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Related Concept Videos

Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

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...
Uncertainty: Overview00:59

Uncertainty: Overview

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.
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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 't,' or...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Uncertainty in Measurement: Accuracy and Precision03:37

Uncertainty in Measurement: Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.

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Related Experiment Video

Updated: May 11, 2026

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
10:22

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Published on: September 7, 2019

Generalised polynomial chaos-based uncertainty quantification for planning MRgLITT procedures.

Samuel J Fahrenholtz1, R Jason Stafford, Florian Maier

  • 1Department of Imaging Physics, The University of Texas M.D. Anderson Cancer Center, Houston, TX 77054, USA.

International Journal of Hyperthermia : the Official Journal of European Society for Hyperthermic Oncology, North American Hyperthermia Group
|May 23, 2013
PubMed
Summary

This study uses a generalized polynomial chaos method to model uncertainties in bioheat transfer for laser therapies. The approach accurately predicts heating, aiding in planning MR-guided laser-induced thermal therapies.

Related Experiment Videos

Last Updated: May 11, 2026

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
10:22

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Published on: September 7, 2019

Area of Science:

  • Biomedical Engineering
  • Computational Biology
  • Medical Physics

Background:

  • Accurate thermal modeling is crucial for MR-guided laser-induced thermal therapies (MRgLITT).
  • Parameter uncertainties in bioheat transfer models can affect treatment predictability.
  • Generalised polynomial chaos (gPC) offers a method to quantify these uncertainties.

Purpose of the Study:

  • To incorporate constitutive parameter uncertainties into the Pennes bioheat transfer model using gPC.
  • To evaluate stochastic temperature predictions against MR thermometry data for MRgLITT planning.
  • To assess the model's potential as a computational tool for thermal therapy planning.

Main Methods:

  • Implemented the Pennes bioheat transfer model with diffusion theory for laser-tissue interaction.
  • Conducted a probabilistic sensitivity study to identify key parameters influencing temperature variance.
  • Compared gPC predictions with MR temperature imaging (MRTI) data from phantom and canine experiments.

Main Results:

  • Optical parameters (anisotropy, absorption, scattering) significantly influenced model temperature output.
  • gPC method captured non-linear dependencies within confidence intervals.
  • Stochastic model predictions showed good agreement with experimental MRTI data.

Conclusions:

  • The statistical framework provides conservative estimates of therapeutic heating.
  • The gPC method effectively handles parameter uncertainties in bioheat modeling.
  • This approach shows promise for computational prediction in thermal therapy planning.