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Bayesian Sensitivity Analysis of a Cardiac Cell Model Using a Gaussian Process Emulator.

Chang ET, Strong M, Clayton RH - PLoS ONE (2015)

Bottom Line: In this study we show that a surrogate statistical model of a cardiac cell model (the Luo-Rudy 1991 model) can be built using Gaussian process (GP) emulators.We found that the GP emulators could be fitted to a small number of model runs, and behaved as would be expected based on the underlying physiology that the model represents.We have shown that an emulator approach is a powerful tool for uncertainty and sensitivity analysis in cardiac cell models.

View Article: PubMed Central - PubMed

Affiliation: Insigneo Institute for in-silico Medicine, University of Sheffield, Sheffield, United Kingdom; Department of Computer Science University of Sheffield, Sheffield, United Kingdom.

ABSTRACT
Models of electrical activity in cardiac cells have become important research tools as they can provide a quantitative description of detailed and integrative physiology. However, cardiac cell models have many parameters, and how uncertainties in these parameters affect the model output is difficult to assess without undertaking large numbers of model runs. In this study we show that a surrogate statistical model of a cardiac cell model (the Luo-Rudy 1991 model) can be built using Gaussian process (GP) emulators. Using this approach we examined how eight outputs describing the action potential shape and action potential duration restitution depend on six inputs, which we selected to be the maximum conductances in the Luo-Rudy 1991 model. We found that the GP emulators could be fitted to a small number of model runs, and behaved as would be expected based on the underlying physiology that the model represents. We have shown that an emulator approach is a powerful tool for uncertainty and sensitivity analysis in cardiac cell models.

No MeSH data available.


Variance in APD90 emulator.(a) Distributions of APD90 resulting from normal distributions of GK when all other maximum conductances were effectively held constant by assigning a mean of 0.5 and a very small variance of 0.0001 in normalised units. GK was assigned a mean value of 0.282 mS cm-2 and variance 0.0014 (blue) 0.0028 (red), 0.0071 (green), 0.0141 (yellow) mS cm-2. (b) Distributions of APD90 obtained from four Monte Carlo analyses, each with 2000 simulator runs, and with GK drawn from distributions with mean value of 0.282 mS cm-2 and variance 0.0014 (blue) 0.0028 (red), 0.0071 (green), 0.0141 (yellow) mS cm-2.
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pone.0130252.g004: Variance in APD90 emulator.(a) Distributions of APD90 resulting from normal distributions of GK when all other maximum conductances were effectively held constant by assigning a mean of 0.5 and a very small variance of 0.0001 in normalised units. GK was assigned a mean value of 0.282 mS cm-2 and variance 0.0014 (blue) 0.0028 (red), 0.0071 (green), 0.0141 (yellow) mS cm-2. (b) Distributions of APD90 obtained from four Monte Carlo analyses, each with 2000 simulator runs, and with GK drawn from distributions with mean value of 0.282 mS cm-2 and variance 0.0014 (blue) 0.0028 (red), 0.0071 (green), 0.0141 (yellow) mS cm-2.

Mentions: We next assessed how the variance of APD90 calculated directly using the emulator depended on the variance of GK. For this calculation, all inputs except GK were effectively fixed by assigning independent normal distributions with a mean in normalised units of 0.5 and a very small variance of 0.0001 in normalised units. GK was then assigned a normal distribution with mean 0.5 in normalised units (0.282 mS cm-2 on the natural scale), but to show the effect of increasing uncertainty in GK, the variance was set at 0.01, 0.02, 0.05 and 0.1 in successive calculations of the mean and variance of APD90. These normalised variances correspond to standard deviations of 0.0014, 0.0028, 0.0071, and 0.0141 mS cm-2 on the natural scale. The output distributions of APD90 for each distribution of GK are shown in Fig 4(a). As would be expected, increasing the variance of GK results in an increase in the variance of APD90.


