Direct measurement of intratumor dose-rate distributions in experimental xenografts treated with 90Y-labeled radioimmunotherapy

Int. J. Radiation

Oncology

Pergamon

l

Biol.

Phys.,

Vol.

Printed

32, No. I, pp. 147- 157, 1995 1995 Elsevier Science Ltd in the USA. All rights reserved 036O-3016195 $9.50 + -00

Physics Original Contribution DIRECT

MEASUREMENT OF INTRATUMOR DOSE-RATE EXPERIMENTAL XENOGRAFTS TREATED %Y-LABELED RADIOIMMUNOTHERAPY

DISTRIBUTIONS WITH

RULON MAYER, PH.D.,* LARRY E. DILLEHAY, PH.D.,* YI SHAO, M.D.,* YONG-GANG ZHANG, M.D.,* SHIYU SONG, M.D.,* RICHARD M. BARTHOLOMEW, DANIEL G. MACKENSON, B.A.+ AND JERRY R. WILLIAMS, Sc.D.*

IN

PH.D.,+

*Division of Radiation Oncology, 600 N. Wolfe St., Johns Hopkins Hospital, Baltimore, MD 21205, +Hybritech Inc., P.O. Box 269006, 11095 Torreyana Road, San Diego, CA 92196-9006 Purpose: To measure, quantify, and evaluate the planar dose-rate distribution for human tumor xenografts implanted into mice that are treated with WY-labeled monoclonal antibodies or biipecific antibodies and v-labeled haptens. Methods and Materials: Twenty-five LS174T human colon carcinoma tumors grown subcutaueously in nude mice were treated with T by either directly labeled ZCE025 or bispecific ECAOOl-DBX antibody systems. A simple, quick technique using GAP radiochromic medium determined the dose-rate distribution in a plane passing through the tumor center. The dose-rate distribution is generated from exposure to activity situated in one-half of the tumor (0.045 to 0.83 g). Results: Planar dose-rate distributions were obtained from the tumor xenografts. Planar dose-rate histograms were computed along with the coefficients of variance and skewness of the distributions. The observed dose-rate distributions were quantitatively compared to those calculated for a uniformly distributed activity in a half-ellipsoid of the same volume and approxhuate shape as the tumor half. The observed dose-rate distributions were usually broader with a more positive coefficient of skewness than the dose-rate distributions calculated from the uniformly active half-ellipsoids. For 9, tumor shape plays an important role in determining the minimum tumor dose. For these tumors, the tumor minimum dose-rate is always observed along the edge, usually where the edge curvature is most convex. Larger tumors tended to have broader dose-rate distributions and more positive coefficients of skewness. Exceptions to this trend were associated with dose-rate maxima displaced from the central regions due to activity heterogeneity or tumor size greatly exceeding the range of emission. Calculations for dose rate from the conventional Medical Internal Radiation Dose (MIRD) formulation exceeded the average and minhuum dose rate derived from radiochromic media. The coefficient of skewness became more positive for increasing time between injection and tumor excision, consistent with the activity evolving into a more uniform activity distribution. Conclusion: Using radiochromic media to measure the spatial dose-rate distribution is a valuable method for comparing the dose-rate heterogeneity among experimental tumor xenografts in animals treated with radiolabeled antibodies. Tumor size (relative to the particle range) and changes in activity distribution affect the dose-rate distribution that are reflected by changes in the coefficients of skewness and variation of the dose-rate area histogram. The increase in coefficients of variation and skewness with tumor size and time results from the size of the 9 beta particle penetration range that either exceeds or is comparable to the tumor dimensions. The minimum dose rate is more dependent, relative to the average and the maximum dose rates, on the curvature of the tumor surface. Dosimetry,

Radioimmunoglobulin

therapy, Yttrium-90,

INTRODUCTION

Xenograft, Image analysis, Colon carcinoma.

example, radiolabeled antibodies targeted to tumor-associated antigens can be used in radioimmunoscintigraphy (RIS) and/or radioimmunotherapy (RIT). Treatment applications have used the antibody as either a primary ther-

Since their introduction, monoclonal antibodies have been widely applied in diagnosis and therapy (10, 19). For

Reprint requests to: Dr. Rulon Mayer. Acknowledgements-This research was supported by NIH Grants CA43791 and CA58974, and by Hybritech, Incorporated.

Accepted for publication 20 October 1994.

