Related Experiment Video
Updated: May 17, 2025
09:20
Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction
Published on: February 13, 2021
6.3K
Numerical accuracy of closed-loop steady state in a zero-dimensional cardiovascular model
Nick van Osta1, Gitte van den Acker1, Tim van Loon1
1Department of Biomedical Engineering, Cardiovascular Research Center Maastricht (CARIM), Maastricht University, Maastricht, The Netherlands.
Summary
Accurate cardiovascular models require careful steady-state convergence assessment. Simulations with homeostatic control need more heartbeats for reliable results, balancing accuracy and computational cost.
Area of Science:
- Computational physiology
- Biomedical engineering
- Cardiovascular modeling
Background:
- Closed-loop cardiovascular models are essential clinical tools, demanding high accuracy and reliability.
- Steady-state simulations are crucial, yet convergence accuracy is often overlooked.
- Numerical errors from integration methods and model assumptions can impact results.
Purpose of the Study:
- To investigate steady-state convergence behavior in a reduced-order cardiovascular model (CircAdapt).
- To quantify numerical errors and assess their impact on steady-state accuracy.
- To evaluate the CircAdapt framework's numerical stability and accuracy under varying conditions.
Main Methods:
- Utilized a reduced-order cardiovascular model within the CircAdapt framework.
- Quantified numerical errors from integration methods and model assumptions.
- Simulated steady-state convergence with and without homeostatic pressure-flow control (PFC).
Main Results:
- Clinically accurate steady states required 7-15 heartbeats without regulatory mechanisms.
- Simulations with homeostatic control (regulating mean arterial pressure and blood volume) needed over twice the heartbeats.
- Numerical errors were quantified to understand their influence on convergence.
Conclusions:
- Achieving accurate steady states in cardiovascular models necessitates understanding convergence behavior.
- Homeostatic control significantly increases the number of heartbeats required for convergence.
- Tailoring simulation length to specific characteristics offers an efficient balance between computational cost and accuracy.
Related Concept Videos
01:30Typical Model Studies
188
Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
188
01:26Linear Approximation in Frequency Domain
80
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
80
01:21Linear Approximation in Time Domain
58
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
58
01:12Modeling and Similitude
151
Scaled modeling is a fundamental technique in engineering, enabling the study of large and complex systems by creating smaller, manageable replicas that recreate critical characteristics of the original. In hydrology and civil infrastructure, for example, scaled models of dams help analyze water flow, turbulence, and pressure. This method allows for accurate predictions of real-world behavior within a controlled environment, significantly reducing the cost and time involved in full-scale...
151
01:17Open and closed-loop control systems
583
Control systems are foundational elements in automation and engineering. They are broadly categorized into open-loop and closed-loop systems. These classifications hinge on the presence or absence of feedback mechanisms, significantly influencing the system's performance, complexity, and application.
An open-loop control system operates without feedback from the output. It consists of two primary elements: the controller and the controlled process. The controller receives an input signal...
An open-loop control system operates without feedback from the output. It consists of two primary elements: the controller and the controlled process. The controller receives an input signal...
583
01:18Second Order systems II
73
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
73