Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

1.3K
Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
1.3K
Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

4.3K
A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...
4.3K
Exponential Equations for Modeling Growth01:26

Exponential Equations for Modeling Growth

459
Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...
459
Introduction to Exponential Functions01:29

Introduction to Exponential Functions

545
Exponential functions are fundamental in modeling dynamic processes where the rate of change is proportional to the current value. Defined by f(x) = bx, where b is a positive constant not equal to one, they form the basis for describing processes of growth and decay depending on whether the base b is greater than or less than one.Exponential models describe situations where change occurs at a rate proportional to the current amount. These include phenomena such as bacterial proliferation,...
545
Exponential Functions with Base e01:30

Exponential Functions with Base e

383
Exponential functions with base e are essential for modeling continuous processes of growth and decay. The constant e, approximately 2.718, naturally arises in systems where change occurs proportionally to the current value. A positive exponent represents continuous growth, while a negative exponent represents continuous decay. These functions are especially useful for describing situations where change happens smoothly over time rather than in discrete steps.One clear example of exponential...
383
Survival Curves01:18

Survival Curves

931
Survival curves are graphical representations that depict the survival experience of a population over time, offering an intuitive way to track the proportion of individuals who remain event-free at each time point. These curves are widely used in fields such as medicine, public health, and reliability engineering to visualize and compare survival probabilities across different groups or conditions.
The Kaplan-Meier estimator is the most common method for constructing survival curves. This...
931

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Investigation of the cortical bone metabolome of C57BL/6J mice with adenine-induced kidney disease.

JBMR plus·2026
Same author

AhR signaling in joint homeostasis and disease.

Biochimie·2026
Same author

Adipose-driven complement-lipid reprogramming controls nociceptive vulnerability in obesity-associated osteoarthritis.

bioRxiv : the preprint server for biology·2026
Same author

A single intra-articular injection of IDO-Gal3 shifts synovial fluid metabolic profiles for up to six weeks in male rats with knee instability.

Biochimie·2026
Same author

Expanded stoichiometric model of chondrocyte metabolism: response to cyclical shear and compressive loading.

bioRxiv : the preprint server for biology·2026
Same author

Viscoelastic recovery time of chondrocytes from monolayer and alginate cultures.

bioRxiv : the preprint server for biology·2026
Same journal

A Rapid, Quantitative Method to Characterize The Human Lymphocyte Concentration for Automated High-Throughput Radiation Biodosimetry.

Biomedical engineering research·2013
See all related articles

Related Experiment Video

Updated: May 1, 2026

Luminescence Resonance Energy Transfer to Study Conformational Changes in Membrane Proteins Expressed in Mammalian Cells
08:31

Luminescence Resonance Energy Transfer to Study Conformational Changes in Membrane Proteins Expressed in Mammalian Cells

Published on: September 16, 2014

11.6K

A Novel Method for Curvefitting the Stretched Exponential Function to Experimental Data.

Ronald K June1, John P Cunningham2, David P Fyhrie3

  • 1Department of Mechanical and Industrial Engineering, Montana State University, Bozeman, MT.

Biomedical Engineering Research
|April 1, 2014
PubMed
Summary
This summary is machine-generated.

A new algorithm accurately fits stretched exponential models to relaxation data, overcoming issues with standard methods. This approach requires fewer parameters and no initial guesses, improving fits for simulated and experimental bone/cartilage data.

Keywords:
Cartilage BiomechanicsCurvefittingOptimizationOsteoarthritisPolymer Dynamics

More Related Videos

Visualizing Intracellular SNARE Trafficking by Fluorescence Lifetime Imaging Microscopy
08:55

Visualizing Intracellular SNARE Trafficking by Fluorescence Lifetime Imaging Microscopy

Published on: December 29, 2017

11.0K
Saccharomyces cerevisiae Exponential Growth Kinetics in Batch Culture to Analyze Respiratory and Fermentative Metabolism
07:38

Saccharomyces cerevisiae Exponential Growth Kinetics in Batch Culture to Analyze Respiratory and Fermentative Metabolism

Published on: September 30, 2018

44.0K

Related Experiment Videos

Last Updated: May 1, 2026

Luminescence Resonance Energy Transfer to Study Conformational Changes in Membrane Proteins Expressed in Mammalian Cells
08:31

Luminescence Resonance Energy Transfer to Study Conformational Changes in Membrane Proteins Expressed in Mammalian Cells

Published on: September 16, 2014

11.6K
Visualizing Intracellular SNARE Trafficking by Fluorescence Lifetime Imaging Microscopy
08:55

Visualizing Intracellular SNARE Trafficking by Fluorescence Lifetime Imaging Microscopy

Published on: December 29, 2017

11.0K
Saccharomyces cerevisiae Exponential Growth Kinetics in Batch Culture to Analyze Respiratory and Fermentative Metabolism
07:38

Saccharomyces cerevisiae Exponential Growth Kinetics in Batch Culture to Analyze Respiratory and Fermentative Metabolism

Published on: September 30, 2018

44.0K

Area of Science:

  • Biophysics
  • Materials Science
  • Computational Modeling

Background:

  • The stretched exponential function is widely used for modeling experimental relaxation data.
  • Standard fitting algorithms for this function can yield inconsistent results due to sensitivity to initial parameter values.
  • This inconsistency poses challenges in accurately characterizing material properties from relaxation experiments.

Purpose of the Study:

  • To develop a novel, robust algorithm for fitting the stretched exponential model to relaxation data.
  • To address the limitations of existing methods, particularly their sensitivity to initial parameter guesses.
  • To provide a more reliable tool for analyzing experimental relaxation data.

Main Methods:

  • Development of a new fitting algorithm for the stretched exponential model.
  • The algorithm requires only a single adjustable parameter and does not need initial parameter values.
  • Validation using simulated datasets and experimental stress-relaxation data from bone and cartilage.

Main Results:

  • The novel algorithm demonstrated strong correlations between simulated and fitted parameters for simulated data, indicating accurate parameter determination.
  • High-quality fits were achieved for experimental stress-relaxation data from bone and cartilage.
  • The new method significantly outperformed a commonly-used Quasi-Newton method in fitting accuracy for experimental data.

Conclusions:

  • The developed algorithm offers a reliable and accurate method for fitting stretched exponential models to relaxation data.
  • This approach mitigates issues associated with parameter initialization and sensitivity in traditional methods.
  • The algorithm shows significant potential for applications in biophysics and materials science, particularly for analyzing biological tissue relaxation.