gapping fields on sloping surfaces

hr. J Radration Oncdogy Bid Ph. Vol. 18. PP. 1183-1190 Printed in the U.S.A. All rights reserved.

0360-3016/90 $3.00 + .oO copyright Q I990 Pergamon Press plc

??Technical Innovations and Notes

GAPPING FIELDS ON SLOPING SURFACES

RICHARD KEYS, M.A. AND PERRY W. GRIGSBY, MS., M.D.

Radiation Oncology Center and Physics Department, Mallinckrodt Institute of Radiology, Washington University School of Medicine, St. Louis, Missouri 63 110

The accurate positioning of treatment fields has always been difficult, and becomes even more important when two fields are adjacent and a gap must be calculated. The standard formula (based on similar triangles) assumes a flat surface. In Hodgkin’s patients the gapping between the mantle and para-aortic fields involve sloping surfaces and the patient thickness can vary as much as 5 or 6 cm between central axis and the lower edge of the mantle field. Due to the divergence of a large mantle field, using the standard formula and gapping on the skin surface can lead to an overlap of 7 to 9 mm and a region which can receive 140% of the midplane dose. A modification of the existing formula which takes into account sloping surfaces has been formulated for both source-skin-distance and isocentric treatments. In addition, problems in positioning related to mantle fields when treating the patient prone and supine have been investigated.

Gapping fields, Mantle field, Hodgkin’s disease.

INTRODUCTION

The gapping of abutting fields in radiation therapy often presents a difficult problem. The consequences of incorrect gapping can be serious, especially if it creates an overdose to the spinal cord or, if gapped too much, an underdose which may lead to recurrence of tumor in an area that is difficult to retreat adequately without complications to normal tissue. Many formulas have been devised for de- termining how much to gap two adjacent fields on the skin surface. All of these formulas assume that the patient surface is flat and that the source-skin-distance (SSD) is the same for the field edge as at central axis (Fig. 1). In Hodgkin’s patients, the gapping between the mantle and para-aortic fields involves sloping surfaces and the patient thickness varies as much as 5 cm or 6 cm between the central axis and the lower edge of the mantle field (Ta- ble 1).

METHODS AND MATERIALS

The radiation therapy records of all patients in the Mallinckrodt Institute of Radiology (MIR) tumor registry with the diagnosis of Hodgkin’s disease from January 1978 through December 1984 were reviewed. The total patient population included 245 patients. From this group, there

were 97 consecutive cases of Hodgkin’s disease in which some portion of the patient’s therapy included a full mantle field. All of these 97 patient charts contained complete information regarding SSD, patient contour (slope), position of the central axis and patient diameter.

Figure 2 is a sagittal contour of the upper neck and chest. For uniformity on all of our Hodgkin’s patients, the central axis of the mantle field is at the sternal notch. The length of the mantle field for this example patient is 26 cm. The patient diameter at central axis is 12 cm and the diameter at the lower field edge 18 cm. The central axis is at 100 cm SSD and therefore, the lower edge of the light field strikes the skin surface 6 cm closer to the source at 94 cm SSD. Because of the beam divergence the field size at 94 cm is only 24.4 cm. This is a difference of 1.6 cm, and indicates that the lower edge of the field has shifted half that distance, or 8 mm, closer to the central axis on the skin surface. When the gap is measured on the skin surface, the para-aortic field will be positioned 8 mm closer to the mantle field than desired, since the standard gap formula used is based on a flat surface. Thus, the anterior para-aortic field will overlap the posterior mantle field by 8 mm at depth.

A close look at the simulation films for this patient indicated that the anterior and posterior mantle fields were parallel opposed as planned. However, the superior edge

Reprint requests to: Perry W. Grigsby, M.D., Radiation On- cology Center, Box 8 13 1,4939 Audubon, Suite 5500, St. Louis, MO 63110. Acknowledgements-The authors wish to thank Elaine Pirkey for her help in preparation of this manuscript.

Dr. P. W. Grigsby has been supported by the American Cancer Society Clinical Oncology Career Development Award.

Accepted for publication 16 November 1989.