147

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0 Physics

apy source or as an adjunct treatment to be combined with other modalities such as hyperthermia or external beams (23) or as a possible radiation sensitizer for cancerous cells (23). Unlike imaging modalities using nuelides with long-range emissions (> 10 cm, 100 to 400 kev gamma rays), RIT requires emissions of much shorter range to deposit dose into the desired regions. Although qualitatively understood, relatively little direct quantitative experimental work has examined the actual dose-rate distribution (as opposed to activity distribution determination, or average dose-rate calculations) for various betaemitting isotopes (maximum range of 0.1 - 1.1 cm). Such studies could support meaningful treatment response predictions and provide optimal strategies for tumor sterilization. Previous work on spatial dose-rate distributions in animal tumors deposited by radiolabeled monoclonal antibodies required elaborate calculations (7, 14-16). Such studies digitize activity distributions in serial autoradiographs of thin slices separated by known distances. Assuming activities for slices represent activities of surrounding slices, a point source function is assigned to the activity, and planar and/or three-dimensional tumor doserate distributions are then computed by summing the contributions to the dose rate from the activities within the examined slices. The extensive work required to calculate the dose-rate distributions makes meaningful comparison of tumor dose-rate distributions difficult for a large number of representative tumors. Recently, we developed another method to measure the dose-rate distribution in animal tissue (12). Instead of slicing thin section samples, a tissue from an animal injected with radiolabeled antibody is halved and the tissue half is placed on radiochromic medium for a time interval of sufficient length to darken the medium. The sources of radiation from all parts of the excised tissue contribute to the dose deposited in the plane, simulating the situation at the time of animal killing. The chromic medium is subsequently scanned and the optical density converted to planar dose following an appropriate calibration. This dose distribution provides a “snap shot” of the dose-rate distribution delivered by the radiolabeled antibody at the time of killing. Such an alternative technique offers a simpler, faster determination of the spatial planar doserate distribution; it is used in the present study of a series of tumors treated under a variety of conditions. We used radiochromic medium to study dose-rate distributions in human colon carcinoma xenografts growing in nude mice treated with V-labeled antibodies. The spatial dose-rate distribution within the tumor depend on such variables as tumor size (8,21), range of radioisotope (4, 9, 10, 19), time interval between injection and dose-

‘Hybritech,

San Diego, CA.

Volume

32. Number

1, 1995

rate measurement (1, 2) and rate of antibody diffusion (1, 2). In 25 tumors we measured the fifth percentile, mean, and 95th percentile dose rates, coefficients of variation, and skewness of the planar dose-rate distribution. Each parameter was compared to parameters characterizing the calculated dose-rate distribution generated by 9 activity uniformly distributed over a half ellipsoid. This type of dose-rate distribution is termed the uniformly active half ellipsoid (UAHE) distribution. Having previously (12) shown an example of a tumor with a planar dose-rate distribution qualitatively resembling the UAHE approximations, we use this approximation as a basis for studying observed dose-rate distributions for two reasons. A concurrent study (5, 6) in our laboratory indicates that this same approximation, when applied to noninvasively determined activity and tumor volume measurements, provides estimates of the minimum dose rate that can account for much of the variability in response between tumors. The UAHE approximation also helps quantify the sources of dose-rate heterogeneities, incorporating heterogeneity due to the finite size and general shape of the tumor. Any additional experimental dose-rate heterogeneity must arise from inhomogeneity in the activity distribution (which is also examined within a simple extension of the UAHE model to activity distributed so that the dominant activity is deposited onto the ellipsoid periphery, but continuously decreases towards the ellipsoid center along the radial direction) and irregularities in the tumor surface. The increase in coefficients of variation and skewness with tumor size and time predominately results from the size of the 9oY beta particle penetration range that either exceeds or is comparable to the tumor length.

METHODS

AND MATERIALS

Animal Model Nine to 11 days prior to antibody injection, 4-5 X lo6 LS 174T human colon carcinoma cells in Hank’s balanced solution were injected subcutaneously into the left upper thighs of 7-week-old nude mice. Some animals were treated with anticarcinoembryonic antigen (CEA) antibody (ZCE025) labeled with WY by Hybritech, as previously described (13). Other animals were treated using a bispecific antibody system (18). Animals were injected intracardially with 100 pg of the bispecific monoclonal antibody ECAOOl’ (13), under metafane anesthesia. This bispecific MoAb has one binding site (same as ZCE025) for CEA and one for a 1037 dalton hapten containing the chelator diethylenetriaminoepentaacetic acid (DTPA). One day later, animals were injected intracardially with 22.5 or 45 picomoles of the hapten, which had been labeled with ?‘. Following sacrifice, the tumors were ex-

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Human tumor xenographs 0 R. MAYER et al.

cised, lightly frozen (to ease tissue cutting), cut in half, the tissue halves weighed, and the activity measured in a well-type counter.’ Preparation of Radiochromic Medium

