Clinical Decision Support

Our research in this area has been funded by the European Research Council and the Synergy-Excellence programme of Sachsen-Anhalt with EFRE support. This is greatly appreciated.

Modeling, simulation, and optimization are important methodological pillars of computational science and have triggered a revolution in the way we approach things. Spearheaded by applications in mechanical engineering, logistics, chemical engineering, and information technologogy, the last two decades saw an explosion of computational approaches being applied to biology and medicine. 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. This trend is further accelerated by availability of data, open source software, hardware improvements, and interdisciplinary approaches and cooperations. Our main contributions are on the level of clinical decision support. Using available data and clinical expert knowledge, we have been modeling relationships between different inputs and relevant biomarkers, and making them accessible for optimization approaches.

A survey paper on the interplay between clinical decision support and optimization was published in Optima. We recommend this paper for an overview of our models, methods, and case studies.

Clinical Decision Support for Blood Cancer

Our long term goal is to provide optimization-driven individual decision support for dosage and treatment scheduling, taking combinations of treatments and practical restrictions into account.

For example, we have been modeling the interplay between chemotherapy, healthy cells, immune system, and blasts in acute myeloid leukemia, as visualized in the following figure.

Mathematical model for AML treatment from Jost2021.

Mathematical model for AML treatment from Jost2021.

The differential equation model was developed, analyzed using advanced methods of parameter estimation, experimental design, uncertainty quantification, sensitivity analysis, and used to calculate personalized and mathematically optimal treatment plans in Jost et al., Model-based optimal AML consolidation treatment, 2021.

As a main result, the new approach can (in-silico) avoid 90% of occuring leukopenias without impairing the long term effect on the cancerous cells. The model makes obviously various simplifying assumptions. We work with different kinds of models for different purposes, following the digital twin paradigm. While above model showed to be a good compromise for real-world application and decision support, we have also developed more involved models based on partial differential equations, which are better suited to understand intrinsic and induced oscillations in the system. As a third line of research we consider machine learning models, with the ultimate goal to achieve accurate, explainable, and applicable models for clinical decision support. The same paradigm applies to other ongoing projects in oncology/hematology, e.g., scheduling of phlebotomia in polycythemia vera or chemotherapy treatment in pediatric acute lymphoblastic leukemia.

Discrimination between Atrial Fibrillation and Atrial Flutter

A similar approach of interacting models applies to applications in cardiology. Here we have been investigating different approaches to classify and treat cardiac arrhytmia. We have been developing and analyzing involved differential equations based on the Hodgkin-Huxley equations with the goal to understand and benchmark simplified mathematical models that can be used in hybrid machine learning approaches and for clinical decision support. As a byproduct of a new automatic classification approach to distinguish ventricular tachycardias, our new mathematical model presented in Sager et al. generalizes several classical and advanced block types (typical Type I block, atypical Type I block, the special cases of 2:1 and 3:2 Type I blocks, Type II block, advanced second-degree AV Block, and multi-level AV block.

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.

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.

Our new 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. Results can be found in this Heart Rhythm publication.

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
Huschto, T., Podolskij, M., Sager, S. The asymptotic error of chaos expansion approximations for stochastic differential equations 2019 Modern Stochastics: Theory and Applications   article DOI
 
BibTeX:
@article{Huschto2019,
    author = {Huschto, T. and Podolskij, M. and Sager, S.},
    title = {The asymptotic error of chaos expansion approximations for stochastic differential equations},
    journal = {Modern {S}tochastics: {T}heory and {A}pplications},
    year = {2019},
    volume = {6},
    number = {2},
    pages = {145--165},
    doi = {10.15559/19-VMSTA133}
}
Jost, F., Sager, S., Le, T. A Feedback Optimal Control Algorithm with Optimal Measurement Time Points 2017 Processes   article
url  
BibTeX:
@article{Jost2017,
    author = {Jost, F. and Sager, S. and Le, T.T.T.},
    title = {A Feedback Optimal Control Algorithm with Optimal Measurement Time Points},
    journal = {Processes},
    year = {2017},
    volume = {5},
    number = {10},
    pages = {1--19},
    url = {http://www.mdpi.com/2227-9717/5/1/10}
}
Matke, C., Bienstock, D., Munoz, G., Yang, S., Kleinhans, D., Sager, S. Robust optimization of power network operation: storage devices and the role of forecast errors in renewable energies 2017 Studies in Computational Intelligence: Complex Networks and Their Applications V   inproceedings DOI
 
