Method of using an orthopaedic fixation device

• US 5,971,984 A
• Filed: 03/17/1998
• Issued: 10/26/1999
• Est. Priority Date: 03/01/1995
• Status: Expired due to Term

• Current Assignee: Smith & Nephew Incorporated (Smith & Nephew PLC)
• Original Assignee: Smith & Nephew Incorporated (Smith & Nephew PLC)
• Inventors: Austin, Gene Edward, Taylor, John Charles, Taylor, Harold S.
• Primary Examiner(s): Buiz, Michael
• Assistant Examiner(s): Shai, Daphna
• Application Number:
  US09/040,022
• Time in Patent Office: 588 Days
• Field of Search: 606/54, 606/55, 606/56, 606/57, 606/58, 606/59, 606/60, 606/61, 128/898
• US Class Current: 606/54
• CPC Class Codes: A61B 17/62 Ring frames, i.e. devices extending around the bones to be positioned A61B17/6433 , A61B17/66 take precedence

Abstract

An external fixator for positioning a first element or the like relative to a second element or the like. The external fixator includes a first base for mounting to the first element; a second base for mounting to the second element; a plurality of adjustable effective length struts; connector structure for rotatably attaching the first ends of a first pair of struts relative to one another and relative to the first base; connector structure for rotatably attaching the first ends of a second pair of struts relative to one another and relative to the first base; connector structure for rotatably attaching the first ends of a third pair of struts relative to one another and relative to the first base; connector structure for rotatably attaching the second ends of the first pair of struts relative to one another and relative to the second base; connector structure for rotatably attaching the second ends of the second pair of struts relative to one another and relative to the second base member; and connector structure for rotatably attaching the second ends of the third pair of struts relative to one another and relative to the second base member.

A unique method of using an external fixation device to reposition a first bone segment relative to a second bone segment is claimed herein. The unique method of using the external fixation device of the current invention includes attaching said first base member to said first bone segment, attaching said second base member to said second bone segment, and adjusting the effective length of at least one of the struts, thereby repositioning said first bone segment relative to said second bone segment.

Claims

1. A method of using an external fixation device to reposition a first tissue segment from an deformed position to a target position relative to a second tissue segment, whereby the fixation device includes a first base member, a second base member, and a plurality of adjustable-length struts interconnecting said first and second base members, wherein the method comprises the steps of:

selecting a cartesian coordinate system with three orthogonal axes, wherein the first axis of the coordinate system is substantially parallel to the centerline of the second tissue segment, and the second and third axes are orthogonal to each other and the first axis;

mathematically correlating the deformed position relative to the target position, wherein the correlation characterizes the deformation in terms of a translational vector and projected rotational angles about the coordinate axes;

attaching the second base member to the second tissue segment and characterizing the location of the second base member;

establishing a neutral length of each strut and characterizing an initial location of the first base member;

calculating an intermediary position for the first base member, wherein the intermediary position bears the same rotational and translational variations relative the initial position as the deformed position of the first tissue bears relative to the target position;

calculating the new effective length of each strut required to orient the first base member at the intermediary position and adjusting the effective lengths of the struts to the new effective lengths, thereby causing the fixation device to mimic the relative positions of the tissue segments;

attaching the first base member to the first tissue segment; and

,

adjusting the effective lengths of the struts to the neutral lengths, thereby repositioning the first tissue segment to the target position;

wherein the calculation of the intermediary position for the first base member includes the following steps, mathematically performed in the sequence set forth;

a) mimicking the angular displacement of the first tissue segment about the first axis;

b) mimicking the angular displacement of the first tissue segment about the second and third axes; and

,

c) mimicking the translational displacement of the first tissue segment.

2. The method set forth in claim 1 further comprising the following steps, performed in the sequence set forth:

a) predetermining an appropriate location on the second tissue segment for the attachment of the second base member;

b) characterizing the positions of the first and second base members based on this predetermined location; and

,

c) mimicking the deformity of the first tissue segment before the first and second base members are attached to the first and second tissue segments.

3. The method of claim 1 wherein angular deformity displacements of the first base member are calculated according the following rotational matrices:

##EQU22## where [R.sub.δ

] [R.sub.θ

] and, [R.sub.φ

] represent the matrices by which the angular deformation of the first base member are calculated about the first, second and third axes, respectively, and where δ

signifies the projected angular displacement of the first tissue segment about the first axis, θ

signifies the projected angular displacement of the first tissue segment about the second axis, and φ

signifies the projected angular displacement of the first tissue segment about the third axis.

