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Tissue Depth to Lung for Electron Beam Boost Therapy of the Breast
Medical Dosimetry, Vol. 19, No.4, pp. 255-258, 1994 Copyright © 1994 American Association of Medical Dosimetrists Printed in the USA. All rights reserved 0958-3947/94 $6.00 + .00
Pergamon
0958-3947(94)00034-4
TISSUE DEPTH TO LUNG FOR ELECTRON BEAM BOOST THERAPY OF THE BREAST L. ROBERSON,l,2 PH.D., GAIL PFEIFFER,l B.S., R.T.(T.)C.M.D., and MICHAEL DWORZANIN 1 B.S., R.T.(T.)C.M.D.
WALDEMAR Dos PASSOS,l,2 PH.D., PETER
'Providence Hospital, Department of Radiation Oncology, Southfield, Michigan, 48075; 2University of Michigan Hospital, Department of Radiation Oncology, Ann Arbor, Michigan, 48109 Abstract-Radiation therapy of the breast frequently employs electron beam boost therapy of the tumor bed. The electron energy is typically chosen based on the location of the tumor and tissue depth to lung within the electron field. This paper proposes a simple technique to estimate the tissue depth to lung using a port film taken orthogonal to the electron beam axis and patient axis for arbitrary electron beam gantry angles and patient table angles. The port film is taken with the patient in standard position (table angle of 0°) and the gantry at right angles to the electron field axis, clearly showing the depth to lung. The mathematical solution for arbitrary electron field gantry angle and patient table angle is presented. Key Words: Radiotherapy, Breast cancer, Electron beam, Boost therapy.
INTRODUCTION
Our proposed solution is to rotate the pedestal to 0° (standard position) and set the gantry axis in the plane perpendicular to the axis of the electron field, passing through the isocenter (Fig. 1). The two possible gantry positions represent the line of intersection of the plane described by the gantry rotation and the plane perpendicular to the electron field axis passing through the isocenter. The resulting film shows the patient anatomy in closer to standard geometry (perpendicular to the patient axis) and includes the tissue depth to lung. To simplify film interpretation, the collimator is rotated so that the graticule axis is coincident with the electron field axis (Fig. 2).
Radiation therapy of the breast is a commonly employed technique. 1 Boost therapy of the tumor bed may be performed with interstitial brachytherapy or electron beam therapy. When one is using electron beam boost therapy, the depth of the breast tissue from the skin surface to the soft-tissue-lung interface may be required to choose the optimum electron energy. This depth can be difficult to estimate in the absence of a multicut computed tomography (CT) study performed with the patient in the treatment position. This paper proposes a simple technique to estimate the tissue depth to lung using a port film taken orthogonal to the central axis of the boost field. The depth to the lung is easily read from the port film. A simple method of generating a view perpendicular to the central axis of the electron field is to rotate the gantry 90° (collimator angle at 0°) and expose a film. The patient position remains fixed with the isocenter at the skin surface. The films shows the depth to the lung as the distance from the isocenter (skin surface) to the lung along the port graticule line lying in the plane of gantry rotation. Unfortunately, problems arise for nonzero table angles. Frequently, the gantry cannot be rotated 90° without conflicting with the patient or patient table. In addition, films taken with large pedestal angles show the patient anatomy at nontypical viewing angles, increasing the difficulty of port interpretation.
METHOD Equations were determined for the two intersecting planes: the plane perpendicular to the electron field axis passing through the isocenter and the plane containing all possible gantry positions. Their intersection describes a line along which the gantry axis must fall (two possible gantry angles). The equation of the line of intersection was derived from the plane equations. The gantry angle solutions result from solving for the slope of the line. The solution is an arctangent function yielding the two possible gantry angles. The collimator angle is derived by determining the angle between the electron beam axis and the axial plane passing through the isocenter. The dot product of the unit-length vectors along the electron beam axis and the vector perpendicular to the axial plane results in the cosine of the complementary angle. The mathematical derivation is presented in the Appendix.
