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Uncertainty: Overview00:59

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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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Experimental Quantification of Interactions Between Drug Delivery Systems and Cells In Vitro: A Guide for Preclinical Nanomedicine Evaluation
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UncertainSCI: Uncertainty quantification for computational models in biomedicine and bioengineering.

Akil Narayan1, Zexin Liu1, Jake A Bergquist2

  • 1Scientific Computing and Imaging Institute, University of Utah, 72 Central Campus Dr, Salt Lake City, UT, 84112, United States; Department of Mathematics, University of Utah, 72 Central Campus Dr, Salt Lake City, UT, 84112, United States.

Computers in Biology and Medicine
|December 15, 2022
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A new software tool, UncertainSCI, quantifies how parameter variability affects biomedical simulations. This open-source Python tool helps analyze uncertainty in models, improving computational biology research.

Keywords:
Biomedical simulationsOpen-source softwareUncertainty quantification

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Area of Science:

  • Computational Biology
  • Biomedical Engineering
  • Scientific Computing

Background:

  • Biomedical simulations rely on parameters with assumed values.
  • Quantifying the impact of parameter variability is crucial but lacks general tools.
  • Parametric uncertainty analysis is a growing area of interest in computational medicine.

Purpose of the Study:

  • To develop a general-purpose software tool for quantifying uncertainty in biomedical simulations.
  • To provide a solution for analyzing the effects of parametric variability on model outputs.
  • To facilitate the study of uncertainty due to parameter variations in computational models.

Main Methods:

  • Developed UncertainSCI, an open-source Python software suite.
  • Utilized advanced parameter sampling and polynomial chaos (PC) emulation.
  • Modeled parameters as random variables to compute output statistics and sensitivities.
  • Employed near-optimal sampling and PC construction techniques using weighted Fekete points.

Main Results:

  • Demonstrated UncertainSCI's utility in analyzing bioelectric potentials in the heart.
  • Showcased application in modeling electric stimulation in the brain.
  • Successfully estimated variability, statistics, and sensitivities for multiple model parameters.

Conclusions:

  • UncertainSCI offers a powerful, lightweight solution for probing parametric variability and uncertainty.
  • The non-intrusive pipeline enables integration with existing biomedical simulation software.
  • Facilitates accurate ascertainment of parametric uncertainty across diverse applications.