4. The method of claim 1 wherein angular deformations of the first base member are calculated according to a rotational matrix which mathematically mimics rotation about the first axis prior to rotation about the second and third axes.

5. The method of claim 4 wherein the angular deformations of the first base member are calculated according to the rotational matrix given by the formula:

space="preserve" listing-type="tabular">______________________________________ Cosδ

* (Cosδ

* Sinθ

* (Sinδ

* Sinβ

) + Cosθ

Cosβ

) - (Sinδ

* (Cosδ

* Sinθ

* Cosβ

) Cosβ

) [R.sub.δ

θ

φ

] = Sinδ

* (Cosδ

* Cosβ

) + (Sinδ

* Sinθ

* Cosβ

) - Cosθ

(Sinδ

* Sinθ

* (Cosδ

* Sinβ

) Sinβ

) -(Sinθ

) Cosθ

* Sinβ

Cosθ

* Cosβ

______________________________________

where δ

signifies the projected angular displacement of the first tissue segment about the first axis, θ

signifies the projected angular displacement of the first tissue segment about the second axis, φ

signifies the projected angular displacement of the first tissue segment about the third axis.

6. The method of claim 1 wherein the angular deformations of the first base member are calculated according to the rotational matrix given by the formula:

space="preserve" listing-type="tabular">__________________________________________________________________________ [(c*e - b*f)]/ [d*(b.sup.2 + c.sup.2) - a*(b*e + c*f)]/ [a*(e.sup.2 + f.sup.2) - d*(b*e + c*f)]/ [a.sup.2 *(e.sup.2 + f.sup.2) - [a.sup.2 *(e.sup.2 + f.sup.2) - [a.sup.2 *(e.sup.2 + f.sup.2) - 2*a*d*(b*e + c*f) + 2*a*d*(b*e + c*f) + 2*a*d*(b*e + c*f) + b.sup.2 *(d.sup.2 + f.sup.2) - 2*b*c*e*f + b.sup.2 *(d.sup.2 + f.sup.2) - 2*b*c*e*f b.sup.2 *(d.sup.2 + f.sup.2) - 2*b*c*e*f + c.sup.2 *(d.sup.2 + e.sup.2)] c.sup.2 *(d.sup.2 + e.sup.2)] c.sup.2 *(d.sup.2 + e.sup.2)] [R.sub.12 ] = [a*f - c*d]/ [a.sup.2 *e - a*b*d - b*c*f + c.sup.2 *e]/ -[a*d*e - b*(d.sup.2 - f.sup.2) + [a.sup.2 *(e.sup.2 + f.sup.2) - [a.sup.2 *(e.sup.2 + f.sup.2) - c*e*f]/ 2*a*d*(b*e + c*f) + 2*a*d*(b*e + c*f) + [a.sup.2 *(e.sup.2 + f.sup.2) - b.sup.2 *(d.sup.2 + f.sup.2) - 2*b*c*e*f + b.sup.2 *(d.sup.2 + f.sup.2) - 2*b*c*e*f 2*a*d*(b*e + c*f) + c.sup.2 *(d.sup.2 + e.sup.2)] c.sup.2 *(d.sup.2 + e.sup.2)] b.sup.2 *(d.sup.2 + f.sup.2) - 2*b*c*e*f + c.sup.2 *(d.sup.2 + e.sup.2)] [b*d - a*e]/ [a.sup.2 *f - a*c*d + b*(b*f - c*e)]/ -[a*d*f + b*e*f - c*(d.sup.2 + [a.sup.2 *(e.sup.2 + f.sup.2) - [a.sup.2 *(e.sup.2 + f.sup.2) - e.sup.2 (]/ 2*a*d*(b*e + c*f0 + 2*a*d*(b*e + c*f) + [a.sup.2 *(e.sup.2 + f.sup.2) - b.sup.2 *(d.sup.2 + f.sup.2) - 2*b*c*e*f + b.sup.2 *(d.sup.2 + f.sup.2) - 2*b*c*e*f) 2*a*d*(b*e + c*f) + c.sup.2 *(d.sup.2 + e.sup.2)] c.sup.2 *(d.sup.2 + e.sup.2)] b.sup.2 *(d.sup.2 + f.sup.2) - 2*b*c*e*f + c.sup.2 *(d.sup.2 + e.sup.2)] __________________________________________________________________________

