Performance of GMRES for the MFS

Karageorghis, Andréas; Smyrlis, Yiorgos–Sokratis

doi:10.2495/be090151

Cited by 2 publications

(5 citation statements)

References 11 publications

(7 reference statements)

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“…In this work, we selected the necessary virtual sources for the MFS following ( Wang and Rudy, 2006 ). However, different virtual source’s choice in the MFS modifies the ill-conditioning of the related inverse problem ( Karageorghis and Smyrlis, 2009 ; Chamorro-Servent et al, 2016 ). And, when the distances of the virtual sources from the boundary are large, the ill-conditioning becomes more severe ( Karageorghis and Smyrlis, 2009 ).…”

Section: Discussionmentioning

confidence: 99%

“…However, different virtual source’s choice in the MFS modifies the ill-conditioning of the related inverse problem ( Karageorghis and Smyrlis, 2009 ; Chamorro-Servent et al, 2016 ). And, when the distances of the virtual sources from the boundary are large, the ill-conditioning becomes more severe ( Karageorghis and Smyrlis, 2009 ). Finally, it is well-known that the number of needed iterations for iterative solvers depends on the ill-conditioning of the problem ( Hansen, 2010 ).…”

Section: Discussionmentioning

confidence: 99%

“…Finally, it is well-known that the number of needed iterations for iterative solvers depends on the ill-conditioning of the problem ( Hansen, 2010 ). GMRES’ solution is not affected by different distance’s choice of the virtual sources ( Karageorghis and Smyrlis, 2009 ). GMRES and RRGMRES are both based on Krylov bases.…”

Section: Discussionmentioning

confidence: 99%

“…The GMRES is currently used to solve the MFS problem in the commercial CardioInsight technologies ECGI system ( Rudy et al, 2011 ; Zeng et al, 2018 ). The performance of this technique for the MFS in a general setting was also shown ( Karageorghis and Smyrlis, 2009 ).…”

Section: Introductionmentioning

confidence: 95%

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Electrocardiographic Imaging: A Comparison of Iterative Solvers

Borràs

Chamorro-Servent

2021

Front. Physiol.

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Cardiac disease is a leading cause of morbidity and mortality in developed countries. Currently, non-invasive techniques that can identify patients at risk and provide accurate diagnosis and ablation guidance therapy are under development. One of these is electrocardiographic imaging (ECGI). In ECGI, the first step is to formulate a forward problem that relates the unknown potential sources on the cardiac surface to the measured body surface potentials. Then, the unknown potential sources on the cardiac surface are reconstructed through the solution of an inverse problem. Unfortunately, ECGI still lacks accuracy due to the underlying inverse problem being ill-posed, and this consequently imposes limitations on the understanding and treatment of many cardiac diseases. Therefore, it is necessary to improve the solution of the inverse problem. In this work, we transfer and adapt four inverse problem methods to the ECGI setting: algebraic reconstruction technique (ART), random ART, ART Split Bregman (ART-SB) and range restricted generalized minimal residual (RRGMRES) method. We test all these methods with data from the Experimental Data and Geometric Analysis Repository (EDGAR) and compare their solution with the recorded epicardial potentials provided by EDGAR and a generalized minimal residual (GMRES) iterative method computed solution. Activation maps are also computed and compared. The results show that ART achieved the most stable solutions and, for some datasets, returned the best reconstruction. Differences between the solutions derived from ART and random ART are almost negligible, and the accuracy of their solutions is followed by RRGMRES, ART-SB and finally the GMRES (which returned the worst reconstructions). The RRGMRES method provided the best reconstruction for some datasets but appeared to be less stable than ART when comparing different datasets. In conclusion, we show that the proposed methods (ART, random ART, and RRGMRES) improve the GMRES solution, which has been suggested as inverse problem solution for ECGI.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

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Electrocardiographic Imaging: A Comparison of Iterative Solvers

Borràs

Chamorro-Servent

2021

Front. Physiol.

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“…Moving to music is seemingly spontaneous, and some prior studies have reported that human vigor response (e.g., a change in step length) to music during walking is positively affected by faster tempos (Karageorghis et al, 2006;Shay , 2022, higher beat salience , higher groove Buhmann, 2016), synchronization with the music (Karageorghis et al, 2009), more familiarity with the music (Leow et al, 2015;, and by more pleasant/enjoyable music . Higher vigor has also been reported for both music and metronome at normal walking tempos that are harmonics of 4 .…”

Section: Introductionmentioning

confidence: 99%

Effect of Sound Intensity on Stepping Vigor During Synchronized Walking: Turn up the Music? Beat the Drum Louder?

Shay¹

2022

Preprint

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The effect of music loudness on human movement vigor in walking, running and some exercise and sports domain activities has been sparsely studied. The few prior studies employed varied experimental conditions and sometimes with mixed results. Although the isochronous beat of a metronome might also be considered music in its simplest form, no previous studies have reported the effect of metronome sound intensity on vigor in physical activities. Employing a single-case experimental design, this study examined the effects of sound intensity on stepping vigor for both music and metronome auditory stimuli. Experimental conditions included stepping to a single tempo of 116 BPM during synchronous walking around a 2-mi greenway loop track. With walking synchrony confirmed at 100% and lap distance a constant, lap speeds for each stimulus-intensity condition were determined from lap times with high precision. Randomized data were collected over a six-month period with six repetitions for each stimulus-intensity pair.For music, intensity level was varied for three different playlists of familiar/enjoyable music at three normal listening levels of 69.3, 75.0, and 80.2 dB (± 0.6 dB at each level). Over this relatively narrow intensity range of 11 dB, step length and commensurate walking speed increased 3.7% - 5.7% (ANOVA pooled p < 0.0001 for each playlist). The speed-dB response for the music composite was approximately linear over the range, and the music was strongly activating (more step-length and proportional speed) relative to a no sound (no stimulus) condition at the same regression tempo/cadence.For metronome, 5 different levels of sound intensity were employed over a range of 58.9 – 82.0 dB (± max of 0.5 dB at each level). An unexpected increase in speed of 12.2% was obtained over the 23 dB range (ANOVA pooled p < 0.0001). The speed-dB response was linear (R2 = 0.993). As expected, vigor response was greater for music than for metronome at equivalent intensity levels. However, another unexpected finding for metronome was that at higher intensity levels the metronome stimulus was activating, and at lower levels it was relaxing relative to the no sound condition at the same regression tempo/cadence. The increase in speed per unit increase in dB for metronome (0.53% / dB) was surprisingly greater than for music (0.34 – 0.52 % / dB). This might be attributed to a higher beat salience for metronome.Within the conditions and parameters of this study, these findings clearly showed a positive effect of sound intensity on vigor response for both music and metronome during synchronous walking. The findings have performance implications for walkers and perhaps for runners and in some other rhythmic physical activities. The findings may also contribute to a further understanding of the human auditory sensorimotor function and for intervention in some human gait disorders.

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Performance of GMRES for the MFS

Cited by 2 publications

References 11 publications

Electrocardiographic Imaging: A Comparison of Iterative Solvers

Electrocardiographic Imaging: A Comparison of Iterative Solvers

Effect of Sound Intensity on Stepping Vigor During Synchronized Walking: Turn up the Music? Beat the Drum Louder?

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