Sensitivity analysis of closed-loop one-chamber and four-chamber models with baroreflex

Figures

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  Fig 1. Schematic representation of information exchange between mechanical model and baroreflex representation proposed by Ursino [10], with particular emphasis on the processing within the nervous system, distinguishing afferent (orange blocks), sympathetic (blue blocks) and vagal (green blocks) components.

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  Fig 2. Electrical analogue representations of the one-(A) and four-chamber (B) cardiovascular models used in this work. In both, the passive circulations are represented by CRC Windkessel’s and the valves by diodes with Ohmic behaviour under both forward and reverse bias. Base parameter values (Rsys, Cart etc.) are declared in Table 1. Ventricular elastance function parameters and, systemic resistance and venous compliance unstressed volumes are regulated, making it convenient to consider certain mechanical model input parameters as time-dependant states with dynamics dictated by the regulation.

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  Fig 3. Results of a local and global sensitivity analysis of the one-chamber model. A: local analysis, unregulated model; B: local analysis, regulated model; C: global analysis, first order indices, unregulated model; D: global analysis, first order indices, regulated model. Results may be interpreted in the interval [0, 1]. Lighter colours (pink, yellow and white) identify the more influential parameters, against a specific output. Empty panels in the first column represent the unregulated models and thus no information may be compared to the regulated model in the second column.

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  Fig 4. Results of global and local sensitivity analysis of the four-chamber model. A: local analysis, unregulated model; B: local analysis, regulated model; C: global analysis, first order indices, unregulated model; D: global analysis, first order indices, regulated model. Results are interpretable on the interval [0, 1]. The lighter colours (pink, yellow and white) identify the more influential parameters within the model against a specific output. The empty panels on the first column represent the unregulated models and thus only mechanical parameters are displayed compared to the regulated model in the second column.

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  Fig 5. Results of global sensitivity analysis, total and higher order indices, of the one-chamber model. A: total order indices, unregulated model; B: total order indices, regulated model; C: higher order indices, unregulated model; D: higher order indices, regulated model. Results are interpretable on the interval [0, 1]. The lighter colours (pink, yellow and white) identify the more influential parameters within the model, against a specific output. The empty panels in the first column represent the unregulated models and thus no information is may be compared to the regulated model in the second column. The second row displaying the higher order indices follows by subtraction of the first order indices in the previous figure, from the total order indices above.

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  Fig 6. Convergence data, one-chamber model. Plots A-D show first order Sobol indices for the regulated model. Plots E-H show total order Sobol indices for the regulated model. Plots I-L show first order Sobol indices, and M-P show total order indices for the unregulated model. The parameters are displayed down the left-hand side of the first column, the parameter influence is displayed against cardiac output (blue), maximum left ventricular pressure (orange) and maximum venous pressure (green). The band around each coloured line represents the sensitivity indices 95% confidence limits of the estimated value.

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  Fig 7. Results of global sensitivity analysis of the four-chamber model. A: total order indices, unregulated model; B: total order indices, regulated model; C: higher order indices, unregulated model; D: high order indices, regulated model. Results are interpretable on the interval [0, 1]. Lighter colours (pink, yellow and white) identify the more influential parameters within the model against a specific output. The empty panels on the first column represent the unregulated models and thus no information is displayed compared to the regulated model in the second column. The second row displaying the higher order indices is the subtraction of the first order indices in the previous figure from the total order indices above. Where there is colour, as in panel D; this indicates higher order interactions associated with a parameter.