Temporal smoothing of a deformation model
A method and apparatus for approximating a path of movement of a target. The method includes referencing a temporal sequence of images, identifying a plurality of data points associated with a selected volume element of the volume of interest, and calculating an estimated location of the selected volume element based on a cost function having a constraint which favors continuous spatial motion of the selected volume element over time. Each of the images of the temporal sequence of images depicts a volume of interest. Each of the plurality of data points corresponds to one of the images.
1. A computer-implemented method, comprising:
indexing a temporal sequence of images taken at different points in time in a motion cycle with a known temporal relationship, wherein each of the images depicts a spatial volume;
identifying three or more data points, wherein each of the data points describes an estimated spatial position of a selected volume element of the spatial volume in the motion cycle, wherein each of the data points corresponds to one of the images; and
calculating, using the identified data points, an estimated location of the selected volume element based on a function having a constraint which favors smooth motion of the selected volume element over time using a processing device.
2. The method of claim 1 , wherein the constraint comprises a time derivative of motion of at least some of the identified data points.
3. The method of claim 1 , wherein the function implements a polynomial approximation of at least some of the identified data points.
4. The method of claim 3 , wherein calculating the estimated location of the selected volume element further comprises calculating a new data point consistent with the polynomial approximation.
5. The method of claim 4 , further comprising replacing one of the identified data points with the new data point.
6. The method of claim 4 , further comprising predicting a future data point associated with the selected volume element based on the new data point.
7. The method of claim 4 , further comprising inserting the new data point between two of the identified data points.
8. The method of claim 4 , further comprising developing a deformation model for a volume of interest structure within the volume of interest based on the new data point.
9. The method of claim 8 , wherein the volume of interest structure comprises a target.
10. The method of claim 8 , wherein the volume of interest structure comprises a critical structure.
11. The method of claim 1 , wherein the motion cycle is at least a portion of a respiratory cycle of a patient.
12. The method of claim 11 , wherein the temporal sequence of images comprises at least three temporally disparate images of the temporal sequence of images.
13. The method of claim 1 , further comprising applying the function to one of the plurality of identified data points to generate a new spatial data point relative to a plurality of spatial data points associated with one of the images.
14. The method of claim 1 , wherein calculating the estimated location of the selected volume element further comprises applying the function to the selected volume element to favor spatial continuity of the selected volume element and surrounding volume elements in a corresponding image.
15. The method of claim 1 , further comprising computing a cumulative deformation field of the data points, wherein the cumulative deformation field comprises a plurality of relative deformation fields, wherein each of the plurality of relative deformation fields relates to a difference between adjacent data points of the data points.
16. The method of claim 1 , further comprising computing individual deformation fields of the data points, wherein each of the individual deformation fields relates to a difference between a reference data point of the data points and another data point of the data points.
17. An apparatus, comprising:
a data storage device to store a plurality of temporally sequential images taken at different points in time in a motion cycle with a known temporal relationship, wherein the plurality of temporally sequential images include a volume of interest structure; and
a digital processing device coupled to the data storage device, the digital processing device to calculate a polynomial approximation of a temporal path of movement of a selected volume element of the volume of interest structure during the motion cycle using three or more of the temporally sequential images taken at three or more points in time in the motion cycle, and to calculate an estimated location of the selected volume element based on the polynomial approximation.
18. The apparatus of claim 17 , wherein the digital processing device is further configured to calculate a new data point consistent with the polynomial approximation, wherein the polynomial approximation represents a deformation model of a part of the selected volume element of the volume of interest structure.
19. The apparatus of claim 18 , wherein the new data point replaces one of the time points in the motion cycle.
20. The apparatus of claim 18 , wherein the new data point supplements the time points in the motion cycle.
21. The apparatus of claim 17 , wherein the polynomial approximation defines a continuous, non-discrete movement over time of the selected volume element of the volume of interest structure.