BibTeX:
@inproceedings{Matke2017,
    author = {Matke, C. and Bienstock, D. and Munoz, G. and Yang, S. and Kleinhans, D. and Sager, S.},
    title = {Robust optimization of power network operation: storage devices and the role of forecast errors in renewable energies},
    booktitle = {Studies in Computational Intelligence: Complex Networks and Their Applications V},
    year = {2017},
    number = {693},
    pages = {809--820},
    doi = {10.1007/978-3-319-50901-3}
}
Matke, C., Medjroubi, W., Kleinhans, D., Sager, S. Structure Analysis of the German Transmission Network Using the Open Source Model SciGRID 2017 Advances in Energy System Optimization   inproceedings
 
BibTeX:
@inproceedings{Matke2017a,
    author = {Matke, Carsten and Medjroubi, Wided and Kleinhans, David and Sager, Sebastian},
    title = {Structure Analysis of the German Transmission Network Using the Open Source Model SciGRID},
    booktitle = {Advances in Energy System Optimization},
    publisher = {Springer International Publishing},
    year = {2017},
    editor = {Bertsch, Valentin and Fichtner, Wolf and Heuveline, Vincent and Leibfried, Thomas},
    pages = {177--188},
    address = {Cham}
}
Huschto, T., Sager, S. Pricing Conspicuous Consumption Products in Recession Periods with Uncertain Strength 2014 European Journal of Decision Processes   article
url  
BibTeX:
@article{Huschto2014,
    author = {Huschto, T. and Sager, S.},
    title = {{P}ricing {C}onspicuous {C}onsumption {P}roducts in {R}ecession {P}eriods with {U}ncertain {S}trength},
    journal = {{E}uropean {J}ournal of {D}ecision {P}rocesses},
    year = {2014},
    volume = {2},
    number = {1--2},
    pages = {3--30},
    url = {http://www.optimization-online.org/DB_HTML/2012/09/3620.html}
}
Huschto, T., Sager, S. Solving Stochastic Optimal Control Problems by a Wiener Chaos Approach 2014 Vietnam Journal of Mathematics   article
url  
BibTeX:
@article{Huschto2014a,
    author = {Huschto, T. and Sager, S.},
    title = {{S}olving {S}tochastic {O}ptimal {C}ontrol {P}roblems by a {W}iener {C}haos {A}pproach},
    journal = {{V}ietnam {J}ournal of {M}athematics},
    year = {2014},
    volume = {42},
    number = {1},
    pages = {83--113},
    url = {https://mathopt.de/publications/Huschto2014a.pdf}
}
Huschto, T. Numerical Methods for Random Parameter Optimal Control and the Optimal Control of Stochastic Differential Equations 2014 School: University Heidelberg   phdthesis
url  
BibTeX:
@phdthesis{Huschto2014b,
    author = {Huschto, T.},
    title = {{N}umerical {M}ethods for {R}andom {P}arameter {O}ptimal {C}ontrol and the {O}ptimal {C}ontrol of {S}tochastic {D}ifferential {E}quations},
    school = {University Heidelberg},
    year = {2014},
    url = {https://mathopt.de/publications/Huschto2014.pdf}
}

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

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Prof. Dr. Sebastian Sager
Head of MathOpt group
at the Institute of Mathematical Optimization
at the Faculty of Mathematics
at the Otto-von-Guericke University Magdeburg

Universitätsplatz 2, 02-224
39106 Magdeburg, Germany

: +49 391 67 58745
:

Susanne Heß

Universitätsplatz 2, 02-201
39106 Magdeburg, Germany

: +49 391 67 58756
:

  • currently no upcoming news

...more

Prof. Dr. Sebastian Sager
Head of MathOpt group
at the Institute of Mathematical Optimization
at the Faculty of Mathematics
at the Otto-von-Guericke University Magdeburg

Universitätsplatz 2, 02-224
39106 Magdeburg, Germany

: +49 391 67 58745
:

Susanne Heß

Universitätsplatz 2, 02-201
39106 Magdeburg, Germany

: +49 391 67 58756
: