U.S. patent application number 12/610070 was filed with the patent office on 2010-07-01 for dental modeling system and method.
Invention is credited to Bruce W. HULTGREN, Michael C. Marshall.
Application Number | 20100169057 12/610070 |
Document ID | / |
Family ID | 38608815 |
Filed Date | 2010-07-01 |
United States Patent
Application |
20100169057 |
Kind Code |
A1 |
HULTGREN; Bruce W. ; et
al. |
July 1, 2010 |
DENTAL MODELING SYSTEM AND METHOD
Abstract
A method for simulating tooth movement utilizes electronic
modeling to represent the teeth. Instant centers of rotation are
determined and projected paths of movement are plotted. The
electronic model provides improved precision and provides a method
for simulating movement in three dimensions. The movement from
growth and/or correction is shown with the electronic model. The
simulation provides for improved correction.
Inventors: |
HULTGREN; Bruce W.;
(Victoria, MN) ; Marshall; Michael C.; (Prior
Lake, MN) |
Correspondence
Address: |
MERCHANT & GOULD PC
P.O. BOX 2903
MINNEAPOLIS
MN
55402-0903
US
|
Family ID: |
38608815 |
Appl. No.: |
12/610070 |
Filed: |
October 30, 2009 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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12299581 |
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PCT/US2007/010838 |
May 4, 2007 |
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12610070 |
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60797911 |
May 4, 2006 |
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Current U.S.
Class: |
703/1 |
Current CPC
Class: |
A61C 7/002 20130101;
A61C 9/0053 20130101; A61C 7/00 20130101 |
Class at
Publication: |
703/1 |
International
Class: |
G06F 17/50 20060101
G06F017/50 |
Claims
1. A method of modeling tooth movement of a patient, comprising:
creating a first virtual model of the patient's teeth; identifying
a first reference point on a first virtual tooth of the model;
identifying a second reference point on the patient's mandible;
creating a second virtual model of the patient's teeth after a time
period; tracking the movement of the first reference point from a
first location to a second location over the time period; tracking
the movement of the second reference point from a third location to
a fourth location over the time period; extending a first segment
between the first location and the second location; extending a
second segment between the third location and the fourth location;
projecting a first perpendicular bisector from the first segment;
projecting a second perpendicular bisector from the second segment;
determining an intersection of the first and second bisectors,
defining a rotational axis; plotting an arc centered on the
rotational axis along which the first reference point will
travel.
2. A method according to claim 1, wherein the computer projects
tooth movement in the future and creates a third virtual model
representing a future tooth position.
3. (canceled)
4. A method of modeling a patient's tooth movement on linkage
configurations, comprising: defining a ground point axis of
rotation; adopting a first point on the patient's ramus as a first
link pivot; adopting a second point on one of the patient's lower
teeth as a second link pivot; tracing a first path of the first
point pivoting about the axis of rotation, tracing a second path of
rotation about the axis of rotation pivoting about the axis of
rotation; moving the first point along the first path a first
distance; applying a relative movement factor to the first distance
to determine a second distance between the first point and the
second point; moving the second point along the second path until
the second point is the second distance from the first point to
arrive at a predicted location.
5. A method according to claim 4, wherein the linkage is oriented
with virtual modeling.
6. A method according to claim 4, wherein the ground point axis of
rotation is determined with virtual models.
7. A method according to claim 4, growth factor to determine
distance between two pivots.
8. A method according to claim 4, wherein coefficient of relative
growth is applied to the first distance to determine the second
distance.
9. A method according to claim 4, further adopting a segment
connecting the axis of rotation and the first point as the first
link; adopting and a segment connecting the axis of rotation and
the second point as the second link; rotating the first point along
the first path a first angle; applying a relative movement factor
to the first angle to determine a second angle between the first
segment and the second segment; moving the second link along the
second path the second angle to arrive at a predicted location.
