Semi automatic vortex extraction in 4 d pc-mri cardiac blood flow data using line predicates

Semi-Automatic Vortex Extraction in 4D PC-MRI Cardiac Blood Flow Data Using Line Predicates

Authors: Benjamin Kohler Rocco Gasteiger Uta Preim Holger Theisel Matthias Gutberlet Bernhard Preim

Presented by: Subhashis Hazarika,

Ohio State University

Motivation

• Many Cardiovascular Diseases (CVD) can be detected based on the blood flow characteristics of the patients.

• The data collected by the 4D PC-MRI allows the quantitative and qualitative analysis of hemodynamics.

• This paper focuses on detection of vortex flow on the human aorta and pulmonary artery.

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Workflow

Data Acquisition & Pre-processing

Vortex Extraction (via local criteria)

Extended Line Predicates

Post-processing

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Workflow(1)

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Line Predicates

• Line predicate P is a boolean function mapping a point p of a pathline to true or false. [Salzbrunn et al.]

• Predicate filters out points that don’t lie within a certain interval. All remaining points (for which value was true) are called characteristic set.

• D is the domain of the flow field . I is the set of all temporal positions.

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Line Predicates(1)

• Basic Intuition : We can apply different set operation on CS to come up with hybrid line predicates.

• Classification of line predicates[Born et al.]:

Line based or Geometry Predicates :

• Depends solely on pathlines’ geometry e.g curvature

Derived or Flow Field Predicates :

• Depends on the underlying flow field parameters e.g velocity, local vortex criteria.

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Line Predicates(2)

• Mesh Predicate : e.g minimal distance of a point to the surface.

• Stream Predicate : depends on surrounding pathlines. E.g no. of pathlines weighted by their distance to each other can be used as density value.

• Sum Predicate :

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Line Predicates(3)

• Mean Predicate : assigns the avg value to each point. i.e, sum predicate divided by N.

• Smoothing Predicate : one- dimensional binomial filter with kernel size 3 in n iterations to the values along an integral line.

• Representation:

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Line Predicates(4)

• Threshold:

• Example:

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Pathline Integration and Vortex Extraction

• Initialization : Put the whole dataset in a segmentation mask with uniformly distributed seed positions.

• Vector Interpolation and Pathline Integration: Trilinear interpolation to get a vector in 3D flow field in one particular temporal position.

Quadrilinear interpolation for vectors in spatio-temporal domain.

• Jacobian Matrix Estimation: Calculation of a Jacobian Matrix for a whole voxel will deliver discontinuities at voxel

boundaries.

Hence use central differences of interpolated vectors, with offset corresponding to one voxel dimension.

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Pathline Integration and Vortex Extraction(1)

• Line Predicate 1 – Finding Vortices:

Leaves behind longer line segment.

Reduces non-swirling regions within a segment.

Fragmentation problem remains to an extent.

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Pathline Integration and Vortex Extraction(2)

• Line Predicate 2 – Refining the Vortex Shapes: Csdc

• Line Predicate 3 – Postprocessing: Cv

This the sum predicate of curvature values.

Proper threshold preserves long curved pathlines.

• Visualization:

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Comparison of Local Vortex Criteria

• Investigate which vortex criterion provides the best results.

• Quality Criteria: Fixed Minimum and Maximum.

Implicit Threshold.

Constant Vortex Core Values.

Correctness.

Helical and Vortical Flow.

Vortex Shape.

Pathline Quality.

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Comparison of Local Vortex Criteria(1)

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Comparison of Local Vortex Criteria(2)

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Comparison of Local Vortex Criteria(3)

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Comparison of Local Vortex Criteria(4)

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Summary

• Final parameters of the model used.

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Thank You

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