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I. J. Radiation Oncology 0 Biology 0 Physics May 1990, Volume 18, Number 5

L, and L, = Field lengths D = Depth of calculation

SSD = Source -Skin distance S, and S,= Field half separations

s=s,+s, S = Field separation

Fig. 1. Standard formula for calculating the gap at the skin surface for a given depth using similar triangles.

of the anterior para-aortic field overlapped the inferior border of the posterior mantle field by approximately the 8 mm predicted by the formula. In addition, the central axis of the anterior para-aortic field was also shifted 8 mm cephalad along the spinal cord in comparison to the central axis of the posterior para-aortic field.

This difference in patient thickness at the central axis and the lower field edge must be taken into account. The standard formula for calculating the gaps between fields is based on similar triangles and assumes a flat surface. The formula is

-P=)Ll(&)+)$&), where Ll and L2 are the field lengths and d is the depth of dose specification. With Hodgkin’s patients this depth at CA is different for the mantle and para-aortic fields.

We are proposing a modified formula which takes into account sloping surfaces and the air gaps due to differences in patient thicknesses. In developing our formula we are attempting to match all four fields at a given point in the patient. We first considered the case of treating the patient supine for both AP and PA fields. This technique is more straightfonvard since it eliminates the problems encoun- tered when turning the patient over and assures that the mantle fields will be parallel opposed. This technique is also becoming more popular since large fields with di- mensions of 40 X 40 cm can be attained at standard treatment distances.

There are three major principles that affect the gapping technique as illustrated in Figure 3. First of all, when treating patients at 100 cm SSD, due to the geometry of the AP and PA mantle fields, the field edges will intersect

at a depth equal to one-half the central axis thickness. If the CA thickness is 12 cm and there is no air gap on the posterior surface of the CA, the field edges will necessarily intersect at a point 6 cm from both the anterior and posterior surfaces in the matched regions.

Second, the gap between fields occurs in the regions of the lower mediastinum and the depth used in the calculation should correspond to the patient thickness in this region and not at the CA depth. Therefore, the depth used for the gap calculation should be one-half the depth of CA thickness (d, ) plus the air gap thickness between the lower field edge and CA; dg = d, + al. The posterior depth of calculation will be just one-half central axis thickness (d, ). The total of these two depths should equal the patient thickness in the gap region. In the previous example the anterior depth should be 6 + 6 = 12 cm and posterior depth = 6 cm, the total is 18 cm.

The third principle is that when trying to match two anterior fields the depth of gap calculation (dg) should be the same for both fields. The air gap between central axis and field edge for the second field (a?) is not important in this case since the ratio of gap width (g2) to depth of calculation (dg) is equal to (L/2)/SSD2 according to similar triangles, see Figure 3.

g2 tL2 _=-

dg SSD2 ’

This principle is very important especially in gapping two posterior fields along the spinal cord at a depth of 5 cm. No correction need be made for sloping surfaces, since the gapping width g2 is dependent only on the field length L2, SSD2 and depth of gap calculation dg. The problem

Table 1.

Actual Actual diK change of in patient

SSD at LM thickness (air gap) (LM-CA)

(cm) Freq. (cm) Freq

1.0 I 1.0 1 1.5 2 1.5 1 2.0 10 2.0 3 2.5 4 2.5 4 3.0 9 3.0 7 3.5 9 3.5 5 4.0 15 4.0 11 4.5 7 4.5 11 5.0 13 5.0 17 5.5 4 5.5 11 6.0 8 6.0 11 6.5 7 6.5 9 7.0 1 7.0 2 1.5 1 7.5 2 8.0 0 8.0 2

Ave. 3.8 cm Ave. 4.8 cm

97 total patients.

Gapping fields 0 R. KEYS AND P. W. GRIGSBY 1185

GAPPING FIELDS ON SLOPING SURFACES

__-___----------_

6cm CEPH

6cm

Fig. 2. Sagittal contour of the upper chest and neck depicting the skin gap calculated using the standard formula for flat surfaces and the new gap calculated using the modified formula for gapping fields on sloping surfaces.

associated with sloping surfaces occurs only when matching both anterior and posterior fields. Thus, the depth of gap calculation (dg) for the anterior mantle and anterior para-aortic fields should be the same (d, + al) and the depth used for the posterior mantle and posterior para- aortic should also be equal to each other but at a depth of one-half the central axis thickness of the mantle field (dr ).