10. A method according to claim 9, wherein the first link is a
driven link.
11. A method according to claim 10, wherein the first link is on
the patient's ramus.
12. A method of modeling tooth movement, comprising: creating a
first virtual model of a tooth; creating a second virtual model of
the tooth after a period of time; identifying a rotational axis of
the tooth; projecting an arc along which the tooth will travel
centered on the rotational axis.
13. A method according to claim 12, wherein the virtual models are
stored on a computer, and wherein the computer performs identifying
the rotational axis and projecting the arc.
14. A method of according to claim 12, further comprising: making a
first positioning location on a patient's mandible; tracking the
movement of the positioning location over the period of time
wherein the rotational axis of the tooth is based on positions of
the tooth and the positioning location before and after the period
of time; projecting an arc along which the tooth will travel
centered on the rotational axis.
15. A method according to claim 13, wherein the virtual models are
stored on a computer, and wherein the computer performs the steps
of identifying the rotational axis and projecting the arc.
16.-17. (canceled)
18. A method of modeling tooth movement, comprising: creating a
virtual model of a patient's mouth; selecting an element for
projecting movement; determining a first instant center of rotation
associated with a first location on the element; determining a
second instant center of rotation associated with a second location
on the element; tracing a path of movement through the first
location and centered on the first instant center of rotation;
tracing a path of movement through the second location and centered
on the second instant center of rotation; and tracing a path of
movement for the element with the first location centered on the
first instant center of rotation and the second location centered
on the second instant center of rotation.
19. A method according to claim 18, wherein the element defines a
link in a virtual four-bar linkage.
20. A method according to claim 19. wherein the pivots in the
four-bar linkage are at the first location, the second location,
the first instant center of rotation and the second instant center
of rotation.
21. (canceled)
22. A method according to claim 18, wherein the virtual model
comprises a three dimensional model.
Description
[0001] This application is being filed on 4 May 2007, as a PCT
International Patent application in the name of Bruce Willard
Hultgren, a citizen of the U.S., applicant for the designation of
all countries, and claims priority to U.S. Provisional Patent
Application No. 60/797,911, filed May 4, 2006.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] The present invention relates to a method and system for
simulating movement of a patient's jaw and teeth.
[0004] 2. Description of the Prior Art
[0005] In the field of orthodontics, simulation is important for
treatment and correction. If the manner in which the teeth and jaw
may form and grow is known, the dental practitioner is better able
to diagnose problems and identify potential problems. In addition,
the limits of moving teeth through braces and other correction
techniques become more apparent and treatment may be carried out
with more precision and greater chance of success.
[0006] Prior simulation techniques consisted of the dental
practitioner observing the patient's teeth and utilizing the
practitioner's knowledge and judgment to predict how the teeth
would move by estimating the effects of braces and other corrective
techniques. Although usually successful in correcting at least some
of the structural problems, greater success rates are possible with
additional information and knowledge about the patient's likely
tooth movement both with and without correction.
[0007] Efforts to model tooth movement have been developed that
proved to be a great aid for practitioners. Some models involve
linear tooth growth, especially for those in the lower jaw.
However, studies and modeling reveal that tooth movement and growth
is not usually truly linearly translational. Although such modeling
is helpful, with greater precision, more accurate simulations could
be achieved.
[0008] Other theories that have been developed involve identifying
an imaginary center of rotation for a particular tooth. Such
theories as stated in papers by Pilgrim, Moses, Erdman and
Hultgren, utilized instant centers of rotation to predict tooth
movement along an arc centered on the instant center of rotation.
It is believed that such a model is typically a better predictor of
actual tooth movement than a model using straight line
movement.
[0009] A further model simulates tooth movement as being governed
by a linkage. The model predicts growth that is not straight line,
but the arc along which the tooth moves is not centered on a single
center of rotation and therefore the tooth behaves as if it was a
segment of a linkage, for example, following a path as if it were
mounted on one link of a four bar linkage.
