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Claims  |
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What is claimed is:
1. A method of optimizing dose delivery involving stereotactic computer
techniques comprising the steps of:
1) generating and displaying graphic simulation of a predetermined volume
to be dosed from image data obtained from a single one of a plurality of
imaging scanners;
2) providing a stereotactic frame and thereby establishing
three-dimensional coordinates about the predetermined volume to be dosed;
3) determining an enclosing volume circumscribing said predetermined volume
to be dosed;
4) meshing said enclosing volume with node points;
5) providing problem variables relating to dosage;
6) calculating the dose to be delivered to each of said node points;
7) formulating an objective function for evaluating the dosage;
8) solving a numerical optimization algorithm minimizing the objective
function;
9) repeating steps 7) and 8) until said problem variables are optimized;
and
wherein the step of determining an enclosing volume circumscribing the
predetermined volume to be dosed further comprises the steps of:
1) graphically simulating a calculated tumor volume as said predetermined
volume;
2) calculating the centroid and major axis dimension of said calculated
tumor volume; and
3) calculating and providing an enclosing volume with said centroid of said
tumor volume at the center of the enclosing volume, said enclosing volume
enclosing said tumor volume plus a nonpathologic margin.
2. The method of claim 1 wherein the step of meshing said enclosing volume
with node points comprises the steps of:
a. assigning three-dimensional stereotactic frame coordinates to said node
points;
b. determining the position of said node points relative to said
predetermined volume; and
c. weighting said nodes according to their position.
3. The method of claim 1 wherein said step of providing problem variables
comprises the steps of:
a. choosing isotopic seed activity;
b. orienting a catheter;
c. locating isotopic seeds along the catheter; and
d. setting upper and lower limits to said variables.
4. The method of claim 3 wherein said step of calculating the dose
delivered to each of said node points comprises the steps of:
a. assigning three-dimensional stereotactic frame coordinates to the
isotopic seeds; and
b. calculating individual node doses by the equation
##EQU7##
wherein: i=current node number,
j=current catheter number,
k=current seed number,
n.sub.c =total number of catheters,
n.sub.s =total number of seeds per catheter,
D.sub.i =total radiation dose at node i,
##EQU8##
node radiation dose from catheter j, s.sub.jk =strength of seed k in
catheter j, and
r.sub.jk =radius from seed k in catheter j to node i.
5. The method of claim 1 wherein said step of providing problem variables
comprises the steps of:
a. choosing a pattern of beam rotation relative to an isocenter;
b. selecting beam strength;
c. selecting beam collimation; and
d. setting upper and lower limits to said problem variables.
6. The method of claim 5 wherein the step of calculating the dose delivered
to each of said node points comprises the steps of:
a. separating each beam path into a predetermined number of individual
beams; and
b. calculating individual node doses by the equation
##EQU9##
wherein: i=current node number
j=current beam number
n.sub.b =total number of beams,
D.sub.i =total radiation dose at node i,
G.sub.j (s.sub.j,c.sub.j,d.sub.j)=node radiation dose from beam j,
s.sub.j =strength of beam j,
c.sub.j =collimation of beam j, and
d.sub.j =direction of beam j.
7. The method of claim 1 whereon the step of formulating an objective
function comprises the steps of:
a. determining whether each said node within said enclosing volume is dead
or alive relative to a predetermined dose;
b. assigning each said node to one of four specific subtotals, including
(1) nodes inside the predetermined volume and alive, (2) nodes inside the
predetermined volume and dead, (3) nodes outside the predetermined volume
and alive, and (4) nodes outside the predetermined volume and dead;
c. dividing each of said specific subtotals by the total number of nodes;
and
d. summing (1) the ratio of nodes outside the predetermined volume and dead
and (2) the ratio of nodes inside the predetermined volume and alive.
8. The method of claim 1 wherein the step of formulating an objective
function comprises the step of assigning status factors to the nodes as
follows: (1) a value of +P for nodes inside the predetermined volume and
dead, (2) a value of -1 for nodes inside the predetermined volume and
alive, (3) a value of -1 for nodes outside the predetermined volume and
dead, and (4) a value of 0 for nodes outside the predetermined volume and
alive, wherein:
P=e-(D.sub.i -D.sub.o).sup.2/.delta..sup.2
D.sub.i =Radiation dose at node i,
D.sub.o =Predetermined dose, and
.delta.=decay factor.