Bayesian Sensitivity Analysis of a Cardiac Cell Model Using a Gaussian Process Emulator.

Chang ET, Strong M, Clayton RH - PLoS ONE (2015)

Variance in APD90 emulator.(a) Distributions of APD90 resulting from normal distributions of GK when all other maximum conductances were effectively held constant by assigning a mean of 0.5 and a very small variance of 0.0001 in normalised units. GK was assigned a mean value of 0.282 mS cm-2 and variance 0.0014 (blue) 0.0028 (red), 0.0071 (green), 0.0141 (yellow) mS cm-2. (b) Distributions of APD90 obtained from four Monte Carlo analyses, each with 2000 simulator runs, and with GK drawn from distributions with mean value of 0.282 mS cm-2 and variance 0.0014 (blue) 0.0028 (red), 0.0071 (green), 0.0141 (yellow) mS cm-2.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4482712&req=5

pone.0130252.g004: Variance in APD90 emulator.(a) Distributions of APD90 resulting from normal distributions of GK when all other maximum conductances were effectively held constant by assigning a mean of 0.5 and a very small variance of 0.0001 in normalised units. GK was assigned a mean value of 0.282 mS cm-2 and variance 0.0014 (blue) 0.0028 (red), 0.0071 (green), 0.0141 (yellow) mS cm-2. (b) Distributions of APD90 obtained from four Monte Carlo analyses, each with 2000 simulator runs, and with GK drawn from distributions with mean value of 0.282 mS cm-2 and variance 0.0014 (blue) 0.0028 (red), 0.0071 (green), 0.0141 (yellow) mS cm-2.
Mentions: We next assessed how the variance of APD90 calculated directly using the emulator depended on the variance of GK. For this calculation, all inputs except GK were effectively fixed by assigning independent normal distributions with a mean in normalised units of 0.5 and a very small variance of 0.0001 in normalised units. GK was then assigned a normal distribution with mean 0.5 in normalised units (0.282 mS cm-2 on the natural scale), but to show the effect of increasing uncertainty in GK, the variance was set at 0.01, 0.02, 0.05 and 0.1 in successive calculations of the mean and variance of APD90. These normalised variances correspond to standard deviations of 0.0014, 0.0028, 0.0071, and 0.0141 mS cm-2 on the natural scale. The output distributions of APD90 for each distribution of GK are shown in Fig 4(a). As would be expected, increasing the variance of GK results in an increase in the variance of APD90.

Bottom Line: In this study we show that a surrogate statistical model of a cardiac cell model (the Luo-Rudy 1991 model) can be built using Gaussian process (GP) emulators.We found that the GP emulators could be fitted to a small number of model runs, and behaved as would be expected based on the underlying physiology that the model represents.We have shown that an emulator approach is a powerful tool for uncertainty and sensitivity analysis in cardiac cell models.

View Article: PubMed Central - PubMed

Affiliation: Insigneo Institute for in-silico Medicine, University of Sheffield, Sheffield, United Kingdom; Department of Computer Science University of Sheffield, Sheffield, United Kingdom.

ABSTRACT
Models of electrical activity in cardiac cells have become important research tools as they can provide a quantitative description of detailed and integrative physiology. However, cardiac cell models have many parameters, and how uncertainties in these parameters affect the model output is difficult to assess without undertaking large numbers of model runs. In this study we show that a surrogate statistical model of a cardiac cell model (the Luo-Rudy 1991 model) can be built using Gaussian process (GP) emulators. Using this approach we examined how eight outputs describing the action potential shape and action potential duration restitution depend on six inputs, which we selected to be the maximum conductances in the Luo-Rudy 1991 model. We found that the GP emulators could be fitted to a small number of model runs, and behaved as would be expected based on the underlying physiology that the model represents. We have shown that an emulator approach is a powerful tool for uncertainty and sensitivity analysis in cardiac cell models.

No MeSH data available.