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Approximation Methods for Molecular Modelling and Diagnosis Tools

Periodic Reporting for period 2 - AMMODIT (Approximation Methods for Molecular Modelling and Diagnosis Tools)

Reporting period: 2017-08-01 to 2019-07-31

In task 1.1 we discuss mathematical algorithms for medical imaging like MPI. The focus is on Fourier methods and approximation results. One of the central ideas in task 1.2 is to consider order relations between values in time series instead of the values themselves, with the advantage of getting simple and robust data analysis methods.

The research task 2.1 deals with the development of integrated multi-scale modelling of biopolymers. Biopolymeric materials have found a wide variety of applications in the biomedical field ranging from sutures, pins and screws for orthopaedic surgery to local drug delivery, tissue engineering scaffolds, and endovascular stents. Biopolymeric properties are dictated by changes at the molecular level which propagate the effects through scales affecting the overall properties at the macroscale. In order to better predict biopolymeric properties, multi-scale material modelling is the overall goal.
The research task 2.2 concerns the development of patient-specific diagnostic tools in the field of cardiac surgery. The diseases affecting left heart valvular apparatuses, i.e. mitral valve (MV) and aortic root (AR), are among the most lethal cardiac pathologies, and affect approximately 10% of the population. The overall objective is the development of computational tools for the quantitative in vivo analysis of MV and AR apparatus, as well as their local blood flow hemodynamics, as a support to the understanding of their pathophysiology, the quantitative diagnosis of pathologies, the planning of surgical repair procedures, and the training of surgeons.

The research tasks 3.1 and 3.2 are related accordingly with the detection of the causality in complex systems and with the prediction\prevention of nocturnal hypoglycemia of diabetes patients. The first problem is of interest in Social Sciences and Biology, where, e. g., it is important to detect the opinion leaders in social networks and reconstruct gene regulatory networks. The second problem is important in view of more than 30 millions of European patients for whom the nocturnal hypoglycemia is one of the most feared complications. Towards these tasks the objectives are to develop new mathematical algorithms by employing recent advances in Regularization Theory, which can be seen as a relevant tool because both the above-mentioned problems can be classified as ill-posed ones.
The published results of task 1.1 include polynomial interpolation on Lissajous-Chebyshev nodes and approximation estimates as well as new Fourier-like fast algorithms which were applied for protein-protein-docking. Moreover, we dealt with the reconstruction problem in non-contact photoacoustic tomography.

In task 2.1 POLIMI developed a combination of homology modeling and molecular dynamics simulations to provide insights into the structural difference between the five FAOX enzymes. In this work, the structure of two enzymes is generated using homology modelling techniques. Then, we used these models and the experimental crystal structures of three other enzymes of the same family to run extensive molecular dynamics simulations in order to compare the structures of these enzymes and assess their interactions with two relevant ligands. Simultaneously, the UzL team developed in task 1.1 improved algorithms for enzyme-ligand docking codes to be used in the framework of enzyme design. Future work is planned to apply the previously developed docking algorithms to molecular modelling problems and test the code on relevant biological problems.

In task 2.2 our team developed high-end numerical methods for the estimation of relative pressure maps from in vivo patient-specific blood flow data in the thoracic aorta. This work was based on the theoretical assumption that relative pressure information can be retrieved from a three-dimensional discrete domain of velocity points. These data was collected in vivo by using the latest evolution of phase contrast magnetic resonance imaging, i.e. 4D Flow, thus measuring in vivo blood hemodynamics in patients characterized by diseases of the aorta. Specifically, a Matlab-based user interface was implemented with ad-hoc Input/Output modules to guide the end-user from data loading to blood velocity post-processing. Data analysis was simplified through novel visualization methods.

It is clear that in Big Data Era the task of causality detection is unavoidably associated with the necessity to deal with big and high-dimensional data. Therefore, in the reported period we have developed prospective mathematical methods for dealing with such data. First results have already been published in the highly ranked journal “Inverse Problems”, and in a new open access Frontiers journal. The later publication has been viewed more than 1000 times in a short period.
A very close cooperation of RICAM with the partner KPI has allowed significant progress towards the prediction of nocturnal hypoglycemia. This fruitful cooperation has led to a publication in a highly ranked journal “Comput Methods Programs Biomed” that has later been highlighted as Editor's choice of the journal. The developed methodology has been summarized in the paper published in the special issue of the medical journal “Journal of Diabetes Science and Technology” devoted to hypoglycemia prevention.
In addition, RICAM and the partner organization IM NASU have contributed to the research task 1.1. As a result, regularized quadrature methods for dealing with the ill-posedness of the underlying model have been proposed and analysed.
All of these results are included in manuscripts which have been prepared and submitted for publication.
The research in task 1.1 directly led to 3 more successful new projects: A DFG-grant for Y. Kolomoitsev, a consortium supported by the VW Foundation on Trilateral Partnership between German, Russian and Ukrainian Partners, and another RISE-project SOMPATY.

As to task 2.1 the combination of molecular modelling simulations performed at Polimi with improved algorithm for molecular docking developed by the project partners at IMath and UzL is aimed at the development of innovative methods for ligand-protein docking. In this view, a secondment of N. Derevianko (IMath) to Polimi was very effective to couple the docking algorithm with molecular modelling. The expected outcome is a novel modelling code that will improve our ability to predict interactions between ligand and proteins.
As to task 2.2 the team is also working on the integration of approaches based on in vivo fluid dynamics with high-end research activity focused on the development of patient-specific mass-spring models to predict the effects of surgical repair on heart valves, as well as on heart chambers. These efforts will lead to software prototypes embedded within proper graphical user interfaces, proposing an innovative multi-perspective approach for surgical planning support.

The mathematical algorithms developed by RICAM together with the partner organization KPI have been implemented in the form of Android Smartphone application “DIA Safe Life” (see the attached image AMMODIT_SMARTPHONE.png). The first trial version of this app has already been demonstrated at the 10th Intern. Conf. on Adv. Tech. & Treat. for Diabetes, ATTD, Paris, Feb. 2017, and received a very positive feedback from the community.
Conference Rivne, September 15-19, 2015
DIA Safe Life of AMMODIT is awarded at the International Startups Contest Sikorsky Challenge
Partners from IM NASU during their secondment at RICAM in August 2018
Conference Kyiv, January 26-30, 2017
Conference Lviv, March 19-23, 2018
Android Smartphone application “DIA Safe Life”
"Final AMMODIT Conference ""Mathematics for Life Sciences"", March 18-22, 2019, Kyiv"
Logo of our project AMMODIT
Conference Hasenwinkel, March 07-11, 2016
Joint poster of AMMODIT and Med. Uni. Innsbruck awarded by Life Science Cluster Tirol