9. A apparatus for optimizing dose delivery involving stereotactic computer
techniques comprising:
means for generating and displaying a graphic simulation of a predetermined
volume to be dosed from image data obtained from a single one of a
plurality or imaging scanners;
stereotactic frame means for establishing three-dimensional coordinates
about the predetermined volume to be dosed;
means for determining an enclosing volume circumscribing said predetermined
volume to be dosed;
means for meshing said enclosing volume with node points;
means for providing problem variables relating to dosage;
means for calculating the dose to be delivered to each of said node points;
means for formulating an objective function for evaluating the dosage;
means for solving a numerical optimization algorithm minimizing the
objective function; and
wherein said means for determining an enclosing volume circumscribing the
predetermined volume to be dosed comprises:
means for graphically simulating a calculated tumor volume as said
predetermined volume;
means for calculating the centroid and major axis dimension of said
calculated tumor volume; and
means for calculating and providing an enclosing volume with said centroid
of said tumor volume at the center of the enclosing volume, said enclosing
volume enclosing said tumor volume plus a nonpathologic margin.
10. The apparatus of claim 9 wherein said means for meshing said enclosing
volume with node points comprises:
means for assigning three-dimensional stereotactic frame coordinates to
said node points;
means for determining the position of said node points relative to said
predetermined volume; and
means for weighting said nodes according to their position.
11. The apparatus of claim 9 wherein said means for providing problem
variable comprises:
means for choosing isotopic seed activity;
means for orienting a catheter;
means for locating isotopic seeds along the catheter; and
means for setting upper and lower limits to said variables.
12. The apparatus of claim 11 wherein said means for calculating the dose
delivered to each of said node points comprises:
means for assigning three-dimensional stereotactic frame coordinates to the
isotopic seeds; and
means for calculating individual node doses by the equation
##EQU10##
wherein: i=current node number,
j=current catheter number,
k=current seed number,
n.sub.c =total number of catheters,
n.sub.s =total number of seeds per catheter,
D.sub.i =total radiation dose at node i,
##EQU11##
node radiation dose from catheter j, s.sub.jk =strength of seed k in
catheter j, and
r.sub.jk =radius from seed k catheter j to node i.
13. The apparatus of claim 9 wherein said means for providing problem
variables comprises:
means for choosing a pattern of beam rotation relative to an isocenter;
means for selecting beam strength;
means for selecting beam collimation; and
means for setting upper and lower limits to said problem variables.
14. The apparatus of claim 13 wherein said means for calculating the dose
delivered to each of said node points comprises:
means for separating each beam path into a predetermined number of
individual beams; and
means for calculating individual node doses by the equation
##EQU12##
wherein: i=current node number,
j=current beam number,
n.sub.b =total number of beams,
D.sub.i =total radiation dose at node i,
G.sub.j (s.sub.j,c.sub.j,d.sub.j)=node radiation dose from beam j,
s.sub.j =strength of beam j,
c.sub.j =collimation of beam j, and
d.sub.j =direction of beam j.
15. The apparatus of claim 9 wherein said means for formulating an
objective function comprises:
means for determining whether each said node within said enclosing volume
is dead or alive relative to a predetermined dose;
means for assigning each said node to one of four specific subtotals,
including (1) nodes inside the predetermined volume and alive, (2) nodes
inside the predetermined volume and dead, (3) nodes outside the
predetermined volume and alive, and (4) nodes outside the predetermined
volume and dead;
means for dividing each of said specific subtotals by the total number of
nodes; and
means for summing (1) the ratio of nodes outside the predetermined volume
and dead and (2) the ratio of nodes inside the predetermined volume and
alive.
16. The apparatus of claim 27 wherein said means for formulating an
objective function comprises assigning status factors to the nodes as
follows: (1) a value of +P for nodes inside the predetermined volume and
dead, (2) a value of -1 for nodes inside the predetermined volume and
alive, (3) a value of -1 for nodes outside the predetermined volume and
dead, and (4) a value of 0 for nodes outside the predetermined volume and
alive, wherein:
P=e-(D.sub.i -D.sub.o).sup.2/.delta..sup.2
D.sub.i =Radiation dose at node i,
D.sub.o =Predetermined dose, and
.delta.=decay factor. |
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Claims |
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Description |
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This application is also related to U.S. patent application Ser. No.
07/428,242, now abandoned, entitled Three-Dimensional Laser Localization
Apparatus and Method for Stereotactic Diagnoses or Surgery, to Hardy, et
al., filed Oct. 27, 1989, the teachings of which are incorporated herein
by reference.
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to an apparatus and method of combining
three-dimensional computer graphic simulation of volumes with computerized
numerical optimization by mathematical computation.
