Computational and Mathematical Methods in Cardiovascular

EditorialComputational and Mathematical Methods inCardiovascular Diseases

Elena G. Tolkacheva,1 Xiaopeng Zhao,2 Sharon Zlochiver,3 and Yoichiro Mori4

1Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN, USA2Department of Mechanical, Aerospace, and Biomedical Engineering, University of Tennessee, Knoxville, TN, USA3Department of Biomedical Engineering, Tel-Aviv University, Tel Aviv, Israel4Department of Mathematics, University of Minnesota, Minneapolis, MN, USA

Correspondence should be addressed to Elena G. Tolkacheva; [email protected]

Received 31 January 2017; Accepted 31 January 2017; Published 19 March 2017

Copyright © 2017 Elena G. Tolkacheva et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

Cardiovascular diseases are a leading cause of death in theworld. Computational and mathematical methods providea useful tool to better understand heart and vessel prob-lems. This special issue focuses on various computationaland mathematical methods to model cardiac disorders, tounderstand the existing mathematical challenges, to explorenew directions in modeling of cardiovascular dynamicsand cardiac rhythm abnormalities, and to develop cardiacrelated mathematical applications in clinical and emergencysituations.

Several key aspects become the main targets for discus-sion in the current special issue.

Several authors presented their research aiming to usecomputational approaches to elucidate the underlying elec-trophysiological mechanisms of different cardiac diseasesleading to increased arrhythmogeneity in the heart. One areaof research includes investigating the roles of hyperkalemiaand calcium handling components played in the genesisof alternans in ischemia at the cellular level. The resultsshow that hyperkalaemic conditions reduced cell excitabilityand delayed recovery from inactivation of depolarizationcurrents, thus leading to alternans formation. In addition,sarcoplasmic reticulum calcium-ATPase (SERCA2a) func-tion decreased in ischemia, thus resulting in intracellular Ca(Cai) alternans of small magnitude. Finally, a strong Na+-Ca2+ exchange current (INCX) increased the magnitude ofCai alternans, leading to APD alternans through excitation-contraction coupling. Another research aimed to investigate

the combined role of Ca2+/calmodulin-dependent proteinkinase II (CaMKII) and 𝛽-adrenergic signaling pathway inregulating early afterdepolarization. Early afterdepolarization(EAD) has tremendous relevance for the onset of arrhythmo-genesis. Simulations of this kind provide insights on therapystrategies to treat EADs related arrhythmogenesis. Finally,there is an interest to determine the potential antiarrhythmiceffects of the green tea catechin Epigallocatechin-3-Gallate(E3G), by employing numerical simulations of cellular andcable models using atrial, Purkinje, and ventricular kinetics.The authors tested the effects of the drug on action potentialproperties and conduction velocity in the settings of twoNa+ channel gain of function mutations that are correlatedwith hyperexcitability and ectopic premature contractions.They concluded that 30 𝜇M E3G reduces and suppressescellular electrical abnormalities that are associated with thosemutations.

Another important aspect was the development andapplication of different methods and techniques to variouscardiovascular recordings in order to differentiate betweendiseased and healthy states. Some studies propose to investi-gate the level of temporal dependency in cardiovascular timeseries using a copula method. The technique was applied tohealthy aging rats as well as aging rats with early developedhypertension. The study shows that copulas and conditionalentropy can reveal dependency of streams, to their numberand to type.The authors highlighted that antiparallel streamsplay an important role between systolic blood pressure and

HindawiComputational and Mathematical Methods in MedicineVolume 2017, Article ID 4205735, 2 pageshttps://doi.org/10.1155/2017/4205735

https://doi.org/10.1155/2017/4205735

2 Computational and Mathematical Methods in Medicine

its pulse interval. Another approach is to use a 3D modelingfor hemodynamic analysis of fluid structure interaction inintima and adventitia. Combining CT, IVUS, and biplane X-ray angiogram images, the authors calculated deformationof intima and adventitia by catheter insertion and generatedvessel bifurcations. Limitations and future directions werealso discussed. Finally, a hybrid classification system usingthe Rough Set and Relief (RSRF) method for diagnosis ofheart diseases can be developed.Numerical experimentswereconducted using the Statlog data. Results that reported on10-fold cross validation demonstrate a high classificationaccuracy.

Several authors used computational approach to studyvarious biomechanical properties and characteristics of thevarious diseased hearts. Some studies evaluate the pumpingefficacy of a left ventricular assist device according to cannu-lation site in heart failure with valvular regurgitation. Theyaimed to analyze the contribution of a left ventricular assistdevice (LVAD) to mitral and aortic valve regurgitation forthe following cannulation sites: from the LA to the aorta(LAAO) and from the LV to the aorta (LVAO) under differ-ent conditions. The results showed that LVAD with LAAOcannulation is appropriate for recovery of the mitral valveregurgitation heart, and the LVAD with LVAO cannulation isappropriate for treating the aortic valve regurgitation heart.Another approach is to investigate the relationship betweenendoleak formation and the surrounding pathological flowfields. Endoleak formation is a major complication forabdominal aortic aneurysm patients. Using computationalfluid dynamics and image processing techniques, the authorsreconstructed 6 patient specific models to study possibleendoleak formation in a location with high local wall stress.The developed models may be adapted for other humancardiovascular surgeries, such as cardiopulmonary bypass,where detailed patient-specific hemodynamics is necessary.

Elena G. TolkachevaXiaopeng Zhao

Sharon ZlochiverYoichiro Mori

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