Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Kinetic Energy for a Rigid Body

Kinetic Energy for a Rigid Body

Imagine a solid object involved in a general planar movement, with its center of mass pinpointed at a spot labeled G. The object's kinetic energy relative to an arbitrary point A can be quantified for each of its particles - the ith particle in this case. This measurement is achieved through the employment of the relative velocity definition. The position vector, known as rA, extends from point A to the mass element i.

Velocity and Position by Integral Method

Velocity and Position by Integral Method

If acceleration as a function of time is known, then velocity and position functions can be derived using integral calculus. For constant acceleration, the integral equations refer to the first and second kinematic equations for velocity and position functions, respectively.
Consider an example to calculate the velocity and position from the acceleration function. A motorboat is traveling at a constant velocity of 5.0 m/s when it starts to decelerate to arrive at the dock. Its acceleration is...

Integration by Parts: Indefinite Integrals

Integration by Parts: Indefinite Integrals

Integration by parts is a fundamental technique in calculus for evaluating integrals involving the product of two functions. It is particularly useful when direct integration is not feasible. The method is based on the product rule for differentiation, which states that the derivative of a product equals the derivative of the first function times the second, plus the first function times the derivative of the second. By integrating this identity and rearranging terms, the integration by parts...

Kinematic Equations - III

Kinematic Equations - III

The first two kinematic equations have time as a variable, but the third kinematic equation is independent of time. This equation expresses final velocity as a function of the acceleration and distance over which it acts. The fourth kinematic equation does not have an acceleration term and provides the final position of the object at time t in terms of the initial and final velocities. This equation is useful when the value of the constant acceleration is unknown.
Using the kinematic equations,...

Kinetic Energy - II

Kinetic Energy - II

The kinetic energy of a particle is one-half of the product of the particle’s mass and the square of its speed. Note that just as Newton’s second law can be expressed as either the rate of change of momentum or mass multiplied by the rate of change of velocity, so too can the kinetic energy of a particle be expressed in terms of its mass and momentum, instead of its mass and velocity.

Linear Differential Equations

Linear Differential Equations

The integrating factor method provides a systematic way to solve first-order linear differential equations, especially those that cannot be handled by separation of variables. This method is particularly useful in modeling time-dependent physical systems influenced by both constant inputs and resistive forces. A common example is the motion of a car subjected to a constant engine force while experiencing air resistance proportional to its velocity.In such scenarios, Newton’s second law yields a...

You might also read

Related Articles

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

Sort by

Same author

Image Reconstruction with Maclaurin Series Expansion.

International journal of biomedical research & practice·2026

Same author

A Higher-Order Ising Model with Gradient-Free Update.

Axioms·2026

Same author

Limited-Angle Tomography Using a Neural Network as the Objective Function.

International journal of biomedical research & practice·2026

Same author

Radon Inversion Reconstruction for Kooshball-Like Sampling Trajectory in Cine.

Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference·2025

Same author

Response to Letter to the Editor.

Journal of nuclear cardiology : official publication of the American Society of Nuclear Cardiology·2025

Same author

Mitigating the Drawbacks of the L<sub>0</sub> Norm and the Total Variation Norm.

Axioms·2025

Search research articles

Related Experiment Video

Updated: May 18, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Kinetic parameter estimation using a closed-form expression via integration by parts.

Gengsheng L Zeng¹, Andrew Hernandez, Dan J Kadrmas

¹Department of Radiology, University of Utah, 729 Arapeen Drive, Salt Lake City, UT 84108, USA. larry@ucair.med.utah.edu

Physics in Medicine and Biology

|September 7, 2012

Summary

This summary is machine-generated.

This study introduces a novel method for dynamic emission computed tomographic imaging. It offers robust kinetic parameter estimation for compartment models, improving in vivo physiologic process quantification.

More Related Videos

Experimental Methods to Study Human Postural Control

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

Related Experiment Videos

Last Updated: May 18, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Experimental Methods to Study Human Postural Control

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

Area of Science:

Nuclear Medicine
Biophysics
Medical Imaging

Background:

Dynamic emission computed tomographic imaging with compartment modeling quantifies in vivo physiologic processes.
Estimating kinetic rate parameters for multi-compartment models is computationally demanding and prone to local minima.
Current kinetic parameter estimation techniques involve tradeoffs between computation time, robustness, and flexibility.

Purpose of the Study:

To develop a novel method for kinetic parameter estimation in dynamic emission computed tomographic imaging.
To overcome computational challenges and improve the robustness of multi-compartment model fitting.
To provide closed-form formulas that reduce sensitivity to data sampling and noise.

Main Methods:

Elimination of differential operations using the integration-by-parts method.
Derivation of a family of closed-form formulas for kinetic parameter estimation.
Computer simulations to evaluate the proposed method's robustness.

Main Results:

Closed-form formulas were obtained, eliminating differential operations.
The proposed method demonstrated robustness in computer simulations.
The method is effective without requiring specification of the initial condition.

Conclusions:

The integration-by-parts method provides a robust approach for kinetic parameter estimation in dynamic emission computed tomographic imaging.
This technique enhances the quantification of in vivo physiologic processes for molecular disease research.
The closed-form formulas offer improved model fitting and reduced sensitivity to data imperfections.