3D planning and prediction method for optimizing facial skeleton symmetry in orthognathic surgery
The method comprises steps of making a plaster dental cast of a patient, reconstructing jaw image assembly models, performing registration between physical stone and image model, adjusting the plaster dental cast based on a x-ray cephalometric plan, tracking movements of the plaster dental cast, obtaining optimal symmetry planes of the upper and lower jaw image assemblies, determining whether a degree of overall symmetry is elevated, and making surgical occlusal splints for surgical guiding. With foregoing method, possible results of executing an orthognathic surgical plan can be predicted and the surgical plan can be considered more carefully to achieve both occlusion function and facial symmetry.
1. A 3D planning and prediction method for optimizing facial skeleton symmetry in orthognathic surgery comprising steps of
making a plaster dental cast according to an oral cavity of a patient, wherein the plaster dental cast has an upper jaw stone assembly and a lower jaw stone assembly;
reconstructing jaw image assembly models in a computer by scanning the patient's facial structure using computer tomography, wherein the jaw image assembly models include an upper jaw image assembly and a lower jaw image assembly;
performing registration between the jaw image assembly models and the plaster dental cast, wherein a coordinate relationship between the virtual jaw image assembly models and the substantial plaster dental cast is established in the computer by coordinate transformation for position synchronization;
adjusting positions of the upper and lower jaw stone assemblies of the plaster dental cast to target positions according to a predetermined x-ray cephalometric plan;
tracking movements of the upper and low jaw stone assemblies with a spatial tracking device to synchronously and correspondingly reappear the same movements of the upper and lower jaw image assemblies to obtain a relative variation between positions of the upper and lower jaw image assemblies;
obtaining optimal symmetry planes of the upper and lower jaw image assemblies by a computer via an asymmetry quantifying process and thereby computing a variation of an included angle and a specific distance between the optimal symmetry planes of the upper and lower jaw image assemblies;
determining whether a degree of overall symmetry is elevated by determining whether the included angle and the specific distance are shortened under a condition of compromising the x-ray cephalometric plan, and recording the included angle and the specific distance and proceeding to next step when the degree of overall symmetry is elevated, otherwise checking if any error occurs while adjusting positions of the upper and low jaw stone assemblies of the plaster dental cast according to the x-ray cephalometric plan and returning to the step of tracking movements of the upper and low jaw stone assemblies of the plaster dental cast; and
making surgical occlusal splints according to the x-ray cephalometric plan and the recorded included angle and specific distance for surgical guiding.
2. The method as claimed in claim 1 , wherein the spatial tracking device is selected from the group consisting of an optical tracking device, a mechanical tracking device, an ultrasonic tracking device, a gyroscope tracking device and an electromagnetic tracking device.
3. The method as claimed in claim 1 , wherein the asymmetry quantifying process is operated in a computer and comprises steps of
importing medical imaging data sets of the patient's facial structure into a computer;
selecting regions of interest of the patient's facial structure in each medical imaging data set locating the regions of interest of the patient's facial structure in each medical imaging data set, and comprising steps of
selecting contrast and threshold arguments that both define the regions of interest of the patient's facial structure in each medical imaging data set; and
image processing using the contrast and threshold arguments to generate binary image data and locates the regions of interest of the patient's facial structure in each medical image data set;
processing those binary image data by executing an error equation and obtaining optimal parameters corresponding to the error equation; and
constructing an optimal symmetry plane with a best symmetry value, wherein the best symmetry value is a ratio value obtained from the error equation.
4. The method as claimed in claim 3 , wherein the step of constructing an optimal symmetry plane further comprising steps of
assuming an equation (sin α sin β)x+(sin β cos β)y+(cos β sin α)z−(sin α sin β)k d =0 being a symmetry plane of the patient's facial structure, wherein parameters α, β and k d are obtained from the step of obtaining the optimal parameters, α is an angle between an x-axis and an intersection line between the symmetry plane and the plane XY, β is an angle between the x-axis and an intersection line between the symmetry plane and the plane XZ and k d is a distance between a point on the symmetry plane and the origin; and
obtaining the symmetry plane by substituting the optimal parameters α, β and k d into the equation (sin α sin β)x+(sin β cos β)y+(cos β sin α)z−(sin α sin β)k d =0 of the symmetry plane.
5. The method as claimed in claim 4 , wherein the step of processing the medical imaging data sets further comprises steps of
executing an error equation
E
(
α
,
β
,
k
d
)
=
(
∑
i
=
0
n
-
1
[
f
(
x
i
,
y
i
,
z
i
)
^
f
(
x
si
,
y
si
,
z
si
)
]
)
/
n
,
wherein
f
(
x
i
,
y
i
,
z
i
)
^
f
(
x
si
,
y
si
,
z
si
)
=
{
1
,
f
(
x
i
,
y
i
,
z
i
)
=
f
(
x
si
,
y
si
,
z
si
)
0
,
f
(
x
i
,
y
i
,
z
i
)
≠
f
(
x
si
,
y
si
,
z
si
)
;
and
obtaining the optimal parameters α, β and k d by executing the error equation.
6. The method as claimed in claim 1 , wherein the asymmetry quantifying process is operated in a computer and comprises steps of
importing medical imaging data sets of the patient's facial structure into a computer;
reconstructing jaw image assembly models under a specific coordinate system by processing the medical image data in each data set; and
obtaining an optimal symmetry plane by initially assuming multiple possible symmetry planes, computing corresponding symmetry voxels of the image model relative to each assumed symmetry plane and taking an assumed symmetry plane that has the most symmetry voxels belonging to the image model as an optimal symmetry plane.
7. The method as claimed in claim 6 , wherein the step of obtaining an optimal symmetry plane comprises a step of executing a minimum equation
min
a
,
b
,
c
,
d
f
(
a
,
b
,
c
,
d
)
=
1
-
∑
P
∈
S
{
1
,
P
′
∈
S
0
,
P
′
∉
S
∑
P
∈
S
1
,
wherein
the assumed symmetry plane equation is E:ax+by+cz+d=0;
a normal vector of the assumed symmetry plane is V≡(a b c);
a voxel of the image model is P:(x i y i z i ), PεS; and
a symmetry point of each voxel is
P
′
:
(
x
′
y
′
z
′
)
=
P
-
2
V
[
P
1
]
[
V
T
d
]
V
2
.
8. The method as claimed in claim 6 , wherein the specific coordinate system is selected from the group consisting of an orthogonal coordinate system, a spherical coordinate system and a cylindrical coordinate system.
9. The method as claimed in claim 1 , wherein the plaster dental cast further has multiple tracking plates mounted on the upper and lower jaw stone assemblies, wherein each tracking plate has at least three recognition spots or at least two vector-based patterns.
10. The method as claimed in claim 9 , wherein each tracking plate is attached with multiple light-emitting diodes.
11. The method as claimed in claim 9 , wherein each tracking plate is attached with multiple reflection balls.
12. The method as claimed in claim 9 , wherein each tracking plate has multiple recognized patterns.