Hemodynamic Force Calculation from Boundary Meshes
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Solution Overview
Problem
Current methods for determining hemodynamic forces within heart chambers, such as Echo-PIV and 4D Flow MRI, are either invasive, costly, or mathematically complex, and often require expensive equipment and time-consuming procedures, limiting their practical application in clinical settings.
Innovation Solution
A computer-implemented method that uses sequences of images to calculate hemodynamic forces by expressing the container boundary as meshes, determining instantaneous velocity vectors, and integrating surface parameters to estimate forces exchanged between the fluid and the container, allowing for non-invasive and efficient estimation of intraventricular pressure gradients and total hemodynamic force vectors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If 4D Flow MRI is used to evaluate hemodynamic forces, then measurement precision and reliability are improved, but device complexity, cost, and procedure time increase
Solution Approach 1:
The patent extracts the essential information needed for hemodynamic force calculation from the boundary surface motion, eliminating the need for complex 4D Flow MRI procedures. By using only the boundary surface sequences and applying the derived mathematical formula, the method achieves accurate force measurement without requiring expensive MRI equipment and time-consuming 3D velocity field acquisition and post-processing.
Solution Approach 2:
The patent creates a simplified mathematical model that copies the essential physics of fluid-force interaction without requiring direct measurement of the complex 3D velocity field. The formula F(t) = ρ · d/dt ∫_S(t) (x(s,t) × v(s,t)) × n(s,t) ds provides a direct computational approach that replicates accurate force calculation while avoiding the complexity of 4D Flow MRI.
2Ease of operation
If Echo-PIV or Doppler-based methods are used, then ease of operation is improved, but measurement precision deteriorates
Solution Approach 1:
The patent introduces an intermediary mathematical relationship that connects boundary surface motion to hemodynamic forces without requiring direct measurement of the complex 3D velocity field. By using the boundary surface sequences and applying the derived formula, the method achieves both ease of operation (using standard echocardiographic imaging) and acceptable precision through the mathematical transformation rather than direct velocity measurement.
3Ease of operation
If simplified methods using boundary motion are used, then ease of operation and cost are improved, but measurement precision may deteriorate
Solution Approach 1:
The patent changes the parameters being measured from complex 3D velocity fields to boundary surface position and normal vectors. By transforming the measurement problem into boundary surface analysis, the method maintains simplicity and reduces equipment requirements while preserving measurement precision through the mathematically derived relationship between boundary motion and hemodynamic forces.
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
This method provides a simple and efficient way to estimate hemodynamic forces, reducing the need for invasive procedures and costly equipment, while offering accurate results comparable to existing methods, making it suitable for clinical practice.
Implementation Method 1
By using the law of conservation of momentum we have F(t) is the hemodynamic force vector, ρ is the fluid density, v(x,t) is the fluid velocity vector field measured at time t at all points x inside the chamber volume V(t)
Implementation Method 2
Using the Reynolds transport theorem, the integral (1) can be rewritten as... where now integration over the fixed points x inside the volume V(t) assumed as instantaneously fixed
Data Source
AI summary
The disclosure relates to a method for determining one or more parameters related to the forces exchanged between a fluid and a surrounding container from sequences of images of the boundary surface of such container, the method comprising: a) expressing the boundary surface S(t) of the container as a series of meshes s, each mesh identified by a position vector x(s,t); b) calculating, or receiving in input, the instantaneous velocity vector v(s,t) at each position x(s,t); c) calculating, or receiving in input, the vector n(s,t) normal to the surface at each position x(s,t); d) calculating at each position x(s,t) a surface parameter f(s,t) as a function of the velocity vector v(s,t), the position vector x(s,t) and the normal vector n(s,t); e) deriving the parameter or the parameters related to the forces exchanged between the fluid and the surrounding container from such surface parameter f(s,t). A corresponding system and computer program are also disclosed.