Methods and systems to produce continuous trajectories from discrete anatomical shapes
A method of estimating changes in an anatomical structure over time. The method includes steps of obtaining a plurality of shapes of an anatomical structure from a plurality of points in time, wherein the plurality of shapes of the anatomical structure includes a baseline shape of the anatomical structure; continuously deforming the baseline shape of the anatomical structure using a growth model parameterized by acceleration; fitting the deformed baseline shape to at least one of the plurality of shapes of the anatomical structure; and using the deformed baseline shape to estimate at least one shape of the anatomical structure at a time corresponding to a time that is different than any of the plurality of points in time.
1. A method of estimating changes in an anatomical structure over time, comprising:
obtaining a plurality of shapes of an anatomical structure from a plurality of points in time, wherein the plurality of shapes of the anatomical structure includes a baseline shape of the anatomical structure;
continuously deforming the baseline shape of the anatomical structure using a growth model parameterized by acceleration comprising modeling shapes as currents comprising modeling an outer surface of the shape as a plurality of shape points, and wherein continuously deforming comprises iteratively calculating an acceleration of the plurality of shape points at a plurality of time points using a gradient descent algorithm, using an initial velocity of zero for each of the plurality of shape points;
fitting the deformed baseline shape to at least one of the plurality of shapes of the anatomical structure; and
using the deformed baseline shape to estimate at least one shape of the anatomical structure at a time corresponding to a time that is different than any of the plurality of points in time.
2. The method of claim 1 , wherein the plurality of shape points has an acceleration field associated therewith, and wherein iteratively calculating an acceleration of the shape points at a plurality of time points further comprises controlling a spatial extent at which the acceleration field varies using a regularity term.
3. The method of claim 2 , wherein fitting the deformed baseline shape to at least one of the plurality of shapes of the anatomical structure comprises fitting the deformed baseline shape to at least one of the plurality of shapes of the anatomical structure using regression.
4. The method of claim 3 , wherein fitting the deformed baseline shape to at least one of the plurality of shapes of the anatomical structure using regression comprises applying a regression criterion, wherein the regression criterion comprises a regularization term which accounts for a total amount of acceleration.
5. The method of claim 1 , wherein modeling shapes as currents comprises calculating growth trajectories as twice differentiable flows of deformations.
6. The method of claim 5 , wherein calculating growth trajectories comprises integrating a second-order ordinary differential equation.
7. The method of claim 1 , further comprising displaying the estimated shape to a user.
8. The method of claim 1 , further comprising measuring a feature of the estimated shape.
9. The method of claim 1 , further comprising at least one of diagnosing and prescribing treatment for a condition based on the estimated shape.
10. The method of claim 9 , wherein the condition is one of autism, Huntington's disease, Alzheimer's disease, Parkinson's disease, schizophrenia, and traumatic brain injury.
11. The method of claim 1 , wherein the plurality of shapes of an anatomical structure are obtained using magnetic resonance imaging, computed tomography, or ultrasound.
12. The method of claim 1 , wherein the plurality of points in time includes at least one of an age of a subject and a timeframe of progression of a disease or disorder, and wherein time is expressed as at least one of days, weeks, months, or years.
13. The method of claim 1 , wherein the anatomical structure is in a human subject.
14. The method of claim 1 , wherein the anatomical structure is one of a brain structure, heart, joint, liver, and kidney.
15. The method of claim 1 , wherein obtaining a plurality of shapes of an anatomical structure from a plurality of points in time comprises co-registering the plurality of shapes of an anatomical structure.
16. A computer-based system for estimating changes in an anatomical structure over time, the system comprising:
a processor; and
a storage medium operably coupled to the processor, wherein the storage medium includes program instructions executable on the processor for
obtaining a plurality of shapes of an anatomical structure from a plurality of points in time, wherein the plurality of shapes of the anatomical structure includes a baseline shape of the anatomical structure;
continuously deforming the baseline shape of the anatomical structure using a growth model parameterized by acceleration comprising modeling shapes as currents comprising modeling an outer surface of the shape as a plurality of shape points, and wherein continuously deforming comprises iteratively calculating an acceleration of the plurality of shape points at a plurality of time points using a gradient descent algorithm, using an initial velocity of zero for each of the plurality of shape points;
fitting the deformed baseline shape to at least one of the plurality of shapes of the anatomical structure; and
using the deformed baseline shape to estimate at least one shape of the anatomical structure at a time corresponding to a time that is different than any of the plurality of points in time.