2. Description of the Related Art Including Information Disclosed under 37
C.F.R. .sctn.1.97-1.99
Currently there are no efficient optizimation techniques or treatment
planning methods for optimizing the dose delivery and shape of e.g.,
radiation zones in the treatment of various tumors in the body, especially
the brain. Current methods involve various means of rough approximation of
dose delivery to a tumor region with severe limitations on tailoring the
radiation dose delivery to fit the exact dimensions and shape of the tumor
volume. In addition, there is no method available which allows treatment
planners to effectively minimize the dose delivery to reasonably normal
brain tissue surrounding a tumor lesion and maximizing the dose to the
tumor itself, other than the rather cumbersome, two-dimensional does
planning systems which rely heavily on dose volume histogram calculations.
As designed, currently used systems involve very tedious iterative
processing by the planner to fit a radiation treatment dose and volume
distribution to a given tumor volume or such similar tissue volume.
Current methods are very laborious, often requiring up to a day or more to
do a single dose plan or any simple iterative adjustment. Such methods are
severely limited and many dose treatment planners are constrained by
current technological limitations to "closely approximate" a given dose
delivery. There are various devices on the market; for example, the
Leksell gamma knife (see L. Leksell, Stereotaxis and Radiosurgery; An
operative system, Springfield, Ill. Charles C. Thomas, 1971) and the
LINAC.RTM. scalpel" (see K. R. Winston, W. Lutz, "Linear Accelerator as a
Neurosurgical Tool for Stereotactic Radiosurgery," Neurosurgery, Vol. 22,
No. 3, 1988; F. Colombo, A. Benedetti, et al., "External Stereotactic
Irradiation by Linear Accelerator," Neurosurgery, Vol. 16, No. 2, 1985;
and W. A. Friedman, F. J. Bova, "The University of Florida Radiosurgery
System," Surg. Neurol., Vol 32, pp. 334-342, 1989) which are capable of
deliverying the dose delivery to the tumor volume and optimizing the
delivery such that dose zones can be tailored to tumor shape,
configuration and size. Similarly, there are currently available methods
for the accurate placement of radioisotopes, contained within catheters,
in strategic areas of the brain for the direct delivery of a radiation
does to a given area of the brain. This method also has similar
limitations in radiation does delivery optimization (see K. Weaver, V.
Smith, et al., "A CT Based Computerized Treatment Planning System for
I-125 Stereotactic Brain Implants," Int. J of Radiation Oncology, Biol.
Phys., Vol 18, pp. 445-454, 1990; P. J. Kelly, B. A. Kall, S. Goerss,
"Computer Simulation for the Stereotactic Placement of Interstitial
Radionuclide Sources into Computed Tomography-Defined Tumor Volumes,"
Neurosurgery, Vol. 14, No. 4, 1984; and B. Bauer-Kirpes, V. Sturm, W.
Schlegel, and W. J. Lorenz, "Computerized Optimization of I-125 Implants
in Brain Tumors," Int. J. Radiat. Oncol. Biol, Phys., Vol. 14 pp.
1013-1023, 1988)
None of the methods or devices described above combine three-dimensional
graphics simulation and actual imaging data, such as disclosed in parent
application, Ser. No. 07/500,788, with computerized numerical optimization
for dose delivery treatment planning. Generally, co-pending applications
Ser. No. 07/500,788 and 07/290,316, now U.S. Pat. No. 5,099,846, involve
acquiring a magnetic resonance (MR), computed tomography (CT), or the
like, image of a volume, such as a tumor volume, in serial sections
through the volume, outlining such sections, and creating a
three-dimensional simulation of the volume.
The concept of mathematical function optimization has existed since the
advent of calculus and over the years has developed into very efficient
and robust algorithms for constrained multidimensional nonlinear
optimization. The word "optimization," when used in this context and in
the specification and claim, means the rigorous use of algorithmic steps,
implemented as computer code, to search for and find a mathematically
defined local minimum (or maximum) or given objective function. An
objective function can take many forms (e.g., calculated stress in a
structural member, aerodynamic loading on a wind, or a calculated dose of
brain cell irradiation), but is simply a chosen measure of the desired
behavior of the object, system, or process being designed. The term
"contrained optimization" then refers to the optimization process, as
explained above, being conducted within certain allowable limits or
constraint. For example, a desired design objective may be to design a car
frame of minimum weight design. If no constraints were put on this design
problem, the minimum weight design would no be able to withstand the
encountered loads during operation and may not even by manufacturable.
Constraints are put on the design problem that require the car frame to
support certain loads under various conditions and to ensure that the
final design will be manufacturable given current technology. Typically,
"real world" design problems are constrained by certain necessary
performance criteria. Modeling the physical behavior or "real world"
objects, systems, and processes requires the use of complex nonlinear
mathematical equations formed from available variable and incorporated
within the computer code. Therefore, using the definitions provided in
this paragraph, the term "constrained multidimensional nonlinear
optimization" is defined.
