Generating scanning spot locations for laser eye surgery

• US 6,673,062 B2
• Filed: 03/13/2001
• Issued: 01/06/2004
• Est. Priority Date: 03/14/2000
• Status: Expired due to Term

• Current Assignee: Amo Manufacturing Usa, Llc (Johnson & Johnson)
• Original Assignee: VISX Incorporated (Johnson & Johnson)
• Inventors: Yee, Kingman, Gross, Erik
• Primary Examiner(s): Dvorak, Linda C. M.
• Assistant Examiner(s): Farah, Ahmed M
• Application Number:
  US09/805,737
• Publication Number:
  US 20020035359A1
• Time in Patent Office: 1,029 Days
• Field of Search: 606/4-6, 606/8-11, 128/898, 351/211-216
• US Class Current: 606/5
• CPC Class Codes: A61F 2009/00844 Feedback systems
• CPC Class Codes: A61F 2009/00872 Cornea
• CPC Class Codes: A61F 2009/0088 based on wavefront
• CPC Class Codes: A61F 2009/00882 based on topography
• CPC Class Codes: A61F 2009/00897 Scanning mechanisms or algorithms
• CPC Class Codes: A61F 9/008 using laser
• CPC Class Codes: A61F 9/00804 Refractive treatments

Abstract

Scanning spot locations are generated for ablating tissue using a scanning laser beam over a treatment region by fitting a target function representing a desired lens profile of ablation with a basis function representing a treatment profile produced by overlapping scanning spots in a particular treatment pattern. Symmetry effects are utilized to simply the process for determining the scanning spot locations. In some embodiments, the basis function is a two-dimensional function representing a two-dimensional section of a tree-dimensional treatment profile which has symmetry with respect to the two-dimensional section extending along the treatment pattern. The target function and the basis function are fitted to produce ablation depths for discrete scanning spots which are used to calculate the number of pulses at each reference position along the two-dimensional section.

Claims

1. A method of generating a treatment table for ablating tissue using a scanning laser beam for generating scanning spots over a treatment region larger in area tan the scanning spots, the method comprising:

providing a target function representing a desired lens profile for ablating the tissue by scanning spots of the laser beam on the tissue to achieve a desired removal of the tissue by ablating the tissue according to the desired lens profile represented by the target function;

providing a user-specified basis function representing a treatment profile produced by scanning with overlapping scanning spots of the laser beam to be centered at a plurality of scanning spot locations on the tissue in a user-specified treatment pattern; and

fitting the target function with the user-specified basis function to obtain a treatment table including scanning spot locations and characteristics for the overlapping scanning spots of the laser beam, such that an ablation employing the user-specified basis function according to the scanning spot locations and characteristics of the treatment table will substantially achieve the desired removal of the tissue as represented by the target function.

2. The method of claim 1 wherein the basis function is a two-dimensional function representing a two-dimensional section of a three-dimensional treatment profile which has symmetry with respect to the two-dimensional section extending along the treatment pattern.

3. The method of claim 2 wherein the treatment pattern is generally linear or generally circular.

4. The method of claim 1 wherein the target function is a two-dimensional function representing a two-dimensional section of a three-dimensional lens profile which has symmetry with respect to the two-dimensional section extending along the treatment pattern.

5. The method of claim 4 wherein the target function represents an ablation depth as a function of a distance from an optical axis of a cornea.

6. The method of claim 1 wherein fitting the target function and the basis function comprises evaluating closeness of the fit and repeating the fitting step if the closeness does not fall within a target closeness.

7. The method of claim 1 wherein the target function and the basis function are fitted using a least square fit.

8. The method of claim 1 further comprising randomizing the scanning spot locations of the treatment table to produce a random scanning order.

9. A The method of claim 1 further comprising refitting the target function with the basis function by varying the size of at least one of the scanning spots to iterate for a best fit.

10. The method of claim 1 wherein the scanning spot characteristics of a scanning spot at a scanning spot location include shape, size, and depth of the scanning spot at the scanning location.

11. The method of claim 1 wherein the scanning spots have different sizes.

12. The method of claim 1 further comprising specifying the treatment pattern for scanning with overlapping scanning spots of the laser beam.

13. The method of claim 1 wherein the target function and the basis function are fitted using a simulated annealing process.