Reprint requests to: Peter L. Roberson, Ph.D., Providence Hospital, Dept. of Radiation Oncology, 22301 Foster Winter Drive, Southfield, MI 48075. 255
256
Medical Dosimetry
Volume 19, Number 4, 1994
Fig. 1. Geometry. With the patient in standard position (table angle of 0°), the port film axis is positioned along the intersection of the plane of gantry rotation, and the plane perpendicular to the electron field. The intersecting planes are shown with circles. The external contour for the oblique plane containing the electron field axis is also shown.
RESULTS
The formulas for the gantry and collimator angles (see Appendix) allow two solutions. A simple computer program was prepared to calculate both solutions. The preferred gantry and collimator angles are easily determined by the therapists during setup. Since the collimator cannot be rotated through all the quadrants, the program chooses an alternative angle that can be achieved, either 180° or 90° from the mathematical solution. CONCLUSIONS
This technique allows optimum film angles for the measurement of tissue depth to lung. A simple computer program allows the therapists to determine the optimum port film angle without having to consult a dosimetrist or physicist, thus reducing setup time for the electron port films.
APPENDIX
Fig. 2. Port film for the detennination of tissue depth to lung. The collimator is rotated so that one of the graticule axes coincides with the projection of the electron axis. Treatment table angle 49° electron gantry angle 37°.
Here we present a derivation of the calculated expressions for the gantry angle ~ and the collimator angle () used for filming the view perpendicular to the electron field axis, from which the tissue depth to the lung may be obtained.
Electron beam boost therapy of the breast. W. Dos
We begin by finding the equation of a line in space along the direction of the electron field axis where the gantry has been rotated by an arbitrary angle (). Consider a gantry coordinate system where the isocenter is set at the origin (0, 0, 0) and SI = (0, 0, 1) and S2 = (0, Ys2, Zs2) are two points in space representing the gantry target position (one unit length from isocenter) at and () degrees, respectively, as shown in Fig. AI. Points S 1 and S2 are related by a standard axial rotation about the x axis given by S2 = R«(})SI, where =
(~ co~ B Si~ B) , o
(0,0,1)
P2
(At)
-sin B cos B
-
so that Xs2 = Xsi = 0, Ys2 = sin (), Zs2 = cos (). The general equation of a line in space through a set of arbitrary points (XI, YI, zd and (X2' Y2, Z2) is given by
~
where a = X2 - Xl, b = Y2 - YI, e = Z2 - Zl. Hence, the equation of a line along the beam axis (i.e., along the S2 isocenter axis) can be reduced to y
= z tan
B.
(A3)
We next want the equation for a plane perpendicular to the beam axis and passing through isocenter. The general equation for a plane with direction vector (A, B, C) is given by Ax + By + CZ + D = 0,
(A4)
where D is an arbitrary constant determined by the actual position of the plane in space. Since this plane
z
(O,y 52 ,Z 52)
/'--------- Y (0,0,0) 150CENTER
x Fig. AI. Gantry coordinate system. The gantry plane ofrotation is chosen to be the y-z plane. Two points in space represent the target position for gantry angles of 0° and B.
Y
P1
(0,0,0) 150CENTER
x Fig. A2. Patient coordinate system. The patient coordinate system is related to the gantry coordinate system by a rotation about the z axis.
4>
passes through the isocenter at (0, 0, 0), we can set D = 0. In general, a line (eq. [A2]) and a plane (eq. [A4]) are perpendicular only if Ala = Bib = Cle. From our geometric configuration, we obtain A
= 0;
B
= C tan B,
(A5)
so that the equation for a plane passing through isocenter and perpendicular to the beam axis is given by
z + y tan B = o.
(0,0,1)
_I
_ _- - L - -_ _ _ _ _ _
"
(A2)
x = 0;
257
et al.
z
°
R(B)
PASSOS
(A6)
We also require an equation for the axial plane of the patient passing through isocenter. In addition to gantry rotation by angle (), let us also introduce a table position determined by a rotation through an angle
(~:;n4>4> ;~:: ~).
(A7)
001
The coordinates of P2 are then (sin
Medical Dosimetry
258
electron field axis
Volume 19, Number 4, 1994
tions (A6) and (A8) allows one to determine the equations for a line in the gantry coordinate system:
x
y
z
tan cf>
1
-tan ()
--=-=--
(A9)
To rotate this line of intersection into the plane of gantry rotation (rotate table to 0°), we multiply any point along the line by R- 1(4)). Thus, cf> sin cf>
COS (
o
0) o ( tan
-sin cf> cos cf>
1
o
1
cf> )
0)
(
=
sec cf> -tan ()
-tan ()
1\
(A 10)
X
The slope of the line in the y-z plane determines the desired gantry angle: tan
x=O
Fig. A3. Collimator angle (6). The dot product of the electron field axis and the vector (x) normal to the plane of gantry rotation (x = 0) yields the cosine of the complementary angle.
cf> -sin cf> COS
R(cf» =
e=
sec cf> = 1 -tan B -cos cf> tan ()
The new gantry angle
= (0,
nience we choose to have coordinates PI Thus, P2 = R(
(
sin cf> cos cf>
0) 0
001
o.
thus, is -1 ) ( cos cf> tan ()
cf> sin cf>
COS
o
-sin cf> cos cf>
The intersection of the two planes given by equa-
(A12)
.
o
0)o ( 0) (Y s2
I
=
Zs2
s2
Y sin cf» cf>
Ys 2cos
,
Zs2
(A13)
(A7)
(A8)
(All)
To determine the collimator angle 8, we first rotate the electron field axis to the table = 0° position (refer to Fig. AI):
1,0).
The coordinates of P2 are then (sin 4>, cos 4>, 0). Substituting the coordinates of each of these three points into the general equation of a plane (eq. [A4]) allows one to determine the constants A, B, C, D, which here are given by D = 0, C = 0, B = -A tan 4> so that the most general equation for the axial plane of the patient passing through isocenter is given by the formula x - Y tan cf> =
~,
~ = tan- 1
(
.
•
and take the dot product of the vector along the electron beam axis and the line perpendicular to the x = 0 plane, (-1,0,0) (Fig. A3). Hence, Ys2 sin 4> = cos(90 - 8). Since Ys2 = sin e, the equation simplifies to sin 8 = sin e = sin
(A14)
REFERENCE 1. Perez, C.A.; Garcia, D.M.; Kuske, R.R.; Levitt, S.H. Breast: stage Tl and T2 tumors. In: Perez, C.A.; Brady, L.W. editors. Principles and practice of radiation oncology. New York: lB. Lippincott; 1992:887-947.
Pergamon
0958-3947(94)00034-4
TISSUE DEPTH TO LUNG FOR ELECTRON BEAM BOOST THERAPY OF THE BREAST L. ROBERSON,l,2 PH.D., GAIL PFEIFFER,l B.S., R.T.(T.)C.M.D., and MICHAEL DWORZANIN 1 B.S., R.T.(T.)C.M.D.
WALDEMAR Dos PASSOS,l,2 PH.D., PETER
'Providence Hospital, Department of Radiation Oncology, Southfield, Michigan, 48075; 2University of Michigan Hospital, Department of Radiation Oncology, Ann Arbor, Michigan, 48109 Abstract-Radiation therapy of the breast frequently employs electron beam boost therapy of the tumor bed. The electron energy is typically chosen based on the location of the tumor and tissue depth to lung within the electron field. This paper proposes a simple technique to estimate the tissue depth to lung using a port film taken orthogonal to the electron beam axis and patient axis for arbitrary electron beam gantry angles and patient table angles. The port film is taken with the patient in standard position (table angle of 0°) and the gantry at right angles to the electron field axis, clearly showing the depth to lung. The mathematical solution for arbitrary electron field gantry angle and patient table angle is presented. Key Words: Radiotherapy, Breast cancer, Electron beam, Boost therapy.
INTRODUCTION
Our proposed solution is to rotate the pedestal to 0° (standard position) and set the gantry axis in the plane perpendicular to the axis of the electron field, passing through the isocenter (Fig. 1). The two possible gantry positions represent the line of intersection of the plane described by the gantry rotation and the plane perpendicular to the electron field axis passing through the isocenter. The resulting film shows the patient anatomy in closer to standard geometry (perpendicular to the patient axis) and includes the tissue depth to lung. To simplify film interpretation, the collimator is rotated so that the graticule axis is coincident with the electron field axis (Fig. 2).
Radiation therapy of the breast is a commonly employed technique. 1 Boost therapy of the tumor bed may be performed with interstitial brachytherapy or electron beam therapy. When one is using electron beam boost therapy, the depth of the breast tissue from the skin surface to the soft-tissue-lung interface may be required to choose the optimum electron energy. This depth can be difficult to estimate in the absence of a multicut computed tomography (CT) study performed with the patient in the treatment position. This paper proposes a simple technique to estimate the tissue depth to lung using a port film taken orthogonal to the central axis of the boost field. The depth to the lung is easily read from the port film. A simple method of generating a view perpendicular to the central axis of the electron field is to rotate the gantry 90° (collimator angle at 0°) and expose a film. The patient position remains fixed with the isocenter at the skin surface. The films shows the depth to the lung as the distance from the isocenter (skin surface) to the lung along the port graticule line lying in the plane of gantry rotation. Unfortunately, problems arise for nonzero table angles. Frequently, the gantry cannot be rotated 90° without conflicting with the patient or patient table. In addition, films taken with large pedestal angles show the patient anatomy at nontypical viewing angles, increasing the difficulty of port interpretation.
METHOD Equations were determined for the two intersecting planes: the plane perpendicular to the electron field axis passing through the isocenter and the plane containing all possible gantry positions. Their intersection describes a line along which the gantry axis must fall (two possible gantry angles). The equation of the line of intersection was derived from the plane equations. The gantry angle solutions result from solving for the slope of the line. The solution is an arctangent function yielding the two possible gantry angles. The collimator angle is derived by determining the angle between the electron beam axis and the axial plane passing through the isocenter. The dot product of the unit-length vectors along the electron beam axis and the vector perpendicular to the axial plane results in the cosine of the complementary angle. The mathematical derivation is presented in the Appendix.
Reprint requests to: Peter L. Roberson, Ph.D., Providence Hospital, Dept. of Radiation Oncology, 22301 Foster Winter Drive, Southfield, MI 48075. 255
256
Medical Dosimetry
Volume 19, Number 4, 1994
Fig. 1. Geometry. With the patient in standard position (table angle of 0°), the port film axis is positioned along the intersection of the plane of gantry rotation, and the plane perpendicular to the electron field. The intersecting planes are shown with circles. The external contour for the oblique plane containing the electron field axis is also shown.
RESULTS
The formulas for the gantry and collimator angles (see Appendix) allow two solutions. A simple computer program was prepared to calculate both solutions. The preferred gantry and collimator angles are easily determined by the therapists during setup. Since the collimator cannot be rotated through all the quadrants, the program chooses an alternative angle that can be achieved, either 180° or 90° from the mathematical solution. CONCLUSIONS
This technique allows optimum film angles for the measurement of tissue depth to lung. A simple computer program allows the therapists to determine the optimum port film angle without having to consult a dosimetrist or physicist, thus reducing setup time for the electron port films.
APPENDIX
Fig. 2. Port film for the detennination of tissue depth to lung. The collimator is rotated so that one of the graticule axes coincides with the projection of the electron axis. Treatment table angle 49° electron gantry angle 37°.
Here we present a derivation of the calculated expressions for the gantry angle ~ and the collimator angle () used for filming the view perpendicular to the electron field axis, from which the tissue depth to the lung may be obtained.
Electron beam boost therapy of the breast. W. Dos
We begin by finding the equation of a line in space along the direction of the electron field axis where the gantry has been rotated by an arbitrary angle (). Consider a gantry coordinate system where the isocenter is set at the origin (0, 0, 0) and SI = (0, 0, 1) and S2 = (0, Ys2, Zs2) are two points in space representing the gantry target position (one unit length from isocenter) at and () degrees, respectively, as shown in Fig. AI. Points S 1 and S2 are related by a standard axial rotation about the x axis given by S2 = R«(})SI, where =
(~ co~ B Si~ B) , o
(0,0,1)
P2
(At)
-sin B cos B
-
so that Xs2 = Xsi = 0, Ys2 = sin (), Zs2 = cos (). The general equation of a line in space through a set of arbitrary points (XI, YI, zd and (X2' Y2, Z2) is given by
~
where a = X2 - Xl, b = Y2 - YI, e = Z2 - Zl. Hence, the equation of a line along the beam axis (i.e., along the S2 isocenter axis) can be reduced to y
= z tan
B.
