Graph-based hemodynamics for biomarkers of neurovascular resilience

1 . An apparatus comprising:

input circuitry configured to acquire imaging data corresponding to a branched biological structure; and

image processing circuitry configured to:

extract, from the imaging data, a configuration of the branched biological structure;

determine graph data indicative of the configuration of the branched biological structure,

wherein the graph data comprises edges corresponding to branches of the branched biological structure and vertices corresponding to connections between said branches of the branched biological structure,

wherein the graph data is non-hierarchical graph data comprising one or more loops and multiple roots, and

wherein the image processing circuitry is configured to, as part of the determining of the graph data:

determine for each said edge, at least one geometrical property of the corresponding branch of the branched biological structure; and

determine a biomechanical lumped parameter associated to the geometrical property;

detect, based on the graph data, a biological characteristic of the branched biological structure,

wherein the image processing circuitry is configured to, as part of the detecting a biological characteristic:

translate the determined biomechanical lumped parameters into an analog closed-circuit configuration; and

simulate approximations of fluid flow and fluid pressure drop in said branched biological structure by solving said analog closed-circuit;

modify the graph data with a biologically plausible modification, wherein the image processing circuitry is configured to modify the graph data to at least one of remove at least one edge of the graph data and remove at least one node of the graph data;

re-detect, based on the modified graph data, the biological characteristic of the branched biological structure;

iteratively repeat the modifying of the graph data and the re-detecting of the biological characteristic;

based on the detection of the biological characteristic and the re-detections of the biological characteristic, determine a statistical likelihood associated with the biological characteristic; and

based on the statistical likelihood, determine a statistical susceptibility of the branched biological structure to a pathology.

2 . An apparatus according to claim 1 , wherein said at least one geometrical property of the corresponding branch comprises at least one of:

a length of the corresponding branch; and

a width of the corresponding branch.

3 . An apparatus according to claim 1 , wherein the image processing circuitry is configured to determine, for each said vertex and based on said geometric properties associated with each said edge, at least one fluid property associated with the corresponding connection of the branched biological structure,

said detecting of the biological characteristic being based on said at least one fluid property of said vertices.

4 . An apparatus according of claim 3 , wherein said at least one fluid property associated with the corresponding connection comprises at least one of:

a fluid pressure at the corresponding connection; and

a fluid flow through the corresponding connection.

5 . An apparatus according to claim 3 , wherein the image processing circuitry is configured to determine at least one fluid property associated with the corresponding connection of the branched biological structure by performing computational fluid dynamical modelling with the graph data as an input.

6 . An apparatus according to claim 1 , wherein the modifying of the graph data, by the image processing circuitry, corresponds to a modification of the configuration of the biological structure.

7 . An apparatus according to claim 6 , wherein the image processing circuitry is configured to determine the modification of the biological structure based on a potential future physical modification of the biological structure.

8 . An apparatus according to claim 6 , wherein the image processing circuitry is configured to modify the graph data to at least one of:

add at least one edge to the graph data;

add at least one node to the graph data;

modify a width associated with at least one edge of the graph data; and

modify a length associated with at least one edge of the graph data.

9 . An apparatus according to claim 1 , wherein said branched biological structure is a network of blood vessels.

10 . An apparatus according to claim 1 , wherein the imaging data is an angiographic image and the image processing circuitry is configured to, as part of the determining of the graph data:

extracting a geometrical centerline, or vascular minimal path, π from a topologically connected set II of the angiographic image; and

obtaining a reformatted volume V rf by intersecting the angiographic image with orthogonal cross-sections to the geometrical centerline, or vascular minimal path, x, the orthogonal cross-sections being further mapped with planar diffeomorphisms.

11 . An apparatus according to claim 1 , wherein the image processing circuitry is configured to, as part of extracting the configuration of the branched biological structure:

delineating and segmenting the acquired imaging data by way of geodesic active contours.

12 . A method comprising:

acquiring imaging data corresponding to a branched biological structure;

extracting, from the imaging data, a configuration of the branched biological structure;

determining graph data indicative of the configuration of the biological structure,

wherein the graph data comprises edges corresponding to branches of the branched biological structure and vertices corresponding to connections between said branches of the branched biological structure, wherein the graph data is non-hierarchical graph data comprising one or more loops and multiple roots, and

wherein determining the graph data comprises:

determining for each said edge, at least one geometrical property of the corresponding branch of the branched biological structure; and

determining a biomechanical lumped parameter associated to the geometrical property;

detecting, based on the graph data, a biological characteristic of the branched biological structure,

wherein detecting the biological characteristic comprises:

translating the determined biomechanical lumped parameters into an analog closed-circuit configuration; and

simulating approximations of fluid flow and fluid pressure drop in said branched biological structure by solving said analog closed-circuit;

modifying the graph data with a biologically plausible modification, wherein modifying the graph data comprises at least one of removing at least one edge of the graph data and removing at least one node of the graph data;

re-detecting, based on the modified graph data, the biological characteristic of the branched biological structure;

iteratively repeating the modifying of the graph data and the re-detecting of the biological characteristic;

based on the detection of the biological characteristic and the re-detections of the biological characteristic, determining a statistical likelihood associated with the biological characteristic; and

based on the statistical likelihood, determining a statistical susceptibility of the branched biological structure to a pathology.

13 . A non-transitory computer-readable medium comprising computer-implementable instructions for causing a computer to become configured to carry out the method of claim 12 .