A General Method to Calculate Dose to Spine in Opposing Anterior Posterior Treatment Setup Without CT

0739-021 l/93 $6.00 + .oO Copyright 0 1993 American Association of MedIcal Doslmetrists

Mrdrcol Dosrm~/r~, Vol. 18. pp. 53-61 Printed in the U.S.A. All nghts reserved.

A GENERAL METHOD TO CALCULATE DOSE TO SPINE IN OPPOSING ANTERIOR POSTERIOR TREATMENT SETUP WITHOUT CT RAMAMURTHI JANAKIRAMAN, PH.D. Department of Radiation Oncology, William Beaumont Hospital, Royal Oak, MI 48073-6769, U.S.A. Abstract-The spinal cord is usually part of the treatment volume in the treatment of the thorax and abdomen areas using antero-posterior (AP) and postero-anterior (PA) ports. Thus it is necessary to know the dose the spinal cord would receive. One needs to locate the spine to calculate the dose at that location. In the absence of CT, a set of orthogonal films is taken at simulation to aid in locating the spine. The relative point dose then is calculated

using irregular field point dose calculation mode of the treatment planning system. The data needed for the calculation are the x and y coordinates of the spine in the coronal plane, air gap, and depth in tissue. Correct entry of these is thus important to obtain the dose accurately. Planning systems assume that the spine is close to the beam axis. There could be possible mislocation of the spine when this assumption is not valid. This presentation describes a procedure to obtain the needed numbers for a general location without any assumptions. To obtain x and y coordinates the suggestion is made to solve numerically using successive approximation series for the coordinates, the series continued until mutually consistent values are obtained. The other parameters, g and d, are obtained from the source to skin distance @SD) above the spine point, with the use of multiple transaxial contours in association with the principle of linear interpolation. Besides providing the correct geometric parameters, this procedure also allows use of transaxial contours with the spine located on them to run isodose plans and thus have an additional way of obtaining the spine dose. Key Words: Dose to spine, Numerical solution, Successive approximation series, Linear interpolation, Transaxial contour.

INTRODUfXION

interest inside tissue is well known. All points on a ray line of constant divergence would cast a shadow at a single point on the radiograph film. Thus it is not unique to identify the location of interest from a single projection film. Taking another film at a different orientation would uniquely locate the point, since there is only one coordinate in space that is common to two intersecting ray lines. Thus locating a point in space using orthogonal films is a direct geometric problem and one can express the coordinates analytically in terms of the projection values.’ The important factors to consider are beam divergence and simultaneous use of the orthogonal films. Many treatment planning systems allow direct use of the AP simulation film to locate the coordinates of the point of interest. The menu of these systems makes an assumption that the point of interest is close to the beam axis near the principal plane, i.e., close to isocenter in SAD setup. It would lead to possible mislocation of the spine when this approximation is not valid. This presentation is thus a “re-look” at the issue of locating the spine using AP and lateral projection films; that is more general in applicability. The primary objective in this presentation is to approach the issue of locating the spine for a general situation without need for specific assumptions. Thus all the geometrical parameters to locate the spine, viz., its coordinates in a given Cartesian frame, depth in tissue, air gap, are all obtained for a general case. We feel this approach is more analytical and less subjective. For the same rea-

This paper describes a general technique to obtain information on spatial location of a given organ from a set of two orthogonal films of diagnostic quality, viz., simulation films. This is a common technique when CT information is not available or needed. The popular example is locating the spinal cord/spine* with the help of these films to obtain dose to spine in the treatment of the thorax and abdomen areas. The treatment delivery is via two opposing ports, antero-posterior (AP) and postero-anterior (PA), either by keeping same field size definition plane for both ports (“SAD setup”) or separate planes for AP and PA ports (“SSD setup”). The only movement to treat AP and PA ports in SAD setup is the gantry rotation about its axis. Thus the point in tissue at the isocenter keeps a constant source-to-axis distance (SAD) for AP and PA setups, and hence the name. Central axis (CAX) source-to-skin distance (&!%&-& is set to be same for both ports in SSD setup, by movement of gantry and treatment table without moving the patient, or, by turning the patient between setups. The simulation films taken are usually AP (or PA for prone position) and a lateral film (right lateral film for supine and left lateral for prone positions), head towards gantry without moving the patient between the films. The use of orthogonal films to locate points of * Spine and spinal cord are used interchangeably in this presentation. 53

54

Medical Dosimetry

son of generality, this presentation suggests obtaining all three coordinates of the spine from simultaneous use of the two simulation films and using the information on SSD above the spine point to obtain other parameters needed to locate spine. SSD information above the spine is obtained by taking more than one transaxial contour on the simulator table. SPINE

DOSE

Volume 18,Number 2, 1993

7

t 1 I

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I

I

I

Spinal cord tolerance dose (TD,,,) to fractionated radiation is around 5,000 cGy.’ It is part of treatment volume in many of the treatments of the thorax and abdomen areas using AP/PA fields. The dose prescription point is usually the midpoint along CAX separation. Thus the dose to spine is different from the prescription dose. How high or low this dose is depends on location of the spine in tissue and relative to the beam axes (Figs. l-3). For an ideally flat surface keeping a constant SSD everywhere, the dose is higher along the CAX away from the midpoint and away from the CAX when the off-axis factor at a given depth is greater than unity (Figs. 4 and 5). These are machine-related factors. Also, in regions of shorter beam traverse the dose is higher due to tissue deficit. How high spine dose is depends on these and related factors like dose profile near the beam or block edge, tissue inhomogeneity, and others. Thus it is useful to

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1

:

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1

:

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P Fig. 2. Lateral projection showing spine location in dashed lines relative to CAX and skin surface for a general case.

Z

Y . I

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-

Ii il , .$ I'1 ,

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1 1

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Fig. 1. AP view of the blocked treatment field showing spine location in dashed lines relative to block edge and CAX for a general case.

Fig. 3. Transaxial slice showing spine location in dotted circle inside the tissue for a general case. Dashed lines represent the field edges of the blocked field. Dotted line is the line of calculation at xAp. Note spine would not lie on this line of calculation when away from principal plane.

Calculating dose to spine 0 R. JANAKIRAMAN

Fig. 5. A typical absorbed dose profile at a given depth for an accelerator with off-axis factor greater than unity. Fig. 4. A typical dose distribution along CAX for equalweighted AP/PA treatment. The scale is relative, chosen to emphasize the increase in dose away from midpoint. The dashed profile is for SAD setup, showing a greater variation because of shorter SSD.

obtain the dose to spine even when the treatment dose is below the prescribed dose limit for spine. A partial or full spine block for the PA port, or on occasions, a two-dimensional compensator,’ like a wedge with heel-to-toe orientation along head to feet, is used to limit the spinal dose. Calculation of spine dose means obtaining all the relevant geometrical information to correctly locate the spine. Besides the variations of the above parameters, additionally the spine can be curved in AP and lateral films. Thus one has to have a general procedure to locate the spine and to calculate its dose. ORIENTATION

AND COORDINATE

SYSTEM

It is helpful at this stage to write a few lines on the orientation and coordinate system used in this presentation. Patient orientation is taken to be supine with head to gantry, so the collimator set fields on the AP simulation film would be positive x axis going from right to left and positive y axis going from feet to head. The positive z axis is set to go from posterior to anterior so the coordinate system is right-handed. We find it simpler to define the axis as going from feet to head for this presentation. This is because the algorithm used to calculate the dose to spine using treatment planning system, viz., irregular field point dose calculation mode, defines x and y this way and this is also the conventional axes nomenclature dosimetrists and therapists are used to. Thus this orientation is a deviation from the conventional patient coordinate sys-

tern, which is a left-handed coordinate system with y and z interchanged from this presentation.‘.4 This does not change the discussion that follows. The origin for this system is the isocenter. The choice of the isocenter as origin is natural, since the simulator reticule is defined with respect to the isocenter and treatment planning system menus also define distances with reference to the isocenter. Because of the definition of the y axis going from feet to head, the expression for y (Eqn. 2, Coia et al. ‘) is equivalent to expression for z in this presentation. CALCULATION

OF DOSE TO SPINE

Dose to spine is obtained through the use of a treatment planning computer system. If CT information is available where the target volume and spine location are seen, it is possible to directly obtain the dose to spine. Since, more often than not, CT information is not used in the AP/PA treatment setup, one has to use a different method to locate the spine point inside the tissue to calculate the dose to that point. Orthogonal simulation films are used to locate the spine and the algorithm of the planning system that would not need the use of contour to calculate dose, viz., irregular field point dose calculation algorithm, is used to calculate the relative dose to spine. In this method the information on the location of the spine from the simulation films is input into the planning system by the dosimetrist. These are the x and y coordinates of the spine in the coronal plane, air gap (g) that is indicative of the location of beam entry point above the spine relative to the one for CAX, and, the depth (d) of the spine in tissue, with or without information on heterogeneous tissue density. The planning system would calculate the dose to spine from

56

Medical Dosimetry

this geometrical information on the location of the spine using the beam data. The planning system calculates the dose to a point in the irregular field point dose calculation mode as follows. Since the contour and location of the interest organ inside it are not available, the planning system assumes, for each calculation point, a flat infinite contour at the point of beam entry orthogonal to the CAX. The dose at this calculation point is obtained for points along the line of calculation, which is a line parallel to CAX, passing through the beam entry point and has the SSD (from information on g) as of the entry point. The spine point is located on this line of calculation from information on d. Usually x and y are obtained from direct use of AP simulation film with the use of a digitizer, g and d are obtained from the lateral film using the sagittal contour above and below the spine point and entered into the system through keyboard entry. The x and y coordinates are obtained from the AP film by locating the point on the ray line of constant divergence at the field size definition (or isocenter) distance. When the spine is away from the principal coronal plane, because the line of calculation at (x, y) is parallel to CAX, the spine point would not lie on this line of calculation (see Fig. 3). The farther the spine point is away from the principal coronal plane and the CAX, the spine point would more be away from the line of calculation. This would be important in SSD setup since the spine is invariably away from the principal coronal plane and when the spine location is away from the CAX. On a similar note, if g and d information is not correct, the spine would not be correctly located on the line of calculation. Thus entry of proper values for x, y, g, and d that would correctly locate the spine on the line of calculation is important to calculate the spine dose using the planning system. The aim of this presentation is to provide a procedure to obtain the correct set of x, y, g, and, d for the planning system, which is valid for a general situation. The data obtained this way are then all input through keyboard entry to the planning system. The spine can be uniquely located from the AP and lateral projection films taking divergence of the beam into consideration.’ The specific details of obtaining the orthogonal films and locating the spine would depend to a certain extent on the treatment setup, viz., SAD or SSD setup. SAD setup is usually preferred over SSD setup because of its ease. SSD setup is used for reasons of practice or machine limitations such as nonisocentric, shorter SAD, large patient separation, and/or large treatment field sizes. COORDINATE SYSTEM OF AXES Let P (xsp, ysp, z,,) be the point in space of a given spine (Fig. 6). As a starting assumption, we consider x,

Volume 18, Number 2, 1993

y, and, z all to be positive.* In the coordinate system with isocenter as origin, the X-ray source (target) is at SAD ( 100 cm) from the origin, and, x, y, and z are the coordinates of a given spine in centimeters (cm) with respect to the isocenter. There are two principal projection planes passing through the origin that are parallel to the two simulation planes. For AP projection the principal plane is the coronal plane (x, y) passing through the isocenter. For lateral projection the principal plane is the sag&al plane (z, y) passing through the isocenter. The ray line from the source to the point P would intersect the principal coronal plane at pAP (xAP~ YAP ) and the principal sagittal plane at PJz,,~, y,,,). These four projection coordinate values on the principal planes are the starting values in this presentation that would provide the true coordinates of the point P. This way the procedure is kept simple, since there is no need to use a magnification factor different from the factor for isocenter when the spine is curved or away from principal planes. Looking down through positive z axis at the coronal plane, the projection of the point P on the xy plane (suffix “AP”) would be at the coordinates x*p = x/( 1 - z/100)?

(la)

YAP

(lb)

and =

y/t

1 -

z/1oo).

So the true x and y are related to the projections on the z = 0 plane as x = x,p x (1 - z/100)

(14

y = yApx (1 - z/100).

(14

and

In a similar way, looking at the lateral plane through the negative x axis, the projection of the point P on the zy plane would be at the coordinates Zlst= z/(1 + x/100)

(24

Yl,,

CW

and =

Y/t

1 +

xl

100).

Doing a reverse transformation tain the true z and y as

as before, we ob-

z = Zlatx (1 + x/100)

(2c)

Y = Yl,,x (1 + x/lo@.

(24

and

Because of the starting assumption that x, y, and * We use x, y, z interchangeably to represent the coordinate system as well as coordinates of the spine as long as there is no conflict of usage. t The equations are for a treatment machine with SAD = 100 cm. For a different situation, 100 in these equations would be replaced by the appropriate SAD or field size definition distance.

57

Calculating dose to spine 0 R. JANAKIRAMAN

4

P(Xsp,Ysp,Zsp) ,/

/ I I I I I I

Y

I

-. pAP

Fig. 6. Spine point at P(xsp, y,, zsp) in a right-hand coordinate system with isocenter as origin. The true coordinates are the edges of the box with dimensions (x.,, ysP, z sp). PAPand p,st are the ray line projections of this point on the principal planes.

z are all positive, the point P is closer than isocenter looking from the positive z axis (AP projection), while it is beyond isocenter looking from the negative x axis (right lateral projection). The true coordinates x, y, z we need to know are obtained from (x, y)V)Ar and (z, y),,, . It is a straightforward measurement to obtain these from the simulation films. On each film the spine point of interest is located. On AP film the distance of this point parallel to the x and y axes is measured using an appropriate ruler for the magnification of the isocenter (e.g., by the use of Rad Mag Ruler*). These with the correct sign notation are the xAp and y,,. In a similar way zla, and y,,, are obtained using the right lateral film. These are then used to obtain the true coordinates using the equations X = XApx (1 - z/100),

@a)

Y=

WI

YAP

x

t1

-

z/1oo),

or,

Y = Yl,, x (1 + x/~OO),

* Rad Care Products, Sunnyvale, CA 94086.

(3c)

and z = Zla,x (1 + x/100).

W

Solving the above equations for x, y, z would provide the true coordinates. Analytical expressions to obtain x and z are given.’ This presentation uses a little deviation from those equations. We would solve for true x, y, and, z numerically. A numerical solution has certain advantages in that the starting values are same for any location of spine, they are simple to use, and they are programmable. This way all four equations in Eqns. 3 are used together. Since we are going to use information on all three coordinates of the spine, we would locate all three coordinates of the spine using the orthogonal films. Since the emphasis in this presentation is on generality and it is possible to have the location of spine such that yAp, is not same as y,,, , there is no restriction that the projection coordinate values along they axis be the same in both simulation films. We would solve for xi y, and, z from the simulation films using a numerical technique. Information on y is used later in association with interpolation to obtain SSD,,. The numerical approximation is taken to successively higher orders until the true

58

Medical Dosimetry

coordinates are obtained. True coordinates are considered to have been obtained when a given order of the series provides the same (x, y, z) as the lower order series within the expected accuracy. This is achieved at a lower order of the series for a point close to isocenter, while one would go to higher order for a point away from the isocenter. We look for solution to Eqns. 3. Solving numerically, we would go from zero order and go up the series. The zero order approximation (x,, , y,, zo) would be to assume the point P is the isocenter itself, viz., x, y, z, and hence xAp, yAp, Y,~,, and z,,, are all equal to zero. The first order approximation is obtained by substituting the zero order x, y, and z values in Eqns. 3. We then have x, = x*p x (1 - zo/lOO),

(4a)

YI =

YAP

(4b)

y,

Yl,,

x

t1

-

(1

+

zO/loo),

or,

=

x

%/1W,

(4c)

and z, = Z,=,x (1 + x0/100).

(4d)

This is the most commonly used approximation. This approximation is valid when x, y, and, z are very close to the isocenter. We shall compare this with the next order of approximation, viz., the second order approximation, which is obtained by substituting the first order values of x, y, z in Eqns. (3). These are x, = x,, x (1 - z,/lOO),

Pa)

y2

(5b)

=

YAP

x

(I

-

(1

+

z,/loo)>

or _v2 =

Ma,

x

x,/100),

(W

and z2 = Z,=,x (1 + x,/100).

(W

Looking at the Eqns. 4 and 5, we see there can be as high as 10% or more error in estimating the true x, y, z, depending on the location of the point P. The error is larger if xAp and/or zla, are away from the isocenter so that either x,/ 100 or z,/ 100 is not negligible compared to 1. Further, it is not self-consistent to assume x = xAp (P is on the z = 0 plane) and have a finite value for z (z,,,). Thus, a second order numerical solution is a better approximation than first. We can continue the series to higher orders. We are looking for mutual consistency in the three coordinates to know we have located the spine correctly. This means the series is continued until the coordinates are the same between that order and the immediately preceding lower order within expected accuracy.

Volume 18, Number 2, 1993

Third order series is obtained by substituting the second order values for x, y, z in Eqns. 3. These are xj = XApx (1 - z,/lOO),

@a)

Y3

(6b)

=

YAP

x

(1

-

z2/1w,

or Y3= Yl,,x ( 1 +

x2/

1 w,

(6~)

and zj = Zla,x ( 1 + x2/ 100).

(6d)

Thus we have a general procedure to obtain x, y, z for any order of approximation through substitution of the lower order approximation value in Eqns. 3. SSD SETUP The above discussion is valid for SAD setup. Since the field size definition planes are different for AP and PA fields in SSD setup, the Eqns. 3 would need redefinition. We consider the setup where there is only gantry and treatment table movement to get to PA port and no patient movement in between. SSDcAx is kept equal to SAD, or field size definition distance (SSD setup) or greater (extended SSD setup). Isocenter location for AP port is separated from the location for PA port by the CAX patient separation for SSD setup and is greater than that for extended SSD setup. Treatment setup parameters are different between AP and PA ports because of this. Simulation films taken are also different. AP simulation film is taken at the treatment setup. Since the isocenter location is outside of the treatment volume, there is need to raise the simulator table from the treatment setup to bring the spine and most of the treatment volume within the field of the lateral film. The amount of shift of the treatment table for lateral simulation is denoted as Z,,i‘, and it is the difference of table top positions for AP and lateral simulations. Similar to air gap, zshlftis defined as negative for shift towards the source. Since simulation setup for AP film is same as treatment setup, xap and y,, are the same as in Fig. 6 and Eqns. la and 1b, i.e., defined with reference to the isocenter. z,,,~~,would alter the value to be used for z,,, in Eqns. 3. If (zlaJodj is the proper zlat value to be used in Eqn. 3d and (zlaJmeasis the z,,, measured with reference to the lateral CAX with table shift, the two are related as (Zd(3d)

=

(Zlat)meas

+

Zshtft.

(7)

Eqns. 3 would then be x =

x,, x (1 - z/100),

(3a)

Y=

YAP

(3b)

Y

Yl,,

=

x

x

(l

-

(1

+

z/1oo),

x/100),

(3c)

59

Calculating dose to spine 0 R. JANAKIFUMAN

gap g and depth under skin d for a general case. Since the correct z with reference to the isocenter is known, we have

and 2 = (Z&d) x ( 1 + xl 1w.

(34

As before, numerical solution would provide x, y, z values with reference to AP isocenter. We are thus locating the true coordinates of the spine for either SAD or SSD setup with reference to field size definition distance, which is at isocenter for SAD setup. The x and y so obtained are the data needed for input into the planning system so that the spine point is on the line of calculation. These values are closer to true value since they are the values consistent in both the AP and lateral films. The following table gives a theoretical example of a spine located away from the isocenter at (20,20,20) cm. The (x, JJ)~~one gets from digitizing AP film at isocenter magnification is (25, 2.9, 25% off if these numbers are input into the planning system uncorrected for divergence. If the spine off-axis location is taken into account for lateral film, the z coordinate would be at 21.2 cm (see Appendix), 6% deviation. Using the suggested successive approximation method, one gets very close to the true value by going up to third order approximation, while fourth order generates the true numbers. This is an illustrative example of possible input of wrong coordinates if input into the planning system uncorrected, when the spine location is far away (Table 1). AIR GAP AND DEPTH IN TISSUE

In a similar manner, we would like to generate a procedure to obtain the other needed values, viz., air

Table 1. Successive approximation method, examples. True coordinates are (20, 20, 20) cm. All units are in cm. The deviation from true value in percentage is shown in parenthesis.

1APPr;;~~~ion Zero

First

Second

(

Third

Fourth

/

x

1 Y(AP) 1Y(lW

1

2

0

0

0

0

(100)

(100)

(100)

(100)

25.0

25.0

16.7

16.7

(20)

(20)

(16.5)

(16.5)

20.8

20.8

20.9

20.9

(4)

(4)

(4.5)

(4.5)

1 l;l.," 1 1';:

20.0

20.0

1 29':

/ 2";:

20.0

20.0

S&SD,,+ d = (100 - z).

Please note z is an algebraic variable and thus the value on the right hand side is greater than 100 cm if z is negative. From Eqn. 8, depth d is obtained if SSD,, is known and vice versa. The methodology in common use to obtain g and d is as follows. A sagittal contour of the skin outline for the anterior and posterior borders is drawn on the lateral film. This is taken to be the contour shape of the skin exactly above and below the spine. Due to the large amount of tissue traversed in the lateral position and the metal frame of the simulator table, there are interfering shadows on the film, and it is difficult on occasions to locate these sag&al contours accurately. It is also a common occurrence that the sag&al outline is beyond the view of the film when the patient separation magnified at the film location is larger than the dimension of the film. Locating the spine on the lateral film is easier than locating the sag&al contour. If the spine is curved in AP projection, the spine magnification factors are different at different lateral projection locations, and likewise for AP film. Thus there is a need to have a general approach to obtain those numbers, too. The basis for the present discussion is Eqn. 8. Since it is more direct to locate the spine in the lateral film, we use information on z to obtain g and d. From Eqn. 8 we see that it is possible to know the depth d if SSD,, is known. A very direct solution is thus to read the actual SSD,, for anterior and posterior skin edges on the simulator table itself for the points of interest, similar to obtaining the SSDs for supra clavicular and axillary points. Air gap g is known from the relation g = SSD,, - SSD,,,.

1

1

(8)

(9)

Thus we have all the relevant information we need to input into the treatment planning system to obtain the dose to spine. However, in practice it is difficult to choose the needed points where the spine dose will be calculated at the stage of simulation. We feel information on SSDsp, directly measured at simulation or obtained later, is a better approach than information from the sagittal contour shapes drawn on the lateral simulation film. The limitation here is that it is not possible to identify the interest spine points and thus to obtain their SSD,, at the stage of simulation. So we have to have a procedure that is general. The solution seems to be to obtain SSD,, at a selected few locations and obtain SSD,, above a given spine point from these measured values using the principle of linear interpolation. This is achieved by taking many transaxial contours of the patient on the

60

Medical Dosimetry

simulation table. The number of contours would be more than one, how many would depend precisely on how close the linear interpolated value of SSD,, is to the real value. This would mean taking more contours around regions of greater variation of SSDs and greater curvature of spine on the AP and lateral films. Transaxial contours are used to obtain g and d for AP and PA ports, thus it is essential that the posterior aspect of the contour is also conforming to patient skin. This requires using an appropriate molding device that would shape to the body contour posteriorly to locate the posterior SSDs accurately. For each of the contours we have the information on the location of CAX, the y value (how far away from CAX on the y direction), and the isocenter. Thus x and z coordinate axes can be drawn on each of the contours the way xsp, y,,, z,, are defined, i.e., with respect to the isocenter. A line of calculation through the spine point parallel to the beam axis is drawn, and we would have the information on g and d for AP and PA ports to obtain the relative dose. The procedure to be established has to be to locate the SSD,, above the spine calculation point from the available transaxial contours. The technique suggested here is linear interpolation (or linear extrapolation). Interpolation would be performed twice to arrive at the SSD,, above the calculating spine point. In the first phase it is necessary to locate the spine point (using interpolation) on each of the given transaxial contours, and later, to obtain the SSD,, (again using interpolation) exactly above the spine calculation point from the spine points located on the contours. Let us consider a transaxial contour at location y = y, and two neighboring spine points whose coordinates obtained numerically are, (x,,, , y,,, , z,,,) and (xspz1J&2 3 zsp2). It is possible to obtain coordinates x, and z, for the spine point on the contour with y = y, from (xspl TYspl9 z,,d and (xsp2, xp2, zsp2)using linear interpolation. Once (x, , z,) is located on this transaxial contour, it is easy to draw a line through this point parallel to CAX and thus obtain (SSD,,),, . Thus we would now have a set of SSDs for the spine points at each of contour locations, [(SSD,,),, vs y]. The next step is to obtain the SSD,,s above the spine points where the dose to spine needs to be calculated. From the data of (SSD),, y), it is again a simple matter of linear interpolation to obtain SSD,, for y = ysp. These SSD,,s would be very close to the true SSD above the spine if interpolation is a valid assumption. This means both spine curvature and SSD slope are linear between any two successive contours. SSD,, for the posterior setup is likewise obtained. Now that SSD,, is known for each spine point, along with the true x, y, z values, one can right way obtain d and g from Eqns. 8 and 9. It is now a routine procedure of inputing these x, y, d, and g through

