Relative Cardiovascular Pressure Computation via Finite Element PPE
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Solution Overview
Problem
Current methods for computing cardiovascular pressure fields from blood flow data are inaccurate due to the need for iterative solutions and boundary conditions, especially when dealing with noisy input data and high Reynolds number flows.
Innovation Solution
A finite element discretization method is applied to the Pressure Poisson Equation (PPE), which defines a higher-order derivative of the pressure field, allowing for direct computation of relative pressure fields from flow-sensitive data without requiring surface fluxes or boundary conditions, using a weak formulation and Galerkin finite element discretization to solve for cardiovascular pressure fields.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If iterative solutions with boundary conditions are used to compute pressure fields, then pressure information can be obtained, but computational complexity increases and accuracy decreases due to sensitivity to boundary conditions
Solution Approach 1:
The patent extracts and eliminates the need for boundary conditions by reformulating the pressure Poisson equation to compute pressure differences directly from velocity fields. This removes the problematic iterative solution process and boundary condition specifications, directly resolving the contradiction between accuracy and computational complexity.
Solution Approach 2:
Instead of computing pressure fields from boundary conditions (traditional approach), the patent inverts the approach by computing pressure differences directly from known velocity fields. This inversion eliminates the need for iterative solutions and boundary condition specifications, simultaneously improving accuracy and reducing computational complexity.
2Ease of manufacture
If viscous terms are neglected in pressure calculation, then computation is simplified, but accuracy deteriorates for low Reynolds number flows
Solution Approach 1:
The patent changes the formulation parameter from neglecting viscous terms (simplified model) to including them in the pressure Poisson equation (comprehensive model). By using the full equation with viscous terms and solving it directly without iteration, the method achieves both accuracy for low Reynolds number flows and computational efficiency.
3Measurement precision
If boundary conditions are imposed on fluid domain, then pressure fields can be determined, but the method becomes less adaptable to actual imaging space
Solution Approach 1:
The patent removes the requirement for boundary condition specification, which eliminates the need to define fluid domain boundaries. This allows direct application to actual imaging spaces without requiring separate fluid domain identification or boundary condition imposition, simultaneously maintaining pressure field determination accuracy and improving adaptability to imaging data.
Data Source
AI summary
The present invention provides a method for the determination of relative pressure fields from flow-sensitive data, the method comprising: applying a finite element discretization to the Pressure Poisson Equation (PPE):b=f+μΔu-ρ(∂u∂t+((u-w)·∇)u)where vecter b is a function of a given blood velocity data, u represents the velocity, w the reference velocity, t the time, f a volume force, p the pressure and ρ and μ the fluid density and viscosity, respectively, and wherein the PPE is now defined as the divergence of the above equation and gives a higher order derivative of the pressure field p: Δp=∇·b.