or to mitigate its manifestation. For this purpose, it is necessary to specify predictors for the complex clinical and hemodynamic relationships with the goal of individualized therapy in the case of cardiac failure. The combination of disease-specific measurements and dynamic modeling approaches can improve sensitivity to characterize the regulatory system behavior. To model and simulate this pathology we want to extend a hemodynamic model with specific clinical measurements. The CircAdapt model describes the heart and circulation in a phenomenological way, calculating beat-to-beat hemodynamics and cardiac mechanics as well as focussing on the interactions of the ventricles via the septum. Thereby, several variables such as compliance and pulmonary vascular resistance should be mirrored. Especially, the longterm objective of this project is to improve the device based cardiac heart failure therapies.

Selected publications



AuthorTitleYearJournal/ProceedingsReftypeLink
Engelhart, M. Modeling, Simulation, and Optimization of Cancer Chemotherapies 2009 School: Heidelberg University   mastersthesis
preprint  
BibTeX:
@mastersthesis{Engelhart2009,
  author = {Engelhart, M.},
  title = {{M}odeling, {S}imulation, and {O}ptimization of {C}ancer {C}hemotherapies},
  school = {Heidelberg University},
  year = {2009},
  url = {http://mathopt.de/PUBLICATIONS/Engelhart2009.pdf}
}
Engelhart, M., Lebiedz, D. & Sager, S. Optimal Control for Cancer Chemotherapy ODE Models: Potential of optimal schedules and choice of objective function 2011 Mathematical Biosciences   article
preprint  
BibTeX:
@article{Engelhart2011,
  author = {Engelhart, M. and Lebiedz, D. and Sager, S.},
  title = {{O}ptimal {C}ontrol for {C}ancer {C}hemotherapy {ODE} {M}odels: {P}otential of optimal schedules and choice of objective function},
  journal = {{M}athematical {B}iosciences},
  year = {2011},
  volume = {229},
  number = {1},
  pages = {123--134},
  url = {http://mathopt.de/PUBLICATIONS/Engelhart2011.pdf}
}
Jost, F., Rinke, K., Fischer, T., Schalk, E. & Sager, S. Optimum Experimental Design for Patient Specific Mathematical Leukopenia Models 2016 IFAC-PapersOnLineProceedings of the Foundations of Systems Biology in Engineering (FOSBE) Conference   inproceedings
 
BibTeX:
@inproceedings{Jost2016,
  author = {Jost, Felix and Rinke, K and Fischer, T and Schalk, E and Sager, S},
  title = {Optimum Experimental Design for Patient Specific Mathematical Leukopenia Models},
  booktitle = {Proceedings of the Foundations of Systems Biology in Engineering (FOSBE) Conference},
  journal = {IFAC-PapersOnLine},
  publisher = {Elsevier},
  year = {2016},
  volume = {49},
  number = {26},
  pages = {344--349},
  organization = {Magdeburg, Germany}
}
König, R., Schramm, G., Oswald, M., Seitz, H., Sager, S., Zapatka, M., Reinelt, G. & Eils, R. Discovering functional gene expression patterns in the metabolic network of Escherichia coli with wavelets transforms 2006 BMC Bioinformatics   article
preprint  
BibTeX:
@article{Koenig2006,
  author = {R. K\"onig and G. Schramm and M. Oswald and H. Seitz and S. Sager and M. Zapatka and G. Reinelt and R. Eils},
  title = {{D}iscovering functional gene expression patterns in the metabolic network of {E}scherichia coli with wavelets transforms},
  journal = {{BMC} {B}ioinformatics},
  year = {2006},
  volume = {7},
  pages = {119},
  url = {http://www.biomedcentral.com/1471-2105/7/119}
}
Lebiedz, D., Sager, S., Bock, H. & Lebiedz, P. Annihilation of limit cycle oscillations by identification of critical phase resetting stimuli via mixed-integer optimal control methods 2005 Physical Review Letters   article
 