22. The apparatus of claim 17 , wherein the data storage device is further configured to store a representation of the polynomial approximation and a new data point corresponding to the estimated location of the selected volume of interest.
23. The apparatus of claim 22 , further comprising a graphical display to display a graphical representation of the polynomial approximation and the new data point corresponding to the estimated location of the selected volume of interest.
24. The apparatus of claim 23 , wherein the graphical display is further configured to display a graphic representation of a plurality of identified data points associated with temporally distinct locations of the selected volume element of the volume of interest structure.
25. The apparatus of claim 17 , further comprising:
a diagnostic imaging system coupled to the digital processing device, the diagnostic imaging system to obtain the plurality of temporally sequential images; and
a treatment delivery system coupled to the digital processing device, the treatment delivery system to deliver radiation treatment to the volume of interest structure according to a deformation model based on the polynomial approximation of the temporal path of movement of the selected volume element of the volume of interest structure.
26. A computer readable storage medium having instructions thereon, which instructions, when executed by a digital processing device, cause the digital processing device to perform the following, comprising:
reference a temporal sequence of images taken at different points in time in a motion cycle with a known temporal relationship, wherein each of the images depicts a volume of interest;
identify three or more data points associated with a selected volume element of the volume of interest in the motion cycle, wherein each of the data points corresponds to one of the images; and
calculate an estimated location of the selected volume element based on a polynomial approximation of at least some of the identified data points.
27. The computer readable storage medium of claim 26 , having further instructions thereon, which further instructions, when executed by the digital processing device, cause the digital processing device to perform the following, comprising calculate a new data point consistent with the polynomial approximation.
28. The computer readable storage medium of claim 27 , having further instructions thereon, which further instructions, when executed by the digital processing device, cause the digital processing device to perform the following, comprising replace one of the identified data points with the new data point.
29. The computer readable storage medium of claim 27 , having further instructions thereon, which further instructions, when executed by the digital processing device, cause the digital processing device to perform the following, comprising predict a future data point associated with the selected volume element based on the new data point.
30. The computer readable storage medium of claim 27 , having further instructions thereon, which further instructions, when executed by the digital processing device, cause the digital processing device to perform the following, comprising develop a deformation model for a volume of interest structure within the volume of interest based on the new data point.
31. The computer readable storage medium of claim 26 , having further instructions thereon, which further instructions, when executed by the digital processing device, cause the digital processing device to perform the following, comprising apply a spatial smoothing function to one of the plurality of identified data points to generate a new spatial data point relative to a plurality of spatial data points associated with one of the images.
32. The computer readable storage medium of claim 26 , having further instructions thereon, which further instructions, when executed by the digital processing device, cause the digital processing device to perform the following, comprising compute a cumulative deformation field of the data points, wherein the cumulative deformation field comprises a plurality of relative deformation fields, wherein each of the plurality of relative deformation fields relates to a difference between adjacent data points of the data points.
33. The computer readable storage medium of claim 26 , having further instructions thereon, which further instructions, when executed by the digital processing device, cause the digital processing device to perform the following, comprising compute individual deformation fields of the data points, wherein each of the individual deformation fields relates to a difference between a reference data point of the data points and another data point of the plurality of data points.
34. An apparatus, comprising:
means for identifying a deformation model for a selected volume element over time, wherein the deformation model comprises three or more data points corresponding to a temporal sequence of images taken at different points in time in a motion cycle with a known temporal relationship, wherein each of the data points describes an estimated spatial position of the selected volume element in the motion cycle; and
means for modifying the deformation model based on an assumption that the selected volume element moves along a continuous path over time.
35. The apparatus of claim 34 , further comprising means for approximating the deformation model.
36. The apparatus of claim 34 , further comprising means for generating a new data point which is consistent with an approximation of the deformation model.
37. The apparatus of claim 36 , further comprising means for replacing one of the data points of the identified deformation model.
38. The apparatus of claim 36 , further comprising means for predicting a future data point of the identified deformation model.