Fast and Reliable Reduced-Order Models for Cardiac Electrophysiology

Mathematical models of the human heart are increasingly playing a vital role in understanding the working mechanisms of the heart, both under healthy functioning and during disease. The aim is to aid medical practitioners diagnose and treat the many ailments affecting the heart. Towards this, modelling cardiac electrophysiology is crucial as the heart's electrical activity underlies the contraction mechanism and the resulting pumping action. The governing equations and the constitutive laws describing the electrical activity in the heart are coupled, nonlinear, and involve a fast moving wave front, which is generally solved by the finite element method. The simulation of this complex system as part of a virtual heart model is challenging due to the necessity of fine spatial and temporal resolution of the domain. Therefore, efficient surrogate models are needed to predict the dynamics under varying parameters and inputs. In this work, we develop an adaptive, projection-based surrogate model for cardiac electrophysiology. We introduce an a posteriori error estimator that can accurately and efficiently quantify the accuracy of the surrogate model. Using the error estimator, we systematically update our surrogate model through a greedy search of the parameter space. Furthermore, using the error estimator, the parameter search space is dynamically updated such that the most relevant samples get chosen at every iteration. The proposed adaptive surrogate modelling technique is tested on three benchmark models to illustrate its efficiency, accuracy, and ability of generalization.Comment: 28 pages, 17 figures, 1 tabl

Analysis of amplitude and slope diffraction coefficients

The diffraction mechanism is used for field prediction in both light and shadowed regions. Slope and amplitude diffraction coefficients are vital to predict the field strength at the receiver accurately. In this paper, amplitude and slope diffraction coefficients for one of the ray theoretical models, the slope uniform theory of diffraction with convex hull (S-UTD-CH) model, are analyzed. Moreover, diffraction coefficients are given for knife-edge and wedge structures

Electromagnetic Wave Propagation Models for Multiple-Diffraction Scenarios

Dijital yayın sistemlerinde daha güvenilir yayın yapmak için kapsama alanı ve alıcı üzerindeki alan şiddetinin kestiriminde yayılım modelleri kullanılmaktadır. Yayılım modelleri temelde nümerik ve ışın izleme tekniğine dayanan modeller olmak üzere iki ana grupta incelenebilir. Elektromanyetik dalga yayılım modellerinde hesaplama zamanı ve kestirilen alan şiddetinin kesinliği arasında bir ödünleşme vardır. Nümerik modeller kesin sonuçlar vermesine karşın, hesaplama zamanı yüksektir, ışın izleme tekniğine dayanan modeller ise kesinliği az olmakla beraber hesaplama zamanı düşüktür. Hesaplama zamanı ve kesinlik açısından optimum olan modellere ihtiyaç duyulmuştur. Bunun için birçok model geliştirilmiştir.Electromagnetic wave propagation models have been used for coverage estimation and field prediction at the receiver to make more reliable and efficient digital broadcasting systems. Propagation models can be classified into two groups as numerical and ray tracing based models. There is a tradeoff between computation time and accuracy of field prediction among electromagnetic wave propagation models. Although numerical models predict accurately, it requires more computation times. Ray tracing based models predicts the field strength less accurately with lower computation time. Many propagation models have been developed to provide optimum solution for accuracy and computation time

Local control of primary oropharyngeal malignant melanomas with limited tissue excision: a report of three cases

WOS: 000227443000002PubMed: 15455245Mucosal malignant melanomas are rare lesions, and they have different characteristics from their cutaneous counterparts. Since extended excisions of mucosal malignant melanomas located in the oropharyngeal region cause significant morbidity, limited surgical excision comes into consideration. Three cases of extensive oropharyngeal malignant melanomas were resected with 0.5-1.5-cm healthy tissue margins. The cases were followed for local recurrences. Case 1 applied radiotherapy and chemotherapy in addition to immunotherapy, and the patient is still alive without any local recurrences 18 months after surgery. The patient in case 2 underwent radiotherapy and immunotherapy and died 6 months after surgery. The patient in case 3 received chemotherapy in addition to immunotherapy and died 12 months after surgery as a result of distant metastasis. All cases were without any local recurrences. Surgical excision with limited tumor-free tissue margins may be the surgery of choice to prevent morbidity associated with wide resection of oropharyngeal malignant melanomas if other authors also reconfirm these results with many more cases in the future

Accuracy of Devereux and Teichholz formulas for left ventricular mass calculation in different geometric patterns: comparison with cardiac magnetic resonance imaging

Abstract Left ventricular (LV) myocardial mass is important in the evaluation of cardiac remodeling and requires accurate assessment when performed on linear measurements in two-dimensional echocardiography (Echo). We aimed to compare the accuracy of the Devereux formula (DEV) and the Teichholz formula (TEICH) in calculating LV myocardial mass in Echo using cardiac magnetic resonance (CMR) as the reference method. Based on preceding mathematical calculations, we identified primarily LV size rather than wall thickness as the main source of bias between DEV and TEICH in a retrospective derivation cohort (n = 1276). Although LV mass from DEV and TEICH were correlated with CMR, TEICH did not show a proportional bias as did DEV (− 2 g/m2 vs. + 22 g/m2). This could be validated in an independent prospective cohort (n = 226) with symptomatic non-ischemic heart failure. DEV systematically overestimated LV mass in all tiers of LV remodeling as compared to TEICH. In conclusion, the TEICH method accounts for the changes in LV geometry with increasing LV mass and thus better reflects the different pattern of LV remodeling than the DEV method. This has important clinical implications, as TEICH may be more appropriate for use in clinical practice, rather than DEV, currently recommended