[0010] Although such models have proven to be successful in
providing guidance for predicting tooth growth and movement,
implementation in a practical manner has proven difficult. Current
techniques do not provide for accurately tracking tooth movement
with sufficient precision and their relationship to the tooth's
reference points. Markers and/or landmarks are necessary to ensure
that the movement of the tooth or of a specific portion of the
tooth are tracked. While such markers provide for improved modeling
and tracking, the insertion and placement of such markers and
tracking of the markers relative to one another is intrusive and
only allows tracking of the marker rather than the entire tooth. A
portion of the tooth moves with the marker, but it is possible that
the orientation in one or more planes may have changed or other
portions of the tooth may have moved in a different manner.
[0011] A further problem with such markers and/or landmarks is the
precision possible in tracking the changes in position. Heretofore,
tracking of markers in teeth has generally been accomplished by
taking x-rays of the markers and teeth and outlining the teeth
and/or markers to establish a current position. The insertion and
removal of markers is intrusive and inconvenient for the patient,
requiring an additional procedure. While such methods do provide
for tracking of position and changes, the accuracy of such methods
is decreased due to quality and resolution available for the images
and the inaccuracy from manually outlining and precisely locating
the markers and/or structural landmarks. As the accuracy and
precision are critical for predicting small movements and in
locating instant centers of rotation, such tools may not be an
acceptable simulator of the teeth and their movement. Due to the
precise measurements and the small distances involved, even minor
errors can have a drastic adverse affect on the position of an
instant center of rotation and therefore, the entire model and
movement simulation, increasing the possibility for improper
diagnosis and treatment.
[0012] Techniques have also been developed in orthodontics modeling
to create a digital three dimensional model by scanning a casting
of a patient's teeth and gums.
[0013] The digital EMODEL.TM. digital model system provides a
precise high resolution digital map of the teeth and gums, but its
use has been limited in creating prostheses. Such three dimensional
digital images have been used as a starting point in treatment, but
have not been used to project and simulate growth and movement.
[0014] It can be seen then that a new and improved system is needed
that overcomes the problems and deficiencies associated with the
prior art modeling systems and methods. A system and method is
needed that precisely models position and accurately simulates
movement of the patient's jaw and teeth. In addition, such a system
and method should provide minimal intrusion for the patient. Such a
system and method should also be practical to utilize and should
achieve sufficient precision and reliability for accurate
simulation by the dental practitioner to diagnose problems and
prescribe proper treatment. The present invention addresses these
as well as other problems associated with simulating tooth growth
and movement.
SUMMARY OF THE INVENTION
[0015] The present invention is directed to a system and method for
modeling tooth movement. Electronic modeling is used to create a
precise and accurate three dimensional virtual model of the
teeth.
[0016] In creating an electronic virtual model, a casting of the
patient's teeth is taken and a plaster model created. A scanner is
used to digitize a three dimensional image of the patient's mouth
for modeling. Alternatively, three dimensional high resolution
digital scanners, such as CT scanners, intra-oral scanners, cone
beam scanners or other digital capture devices may scan the
patient's facial structure to create a three dimensional virtual
model. A computer database stores the digital image and the image
may be viewed as a three dimensional virtual model that may be
manipulated on the computer screen. Moreover, the system provides
for separating the teeth into discrete elements for modeling
movement of an individual tooth and for modeling movement of all
teeth to help in providing proper diagnosis for treatment and
correction. The images may be manipulated to model projected growth
or movement over time.
[0017] According to the present invention, modeling of tooth
movement is accomplished by identifying an instant center of
rotation for a particular tooth or other structure of the patient's
jaw. The movement that the tooth would follow at that point in time
is an arc centered about the instant center of rotation. The
instant center of rotation can be plotted in three dimensions so
that the model tooth movement follows the surface of an imaginary
sphere centered about the instant center of rotation. As the image
is digitized, the teeth or other structures and their respective
instant centers of rotation can be mathematically represented with
a set of coordinates so that the plotting of movement is
accomplished with great precision. Locating the instant center of
rotation is accomplished utilizing a number of factors based on the
patient's tooth and jaw physiology and the knowledge and experience
of the dental practitioner. It can be appreciated that the instant
center of rotation varies from patient to patient and an instant
center may be above or below the position of the tooth as well as
to one side or the other, or forward or behind a tooth. The
position may be quite close to the tooth or may approach infinity
so that the virtual tooth substantially models straight line
movement.
[0018] The position of the instant center of rotation may be moved
to reflect different types and sets forces applied to the tooth,
such as movement to changing position of surrounding teeth or the
application of braces to the tooth. Instant centers may also be
determined for larger structures in the mouth or jaw whose movement
may be simulated. Moreover, the forces of growth and passage of
time are typically different than the forces acting on the tooth or
structure due to correction. Therefore, depending on the evaluation
and analysis required, different instant centers of rotation may be
determined for analyzing different sets of kinematic and dynamic
factors. As an instant center of rotation shifts, the projected
path also shifts and the radius from the instant center to the
projected arc may lengthen or shorten. With the digital image
stored, the treatment and the modeling provides for application of
varied forces and in various directions with different projected
paths of movement so that the diagnosis and treatment may be
optimized.
[0019] The present invention also contemplates modeling for
movement of some teeth wherein a tooth substantially pivots about
two axes of rotation and models the movement of a virtual four bar
linkage. The modeling is similar to the modeling for rotation about
a single axis, but two points on the tooth or other structure are
plotted. Using the same techniques discussed above, the instant
centers of rotation are located for both points on the tooth. The
entire tooth is then moved with each plotted point on the tooth
following a path of movement along an arc centered on the
associated instant center of rotation, so that the tooth
substantially follows the movement of a four bar linkage type
model.
[0020] These features of novelty and various other advantages that
characterize the invention are pointed out with particularity in
the claims annexed hereto and forming a part hereof. However, for a
better understanding of the invention, its advantages, and the
objects obtained by its use, reference should be made to the
drawings that form a further part hereof, and to the accompanying
descriptive matter, in which there is illustrated and described a
preferred embodiment of the invention.
BRIEF DESCRIPTION OF THE DRAWINGS
[0021] Referring now to the drawings, wherein like reference
numerals and letters indicate corresponding structure throughout
the several views:
[0022] FIG. 1 is a perspective view of a three-dimensional digital
model of a patient's dentition;
[0023] FIG. 2 is a diagrammatic view of a system for modeling tooth
movement according to the principles of the present invention;
[0024] FIG. 3 is a diagrammatic view of a portion of the virtual
model shown in FIG. 1 with an instant center of rotation shown for
a selected tooth;
[0025] FIG. 4 is a diagrammatic view of a projected path of
movement for a selected portion of the selected tooth shown in FIG.