where,

a=c* TAN (θ

);

b=c* TAN (φ

);

c=1/[TAN² (θ

)+TAN² (φ

)+1]^1/2 ;

d=e/η

;

e=(c² *η

²)/[c² *(1+η

²)+a² +2*a*b*η

+b² *η

² ];

f=(-1/c)*e*((a/η

)+b);

η

=TAN (π

/2+δ

);

θ

=LAT angulation (taken off AP view) in radians;

φ

=AP angulation (taken off LAT view) in radians; and

,

δ

=Axial rotation in radians;

wherein the step of mimicking the angular displacement of the first tissue segment about the first axis is accomplished by setting the θ and

φ

values to zero before the R₁₂ matrix is applied to the location of the first base member; and

,

wherein the step of mimicking the angular displacement of the first tissue segment about the second and third axes is accomplished by setting the δ

value to zero before the R₁₂ matrix is applied to the location of the first base member.

7. The method of claim 1 wherein the translational displacements are calculated according to the vector component:

##EQU23## where "AP trans" signifies the linear displacement of the first tissue segment along the third axis;

"LAT trans" signifies linear displacement of the first tissue segment along the second axis and "axial trans" signifies linear displacement of the first tissue segment along the first axis.

8. The method of claim 1 wherein the new lengths of the adjustable struts are determined using the pythagorean theorem.

9. The method of claim 1 wherein said first and second tissue segments include hard tissue and soft tissue.

10. The method of claim 9 wherein said first and second tissue segments are bone.

11. The method of claim 1 wherein said struts have initial effective lengths defined by the effective lengths prior to the adjustment to said new effective lengths, wherein said initial effective lengths of the struts are not all the same and the new effective lengths of the struts are not all the same.

12. The method of claim 1 wherein a safe rate at which the effective lengths of said struts are adjusted to said new effective lengths is determined by the steps including:

(1) determining a total displacement of a structure at greatest risk;

(2) dividing the total displacement by a clinically determined safe correction velocity to yield the total number of days required for correction;

(3) calculating the sum of the absolute value of the difference between each new strut length and its corresponding initial length to provide the total excursion of all struts that is required to correct the deformity; and

(4) dividing the total excursion by the total number of days required for correction to obtain said safe rate in terms of an amount of daily adjustment.

13. The method of claim 12 wherein said struts are adjusted to said new effective lengths at said safe rate.

14. A method of using an external fixation device to reposition a first tissue segment from an deformed position to a target position relative to a second tissue segment, whereby the fixation device includes a first base member, a second base member, and a plurality of adjustable-length struts interconnecting said first and second base members, wherein the method comprises the steps of:

selecting a cartesian coordinate system with three orthogonal axes, wherein the first axis of the coordinate system is substantially parallel to the centerline of the second tissue segment, and the second and third axes are orthogonal to each other and the first axis;

mathematically correlating the deformed position relative to the target position, wherein the correlation characterizes the deformation in terms of a translational vector and projected rotational angles about the coordinate axes;

attaching the second base member to the second tissue segment and characterizing the location of the second base member;

attaching the first base member to the first tissue segment and characterizing the location of the first base member;

calculating an intermediary position for the first base member, wherein the intermediary position bears the same rotational and translational variations relative the initial position as the target position of the first tissue bears relative to the deformed position;

calculating the new effective length of each strut required to orient the first base member at the secondary position;

adjusting the effective lengths of the struts to the new effective lengths, thereby causing the fixation device to mirror the relative positions of the tissue segments and thereby repositioning the first tissue segment to the target position;

wherein the calculation of the intermediary position for the first base member includes the following steps, mathematically performed in the sequence set forth;

a) mirroring the translational displacement of the first tissue segment;

b) mirroring the angular displacement of the first tissue segment about the second and third axes; and

,

c) mirroring the angular displacement of the first tissue segment about the first axis.

