Regularization of blood motion fields by modified Navier-Stokes equations.

Area of Science:

• Fluid Dynamics
• Computational Mechanics
• Biomedical Engineering

Background:

• Accurate estimation of incompressible fluid motion fields is crucial in various scientific and engineering disciplines.
• Existing methods may struggle with noisy or scattered data, limiting their applicability.
• Navier-Stokes equations are fundamental but require regularization for practical, data-driven applications.

Purpose of the Study:

• To present a novel regularization technique for incompressible fluid motion fields.
• To validate the technique using a known fluid dynamics problem (Couette flow) with simulated noisy data.
• To apply the method for estimating blood velocity fields from echocardiographic data.

Main Methods:

• Development of a regularization technique based on modified Navier-Stokes equations.
• Classification of the technique within Tikhonov-type regularization methods.
• Application to Couette flow with generated noisy and scattered velocity fields for accuracy evaluation.

Main Results:

• The regularization technique demonstrates excellent accuracy in reconstructing analytical velocity fields.
• Accuracy is dependent on a regularization parameter, with an optimal value identified based on noise levels.
• Successful application to real-world echocardiographic data for left ventricle blood flow estimation.

Conclusions:

• The proposed regularization method effectively handles noisy and scattered fluid motion data.
• The technique offers a robust approach for fluid field reconstruction in challenging conditions.
• This method shows promise for quantitative analysis of blood flow dynamics in cardiovascular imaging.