3;
[0026] FIG. 5 is a diagrammatic view of a projected path of
movement for growth;
[0027] FIG. 6 is a perspective view of a projected path of movement
for correction (with the instant center shifted-show 2);
[0028] FIG. 7 shows a flow chart of the steps to create a digital
model;
[0029] FIG. 8 is a flow chart showing the steps to model tooth
movement according to the principles of the present invention;
[0030] FIG. 9 is a diagrammatic view of the virtual model shown in
FIG. 3 at two points in time to determine an instant center of
rotation; and
[0031] FIG. 10 is a diagrammatic view of a tooth with two points
plotting a path of movement about an instant center of rotation for
each point.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
[0032] Referring now to the drawings, and in particular to FIG. 1,
there is shown a digital image of a patients dentition 20 including
an upper arch having a portion of the upper gums 22, and the
exposed surfaces of the upper teeth 26. In a similar manner, a
lower arch including a portion of the teeth and lower gums 24 is
also created in a digitized model along with the exposed upper
surfaces of the lower teeth 28. Such an image of the dentition 20
is digitized and provides a virtual three dimensional image of the
patient's teeth for diagnosis, treatment and correction. Such a
method and system for creating such a virtual image of the
patient's mouth is shown and described in U.S. Pat. No. 6,579,059,
incorporated herein by reference. One method of creating digital
images is taking a casting of the patients teeth and creating a
plaster model and scanning the plaster cast. The digitizing system
70 is shown in FIG. 2 and includes a scanner 72 that passes a laser
over the plaster model held by fixture 74. A rotatable support 76
mounts on a base 78 and provides for moving the plaster model
relative to the scanner so that the outer contour of the patient's
teeth and gums can be stored in a digital format of a memory device
86. A central processor 82 provides for converting the data from
the scanner to a digital image of the exterior of the patient's
teeth and gums. An input device 80 provides for manipulating images
88 and a display 84 provides a screen for viewing the virtual image
of the teeth and gums. It can be appreciated that the digital image
provides for modeling with each tooth represented by sets of
coordinates in three dimensions so that the tooth may be
manipulated independently such as to model tooth movement.
Moreover, when a digitized virtual model is created in three
dimensions, mathematical calculations may be performed and then
displayed to provide the dentist or orthodontist with sufficient
precision for meaningful diagnosis and treatment. Mapping in three
dimensions and greater precision provide for meaningful treatment
that is not possible with prior methods based on markers and/or
x-rays.
[0033] More recently, high resolution three dimensional scanners
have been developed that provide direct three dimensional
craniofacial imaging that may be used to create a digital
representation of a patient's teeth with a high degree of precision
without plaster casts and without using landmarks or markers. Such
scanners include cone beam tomography scanners, intra-oral
scanners, CT scanners and other technologies that provide high
resolution precision three dimensional digital models. Examples of
commercial available scanners include cone beam scanners sold under
the trade names ILUMA.TM. from Kodak and i-CAT from Imaging
Sciences International. Cone beam tomography scanners are well
suited for such applications as they emit lower radiation than
traditional dental x-rays and may eliminate the need for creating
plaster casts.
[0034] Referring now to FIG. 3, there is shown a portion of the
patient's dentition including representative upper incisors and
molars 26 and lower incisors and molars 28. A selected tooth 30
having a complementary lower tooth 34 shown as an upper molar in
FIG. 3 is modeled and movement of the tooth may be determined. It
has been found that the path of movement of a tooth may be more
accurately modeled as rotating about an imaginary point, forming an
axis of rotation, represented as center point C1 in FIG. 4. Each
tooth has various forces acting on the tooth and other structure in
the jaw that affect movement. A kinematic and dynamic analysis and
synthesis is performed based on the patient's facial structures to
determine the imaginary instant center. An imaginary instant center
of rotation may be calculated for each tooth. In addition to an
individual tooth, the jaw, groups of teeth and other structures in
the jaw and mouth may also have an imaginary instant center point
about which such structures move. Moreover, the forces due to
growth may act differently on the tooth or structure so that a
tooth or structure in a patient that is growing may have an instant
center for corrective or restorative procedures and a different
instant center to simulate movement for passage of time and growth.
The center point C1 may be represented as a set of X, Y and Z
coordinates in the digital model. The movement of the tooth 30 is
limited by the gums, jaw, surrounding teeth and other structures
and forces acting on it. Therefore, the movement of point 32 will
occur along an arcing path P1 centered on the instant center of
rotation C1. The tooth will move along this path and correction,
growth or other forces acting on the tooth may direct it a distance
along this path. The path may be charted along a set of coordinates
in the digital model with great precision. Such a virtual model may
be utilized to predict repositioning of the tooth or structure from
the passage of time and growth. In addition, a virtual model that
may have a different instant center of rotation may be utilized to
predict repositioning of the tooth or structure due to forces
applied by the other teeth and structures in the mouth or the
addition of orthodontic structures. Predicting the distance along
the projected path P1 that a tooth will move, a new position of the
tooth 30 may be projected and also represented mathematically as a
new set of coordinates stored in the memory device 86. Such a three
dimensional representation may be shown and manipulated by the
dental practitioner in selecting and optimizing treatment.