BibTeX:
@article{Lebiedz2005,
  author = {Lebiedz, D. and Sager, S. and Bock, H.G. and Lebiedz, P.},
  title = {{A}nnihilation of limit cycle oscillations by identification of critical phase resetting stimuli via mixed-integer optimal control methods},
  journal = {{P}hysical {R}eview {L}etters},
  year = {2005},
  volume = {95},
  pages = {108303}
}
Rinke, K., Jost, F., Findeisen, R., Fischer, T., Bartsch, R., Schalk, E. & Sager, S. Parameter estimation for leukocyte dynamics after chemotherapy 2016 IFAC-PapersOnLineProceedings of the Foundations of Systems Biology in Engineering (FOSBE) Conference   inproceedings
 
BibTeX:
@inproceedings{Rinke2016,
  author = {Rinke, Kristine and Jost, F and Findeisen, R and Fischer, T and Bartsch, R and Schalk, E and Sager, S},
  title = {Parameter estimation for leukocyte dynamics after chemotherapy},
  booktitle = {Proceedings of the Foundations of Systems Biology in Engineering (FOSBE) Conference},
  journal = {IFAC-PapersOnLine},
  publisher = {Elsevier},
  year = {2016},
  volume = {49},
  number = {26},
  pages = {44--49},
  organization = {Magdeburg, Germany}
}
Scholz, E., Kehrle, F., Vossel, S., Hess, A., Zitron, E., Katus, H. & Sager, S. Discriminating atrial flutter from atrial fibrillation using a multilevel model of atrioventricular conduction 2014 Heart Rhythm   article
preprint  
BibTeX:
@article{Scholz2014,
  author = {Scholz, E.P. and Kehrle, F. and Vossel, S. and Hess, A. and Zitron, E. and Katus, H.A. and Sager, S.},
  title = {{D}iscriminating atrial flutter from atrial fibrillation using a multilevel model of atrioventricular conduction},
  journal = {{H}eart {R}hythm},
  year = {2014},
  volume = {11},
  number = {5},
  pages = {877--884},
  url = {https://www.mathopt.de/PUBLICATIONS/Scholz2014.pdf}
}
Shaik, O., Sager, S., Slaby, O. & Lebiedz, D. Phase tracking and restoration of circadian rhythms by model-based optimal control 2008 IET Systems Biology   article
 
BibTeX:
@article{Shaik2008,
  author = {Shaik, O.S. and Sager, S. and Slaby, O. and Lebiedz, D.},
  title = {{P}hase tracking and restoration of circadian rhythms by model-based optimal control},
  journal = {{IET} {S}ystems {B}iology},
  year = {2008},
  volume = {2},
  pages = {16--23}
}
Weber, T., Katus, H., Sager, S. & Scholz, E. Novel algorithm for accelerated electroanatomical mapping and prediction of earliest activation of focal cardiac arrhythmias using mathematical optimization 2017 Heart Rhythm   article DOI
preprint  
BibTeX:
@article{Weber2017,
  author = {T. Weber and H.A. Katus and S. Sager and E.P. Scholz},
  title = {{N}ovel algorithm for accelerated electroanatomical mapping and prediction of earliest activation of focal cardiac arrhythmias using mathematical optimization},
  journal = {Heart Rhythm},
  year = {2017},
  url = {https://www.mathopt.de/PUBLICATIONS/Weber2017.pdf},
  doi = {http://dx.doi.org/10.1016/j.hrthm.2017.03.001}
}
Zeile, C., Scholz, E. & Sager, S. A Simplified 2D Heart Model of the Wolff-Parkinson-White Syndrome 2016 Proceedings of the Foundations of Systems Biology in Engineering (FOSBE) Conference   inproceedings
 
BibTeX:
@inproceedings{Zeile2016,
  author = {Zeile, Clemens and Scholz, Eberhard and Sager, Sebastian},
  title = {A Simplified 2D Heart Model of the Wolff-Parkinson-White Syndrome},
  booktitle = {Proceedings of the Foundations of Systems Biology in Engineering (FOSBE) Conference},
  publisher = {Elsevier},
  year = {2016},
  volume = {49},
  number = {26},
  pages = {26--31},
  organization = {Magdeburg, Germany}
}

Further references of the MathOpt group can be found on this page.

Last Modification: 2017-07-19 - Contact Person: Sebastian Sager - Impressum