15. The method of claim 14 wherein angular deformity displacements of the first base member are calculated according the following rotational matrices:

##EQU24## where [R.sub.δ

] [R.sub.θ

] and, [R.sub.φ

] represent the matrices by which the angular deformation of the first base member are calculated about the first, second and third axes, respectively, and where δ

signifies the projected angular displacement of the first tissue segment about the first axis, θ

signifies the projected angular displacement of the first tissue segment about the second axis, and φ

signifies the projected angular displacement of the first tissue segment about the third axis.

16. The method of claim 14 wherein angular deformations of the first base member are calculated according to a rotational matrix which mathematically accomplishes the sequential mirroring of rotation about the first axis prior to rotation about the second and third axes.

17. The method of claim 16 wherein the angular deformations of the first base member are calculated according to the rotational matrix given by the formula:

space="preserve" listing-type="tabular">______________________________________ Cosδ

* Cosθ

-(Sinδ

* Cosθ

) Sinθ

[R.sub.φ

θ

δ

] = (Sinδ

* Cosβ

) + (Cosδ

* Cosβ

) - -(Cosθ

* (Cosδ

* Sinθ

* Sinβ

) (Sinδ

* Sinθ

* Sinβ

) Sinβ

) (Sinδ

* Sinβ

) - (Cosδ

* Sinβ

) + Cosθ

* (Cosδ

* Sinθ

* Cosβ

) (Sinδ

* Sinθ

* Cosβ

Cosβ

) ______________________________________

where δ

signifies the projected angular displacement of the first tissue segment about the first axis, θ

signifies the projected angular displacement of the first tissue segment about the second axis, and φ

signifies the projected angular displacement of the first tissue segment about the third axis.

18. The method of claim 14 wherein the angular deformations of the first base member are calculated according to the rotational matrix given by the formula:

space="preserve" listing-type="tabular">__________________________________________________________________________ [(c*e - b*f)]/ [d*(b.sup.2 + c.sup.2) - a*(b*e + c*f)]/ [a*(e.sup.2 + f.sup.2) - d*(b*e + c*f)]/ [a.sup.2 *(e.sup.2 + f.sup.2) - [a.sup.2 *(e.sup.2 + f.sup.2) - [a.sup.2 *(e.sup.2 + f.sup.2) - 2*a*d*(b*e + c*f) + 2*a*d*(b*e + c*f) + 2*a*d*(b*e + c*f) + b.sup.2 *(d.sup.2 + f.sup.2) - 2*b*c*e*f + b.sup.2 *(d.sup.2 + f.sup.2) - 2*b*c*e*f b.sup.2 *(d.sup.2 + f.sup.2) - 2*b*c*e*f + c.sup.2 *(d.sup.2 + e.sup.2)] c.sup.2 *(d.sup.2 + e.sup.2)] c.sup.2 *(d.sup.2 + e.sup.2)] [R.sub.12 ] = [a*f - c*d]/ [a.sup.2 *e - a*b*d - b*c*f + c.sup.2 *e]/ -[a*d*e - b*(d.sup.2 - f.sup.2) + [a.sup.2 *(e.sup.2 + f.sup.2) - [a.sup.2 *(e.sup.2 + f.sup.2) - c*e*f]/ 2*a*d*(b*e + c*f) + 2*a*d*(b*e + c*f) + [a.sup.2 *(e.sup.2 + f.sup.2) - b.sup.2 *(d.sup.2 + f.sup.2) - 2*b*c*e*f + b.sup.2 *(d.sup.2 + f.sup.2) - 2*b*c*e*f 2*a*d*(b*e + c*f) + c.sup.2 *(d.sup.2 + e.sup.2)] c.sup.2 *(d.sup.2 + e.sup.2)] b.sup.2 *(d.sup.2 + f.sup.2) - 2*b*c*e*f + c.sup.2 *(d.sup.2 + e.sup.2)] [b*d - a*e]/ [a.sup.2 *f - a*c*d + b*(b*f - c*e)]/ -[a*d*f + b*e*f - c*(d.sup.2 + [a.sup.2 *(e.sup.2 + f.sup.2) - [a.sup.2 *(e.sup.2 + f.sup.2) - e.sup.2 (]/ 2*a*d*(b*e + c*f0 + 2*a*d*(b*e + c*f) + [a.sup.2 *(e.sup.2 + f.sup.2) - b.sup.2 *(d.sup.2 + f.sup.2) - 2*b*c*e*f + b.sup.2 *(d.sup.2 + f.sup.2) - 2*b*c*e*f) 2*a*d*(b*e + c*f) + c.sup.2 *(d.sup.2 + e.sup.2)] c.sup.2 *(d.sup.2 + e.sup.2)] b.sup.2 *(d.sup.2 + f.sup.2) - 2*b*c*e*f + c.sup.2 *(d.sup.2 + e.sup.2)] __________________________________________________________________________