[0035] To determine a path of rotation for modeling the tooth and
tooth movement, a point 32 on or in the tooth is selected as the
tracing point for projecting a path of movement. An instant center
of rotation is established with published methods and using the
expertise and estimation from the dental practitioner based on
features of the virtual image of the dentition 20 as well as the
type and overall structure of the patient's skull and jaw. The
instant center is established by analyzing the various static and
dynamic forces acting on the tooth. In one embodiment, the center
point C1 is selected based on the occlusal plane of the teeth 30
and 32, the structure of the patient's jaw, and patterns of
movement generally associated with similar physiology. Centers of
rotation have been previously charted from studies conducted using
prior art markers that provide guidance for the dental practitioner
locating the instant center. Similar jaw structures for comparison
provide guidance to locate centers of rotation, so that the axis
may be accurately approximated with the available information and
an accurate virtual model of the patient's dentition 20.
[0036] As shown in FIG. 7, the point of projection 32 is entered
and stored as a set of coordinates in the memory device 86, shown
in FIG. 2. In addition, the orientation of the remainder of the
exposed portion of the tooth 30 is also entered and stored as a set
of coordinates in three dimensions. This orientation is in relation
to a radius R1 extending from the point of projection 32 to the
center C1. As the tooth moves along the projected path of movement
P1, the radius distance remains constant and the position and
orientation of the tooth structure 30 translates with respect to
the radius R1. A direction of movement is also determined by the
dental practitioner using knowledge of the patient's physiology and
the forces applied by the selected treatment.
[0037] Based on the repositioning of the tooth 30 as it rotates
about the center point C1, various treatments and/or decisions may
be made regarding alignment and positioning of the tooth. Moreover,
by performing the same analysis on other teeth, an overall
treatment plan may be devised in a coordinated manner so that
treatment is more effective.
[0038] Referring now to FIG. 5, in some instances, the rotational
center of the plotted point 32 may move closer to the tooth due to
changes in forces applied, such as for example, braces. For
example, C1 may shift from position C1 to position C2. Therefore,
the path of rotation moves from the projected path P1 to the
projected path P2. The movement of the projected path allows for
recalculating movement and more precise diagnosis and treatment for
more properly positioning the teeth. Although the center is shown
to be moved closer to the tooth 30 in FIG. 5, it can be appreciated
that the center of rotation may shift in any direction. Moreover,
the instance center may be above, below, behind or in front of the
tooth and that the illustrated center C1 and C2 and the
corresponding paths P1 and P2 and radial cords R1 and R2 are shown
as examples only. Positioning will depend upon the particular
physiology of the patient's teeth and jaws.
[0039] Referring now to FIG. 6, there is shown a further example of
a projected path and changes that may occur to move the instant
center of rotation. For example, with some treatments, such as the
application of corrective braces to the tooth, the instant center
of rotation may move from a rotational axis shown at C1 in FIG. 4
to a rotational axis centered at C3, as shown in FIG. 6. The forces
change the instant center of rotation and move the projected path
of movement from path P1 to path P3. Although the rotational axis
at the instant center C1 is moved from slightly above and behind
the tooth 30 to a location in front of and below the tooth 30 to
rotational axis point C3, the instant center of rotation may begin
and end in any combination of places and it can be readily
appreciated that the locations are shown only as examples. Other
surrounding physiology and corrective devices may alter the center
of rotation and/or the projected path. In a method of the present
invention, the change is factored as a force vector acting on the
tooth. For patients where tooth growth will occur, a growth
coefficient may be factored to determine how much movement will
occur over a predetermined period.
