UncertainSCI: Uncertainty quantification for computational models in biomedicine and bioengineering

Abstract

Background: Computational biomedical simulations frequently contain parameters that model physical features, material coefficients, and physiological effects, whose values are typically assumed known a priori. Understanding the effect of variability in those assumed values is currently a topic of great interest. A general-purpose software tool that quantifies how variation in these parameters affects model outputs is not broadly available in biomedicine. For this reason, we developed the 'UncertainSCI' uncertainty quantification software suite to facilitate analysis of uncertainty due to parametric variability.

Methods: We developed and distributed a new open-source Python-based software tool, UncertainSCI, which employs advanced parameter sampling techniques to build polynomial chaos (PC) emulators that can be used to predict model outputs for general parameter values. Uncertainty of model outputs is studied by modeling parameters as random variables, and model output statistics and sensitivities are then easily computed from the emulator. Our approaches utilize modern, near-optimal techniques for sampling and PC construction based on weighted Fekete points constructed by subsampling from a suitably randomized candidate set.

Results: Concentrating on two test cases-modeling bioelectric potentials in the heart and electric stimulation in the brain-we illustrate the use of UncertainSCI to estimate variability, statistics, and sensitivities associated with multiple parameters in these models.

Conclusion: UncertainSCI is a powerful yet lightweight tool enabling sophisticated probing of parametric variability and uncertainty in biomedical simulations. Its non-intrusive pipeline allows users to leverage existing software libraries and suites to accurately ascertain parametric uncertainty in a variety of applications.

Keywords: Biomedical simulations; Open-source software; Uncertainty quantification.

Figure 1:

Cardiac bioelectric simulations with the passive bidomain model: UQ of simulated zones of myocardial ischemia relative to measured potentials. A: Isosurfaces of 1) the measured ischemic regions (black line shows cut plane for subsequent visualization, with eye glyph pointing in direction of visualization), 2) measured extracellular potentials, 3) the mean forward solution, and 4) the standard deviation due to variation in the four ischemic conductivity values. B: Sensitivity due to variation in 1) the extracellular longitudinal conductivity (σ_eL), 2) extracellular transverse conductivity (σ_eT), 3) intracellular longitudinal conductivity (σ_iL), and 4) intracellular transverse conductivity (σ_iT). Results adapted with permission from [3].

Figure 2:

A: Activation sequence for an epicardial stimulation location, showing 1) the activation sequence for default fiber orientations, 2) the mean activation sequence, and 3) the total standard deviation of the activation sequence. The top row of each pair contains left-ventricular views and the bottom row contains right-ventricular views. B: Parameter sensitivities for an epicardial stimulation location, showing the standard deviation contributions of the 1) epicardial and 2) endocardial fiber orientation, and 3) the global sensitivities of the activation sequence due to both parameters. Views are the same as in panel A. Results adapted with permission from [35].

Figure 3:

Quantification of uncertainty in simulations of transcranial direct current stimulation (tDCS). A: Head model with two electrodes through which current flow was simulated. The vertical plane indicates where the model was cut for all subsequent figures. The model includes skin (pink), skull (yellow), CSF (blue), gray matter (gray) and white matter (white). B: Mean and standard deviation of electric field strength in 1297 simulations of tDCS with all tissue conductivities modeled with uncertainty. C: Total sensitivity values for each tissue conductivity indicate their relative contributions to the standard deviation.

Figure 4:

Quantification of uncertainty in tissue conductivities and electrode locations on the voltage resulting from direct electrocortical stimulation. A: Sagittal slice through the finite element model, which includes CSF (blue), gray matter (gray) and white matter (white). The nodes used as possible locations for the cathode (blue) and anode (red) are shown on the CSF surface. The mean voltage and standard deviation due to uncertainty in tissue conductivities and electrode locations are shown on the same sagittal slice. B: Total sensitivity values for each uncertain parameter indicate their relative contributions to the standard deviation.