Distributed Lumped Parameter Model for Blood Flow Dynamics
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Solution Overview
Problem
Current image-based computational fluid dynamics (CFD) for blood flow dynamics is computationally expensive, prone to numerical instabilities, and limited in clinical translation due to its complexity, making it challenging for parametric analyses and uncertainty quantification in cardiovascular applications.
Innovation Solution
A distributed lumped parameter (DLP) modeling framework that uses analytical expressions to describe energy losses along vascular segments, incorporating viscous dissipation, unsteadiness, flow separation, vessel curvature, and bifurcations, reducing the computational effort and complexity compared to traditional CFD methods.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If image-based computational fluid dynamics (CFD) is used to study blood flow dynamics, then comprehensive hemodynamic analysis is enabled, but computational cost and complexity increase significantly
Solution Approach 1:
The vascular system is divided into discrete vascular segments, each represented by a lumped parameter model (resistor, capacitor, inertance elements). This segmentation transforms the continuous CFD problem into a discrete network of simple elements, reducing computational complexity while preserving hemodynamic analysis capabilities.
Solution Approach 2:
A lumped parameter network (LPN) model is created as a simplified copy of the full CFD model. The LPN replicates the essential hemodynamic behavior (pressure-flow relationships) using ordinary differential equations and algebraic equations, providing a computationally efficient surrogate that maintains measurement precision for clinical decision-making.
2Measurement precision
If image-based computational fluid dynamics (CFD) is used for blood flow analysis, then comprehensive hemodynamic features are resolved, but numerical instabilities and sensitivity to parameters increase
Solution Approach 1:
The lumped parameter model uses simple, computationally inexpensive elements (resistors, capacitors, inertances) that are numerically stable and less sensitive to parameter variations. These simplified models replace the complex, computationally expensive CFD simulations that suffer from numerical instabilities, providing reliable results for clinical applications.
3Productivity
If lumped parameter network (LPN) models are used to describe vascular territories, then computational cost is reduced, but continuous spatial variations in flow and pressure are not resolved
Solution Approach 1:
The LPN model incorporates local quality by assigning different parameter values (resistance, capacitance, inertance) to each vascular segment based on its specific geometric and physiological characteristics. This allows the model to capture local hemodynamic variations while maintaining computational efficiency, and can be refined by adding more segments to resolve specific spatial variations of interest.
4Device complexity
If traditional Poiseuille flow assumptions are used in LPN models, then model simplicity is maintained, but energy dissipation from unsteadiness, kinetic effects, and vessel curvature is not captured
Solution Approach 1:
The model transitions from simple Poiseuille resistance to more sophisticated resistance formulations that account for unsteady flow effects, kinetic energy changes, and vessel curvature. This is achieved by modifying the resistance parameter to include additional terms that capture these physical effects, thereby improving energy loss accuracy while maintaining the LPN framework's computational efficiency.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The DLP framework achieves consistent agreement with CFD simulations with mean errors less than 7% in flow rate and pressure, significantly lowering computational costs, enabling timely decision support and broader clinical applications for hemodynamics modeling.
Implementation Method 1
The proposed techniques generally rely on principles of fluid mechanics to develop a subject-specific lumped parameter network (LPN) of resistors (a surrogate model) describing expected energy losses along vascular segments, including from viscous dissipation
Implementation Method 2
The proposed techniques generally rely on principles of fluid mechanics to develop a subject-specific lumped parameter network (LPN) of resistors (a surrogate model) describing expected energy losses along vascular segments, including from viscous dissipation, unsteadiness, flow separation, vessel curvature and vessel bifurcations
Data Source
AI summary
A computer-implemented method can include generating centerlines of a patient's cardiovascular network, determining geometric features of the cardiovascular network based on the centerlines and a three-dimensional (3D) computer model of the cardiovascular network, constructing a lumped parameter network (LPN) of resistors corresponding to the cardiovascular network, and solving a system of equations corresponding to flow and pressure for the LPN model.