Related Experiment Video

Updated: Jul 6, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

[An aggregation method for determination of parameters of mathematical models]

L Ia Klepper

    Meditsinskaia Tekhnika
    |March 22, 2008
    PubMed

    Related Concept Videos

    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...
    Mathematical Modeling: Problem Solving01:29

    Mathematical Modeling: Problem Solving

    Mathematical modeling transforms real-world scenarios into mathematical expressions, allowing for structured problem-solving and analysis. This process involves defining the situation, assigning variables to measurable quantities, selecting an appropriate model, and solving the resulting equation. Such models are invaluable in finance, providing precise methods to evaluate investments, loans, and repayment structures.A widely used example is the calculation of fixed monthly payments on a loan,...
    Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

    Mechanistic Models: Compartment Models in Individual and Population Analysis

    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 squares (OLS)...
    Fundamental Mathematical Principles in Pharmacokinetics: Calculus and Graphs01:21

    Fundamental Mathematical Principles in Pharmacokinetics: Calculus and Graphs

    The fundamental mathematical principles, such as calculus and graphs, play crucial roles in analyzing drug movement and determining pharmacokinetic parameters. Differential calculus examines rates of change and helps to determine the dissolution rate of drugs in biofluids, as well as how drug concentrations change over time. For instance, it can help calculate the rate of elimination of a drug from the body based on its concentration-time profile.
    On the other hand, integral calculus focuses on...
    Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

    Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

    Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
    The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
    Linearization and Approximation01:26

    Linearization and Approximation

    Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...