Mechanical modules of catheters for sensor fusion processes
Systems and methods are described for implementing a catheter model to estimate shape of a deformable catheter in a three-dimensional space. The catheter model includes two or more model segments that correspond to two or more segments of the deformable catheter. Each model segment includes a length and location of model electrode(s) and/or model magnetic sensor(s) corresponding electrodes and/or magnetic sensors of the deformable catheter. Variable shape parameter define a curvature of the segment. Varying the shape parameters generates a plurality of potential catheter shapes. In conjunction with generating the potential catheter shapes, impedance and/or magnetic responses (e.g., measured responses) are obtained for the physical electrodes and/or physical magnetic sensors of the deformable catheter. Using a selected one (e.g., most likely) of the potential catheter shapes and the measured responses, the shape parameters are updated and a catheter shape is generated and displayed.
1. A method for modeling a catheter and estimating catheter shapes, the method comprising:
defining a first model segment and a second model segment corresponding to first and second segments, respectively, of a deformable catheter disposed in a three-dimensional space, each model segment including a segment length and a location along the segment length of a model electrode or model magnetic sensor corresponding to a location of an electrode or magnetic sensor on a corresponding segment of the deformable catheter;
defining a first variable shape parameter for the first model segment and a second variable shape parameter for the second model segment, wherein the variable shape parameters describe curvatures of the first model segment and second model segment, respectfully;
varying, with a computer, the first and second variable shape parameters of the first and second model segments to generate a plurality of potential catheter shapes, where each potential catheter shape includes a model electrode location or a model magnetic sensor location;
obtaining a measured response of an electrode or a magnetic sensor of the deformable catheter while the deformable catheter is disposed in the three-dimensional space;
updating the variable shape parameters based on the measured response and a model electrode location or model magnetic sensor location from a selected one of the plurality of potential catheter shapes; and
generating a catheter shape based on the updating of the variable shape parameters and outputting the catheter shape to a display.
2. The method of claim 1 , for each segment, further comprising:
defining a plurality of model electrode locations along the length of at least one of the first and second model segments.
3. The method of claim 1 , where defining each of the variable shape parameters comprises:
defining a curvature and a torsion for each model segment.
4. The method of claim 1 , wherein the first model segment and the second model segment are continuous.
5. The method of claim 1 , wherein the first variable shape parameter has a first range of curvatures and the second variable shape parameter has a second range of curvatures.
6. The method of claim 1 , wherein modeling further comprises, for each model segment, defining a moving frame that follows an arc of the model segment.
7. The method of claim 6 , wherein the moving frame comprises a Frenet frame.
8. The method of claim 1 , wherein the plurality of catheter shapes are defined in a catheter reference frame.
9. The method of claim 8 , further comprising:
transforming the selected one of the plurality of catheter shapes from the catheter reference frame to a reference frame of the three-dimensional space; and
determining a predicted location of the model electrode of the catheter shape in the three-dimensional space.
10. The method of claim 9 , further comprising:
generating a predicted impedance response for predicted location of the model electrode in the three-dimensional space.
11. The method of claim 10 , wherein the predicted impedance response is utilized with the impedance response of the electrode of the deformable catheter as measured in the three-dimensional space to update the shape parameters.
12. The method of claim 1 , wherein the variable shape parameters comprise state variables, wherein varying the variable shape parameters comprises applying a transformation matrix to the state variables.
13. The method of claim 12 , wherein a Kalman Filter is used to infer the state variables.
14. The method of claim 12 , wherein the plurality of potential catheter shapes comprises a state distribution of potential catheter shapes.
15. The method of claim 14 , further comprising:
applying a function to the estimated state distribution to remove unlikely states from the estimated state distribution and generate an updated state distribution.
16. The method of claim 15 , wherein the selected one of the plurality of potential catheter shapes comprises a mean of the updated state distribution.
17. The method of claim 1 , further comprising:
based on the measured response and a model electrode location or a magnetic sensor location from the selected one the plurality of potential catheter shapes identifying a location of the electrode or the magnetic sensor in the three-dimensional space.
18. The method of claim 1 , wherein the updating of the variable shape parameters occurs at least 50 times per second.
19. A system for modeling a catheter and estimating shapes of the catheter, the system including:
a deformable catheter having an electrode and a magnetic sensor;
a medical positioning system to measure responses of the electrode and magnetic sensor in a three-dimensional space;
a processor and memory for storing non-transitory computer readable instruction to:
access a stored definition of first and second model segments corresponding to first and second segments, respectively of the deformable catheter disposed in a three-dimensional space, each model segment including a segment length and a location along the segment length of a model electrode or model magnetic sensor corresponding to a location of an electrode or magnetic sensor of the deformable catheter;
vary a first variable shape parameter for the first model segment and vary a second variable shape parameter for the second model segment, wherein the variable shape parameters describe curvatures of the first model segment and second model segment, respectfully;
generate a plurality of potential catheter shapes based on the varying of the variable shape parameters, where each potential catheter shape includes a model electrode location or model magnetic sensor location for the first and second model segments;
obtain a measured response of an electrode or a magnetic sensor of the deformable catheter while the deformable catheter is disposed in the three-dimensional space;
update the first and second shape parameters based on the measured response and a model electrode location or magnetic sensor location from a selected one of the plurality of potential catheter shapes; and
generate an updated catheter shape based on the update of the first and second shape parameters; and
a display configured to display the updated catheter shape.
20. The system of claim 19 , further comprising instructions to identify a location of the electrode or magnetic sensor in the three dimensional space based on the measured response a predicted impedance response for the model electrode location or a predicted magnetic response for the model magnetic sensor location.