Exploiting GPUs to investigate an inversion method that retrieves cardiac conductivities from potential measurements

Barbara Johnston, Josef Barnes


Accurate cardiac bidomain conductivity values are essential for realistic simulation of various cardiac electrophysiological phenomena. A method was previously developed that can determine the conductivities from measurements of potential on a multi-electrode array placed on the surface of the heart. These conductivities, as well as a value for fibre rotation, are determined using a mathematical model and a two-pass process that is based on Tikhonov regularisation. Using simulated potentials, to which noise is added, the inversion method was recently shown to retrieve the intracellular conductivities accurately with up to 15% noise and the extracellular conductivities extremely accurately even with 20% noise. Recent work investigated the sensitivity of the method to the choice of the regularisation parameters. Such a study only became possible due to modifications that were made to the C++ code so that it could run on graphical processing units (GPUs) on the CUDA platform. As the method required the solution of a large number of matrix equations, the highly parallel nature of GPUs was exploited to accelerate execution of the code. Reorganisation of the code and more efficient memory management techniques allowed the data to completely fit in the GPU memory. Comparison between the execution time on the GPU versus the original CPU code shows a speedup of up to 60 times. In the future, the speedup could be further increased with greater use of shared memory, which has a much lower latency (access time) than global memory.

  • Clayton, R. H., Bernus, O., Cherry, E. M., Dierckx, H., Fenton, F. H., Mirabella, L., Panfilov, A. V., Sachse, F. B., Seemann, G., and Zhang, H. Models of cardiac tissue electrophysiology: Progress, challenges and open questions. Progress in Biophysics and Molecular Biology, 104(1–3):22–48, 2011. doi:10.1016/j.pbiomolbio.2010.05.008
  • Arthur, R. M. and Geselowitz, D. B. Effect of inhomogeneities on the apparent location and magnitude of a cardiac current dipole source. IEEE Transactions on Biomedical Engineering, 17:141–146, 1970. doi:10.1109/TBME.1970.4502713
  • Clerc, L. Directional differences of impulse spread in trabecular muscle from mammalian heart. Journal of Physiology, 255:335–346, 1976. http://jp.physoc.org/content/255/2/335
  • Roberts, D. E., Hersh, L. T., and Scher, A. M. Influence of cardiac fiber orientation on wavefront voltage, conduction velocity and tissue resistivity in the dog. Circ. Res., 44:701–712, 1979. doi:10.1161/01.RES.44.5.701
  • Roberts, D. E. and Scher, A. M. Effects of tissue anisotropy on extracellular potential fields in canine myocardium in situ. Circ. Res., 50:342–351, 1982. doi:10.1161/01.RES.50.3.342
  • Hooks, D. A. Myocardial segment-specific model generation for simulating the electrical action of the heart. BioMedical Engineering OnLine, 6(1):21–21, 2007. doi:10.1186/1475-925X-6-21
  • MacLachlan, M. C., Sundnes, J., and Lines, G. T. Simulation of ST segment changes during subendocardial ischemia using a realistic 3-D cardiac geometry. IEEE Transactions on Biomedical Engineering, 52(5):799–807, 2005. doi:10.1109/TBME.2005.844270
  • Roth, B. J. Electrical conductivity values used with the bidomain model of cardiac tissue. IEEE Transactions on Biomedical Engineering, 44(4):326–328, April 1997. doi:10.1109/10.563303
  • Johnston, P. R. and Kilpatrick, D. The effect of conductivity values on ST segment shift in subendocardial ischaemia. IEEE Transactions on Biomedical Engineering, 50(2):150–158, February 2003. doi:10.1109/TBME.2002.807660
  • Johnston, P. R. Cardiac conductivity values–-a challenge for experimentalists? Noninvasive Functional Source Imaging of the Brain and Heart and 2011 8th International Conference on Bioelectromagnetism (NFSI and ICBEM), pages 39–43, 13-16 May 2011. doi:10.1109/NFSI.2011.5936816
  • Hooks, D. A. and Trew, M. L. Construction and validation of a plunge electrode array for three-dimensional determination of conductivity in the heart. IEEE Transactions on Biomedical Engineering, 55(2):626–635, 2008. doi:10.1109/TBME.2007.903705
  • Trew, M. L., Caldwell, B. J., Gamage, T. P. B., Sands, G. B., and Smaill, B. H. Experiment-specific models of ventricular electrical activation: Construction and application. In 30th Annual International IEEE EMBS Conference, pages 137–140, 2008. doi:10.1109/IEMBS.2008.4649109
  • Caldwell, B. J., Trew, M. L., Sands, G. B., Hooks, D. A., LeGrice, I. J., and Smaill, B. H. Three distinct directions of intramural activation reveal nonuniform side–to–side electrical coupling of ventricular myocytes. Circulation: Arrhythmia and Electropysiology, 2:433–440, 2009. doi:10.1161/CIRCEP.108.830133
  • Pollard, A. E., Ellis, C. D., and Smith, W. M. Linear electrode arrays for stimulation and recording within cardiac tissue space constants. IEEE Transactions on Biomedical Engineering, 55(4):1408–1414, 2008. doi:10.1109/TBME.2007.912401
  • Pollard, A. E. and Barr, R. C. A biophysical model for cardiac microimpedance measurements. American Journal of Physiology-Heart and Circulatory Physiology, 298:H1699–H1709, 2010. doi:10.1152/ajpheart.01131.2009
  • Johnston, B. M. Design of a multi–electrode array to measure cardiac conductivities. ANZIAM Journal, 54:C271–C290, 2013. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/viewFile/6278/1694
  • Johnston, B. M. and Johnston, P. R. A multi-electrode array and inversion technique for retrieving six conductivities from heart potential measurements. Medical and Biological Engineering and Computing, 51(12):1295–1303, 2013. doi:10.1007/s11517-013-1101-2
  • Johnston, B. M. Using a sensitivity study to facilitate the design of a multi–electrode array to measure six cardiac conductivity values Mathematical Biosciences, 244:40–46, 2013. doi:10.1016/j.mbs.2013.04.003
  • Plonsey, R. and Barr, R. The four-electrode resistivity technique as applied to cardiac muscle. IEEE Transactions on Biomedical Engineering, 29(7):541–546, 1982. doi:10.1109/TBME.1982.324927
  • Johnston, B. M., Johnston, P. R., and Kilpatrick, D. A new approach to the determinination of cardiac potential distributions: Application to the analysis of electrode configurations. Mathematical Biosciences, 202(2):288–309, 2006. doi:10.1016/j.mbs.2006.04.004
  • Johnston, B. M., Johnston, P. R., and Kilpatrick, D. Analysis of electrode configurations for measuring cardiac tissue conductivities and fibre rotation. Annals of Biomedical Engineering, 34(6):986–996, June 2006. doi:10.1007/s10439-006-9098-4
  • Kuntsevich, A. and Kappel, F. SolvOpt: The solver for Local Nonlinear Optimisation Problems, version 1.1 in C. Technical Report, Institute for Mathematics: Karl–Franzens University of Graz, 1997. http://uni-graz.at/imawww/kuntsevich/solvopt/ps/manual.pdf


bidomain model; cardiac conductivity values; GPU computing

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DOI: http://dx.doi.org/10.21914/anziamj.v55i0.7790

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