Thus, the modified gap formula for supine patients with sloping surfaces for the anterior fields is

Fig. 3. Modified formula for calculating the gap for matching four fields on a sloping surface.

where

d, = 4 CA thickness of mantle fields: al = anterior air gap between central axis and lower field

edge; Lz = para-aortic field length: L, = mantle field length.

The formula for the posterior gap is

garb= fL&$-)+ 14(&j-).

Thus, to match four fields at a common point when treating the patient supine at 100 SSD the gap on the anterior will be much greater than the posterior because of the anterior air gap.

RESULTS

As a comparison of the two methods both formulas are applied to the patient in Figure 2. The mantle field length is 26 cm, the patient thickness at CA axis is 12 cm and the patient is treated at 100 SSD with an air gap of 6 cm between the lower field edge and CA. The para-aortic field length is 20 cm, the patient thickness is I7 cm at CA with an air gap of 1 .O cm. Note that the patient thickness is 18 cm at the gap region. Using the standard formula, the gap on the skin surface is calculated to be

i (26) -6- + i (20) K = .78 + .85 = 1.63 cm (100) 2 (100)

for both the anterior and posterior fields. Using the modified formula the anterior gap is:

1186 1. J. Radiation Oncology 0 Biology 0 Physics May 1990, Volume 18, Number 5

CEPH

CAUD

Fig. 4. Isodose curves obtained in a phantom using film dosimetry illustrating the region of overlap for a standard and modified gap.

= 1.56 + 1.20 = 2.76 cm.

This is a difference of 2.76 - 1.63 = 1.13 cm. The gap on the posterior would be

i (26) -? + 1 (20) 6 = 0.78 + 0.6 = 1.38 cm. (100) 2 (100)

1.38 - 1.63 = -0.25 cm.

To estimate the effect of an overlap of 9- 12 mm, a phantom was designed to simulate the contour. Film* was cut to match the contour shape. Each mantle and para-aortic field was given 40 cGy to the depth of calculation. Thus, 80 cGy corresponds to 100% of the dose. Figure 4 indicates the isodose curves using the standard formula if no blocking had been performed. Note the maximum dose is approximately 145% of the central axis dose. At a depth of 5 cm from the posterior, which is the approx- imate depth of the spinal cord, the dose is 125% of the central axis dose. If the dose to the mantle and para-aortic fields were 4000 rad, the spinal cord would receive 5000 rad. The patient in this example did not receive this dose since a one half value layer spinal cord block was used throughout the posterior mantle treatment and a 2 cm X 2 cm five half value layer “notch” was used to block the spinal cord on the superior border of both the anterior and posterior para-aortic fields. However, there are several cases in which no spinal cord block is used and great care must be used in gapping these fields correctly. The isodose

curves using the modified formula and the one half value layer spinal cord block on the posterior mantle and the 2 cm five half value notches on both para-aortic fields indicate that the midplane mantle dose is approximately 80%, and the dose in a 2 cm region at the junction is less than 30% of the tumor dose due to the 2 cm “notches”. This adequately protects the spinal cord from errors in patient setup, but substantially reduces the dose in this region.

Figure 5 indicates the isodose curves using the modified formula on a similar phantom with the length of the mantle field 30 cm and para-aortic field 20 cm. The standard formula ( 1) calculated a gap of 1.8 cm. The modified formula with an air gap of 6 cm calculated a gap of 3.0 cm. The dose is much more uniform at the junction. The region near the spinal cord received 115% of the central axis dose. This is due to the difference in field sizes between the mantle and para-aortic fields. The greater divergence of the mantle beam edge does produce a small overlap region. This is also an idealized case in a phantom treating the patient supine only and does not indicate other problems in patient set up such as treating the patient prone and supine and daily set up errors.