14. The method of claim 1 further comprising specifying a merit function representing an error of fit between the target function and the basis function;

and minimizing the merit function.

15. The method of claim 1 further comprising specifying a merit function representing an error of fit between the target function and the basis function;

monitoring a total number of the scanning spots in the treatment table; and

minimizing the merit function and the total number of the scanning spots in the treatment table.

16. The method of claim 1 further comprising refitting the target function with the basis function by selecting a scanning spot location and varying the characteristics of the scanning spot at the selected location to iterate for a best fit.

17. A method of generating a treatment table for ablating tissue using a scanning laser beam for generating scanning spots over a treatment region larger in area than the scanning spots, the method comprising:

providing a target function representing a desired lens profile for ablating the tissue by scanning spots of the laser beam on the tissue;

providing a basis function representing a treatment profile produced by scanning with overlapping scanning spots of the laser beam to be centered at a plurality of locations on the tissue in a treatment pattern; and

fitting the target function with the basis function to obtain a treatment table including scanning spot locations and characteristics for the overlapping scanning spots of the laser beam;

wherein fitting the target function with the basis function includes fitting at N discrete evaluation points.

18. The method of claim 17 wherein fitting the target function and the basis function comprises specifying a deviation for each of the N discrete evaluation points.

19. The method of claim 18 further comprising refitting the target function with to basis function by varying the deviations to iterate for a best fit.

20. The method of claim 17 wherein the target function is:

(A) for myopia and myopic cylinder, $f<br><br>\left(x_j\right)=\sqrt{R_1^2-x_j^2}-\sqrt{\left(\frac{R_1<br><br>\left(n-1\right)}{n-1+R_1<br><br>D}\right)-x_j^2}+C<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{or}$

(B) for hyperopia and hyperopic cylinder, $f<br><br>\left(x_j\right)=R_1-\frac{R_1<br><br>\left(n-1\right)}{n-1+R_1<br><br>D}-\sqrt{R_1^2-x_j^2}+\sqrt{\left(\frac{R_1<br><br>\left(n-1\right)}{n-1+R_1<br><br>D}\right)-x_j^2}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{or}$

(C) for phototherapeutic keratectomy,

21. The method of claim 20 wherein the shift is about 0 to about 0.2.

22. The method of claim 20 wherein x_j=j*[(L−

shift)/N].

23. The method of claim 20 wherein the basis function includes M discrete basis functions representing M overlapping scanning spots, and wherein fitting to target function with the basis function comprises solving the following equation for coefficients a_i representing treatment depth for the i^th scanning spot:

$f<br><br>\left(x_j\right)=\underset{i=1}{\overset{M}{\sum <br><br>}}<br><br>a_i<br><br>X_i<br><br>\left(x_j\right)$

where

X_i(x_i) is the i^th basis function; and

i=1, . . . ,M.

24. The method of claim 17 herein the basis function includes M discrete basis functions representing M overlapping scanning spots.

25. The method of claim 24 wherein M is equal to about 7 to about 97.

26. The method of claim 24 further comprising refitting the target function with the basis function by varying the number of scanning spots M to iterate for a best fit.

27. The method of claim 24, wherein the M discrete basis functions represent M overlapping scanning spots across a treatment zone length representing the length across a generally two-dimensional section which is oriented normal across a generally straight treatment pattern or which is oriented radially across a gene ly circular treatment pattern.

28. The method of claim 27 wherein the scanning spots are generally circular and have a generally uniform energy profile.

29. The method of claim 28 wherein

(A) for a treatment profile having a generally uniform two-dimensional section oriented normal across a generally straight treatment pattern, the discrete basis functions represent the two-dimensional section as

30. The method of claim 29 wherein x_0i is specified for M number of equally spaced scanning spots as x_0i=i*[(L−

s+e)/M],

where

L is the treatment zone length;

e is an extended zone; and

i=1, . . . ,M.