Such algorithms are discussed above were designed to replace the
traditional "hunt and peck" process with efficient, non-random techniques
for gleaning information from the computer model in the form of slopes and
curvature of the objective function "hyper-surface" (a surface with three
or more variables). When coupled in this manner, the algorithms take the
place of the user and autonomously search and find the optimal combination
of variables to maximize or minimize a desired objective.
Two robust and efficient nonlinear optimization algorithms available in the
art are the Generalized Reduced Gradient (GRG) algorithm and the
Sequential Quadratic Programming (SQP) algorithm. Since the algorithms
themselves are in the public domain, many private versions of these
algorithms are currently available as software package.
The present invention applies these numerical optimization techniques to
help improve the planning process generally for optimal dose distribution
planning and specifically for the radiation treatment of brain tumors. The
current techniques of radiation therapy require the designers
(neurosurgeons and radiation oncologists) to perform tedious design
iterations in their search for the optimal placement of radioisotope seeds
and external beam trajectories. By incorporating numerical optimization
algorithms into the existing framework, the operation planning process
becomes virtually automatic and produces better planning designs than
current techniques and in less time.
SUMMARY OF THE INVENTION
The preferred embodiment of the invention comprises a method and apparatus
for optimizing dose delivery involving stereotactic computer techniques
comprising: (a) determining an enclosing volume circumscribing a
predetermined volume to be dosed; )b) meshing the enclosing volume with
node points; (c) providing problem variables; (d) calculating the dose to
be delivered to each of the node points; (e) formulating an objective
function; (f) solving a numerical optimization algorithm minimizing the
objective function; and (g) repeating (e) and (f) until the problem
variables are optimized.
The preferred method and apparatus for determining an enclosing volume
comprises: (a) graphically simulating a calculated tumor volume as the
predetermined volume; (b) calculating the centroid and major axis
dimensions of the calculated tumor volume; and (c) calculating and
providing an enclosing volume with the centroid of the tumor volume at the
center of the enclosing volume, the enclosing volume enclosing the tumor
volume plus a nonpathologic margin.
The preferred method and apparatus for meshing the enclosing volume with
node points comprises: (a) assigning three-dimensional coordinates to the
node points; (b) determining the position of the node points relative to
the predetermined volume; and (c) weighting the nodes according to their
position.
The preferred apparatus and method for providing problem variables
comprises (a) choosing isotopic seed activity; (b) orienting a catheter;
(c) locating isotopic seeds along the catheter; and (d) setting upper and
lower limits to the variables. The preferred apparatus and method for
calculating the dose delivered to each of the node points comprises: (a)
assigning three-dimensional coordinates to the isotopic seeds; and (b)
calculating individual node doses by the equation:
##EQU1##
wherein:
i=current node number,
j=current catheter number,
k=current seed number,
n.sub.c =total number of catheters,
n.sub.s =total number of seeds per catheter,
D.sub.i =total radiation dose at node i,
##EQU2##
node radiation dose from catheter j,
s.sub.jk =strength of seed k in catheter j, and
r.sub.jk =radius from seek k in catheter j to node i.
An alternative apparatus and method for providing problem variables
comprises: (a) choosing a pattern of beam rotation relative to an
isocenter; (b) selecting beam strength; (c) selecting beam collimation;
and (d) setting upper and lower limits to the problem variables. The
preferred apparatus and method for calculating the dose delivered to each
of the node comprises: (a) separating each beam path into a predetermined
number of individual beams; and (b) calculating individual node doses by
the equation:
##EQU3##
wherein:
i=current node number,
j=current beam number,
n.sub.b =total number of beams,
D.sub.i =total radiation dose at node i,
G.sub.j (s.sub.j, c.sub.j, d.sub.j)=node radiation dose from beam j,
s.sub.j =strength of beam j,
c.sub.j =collimation of beam j, and
d.sub.j =direction of beam j.
The preferred apparatus and method for formulation the objective function
comprises: (a) determining whether each node within the enclosing volume
is dead or alive relative to a predetermined dose; (b) assigning each node
to one of four specific subtotals, including (1) nodes inside the
predetermined volume and alive, (2) nodes inside the predetermined volume
and dead, (3) nodes outside the predetermined volume and alive, and (4)
nodes outside the predetermined volume and dead; (c) dividing each of the
specific subtotals by the total number of nodes; and (d) summing (1) the
ratio of nodes outside the predetermined volume and dead and (2) the ratio
of nodes inside the predetermined volume and alive. In this embodiment,
the node error or tumor fit error objective function is minimized.