Table 1 indicates the frequency of patients with a given difference in thickness between the central axis and lower mediastinum and also the actual air gap used in the off- axis calculation of dose to the lower mediastinum. The corresponding shift in the edge of the field due to the air gap is tabulated in Table 2. For the majority of patients the air gap equals the difference in patient thicknesses since the patient’s posterior surface at the central axis is also on the table top. However, 34 patients used the Alpha- Cradle+ immobilization device which tends to elevate the

* Kodak XV film, Rochester, NY. + Smithers Corporation, Akron, OH.


GAP 3Ocm

CAUD

GAP 1.5cm

Fig. 5. Isodose curves obtained in a phantom employing film dosimetry using the modified formula to calculate the gap.

central axis in relation to the lower mediastinum. Con- sequently, the air gap is less than the actual difference in patient thicknesses for these patients. Column 2 in Table 2 indicates the shift in the lower edge of the mantle based on these actual thicknesses if the immobilization device was not used. Note that 85% of the patients have possible shifts greater than or equal to 5 mm, 7 1% greater than or equal to 8 mm and 30% greater than 12 mm. The average change of patient thickness at the lower field edge is 4.8 cm. Assuming an average mantle field length of 30 cm there is an overlap of 7.6 mm between the anterior para- aortic and posterior mantle fields.

The data from a beams at 10 cm depth for a 30 X 30 cm field at 80 cm SSD indicates that the dose at a point 5 mm inside the field is 8 1% and at 8 mm it is 88% of the dose at central axis.

Table 3 indicates the percentage dose if a patient is 20 cm thick and two fields are incorrectly abutted. With an overlap of 5 mm at 10 cm depth the percent dose at one field edge at the junction would be 50% + 8 1% = 13 1% of the dose at central axis. An overlap of 2 mm gives a dose of 116%. and a 10 mm overlap gives 140% of the dose. Note in column 6 that the highest dose occurs in the middle of the overlap region and receives 8 1% + 8 1% = 162% if there is a 10 mm overlap. In contrast, if the gap is too large by 5 mm the dose will only be 50% + 22% = 72% of the dose at central axis on a field edge and 36% + 36% = 72% in the middle. Thus, to get a uniform dose in the match region, it is important to gap correctly.

DISCUSSION

On most linear accelerators it is difficult to get a large enough field size (40 cm width) to treat the posterior

mantle field without turning the patient over and treating the patient in a prone position. This creates two major difficulties. We now have the same problem with sloping surfaces that we had on the anterior surface. The air gap between central axis and the lower field edge on the posterior surface varies from 50% to 100% of the air gap on the anterior, and shifts in the lower field edge of 4 mm to 7 mm are common. Now we have both the anterior and posterior para-aortic fields overlapping the mantle fields.

A second difficulty is that we now need to make sure that the mantle fields are truly parallel opposed, and that the central axis and lower edge of the posterior mantle fields have not shifted in relation to the anterior field. This also can result in overlapping of fields. One method

Table 2.

Overlap of Frequency % of patients paraaortic

and mangle Due to Due to Overlap Due to Due to fields (cm) air gap LM-CA (cm) air gap LM-CA

.l 4 1 >.5 70 85

.2 7 5 >.8 27 44

.3 9 5 >I.0 6 15

.4 9 3

.5 18 14

.6 14 13

.7 10 13

.8 14 14

.9 6 14 1.0 1 7 1.1 2 5 1.2 1 2 1.3 2 I

Ave. 0.58 cm 0.70 cm

97 total patients.

* Varian Clinac 6X, Palo Alto, CA.

1188 I. J. Radiation Oncology 0 Biology 0 Physics May 1990, Volume 18. Number 5

Table 3.