31. The method of claim 30 wherein e is set to about 0.1 to about 0.5 mm.

32. A method of generating a treatment table for ablating tissue using a scanning laser beam for generating scanning spots over a treatment region larger in area than the scanning spots, the method comprising:

providing a lens function representing a desired lens profile for ablating the tissue by scanning spots of the laser beam on the tissue to achieve a desired removal of the tissue by ablating the tissue according to the desired lens profile represented by the target function;

providing a user-specified basis function representing a treatment profile produced by the overlapping scanning spots along a treatment path, the user-specified basis function representing a section oriented across the treatment path; and

fitting the lens function with the user-specified basis function to obtain a treatment table including scanning spot locations and characteristics for the overlapping scanning spots of the laser beam, such that an ablation employing the user-specified basis function according to the scanning spot locations and characteristics of the treatment table will substantially achieve the desired removal of the tissue as represented by the target function.

33. The method of claim 32 wherein the scanning spots have a fixed spot size and a fixed spot shape.

34. The method of claim 32 wherein at least one of the spot size and spot shape of the scanning spot is variable.

35. A method of generating a treatment table for ablating tissue using a scanning laser beam for generating scanning spots over a treatment region larger in area than the scanning spots, the method comprising:

providing a lens function representing a desired lens profile for ablating the tissue by scanning spots of the laser beam on the tissue;

providing a basis function representing a treatment profile produced by the overlapping scanning spots along a treatment path, the basis function representing a section oriented across the treatment path; and

fitting the lens function with the basis function to obtain a treatment table including scanning spot locations and characteristics for the overlapping scanning spots of the laser beam;

wherein the scanning spots are generally circular and have a generally uniform energy profile, and the basis function includes M discrete basis functions representing M overlapping scanning spots.

36. The method of claim 35 wherein the treatment profile is symmetrical with respect to an axis of symmetry, and the discrete basis functions are ${\theta }_{}$

i

(x)=cos-1

(x2+x0

i2-(s/2)22·

x0

i·

x)

where

s is the diameter of the scanning spot;

x is an x-coordinate measured from the axis of symmetry;

x_0i is an x-coordinate for a center of an i^th scanning spot;

(x_0i−

s/2)≦

x≦

(x_0i+s/2); and

θ

_i(x) is a coverage angle of the i^th basis function.

37. The method of claim 36 wherein x_0i is specified for M number of equally spaced scanning spots as:

38. The method of claim 36 wherein fitting the lens function with the basis function comprises solving the following equation for coefficients a_i representing treatment depth for the i^th scanning spot:

$f<br><br>\left(x\right)=\underset{i=1}{\overset{M}{\sum <br><br>}}<br><br>a_i<br><br>X_i<br><br>\left(x\right)$

where

f(x) is the lens function; and

i=1, . . . ,M.

39. The method of claim 38 wherein the lens function is:

(A) for myopia, $f<br><br>\left(x\right)=\sqrt{R_1^2-x^2}-\sqrt{\left(\frac{R_1<br><br>\left(n-1\right)}{n-1+R_1<br><br>D}\right)-x^2}+C<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{or}$

(B) for hyperopia, $f<br><br>\left(x\right)=R_1-\frac{R_1<br><br>\left(n-1\right)}{n-1+R_1<br><br>D}-\sqrt{R_1^2-x^2}+\sqrt{\left(\frac{R_1<br><br>\left(n-1\right)}{n-1+R_1<br><br>D}\right)-x^2}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{or}$

(C) for phototherapeutic keratectomy,

40. The method of claim 38 further comprising dividing the depth (a_i) for the i^th scanning spot by a dept per pulse of the laser beam to obtain a number of pulses per an i^th treatment ring for the i^th scanning spot;

and dividing the number of pulses per treatment ring ring by 2π

to obtain an angular spacing between pulses for the i^th treatment ring.

41. A method of generating a treatment table for ablating tissue using a scanning laser beam for generating scanning spots over a treatment region larger in area tan the scanning spots, the method comprising:

providing a target function representing a desired lens profile for ablating the tissue by scanning spots of the laser beam on the tissue;

providing a basis function representing a treatment profile produced by scanning with overlapping scanning spots of the laser beam to be centered at a plurality of locations on the tissue in a treatment pattern; and

fitting the target function with the basis function to obtain a treatment table including scanning spot locations and characteristics for the overlapping scanning spots of the laser beam;

wherein fitting the target function and the basis function comprises evaluating closeness of the fit and repeating the fitting step if the closeness does not fall within a target closeness.