An alternative apparatus and method for formulating another objective
function comprises assigning status factors to the nodes as follows: (1) a
value of +P for nodes inside the predetermined volume and dead, (2) a
value of -1 for nodes inside the predetermined volume and alive, (3) a
value of -1 for nodes outside the predetermined volume and dead, and (4) a
value of 0 for nodes outside the predetermined volume and alive, wherein
P=e.sup.-(D.sub.i -D.sub.o).sup.2.delta.2
D.sub.i =Radiation dose at node i,
D.sub.o =Predetermined dose, and
.delta.=decay factor.
This embodiment for solving the numerical optimization algorithm comprises
maximizing the node status objective function.
A primary object of the present invention is to provide optimization of
dose delivery in various treatments, such as treatment of brain tumors.
A further object of the present invention is to maximize dose delivery in
pathologic tissue while minimizing dosage in nonpathlogic tissue.
An advantage of the present invention is that dose delivery systems can be
employed with diverse therapies.
Yet another advantage of the present invention is the extremely rapid
solution of the dosage delivery problem.
Other objects, advantages and novel features, and further scope of
applicability of the present invention will be set forth in part in the
detailed description to follow, taken in conjunction with the accompanying
drawing, and in part will become apparent to those skilled in the art upon
examination of the following, or may be learned by practice of the
invention. The objects and advantages of the invention may be realized and
attained by means of the instrumentalities and combinations particularly
pointed out in the appended claims.
BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings, which are incorporated into and form a part of
the specification, illustrate several embodiments of the present invention
and, together with the description, serve to explain the principles of the
invention. The drawings are only for the purpose of illustrating a
preferred embodiment of the invention and are not to be construed as
limiting the invention.
FIG. 1 is a perspective view of a form of a dose delivery system showing a
simulated tumor volume, brachytherapy catheters, and radioisotope seeds;
FIG. 2 is a perspective view of a simulated enclosing volume circumscribing
the simulated tumor volume of FIG. 1;
FIG. 3 is a perspective view of the enclosing volume and tumor volume of
FIGS. 1 and 2 meshed with node points;
FIG. 4 is a perspective view of parametric seed positioning relative to the
enclosing volume and tumor volume of FIGS. 1 and 2;
FIG. 5 is a flow diagram of the calculation of the tumor fit error
(objective) function of the present invention useful for brachytherapy;
FIG. 6 is a flow chart of the optimization loop of the invention;
FIG. 7 is a graph showing a curve of the "inside and dead" overkill penalty
function of the present invention.
FIG. 8 is a flow diagram of the calculation of the tumor fit error function
of the present invention useful for external beam radiation.
FIG. 9 is a preferred hardware block diagram in accordance with the
invention; and
FIG. 10 is a photograph of a computer screen display of an actual CT image
section or scan slice combined with a stereotactic frame and a
stereotactic surgical probe directed towards a tumor lesion within the
confines of the head.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS OF THE INVENTION
The present invention relates generally to the optimization of a dose
delivery system. Specifically, the dose to be delivered can be any dosing
agent or physical phenomena, such as radiation, poisons, chemical
compounds, hypothermia compounds, hyperthermia compounds, antimatter, in
the form of antiprotons, photosensitive compounds, and the like. The
invention is not limited to the dosing agents listed above, as the
optimization techniques of the invention may be used with a variety of
dosing agents and treatment plans. The invention is particularly useful
for the radiation treatment of brain tumors using stereotactic techniques
and thus the detailed description below is directed to such techniques and
thus the detailed description below is directed to such treatment.
Although the use of a stereotactic frame and brachytherapy catheters are
discussed herein, other reference frames and other dose delivery systems
may also be used in accordance with the invention.
FIGS. 1-4 depict a tumor volume 10 calculated and graphically simulated.
Methods for simulating the tumor volume 10 are disclosed in parent
application Ser. No. 07/500,788, although other simulation methods which
might be available can also be employed. Centroid 11 and major axis 12 of
tumor volume 10 are calculated. Depending upon the dose delivery system
contemplated, line 13 could comprise, e.g., the center line of
brachytherapy catheter bundle 14 or the center beam of a major beam path
employed in external beam radiation therapy.
An enclosing volume 21 is calculated with tumor volume centroid 11 at the
center of such volume. The preferred configuration for volume 21 is a
cube, but other geometric shapes, such as a sphere, as shown in FIGS. 2-4,
may be employed. A volume which will enclose tumor volume 10 is chosen
such that a predetermined nonpathological margin 32 of presumably healthy
tissue is created. This margin is variable depending upon the dose
delivery system employed. Normally, a high percentage of healthy tissue
margin is required for external beam radiation therapy to better track the
dose deposited in the nonpathlogic tissue.