Gap (cm)

2.5 2.3 2.0 1.7 1.5 3.0 3.5

Overlap at 10 cm depth

(cm)

0.0 0.2 0.5 0.8 1.0

-0.5 -1.0

% dose at edge of field 1

50 50 50 50 50 50 50

% dose due to overlap

from field 2

50 66 81 88 90 22 16

Total dose at edge Dose in middle of field 1 of overlap region

100 100 116 116 131 136 138 150 140 162 72 72 66 44

we have used is to mark the anterior central axis with a wire and then turning the patient prone and using fluoroscopy to match the central axis of the posterior field to this point. This ensures that the entrance point of the anterior mantle field and exit point of posterior field align. This method works well unless the patient is tilted from resting the chin on the table or a sponge. In reviewing simulation films of Hodgkin’s patients, and viewing where the central axis position hits the vertebral bodies, it was noted that some patients have a difference as much as 1 cm between the anterior and posterior mantle fields at the spinal cord. Since the spinal cord lies close to midplane at the sternal notch, the entrance point of the posterior field can be shifted more than a centimeter from the ex- iting anterior central axis (Fig. 6). To ensure truly parallel opposed fields not only should the exit point be the same, but also the position of central axis along the spinal cord should be the same. However, this is often difficult to achieve in practice because of the patient’s position when prone. In addition, when the patient is turned over the skin moves. Any marking on the anterior surface can move by as much as 1 cm. This was verified taking a cross table lateral film of several Hodgkin’s patients.

Anytime the patient must be treated both prone and supine, the correct abutment of four fields is very difficult

and can be accurate only if the same relative position is maintained. Thus, the air gap between central axis and lower mediastinum on the posterior should ideally be zero for both anterior and posterior treatments. If there is an air gap between central axis and the lower mediastinum on the posterior field it, too, must be calculated into the gap formula.

A method utilized in some clinics is to simulate the patients to match the fields on the same geometric position on the spinal cord, thus eliminating the need for a gap calculation. A method used to solve the problem of align- ing fields when the patient is treated both prone and supine was presented by Lutz et al. (3). Their method tries to match the field edges of all four fields at midplane in the patient by picking a reference point in relation to the vertebral body in the match region. After the anterior mantle field is set up isocentrically the gap is calculated using the standard formula with the isocenter depth equal to one- half the patient thickness in the match region, and the field size equal to the collimator setting at treatment SAD. A mark is then placed on the patient’s anterior surface at point P which is a distance equal to the gap from the inferior beam edge. The simulator table is then positioned so that the central axis of the vertical beam goes through this point P and an X ray is obtained. The point where

field edge 1.5 cm

neck illustrating the relative change in position of the spinal cord Fig. 6. Sag&al contour of the upper chest and in the neck with respect to the chest.


the central axis crosses the vertebral column, point M, is used as a reference point. When the patient is turned over for the posterior mantle field this reference point M is located using fluoroscopy along the vertebral column. The lower field edge is then positioned by calculating the gap needed for the posterior mantle fields. This method ensures that no matter how the patient is tilted in the prone position that the field edges cross at a particular point M midline in the patient in the match region. Note that if the patient is treated SSD, or if the isocenter is not based on the depth in the match region, due to the sloping surfaces, the anterior and posterior mantle fields will not be parallel opposed and will be shifted by the same amount as the shift in field edge due to the air gap. The isodose curves produced by the method by Lutz indicated that the spinal cord could also receive I 15% of the central axis dose and consequently Lutz et al. (3) recommended using small blocks to reduce this dose.

Our physicians prefer to treat the mantle fields with parallel opposed fields. Because of the sloping surfaces the air gap from both anterior and posterior fields must be considered in the gap formula.

The major principle to keep in mind when treating a patient both prone and supine is that due to geometry the field edges will necessarily meet at a depth midway between the anterior and posterior central axis. If the patient diameter at central axis is 12 cm, the fields should meet at 6 cm depth. However, if the patient is also treated prone and there is an air gap of 3 cm between central axis and lower mediastinum, the lower field edges will not meet at 6 cm from the posterior. The intersection point is shifted anteriorly one-half the distance of the posterior air gap. With a 3 cm air gap the intersection occurs at 6 cm + $(3 cm) = 7.5 cm from the posterior. Since the patient thickness was 18 cm at the lower mediastinum, the anterior depth should be 18 - 7.5 = 10.5 cm. The formula for finding the depth of calculation in the gap region when treating patients both prone and supine is

where

Ant d, = d, + a, - {a,,

Post d, = d, + fa,,

a, = air gap (anterior mantle)

aPl = air gap (posterior mantle)

thus the anterior gap for the patient in Figure 1 is

; (30) 6 + 6 100 - t(3) 6 + 6 100 - t(3)

= i,,,)(z) +;(20)(%)

= 1.58 + 1.05

= 2.63 cm.