[0040] For some patients, the center of rotation may be positioned
far from the tooth 30 and the length of the associated radius may
approach infinity so that substantially linear motion is projected
for the path of movement. The projected path of movement may be
modeled with the digitized virtual model to occur on all three
planes so that the projected center of rotation may also be
positioned laterally from the patient's face. Such projected path
of movement is easier to plot and represent in a digitized virtual
model with greater precision, such as shown in FIG. 1, and provides
greater feedback and improved information for the dental
practitioner to evaluate for proper treatment. Moreover, as the
present invention provides for plotting paths of movement about
various potential shifted centers of rotation, multiple different
treatment approaches having different forces may be modeled.
Therefore, different types of braces or other corrective measures
may be evaluated by plotting the different centers of rotation and
the corresponding projected path of movement. Modeling movement
with precision leads to optimizing tooth position, diagnosis and
correction.
[0041] Referring now to FIG. 8, to create a projection of tooth
movement about an instant center of rotation, the model of the
casting of the tooth is made and scanned into the memory 86 of the
scanning system 80 as shown in FIG. 7. The patient's physiology and
the virtual model are analyzed to locate an instant center of
rotation for a particular tooth. Based upon the instant center of
rotation, a projected path of movement is plotted. Using a time and
force factor, a direction and distance along the projected path of
movement is selected. The tooth is then repositioned with the
projection point located along the path of movement the selected
distance in the selected direction. A digital image is then created
showing the tooth at the new location. It can be appreciated that
such an image can be superimposed over the old location and
combined with individual digital images of the other teeth and
facial structures to create a complete new three dimensional image
of the patient's teeth to simulate movement. Many virtual images
can be superimposed to compare and optimize treatments.
[0042] Referring now to FIG. 9, the present invention also provides
for tracking of tooth movement through time by comparing and
mapping the position of a tooth 30 over time. Such changes in
position allow for further projection by locating a center of
rotation by triangulating the center point from the tooth
orientation at each of the positions. Such triangulation provides a
center of rotation that can be used to plot a path of movement P4
about a center of rotation C4 and having a radial cord R4. The
historical movement also provides for modifying the selected center
of rotation and for reevaluating treatment.
[0043] Referring now to FIG. 10, the present invention also
provides for modeling growth for movement that does not follow
rotation about a single center of rotation for a particular
structure, such as a tooth 100. The tooth 100 and its movement may
be represented as having a first point 102 following a path of
movement centered about a first rotational axis C5 while a second
point 104 of the tooth structure 100 may follow movement centered
about a second instant center of rotation C6. Each of the locations
102 and 104 has a corresponding path of rotation, P5 and P6
respectively, and radial cords R5 and R6. In this manner, it can be
appreciated that the movement of the tooth 100 over time may still
be plotted with the tooth 100 having the same motion as a four bar
linkage. It can be appreciated that the centers of rotation C5 and
C6 act as the ground or first link while the radial chords R5 and
R6 represent two other links. A tooth structure itself 100
represents a virtual fourth link. It can be appreciated that the
rotational center points C5 and C6 may shift as explained above.
The paths of movement P5 and P6 would also shift and movement of
the two points 102 and 104 would follow a different four bar
linkage, with the tooth reorienting and/or moving. Modeling
techniques and treatment discussed above for a single instant
center may also be employed for a tooth having movement behaving as
a virtual four bar linkage.
[0044] It is to be understood, however, that even though numerous
characteristics and advantages of the present invention have been
set forth in the foregoing description, together with details of
the structure and function of the invention, the disclosure is
illustrative only, and changes may be made in detail, especially in
matters of shape, size and arrangement of parts within the
principles of the invention to the full extent indicated by the
broad general meaning of the terms in which the appended claims are
expressed.
* * * * *