where,

a=c* TAN (θ

);

b=c* TAN (φ

);

c=1/[TAN² (θ

)+TAN² (φ

)+1]^1/2 ;

d=e/η

;

e=(c² *η

²)/[c² *(1+η

²)+a² +2*a*b*η

+b² *η

² ];

f=(-1/c)*e*((a/η

)+b);

η

=TAN (π

/2+δ

);

θ

=LAT angulation (taken off AP view) in radians;

φ

=AP angulation (taken off LAT view) in radians; and

,

δ

=Axial rotation in radians;

wherein the step of mirroring the angular displacement of the first tissue segment about the second and third axes is accomplished by setting the δ

value to zero before the R₁₂ matrix is applied to the location of the first base member; and

,

wherein the step of mimicking the angular displacement of the first tissue segment about the first axis is accomplished by setting the θ and

φ

values to zero before the R₁₂ matrix is applied to the location of the first base member.

19. The method of claim 14 wherein the translational displacements are calculated according to the vector component:

##EQU25## where "AP trans" signifies the linear displacement of the first tissue segment along the third axis;

"LAT trans" signifies linear displacement of the first tissue segment along the second axis and "axial trans" signifies linear displacement of the first tissue segment along the first axis.

20. The method of claim 14 wherein the new lengths of the adjustable struts are determined using the pythagorean theorem.

21. The method of claim 14 wherein said first and second tissue segments include hard tissue and soft tissue.

22. The method of claim 21 wherein said first and second tissue segments are bone.

23. The method of claim 14 wherein said struts have initial effective lengths defined by the effective lengths prior to the adjustment to said new effective lengths, wherein said initial effective lengths of the struts are not all the same and the new effective lengths of the struts are not all the same.

24. The method of claim 14 wherein a safe rate at which the effective lengths of said struts are adjusted to said new effective lengths is determined by the steps including:

(1) determining a total displacement of a structure at greatest risk;

(2) dividing the total displacement by a clinically determined safe correction velocity to yield the total number of days required for correction;

(3) calculating the sum of the absolute value of the difference between each new strut length and its corresponding initial length to provide the total excursion of all struts that is required to correct the deformity; and

(4) dividing the total excursion by the total number of days required for correction to obtain said safe rate in terms of an amount of daily adjustment.

25. The method of claim 24 wherein said struts are adjusted to said new effective lengths at said safe rate.

26. A method of using an external fixation device to reposition a first tissue segment from an deformed position to a target position relative to a second tissue segment, whereby the external fixation device includes a first base member, a second base member, a plurality of adjustable-length struts interconnecting said first and second base members, wherein the method comprises the steps of:

attaching the first base member to the first tissue segment, wherein the connections between the adjustable struts and the first base member define a first plane, and wherein the centerline of the first tissue segment is normal to the first plane;

attaching the second base member to the second tissue segment, wherein the connections between the adjustable struts and the second base member define a second plane, and wherein the centerline of the second tissue segment is normal to the second plane;

selecting a first reference point on the first tissue segment and a second reference point on the second tissue segment, wherein the first and second reference points will meet after the first tissue segment repositioned to the target position;

calculating the distances between the first plane and the first reference point, and between the second plane and the second reference point;

calculating the neutral strut lengths that will orient the first plane parallel to the second plane at a distance equal to the sum of the distances between the first plane and the first reference point, and between the second plane and the second reference point; and

,

adjusting the effective lengths of the struts to the neutral lengths, thereby repositioning the first tissue segment to the target position.

27. The method of claim 26 wherein the new lengths of the adjustable struts are determined using the pythagorean theorem.

28. The method of claim 26 wherein said first and second tissue segments include hard tissue and soft tissue.

29. The method of claim 26 wherein said first and second tissue segments are bone.