42. A method of generating a treatment table for ablating tissue using a scanning laser beam for generating scanning spots over a treatment region larger in area than to scanning spots, the method comprising:

providing a target function representing a desired lens profile for ablating the tissue by scanning spots of the laser beam on the tissue;

providing a basis function representing a treatment profile produced by scanning with overlapping scanning spots of the laser beam to be centered at a plurality of locations on the tissue in a treatment pattern;

fitting the target function with the basis function to obtain a treatment table including scanning spot locations and characteristics for the overlapping scanning spots of the laser beam; and

randomizing the scanning spot locations of the treatment table to produce a random scanning order.

43. A method of generating a treatment table for ablating tissue using a scanning laser beam for generating scanning spots over a treatment region larger in area than the scanning spots, the method comprising:

providing a target function representing a desired lens profile for ablating the tissue by scanning spots of the laser beam on the tissue;

providing a basis function representing a treatment profile produced by scanning with overlapping scanning spots of the laser beam to be centered at a plurality of locations on the tissue in a treatment pattern;

fitting the target function with the basis function to obtain a treatment table including scanning spot locations and characteristics for the overlapping scanning spots of the laser beam; and

refitting the target function with the basis function by varying the size of at least one of the scanning spots to iterate for a best fit.

44. A system for ablating tissue, the system comprising

a laser for generating a laser beam;

a delivery device for delivering the laser beam to a tissue;

a controller configured to control the laser and the delivery device; and

a memory, coupled to the controller, comprising a computer-readable medium having a computer-readable program embodied therein for directing operation of the system, the computer-readable program including a first set of instructions for generating a treatment table including scanning spot locations and characteristics for ablating the tissue over a treatment region larger in area than the spot size of the laser beam to achieve a desired lens profile for ablating the tissue using scanning spots of the laser beam which are centered at a plurality of scanning spot locations on the tissue, a second set of instructions for controlling the laser to generate the laser beam, and a third set of instructions for controlling the delivery device to deliver the laser beam to the tissue according to the treatment table;

wherein the first set of instructions of the computer-readable program includes;

a first subset of instructions for providing a target function representing the desired lens profile for ablating the tissue by scanning spots of the laser beam on the tissue to achieve a desired removal of the tissue by ablating the tissue according to the desired lens profile represented by the target function;

a second subset of instructions for providing a user-specified basis function representing a treatment profile produced by scanning with overlapping scanning spots of the laser beam to be centered at a plurality of scanning spot locations on the tissue in a user-specified treatment pattern; and

a third subset of instructions for fitting the target function with the user-specified basis function to obtain the treatment table including the scanning spot locations and characteristics for the overlapping scanning spots of the laser beam, such that an ablation employing the user-specified basis function according to the scanning spot locations and characteristics of the treatment table will substantially achieve the desired removal of the tissue as represented by the target function.

45. The system of claim 44 wherein the second subset of instructions provide a basis function which is a two-dimensional function representing a two-dimensional section of a three-dimensional treatment profile having symmetry with respect to the two-dimensional section extending along the treatment pattern.

46. The system of claim 44 wherein the first set of instructions of the computer-readable program includes a fourth subset of instructions for refitting the target function with the basis function by varying the spot of laser beam to iterate for a best fit.

47. The system of claim 44 wherein the first set of instructions of the computer-readable program includes a fifth subset of instructions for evaluating closeness of the fit and repeating the fitting step if the closeness does not fall within a target closeness.

48. The system of claim 44 wherein the first set of instructions of the computer-readable program includes a sixth subset of instructions for randomizing the scanning spot locations forte treatment table to produce a random scanning order.

49. The system of claim 44 wherein the first set of instructions of the computer-readable program includes a seventh subset of specifying the treatment pattern for scanning with overlapping scanning spots of the laser beam.

50. The system of claim 49 wherein the scanning spot characteristics of a scanning spot at a scanning location include shape, size, and depth of the scanning spot at the scanning location.

51. The system of claim 44 wherein the desired lens profile is selected from to group consisting of an elliptical profile, a hyperopic elliptical profile, a myopic elliptical profile, a circular profile, and a linear profile.

52. The system of claim 44 wherein the desired lens profile is asymmetric.

53. The system of claim 44 wherein the desired lens profile comprises an arbitrary two-dimensional lens profile.