Volume 18, Number 2, 1993

keyboard entry into the planning system and obtain the relative dose to spine from AP and PA setups. The spine would definitely fall on the line of calculation at the correct location within limits of measurement accuracy if these values are used in the calculation of dose to spine using irregular field point dose calculation algorithm. There are other advantages to locating the spine using transaxial contours. It is now possible to locate the spine for each contour and run an isodose plan as with using CT. Thus there is now an alternative to obtaining the dose to spine in the absence of CT. It is possible to run the isodose plans on the transaxial slices and obtain the dose to spine through isodose distribution. For the cases where a wedge or compensator is used, one can run the isodose plans as for a wedge or a compensator on the various transaxial slices and be able to obtain the dose to spine in each slice. This is not possible in the irregular field point dose calculation mode. In many instances oblique field boost is planned that would increase dose to the designated tumor volume, that avoids the spine, by appropriately blocking’ the spine from the direct field. It is necessary in this case to run an isodose plan to look at the dose distribution, hot spots outside of the volume, and, the dose to spine. It is possible to do all that, if a transaxial contour is taken through CAX for the boost field at the time of initial AP/PA treatment. The spine can be located as suggested on the contour to provide the dose distribution for boost as well as composite treatment. CONCLUSION In conclusion, we have tried to eliminate or minimize the common errors associated with locating the spine by use of a set of two orthogonal films during simulation. The aim has been to keep the procedure general so it is valid for any situation. The use of successive approximations to locate the x, y, and z can, if necessary, be taken to any order of approximation. In obtaining SSD,, , and from that g and d, the assumption is that the use of linear interpolation is valid, which would require more contours in areas ofgreater contour slope and spine curvature. If information on posterior air gap is known from the use of a mold that conforms to the contour of the skin, we can directly obtain SSD,, for posterior setup and thus the dose from PA port. REFERENCES 1. Coia, L.; Chiu, J.; Larsen, R.; Myerson, R. Spinal cord protection during radiation therapy. Int. .I. Radiat. Oncol. Biol. Phys. 12:1697-1705; 1986. 2. Rubin, P.; Constine, L. S.; Nelson, D. F. Late effects of cancer treatment: Radiation and drug toxicity. In: Perez, C. A. and Brady, L. W., editors. Principles of radiation oncology. Philadelphia: J. B. Lippincott; 1992: 15 1.

Calculating dose to spine 0 R. JANAKIRAMAN 3. Gerbi, B. J.; Levitt, S. H. Treatment planning of radiotherapy for lung cancer. Front. Radiat. Ther. Oncol. 21:152-180; 1987. 4. Sherouse, G. W.; Bourland, J. D.; Reynolds, K.; McMurry, H. L.; Mitchell, T. P.; Chaney, E. L. Virtual simulation in the clinical setting: some practical consideration. Int. J. Radial. Oncol. Biol. Phys. 19:1059-1065; 1990.

APPENDIX Following is a typical procedure for obtaining x, y, g, and, d from simulation films, for spine point location close toy axis on AP film and curved on lateral film. We have intentionally taken a faraway location that would lead to mislocation of spine if the numbers obtained this way are entered into the planning system uncorrected.

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Let us assume the source to film distance for AP and lateral films is 140 cm, so the magnification factor at isocenter distance is 1.40.Since the z value of the spine is 20 cm., the magnification for the spine [z = (100 - 20)] cm at 140 cm is 1.750. Thusxcoordinate as measured on the film would be at 20 X 1.75 = 35 cm. This corrected for the isocenter distance would be at 35/l .40 = 25 cm. Because the spine location is off beam axes on AP film, the magnification is accordingly different from the factor for the isocenter distance. Since x,,, is 25 cm, spine magnification is 140/( 100 - 25) viz.. 1.12 (almost 1.10). Location of spine on lateral film would be at 23.3 cm, from the expression [20 X 140/( 100 + 20)]. When corrected for the magnification of I. 10 for spine, the z coordinate is 21.1 cm. In this illustration, input x is 20% off, and, input z is off 6%, if no specific corrections are made for beam divergence, which is more pronounced when the spine is away from the principal axes.