(A3)
We next want the equation for a plane perpendicular to the beam axis and passing through isocenter. The general equation for a plane with direction vector (A, B, C) is given by Ax + By + CZ + D = 0,
(A4)
where D is an arbitrary constant determined by the actual position of the plane in space. Since this plane
z
(O,y 52 ,Z 52)
/'--------- Y (0,0,0) 150CENTER
x Fig. AI. Gantry coordinate system. The gantry plane ofrotation is chosen to be the y-z plane. Two points in space represent the target position for gantry angles of 0° and B.
Y
P1
(0,0,0) 150CENTER
x Fig. A2. Patient coordinate system. The patient coordinate system is related to the gantry coordinate system by a rotation about the z axis.
4>
passes through the isocenter at (0, 0, 0), we can set D = 0. In general, a line (eq. [A2]) and a plane (eq. [A4]) are perpendicular only if Ala = Bib = Cle. From our geometric configuration, we obtain A
= 0;
B
= C tan B,
(A5)
so that the equation for a plane passing through isocenter and perpendicular to the beam axis is given by
z + y tan B = o.
(0,0,1)
_I
_ _- - L - -_ _ _ _ _ _
"
(A2)
x = 0;
257
et al.
z
°
R(B)
PASSOS
(A6)
We also require an equation for the axial plane of the patient passing through isocenter. In addition to gantry rotation by angle (), let us also introduce a table position determined by a rotation through an angle
(~:;n4>4> ;~:: ~).
(A7)
001
The coordinates of P2 are then (sin
Medical Dosimetry
258
electron field axis
Volume 19, Number 4, 1994
tions (A6) and (A8) allows one to determine the equations for a line in the gantry coordinate system:
x
y
z
tan cf>
1
-tan ()
--=-=--
(A9)
To rotate this line of intersection into the plane of gantry rotation (rotate table to 0°), we multiply any point along the line by R- 1(4)). Thus, cf> sin cf>
COS (
o
0) o ( tan
-sin cf> cos cf>
1
o
1
cf> )
0)
(
=
sec cf> -tan ()
-tan ()
1\
(A 10)
X
The slope of the line in the y-z plane determines the desired gantry angle: tan
x=O
Fig. A3. Collimator angle (6). The dot product of the electron field axis and the vector (x) normal to the plane of gantry rotation (x = 0) yields the cosine of the complementary angle.
cf> -sin cf> COS
R(cf» =
e=
sec cf> = 1 -tan B -cos cf> tan ()
The new gantry angle
= (0,
nience we choose to have coordinates PI Thus, P2 = R(
(
sin cf> cos cf>
0) 0
001
o.
thus, is -1 ) ( cos cf> tan ()
cf> sin cf>
COS
o
-sin cf> cos cf>
The intersection of the two planes given by equa-
(A12)
.
o
0)o ( 0) (Y s2
I
=
Zs2
s2
Y sin cf» cf>
Ys 2cos
,
Zs2
(A13)
(A7)
(A8)
(All)
To determine the collimator angle 8, we first rotate the electron field axis to the table = 0° position (refer to Fig. AI):
1,0).
The coordinates of P2 are then (sin 4>, cos 4>, 0). Substituting the coordinates of each of these three points into the general equation of a plane (eq. [A4]) allows one to determine the constants A, B, C, D, which here are given by D = 0, C = 0, B = -A tan 4> so that the most general equation for the axial plane of the patient passing through isocenter is given by the formula x - Y tan cf> =
~,
~ = tan- 1
(
.
•
and take the dot product of the vector along the electron beam axis and the line perpendicular to the x = 0 plane, (-1,0,0) (Fig. A3). Hence, Ys2 sin 4> = cos(90 - 8). Since Ys2 = sin e, the equation simplifies to sin 8 = sin e = sin
(A14)
REFERENCE 1. Perez, C.A.; Garcia, D.M.; Kuske, R.R.; Levitt, S.H. Breast: stage Tl and T2 tumors. In: Perez, C.A.; Brady, L.W. editors. Principles and practice of radiation oncology. New York: lB. Lippincott; 1992:887-947.