Computer-implemented method for estimating range of motion of a joint connecting bones
A system and method ( 100 ) for estimating range of motion of a joint ( 3 ) connecting a first bone ( 5 ) to a second bone ( 7 ), the joint comprising a point of rotation ( 9 ) defining rotation of the first bone relative to the second bone. The method comprises: obtaining ( 110 ) a digital model of the joint that includes, for each bone ( 5, 7 ), respective mesh models with sets of mesh points that represent the bone; determining ( 120 ) polar coordinates for the set of mesh points, with the point of rotation ( 9 ) as a pole ( 21 ) of the polar coordinates; and calculating ( 130 ), based on the polar coordinates, multiple angular distance values relating to rotation of the joint, where the multiple angular distance values are indicative of an angular distance between points in the set of mesh points, and the angular distance being indicative of the range of motion of the joint.
1 . A computer-implemented method for estimating range of motion of a joint connecting a first bone to a second bone, the joint comprising a point of rotation defining rotation of the first bone relative to the second bone about the point of rotation, the method comprising:
generating a digital model of the joint, the digital model comprising:
a first mesh model representing the first bone and comprising a first set of mesh points; and
a second mesh model representing the second bone and comprising a second set of mesh points;
determining polar coordinates for at least one of the first set of mesh points and the second set of mesh points, with the point of rotation as a pole of the polar coordinates;
calculating, based on the polar coordinates, multiple angular distance values relating to rotation of the joint, each of the multiple angular distance values being indicative of an angular distance between one point in the first set and one point in the second set, and the angular distance being indicative of the range of motion of the joint; and
generating a visualization of the digital model, wherein a visual appearance of the first set of mesh points and the second set of mesh points is indicative of the angular distance value, wherein the visual appearance is a color value, and wherein the color value represents attainment, or failure to attain, a specified anatomic range of motion value.
2 . The method of claim 1 , wherein calculating the multiple angular distance values comprises selecting for a point in the first set, a point in the second set that is the nearest neighbor of the point in the first set based on the polar coordinates.
3 . The method of claim 1 , wherein the method comprises performing a nearest neighbor search.
4 . The method of claim 3 , wherein the nearest neighbor search is based on a space-partitioning data structure.
5 . The method of claim 4 , wherein the space-partitioning data structure comprises a k-d tree.
6 . The method of claim 1 , wherein the method comprises determining an angular distance value for multiple points on opposing surfaces of the first bone and the second bone.
7 . The method of claim 1 , wherein the angular distance value is a difference in an angle between the first set of mesh points and the second set of mesh points.
8 . The method of claim 1 , wherein the polar coordinates are two-dimensional comprising one distance value and one angle value.
9 . The method of claim 1 , wherein the polar coordinates are supplemented with an azimuthal angle to define spherical coordinates in three-dimensional space.
10 . The method of claim 1 , wherein the digital model of the joint comprises a digital model of an implant that replaces a part of at least one of the first bone, the second bone, or another implant, and defines the rotation of the first bone relative to the second bone.
11 . The method of claim 10 , wherein the method comprises:
receiving an update on the digital model of the implant; and
re-calculating the multiple angular distance values based on the update.
12 . The method of claim 11 , wherein the update comprises position information of the implant.
13 . The method of claim 12 , wherein the update comprises a cut angle of the first bone or the second bone.
14 . The method of claim 1 , wherein at least one of the first mesh model and the second mesh model is a triangular mesh model defined by multiple triangles approximating a surface of the respective first bone and second bone.
15 . The method of claim 14 , wherein at least one of the first set of mesh points and the second set of mesh points comprise one or more of:
vertices of the triangles, and centroids of the triangles.
16 . A computer system for estimating range of motion of a joint connecting a first bone to a second bone, the joint comprising a point of rotation defining rotation of the first bone relative to the second bone about the point of rotation, wherein the computer system comprises:
at least one processor configured to:
generate a digital model of the joint, the digital model comprising:
a first mesh model representing the first bone and comprising a first set of mesh points; and
a second mesh model representing the second bone and comprising a second set of mesh points;
determine polar coordinates for at least one of the first set of mesh points and the second set of mesh points, with the point of rotation as a pole of the polar coordinates;
calculate, based on the polar coordinates, multiple angular distance values relating to rotation of the joint, each of the multiple angular distance values being indicative of an angular distance between one point in the first set and one point in the second set, and the angular distance being indicative of the range of motion of the joint; and
generate a visualization of the digital model, wherein a visual appearance of the first set of mesh points and the second set of mesh points is indicative of the angular distance value, wherein the visual appearance is a color value, and wherein the color value represents attainment, or failure to attain, a specified anatomic range of motion value.
17 . The computer system of claim 16 , wherein the at least one processor is configured to:
select, for a point in the first set, a point in the second set that is the nearest neighbor of the point in the first set based on the polar coordinates.
18 . The computer system of claim 16 , wherein the at least one processor is configured to:
receive an update on the digital model of the implant; and
re-calculating the multiple angular distance values based on the update.