The posterior gap is

= 1.88 cm.

Since the patient thicknesses in the match region de- termines the total depth for the gap calculation we are tempted to just use the patient thickness at the gap region in the standard formula without trying to line up these field edges about the reference point M. If the anterior and posterior mantle fields are set up to be parallel opposed, this method does not work. Due to the divergence problem on sloping surfaces, if the air gap on the anterior is greater than the posterior, the gap between fields on the anterior surface should be greater than the gap on the posterior. For the patient in Figure 1, this method calculated the gap to be l/2(30) (9/100) + l/2(20) (9/100) = 1.35 + 0.9 = 2.25 cm. Our modified formula indicated a gap of 3.0 cm is needed for the anterior and 1.5 cm for the posterior. Thus, the gap will be 7.5 mm too small on the anterior and 7.5 mm too large for the posterior which will increase the region of overdose and underdose compared to the modified formula. This particular method also does not take into account the positioning problems involved in treating the patient prone and supine.

One other method which circumvents the problem of the sloping surfaces is to treat the anterior mantle field with a compensating filter and use the patient thickness in the match region at the lower field edge as the point of calculation. One hundred SSD is then set to this high point and not at central axis. The standard formula will work in this case since there is no air gap between the central axis and the lower field edge. We have used this technique on several of our patients at Mallinckrodt.

Even with a “perfect” match between all four fields there will be regions of overlap of the fields due to beam divergence. Note in Figure 1 that the dotted line indicating the correct position of the anterior para-aortic field edge does not coincide with the field edge of the posterior mantle. This difference of approximately 6 mm is due to the greater divergence of the mantle field which is 26 cm long compared to the 20 cm long para-aortic field. Hopfan et al. (2) suggest a rule of thumb of using a ratio of Ll to L2 of 1 to 1.5. The actual formula they suggest is L2 - Ll < 2(SSD/d) to avoid an overlap of 1 cm due to beam divergence and field size.

The dose in this overlap region due to beam divergence is approximately 15-20%. For this reason and because of the other difficulties involved with day to day set up, such as the moving of field edges on the patient surface due to changes in the patient’s weight, or changes in the light field-radiation field coincidence, it is recommended to protect the spinal cord in the match region with a block. At Mallinckrodt we have used a 1 HVL spinal cord block

1190 I. J. Radiation Oncology 0 Biology 0 Physics May 1990, Volume 18, Number 5

Fig. 7. Overall comparison of the standard formula, the Lutz method, and the modified gap formula.

along the entire cord on the posterior mantle field and a 2 cm X 2 cm X 5 HVL “notch” in both para-aortic fields. Lutz et al. (3) recommend a 2 cm X 2 cm X one half value layer block on both posterior fields. Figure 7 gives an overall comparison of three methods for calculating the appropriate gap.

The accurate gapping of four fields is a very difficult problem to implement in a clinical setting. If the patient surfaces are sloping the problem becomes more complex.

Due to the differences in patient thicknesses at central axis and the lower mediastinum, the lower edge of the diverging mantle field can be shifted on the skin surface. Using the standard formula can lead to overlaps of the para-aortic and mantle fields of 9 mm to 12 mm. Our modifjed formula corrects for this difference due to sloping surfaces. Not only is it easy to implement, the formula tends to increase the gap which ensures no large regions ever overlap.

1.

2.

REFERENCES

Glenn, D. W.; Faw, F. L.; Kagan, A. R.; Johnson, R. E. fields: physical and technical considerations. Int. J. Radiat. Field Separation in multiple portal radiation therapy. Am. Oncol. Biol. Phys. 2:801-808; 1977. J. Roentgenol. 102: 199-206; 1968. 3. Lutz, W. R.; Larsen, R. D. Technique to match mantle and Hopfan, S.; Reid, A.; Simpson, L.; Ager, P. J. Clinical com- para-aortic fields. Int. J. Radiat. Oncol. Biol. Phys. 9: 1753- plications arising from overlapping of adjacent radiation 1756; 1983.

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