Subsequent to calculation of the enclosing volume, enclosing volume 21 is
meshed with a plurality of node points, as depicted by the mesh
intersections in FIG. 3. The number of node points is variable depending
upon mesh dimensions, desired accuracy, and computation time available. A
determination is then made as to whether each node point is within or
without tumor volume 10. This is accomplished by determining the size of
each voxol according to the dimension of the mesh and the number of nodes
defined; determining the distinct stereotactic frame coordinates (x, y,
and z) of each of these nodes; determining whether each node is located
within or without tumor volume 10; and flagging each node accordingly (0
or 1).
Initially there are some values or variables that must be chosen by the
user (e.g., physician, surgeon, or technician) to start the optimization
process. For brachytherapy or radioisotopic seed used, the number of seeds
per catheter, the configuration of the catheters within the available
catheter block hole pattern, and the dose delivery time. Treatment
planning may further include choosing radioisotope seed type (e.g., I-125,
irridium, or the like) and radioactivity level; using a nomogram to obtain
a preliminary number and spacing of seeds relative to a given tumor
volume; a computerized numerical optimization program to "best fit"
radioisotopic seeds to the given tumor volume; visually inspecting
graphically simulated dose zone delivery within the tumor volume; and
confirming or adjusting the constraints of the computerized numerical
optimization program.
For external beam radiation therapy, the values or variables include the
number of isocenters to be used and the location of the isocenters within
the tumor. Treatment planning may further dictate determination of
collimator size and shape and a preliminary number of isocenters for
radiation beam delivery; a computerized numerical optimization program to
"best fit" intended dose to tumor volume, visually inspecting graphically
simulated dose zone delivery within the tumor volume, and confirming or
adjusting the constraints of the computerized numerical optimization
program.
With specific reference to FIG. 5, the preferred initial treatment method
for use of the invention for brachytherapy comprises the following steps:
Tumor surface data 10 is obtained 50. This tumor surface data 10 is used
to determine 51 an enclosing volume 21, such as shown in FIG. 3. The
enclosing volume 21 is meshed into mode points (tumor plus healthy tissue)
52, such as shown in FIG. 3. Initial problem variables, such as choosing
the initial individual seed activity, the initial orientation of the
catheter bundle and the initial location of the seeds along each catheter,
are input 53. Providing the initial treatment plan or design may be done
automatically using a nomogram incorporated into the softwave or input by
the user. The initial treatment plan or design is used as a starting point
for the optimization algorithm of the invention. The performance of the
optimization algorithm is not all that sensitive to the initial design;
however, should be noted that poor initial input requires the optimization
algorithm to look harder and longer for the optimal design. Upper and
lower bounds on the design variables are either arbitrarily set or set to
remain within available bounds (e.g., a chosen type of isotope seed will
have a certain activity range in which it is available).
The isotope seed positions are then calculated and located 54 in x, y, and
z frame coordinates. The orientation of the catheter bundle is defined by
two rotation angles about the x and y axes respectively. Depending on the
stereotactic frame design, the stereotactic frame may be positioned in
such a way that the center of its rotation angles coincides or intersects
with the centroid 11 of the tumor 10. This allows the centroid line 13 of
the catheter bundle 14 to intersect with the tumor centroid 1 (see FIG.
1). An enclosing cube or other volume 21 is then located with its center
at the tumor centroid 11 and a sphere with a radius just large enough to
totally enclose the tumor volume, as in FIG. 3. Knowing the radius of the
sphere and the catheter pattern, the intersection points of each catheter
with the enclosing sphere 31 and the length of each catheter within the
sphere 31 can easily be calculated. Since the lengths of each catheter
enclosed within the sphere 31 will remain constant as the bundle 14
orientation angles are varied, these lengths can be used to parametrically
locate the radioisotope seeds along the catheter. This is done by
designating the entrance points 34 of each catheter into the enclosing
volume 21 as a "0" in parametric space, and the exit points 36 as "1".
Therefore, a number between 0 and 1 for a specific seed 38 along one of
the catheters can be used to uniquely define its x, y, and z coordinates
in the frame system. This concept is represented as a two-dimensional view
in FIG. 4. This parametric location process using an enclosing sphere 31
(or other volume) it implemented for two reasons: (1) to reduce the number
of design variables (there is only one location variable for each seed,
instead of its actual x, y and z, coordinates), and (2) to insure that the
relationship between the catheter bundle orientation angles and the seed
positioning would remain decoupled when using a parametric location
scheme.
Given the x, y, z coordinates of each isotope seed, the radiation dose to
each individual node within the meshed volume can be calculated 55 as the
sum of each seed's dose contribution to that particular node location (see
Equation 1).
##EQU4##
where:
i=current node number
j=current catheter number
k=current seed number
n.sub.c =total number of catheters
n.sub.s =total number of seeds per catheter
D.sub.i =total radiation dose at node i
##EQU5##
node radiation dose from catheter j
s.sub.jk =strength of seed k in catheter j
r.sub.jk =radius from seed k catheter j to node i
The calculated dose received by each node in the meshed volume can be used
in a number of ways to evaluate the "goodness" of the current treatment
plan.
Given the dose calculated at each node, it is determined whether each
individual node within the meshed volume is "dead" or "alive" based on a
predetermined "kill" dose of radiation. As each node 31 is inquired, that
node is recorded as "dead" or "alive" by adding a "1" to the values of
various subtotals. The four subtotals are identified as: (1) the number of
nodes inside the tumor and alive; (2) the number of nodes inside the tumor
and dead; (3) the number of nodes outside the tumor and alive; and (4) the
number of nodes outside the tumor and dead.
Using the information stored in the subtotals, the "dead" and "alive"
ratios are calculated by dividing the number in each bin by the total
number of nodes. These ratios are then combined to formulate 56 an
objective function for the optimization process. This objective function
for tumors is referred to herein as "tumor fit error" value. It is defined
as the sum of the ratio of nodes outside the tumor and dead, plus the
ratio of nodes inside the tumor and alive (see Equation 2).
Tumor Fit Error=Out.sub.d +In.sub.a (2)
where:
Out.sub.d =Ratio of nodes outside the tumor and dead
In.sub.a =Ratio of nodes inside the tumor and alive
As shown in FIG. 6, when a value of tumor fit error is obtained 60 for the
current seed placement and bundle orientation, a numerical optimization
algorithm (e.g., Generalized Reduced Gradient or Sequential Quadratic
Programming) is then used 62 to determine the optimal seed placement,
activity and bundle orientation. Obviously, as the tumor fit error value
approaches zero, the radiation kill zone created by the isotope seeds
approaches the actual shape of the tumor. Therefore, the optimization
problem can be stated: "Minimize the tumor fit error such that all nodes
inside the tumor are dead." As shown in FIG. 6, the optimization algorithm
iterates through a number of designs by perturbing the variable values
(seed location, strength, bundle orientation, and other associated
variables) and executing these steps until it reaches the best combination
of variables to minimize the tumor fit error.
With specific reference to FIG. 7, an alternative brachytherapy dose
delivery method designed to provide homogeneous dose delivery comprises
assigning status factors as follows:
Calculate the individual node radiation doses in the same manner as
detailed above. By comparing against the predetermine "kill" dose, decide
if the node is "dead" or "alive" and assign it a status factor as defined
below.
If the node is:
Inside the tumor and dead, assign the node +P
Inside the tumor and alive, assign the node as -1
Outside the tumor and dead, assign the node as -1
Outside the tumor and alive, assign the node as O
where
P=e.sup.-(D.sub.i -D.sub.o).sup.2/.delta..sup.2 (3)
D.sub.i =Radiation dose at node i
D.sub.o =Predetermined lethal radiation dose .delta.=decay factor of the
overkill penalty
The P function is used to define an "overkill" penalty to a node inside the
tumor with a dose above that of the lethal dose; that is, when the dose
level is below the lethal dose, the value of P is zero, but as it passes
the lethal dose, its value jumps to 1 and then starts to decrease as the
node dose level increases above the lethal limit. The parameter .delta. is
used to change the amount of dwell nearer to a P value of 1 before the
exponential decay becomes effective and quickly decreases the "utility" of
an inside node that has been overkilled. As can be seen, only the nodes
that are inside and dead receive a factor greater than zero with the
undesirable conditions of inside and alive and outside and dead being
assigned negative status factors.
After assigning a status factor to each node, an objective function for the
optimization process can be formed by summing all of the node status
factors (see Equation 5). This "tumor status" objective function will be
different for each seed placement design and would reach its maximum when
there are few "outside dead" and "inside alive" nodes and most of the
inside dead" nodes have a status factor of 1 (meaning they have just
attained a level of "dead"). Notice that maximizing the "tumor status"
function will have the effect of homogenizing the dose distribution within
the tumor boundaries because the maximum value of the node status factor
is assigned only to those nodes that are not "overkilled" by too much.
Therefore, the optimization problem can be stated: "Maximize the tumor
status function." Insuring that all the nodes inside are dead could be
accomplished by increasing the negative value of the "inside alive" status
factor and more heavily penalizing the "tumor status" function when
"inside alive" nodes exist. The optimization algorithm will iterate
through a number of designs or treatment plans be perturbing the variable
values (seed location, strength, bundle orientation, and other associated
variables) until it reaches the best combination of variables to maximize
the "tumor status" function.
Employment of external beam radiotherapy also requires an initial design or
treatment plan comprising problem variables. With specific reference to
FIG. 8, and as in FIG. 5, tumor surface data is obtained 80, which is used
to determine 81 an enclosing volume. Initial program variables are chosen
and input 82. These program variables include a pattern of beam rotation
for each isocenter, the beam strength and beam collimation (either or both
of the last two could be provided as a function of beam rotation with the
variables then becoming the coefficients of polynomial functions or
control points of Bezier curves). An initial treatment plan appropriate
for this type of therapy is used as a starting point for the optimization
algorithm. The performance of the optimization algorithm is not all that
sensitive to the initial treatment plan; however, it should be noted that
poor initial input will again require the optimization algorithm to look
harder and longer for the optimal design. Upper and lower bounds on the
design variables are either arbitrarily set or set to remain within
available bounds (e.g., a beam rotation pattern may be constrained to
remain between certain angles to avoid sensitive areas of the brain).
Each major beam path within each isocenter's application pattern is
separated 84 into a predetermined number of individual beams. This is done
so that the actual continuous beam paths can be approximated and evaluated
by the dose function.
Given the orientation angles (direction cosines) of each discrete beam, the
radiation dose to each individual node is calculated 85 within the meshed
volume by summing each beam's dose contribution to each node as follows:
##EQU6##
where:
i=current node number
j=current beam number
n.sub.b =total number of beams
D.sub.i =total radiation dose at node i
G.sub.j (s.sub.j,C.sub.j,d.sub.j)=node radiation dose from beam j
s.sub.j =strength of beam j
c.sub.j =collimation of beam j
d.sub.j =direction of beam j
The objective function (e.g., tumor fit function) is formulated 86 as
discussed above. Given the dose calculated at each node, it is determined
whether each individual node within the meshed volume is "dead" or "alive"
based on a predetermined "kill" dose of radiation. As each node is
inquired, that node is recorded as "dead" or "alive" by adding a "1" to
the values of various collection subtotals. The four subtotals identified
are: (1) the number of nodes inside the tumor and alive; (2) the number of
nodes inside the tumor and dead; (3) the number of nodes outside the tumor
and alive; and (4) the number of nodes outside the tumor and dead.
Using the information stored in the subtotals, the "dead" and "alive"
ratios are calculated by dividing the number in subtotal by the total
number of nodes. These ratios are then combined to form an objective
function for the optimization process. This objective function for tumors
is referred to herein as the "tumor fit error" value. It is defined as the
sum of the ratio of nodes outside the tumor and dead, plus the ratio of
nodes inside the tumor and alive (see Equation 5).
Tumor Fit Error=Out.sub.d +In.sub.a (5)
where:
Out.sub.d =Ratio of nodes outside the tumor and dead
In.sub.a =Ratio of nodes inside the tumor and alive
When a tumor fit error value is obtained for the given beam variables and
isocenters, a numerical optimization algorithm (e.g., Generalized Reduced
Gradient or Sequential Quadratic Programming algorithms) is used to
determine the optimal combination of beam variables. As the tumor fit
error value approaches zero the radiation kill zone created by the beam
trajectories approaches the actual shape of the tumor. Therefore, the
optimization problem can be stated: "Minimize the tumor fit error such
that all nodes inside the tumor are dead." Again, as shown in FIG. 6, the
optimization algorithm iterates through a number of designs by perturbing
the variable values (beam rotation pattern, strength, and collimation, the
other associated variables) until it reaches that best combination of
variables to minimize the tumor fit error.
Alternatively, a homogeneous dose delivery method can also be used with
external beam radiotherapy using status factors, as previously discussed.
The apparatus can further comprise structure for simulating a brain probe
and structure for simulating manipulation of the probe within a video
presentation; structure for simulating one or more electrodes and for
simulating manipulation of electrodes within a video presentation.
Additionally, it can comprise structure for storing representations of
physiological response points and for selectively recalling and displaying
any of the response points within a video presentation. The apparatus can
further comprise structure for providing stereotactic coordinates for a
user selected point of a video presentation.
With reference to FIG. 9, the image acquiring structure preferably
comprises structure for acquiring an image from a CT scanner, an NMR
scanner, and PET scanner, an X-ray scanner, a DSA scanner and/or an
isotope scanner 40. This scanning data, which is in various, typically
non-standard formats, it convertible to a standard format using a PROM
computer video signal processor 42. The converted scanning data is made
available, through programmable relay control 45, to a central processing
unit (CPU) 44, preferably comprising hard disc storage, floppy disc
storage, streamer tape storage, and high-resolution frame grabber with a
high speed graphics and video image processor. The image acquisition
structure is preferably uniquely programmable to acquire any of a
predetermined number of image types. The apparatus preferably further
comprises structure providing for user to input 47 within a sterile
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