17. The computer-based system of claim 16 , wherein the plurality of shape points has an acceleration field associated therewith, and wherein program instructions executable on the processor for iteratively calculating an acceleration of the shape points at a plurality of time points further comprise program instructions executable on the processor for controlling a spatial extent at which the acceleration field varies using a regularity term.
18. The computer-based system of claim 17 , wherein program instructions executable on the processor for fitting the deformed baseline shape to at least one of the plurality of shapes of the anatomical structure comprise program instructions executable on the processor for fitting the deformed baseline shape to at least one of the plurality of shapes of the anatomical structure using regression.
19. The computer-based system of claim 18 , wherein program instructions executable on the processor for fitting the deformed baseline shape to at least one of the plurality of shapes of the anatomical structure using regression comprise program instructions executable on the processor for applying a regression criterion, wherein the regression criterion comprises a regularization term which accounts for a total amount of acceleration.
20. The computer-based system of claim 16 , wherein program instructions executable on the processor for modeling shapes as currents comprise program instructions executable on the processor for calculating growth trajectories as twice differentiable flows of deformations.
21. The computer-based system of claim 10 , wherein program instructions executable on the processor for calculating growth trajectories comprise program instructions executable on the processor for integrating a second-order ordinary differential equation.
22. The computer-based system of claim 16 , wherein the system further comprises a graphical user interface and wherein the storage medium further comprises program instructions executable on the processor for displaying the estimated shape to a user on the graphical user interface.
23. The computer-based system of claim 16 , wherein the storage medium further comprises program instructions executable on the processor for measuring a feature of the estimated shape.
24. The computer-based system of claim 16 , further comprising at least one of diagnosing and prescribing treatment for a condition based on the estimated shape.
25. The computer-based system of claim 24 , wherein the condition is one of autism, Huntington's disease, Alzheimer's disease, Parkinson's disease, schizophrenia, and traumatic brain injury.
26. The computer-based system of claim 16 , wherein the plurality of shapes of an anatomical structure are obtained using magnetic resonance imaging.
27. The computer-based system of claim 16 , wherein the plurality of points in time includes at least one of an age of a subject and a timeframe of progression of a disease or disorder, and wherein time is expressed as at least one of days, weeks, months, or years.
28. The computer-based system of claim 16 , wherein the anatomical structure is in a human subject.
29. The computer-based system of claim 16 , wherein the anatomical structure is one of a brain structure, heart, joint, liver, and kidney.
30. The computer-based system of claim 16 , wherein obtaining a plurality of shapes of an anatomical structure from a plurality of points in time comprises co-registering the plurality of shapes of an anatomical structure.
31. A method of estimating changes in an anatomical structure over time, comprising:
obtaining a plurality of shapes of an anatomical structure from a plurality of points in time, wherein the plurality of shapes of the anatomical structure includes a baseline shape of the anatomical structure;
continuously deforming the baseline shape of the anatomical structure using a growth model parameterized by acceleration comprising modeling shapes as currents comprising modeling an outer surface of the shape as a plurality of shape points, and wherein continuously deforming comprises iteratively calculating an acceleration of the plurality of shape points at a plurality of time points using a gradient descent algorithm, further comprising determining an initial velocity for each of the plurality of shape points using geodesic diffeomorphic registration between the baseline and at least one of the plurality of shapes of the anatomical structure,
fitting the deformed baseline shape to at least one of the plurality of shapes of the anatomical structure; and
using the deformed baseline shape to estimate at least one shape of the anatomical structure at a time corresponding to a time that is different than any of the plurality of points in time.