Medium preparation, handling, and procedures to determine dose and dose-rate distributions were as previously described (12), and may be summarized as follows: the radiochromic medium is prepared before exposure to the radioactive tissues to minimize the thermal effects from the freezer, eliminate spurious discolorations of the medium, and ensure proper alignment of the doserate distribution and tissue outline. Fiducial marks, placed at fixed positions on the dosimetry medium with a sharp, smudgeless black pen, provide registration between doserate distribution and tissue outline. Radiochromic medium is sandwiched between pieces of clear plastic, tightly taped to help reduce exposure to moisture and radioactive contamination of the dosimetry medium. Tissues are placed with the flat (cut) side against the sensitive side of the dosimetry medium and within the spatial markers, and the medium is taped to a tissue-equivalent acrylic block. The tissues, radiochromic medium, and acrylic block are chilled in the freezer, plastic wrap is placed over the tissues, and a 1 cm-thick sheet of the supertlab (flexible tissue-equivalent material used in radiotherapy to enhance surface dose) is placed on top to simulate surrounding tissue backscattering. After l-2 weeks (several physical radioactive decay half lives), the superflab is lifted and the tissues, radiochromic medium, and acrylic mount are carefully removed from the freezer without any relative movement between the tissues and the radiochromic medium. Before the tissues can “melt” and change shape, they are photographed through the clear acrylic block. The fiducial marks on the dosimetry medium and the outline depicted in the photographic slides are digitized to provide an outline of the tissues and an accurate record of the tissue’s placement within the spatial markers. Subsequent calculations assume the tissue outline depicts the tissue perimeter in direct contact with the dosimetry medium. Quanti@ation of Results

After removal of the tissue and plastic wrap, the dosimetry medium is optically scanned with a commercial flatbed scanner to quantify the degree of medium darkening due to radiation exposure. To account for varying light levels and digital manipulation of the image processing software, the sample is simultaneously scanned with dosimetry media previously exposed to a known dose of radiation from a calibrated3 external therapy machine. The digital image is stored with eight-bit greyscale levels and

‘Model 1185 Automatic Gamma Counter, G. D. Searle, Des Plaines, IL.

a spatial resolution of 200 dots per inch (dpi, or 127 micron) except for the largest tumors, which were scanned at 100 dpi. The chosen resolution permits the highest spatial resolution (relative to the range of the radiation) compatible with the graphics software limitations in handling the large data array. Dose measured at a particular point reflects the dose rate received for this point at the time the sample is placed on the medium. The digitized tissue outline (taken from photographic slides of the tissue) is digitally juxtaposed onto the darkening pattern of the dosimetry medium with the aid of the fiducial marks. The dose-rate distribution is quantified by computing the dose-rate frequency histogram for pixels inside the tissue outline. The average dose-rate inside the tissue outline, the fifth and the 95th percentile dose rates, the standard deviation, and coefficient of skewness of the dose-rate distribution are then determined. Uniformly Active Half Ellipsoid (UAHE) and Radially Distributed Active Half Ellipsoid (RDAHE) Dose-Rate Distributions

To help determine the influence on dose-rate distributions of shape irregularity and activity heterogeneities, the observed distributions were compared to those of uniformly active half ellipsoids, each with the same total activity and approximate size and shape as one of the half tumors. Two dimensions of the half ellipsoid were calculated by fitting an ellipse (by eye) to the tumor outline (taken from the photographic slide). The weight of the sample was then used to calculate the height (third dimension). The fraction Rf of nuclide that decays during the exposure of the dosimetry medium is ‘2

-fh21T,,,dt

R,=“a s e

e

-tin~T,adt

m.1)

0

Rf= e- “QJT,,z’,-e-ln2JT,,,2

0%. 2)

where t, and t2 are the time points of tissue placement and removal from the dosimetry medium, respectively. Tin is the half-life of the radionuclide, and t = 0 the time at which the activity was measured at time zero. The dose rate D, is related to the dose D by D

=

D

ln(2)

r

ml. 3)

W-m

If the radionuclide

activity density A (,uCi/cm3) uni-

‘Varian Clinac 4180, Palo Alto, CA.

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formly distributes on one side of the dosimetry medium, then the dose D (in Gy) deposited in the chromic medium would be uniform and equal to

0%. 4)

where C is the mean energy emitted per unit cumulated activity and the factor (l/2) is inserted into the equation because activity is only located on one side of the dosimetry medium. For a finite source such as a half ellipsoid, the dose deposited to the dosimetry medium is guaranteed to be less than D in Eq. 4 on average and distributed inhomogeneously inside the tissue outline. The expected dose-rate distribution was calculated by dividing the half ellipsoid into a cubic grid, assigning a point source function (11) with the same activity to each grid point within the half ellipsoid, and calculating the dose rate delivered to each point in a square grid in the plane abutting the half ellipsoid by summing the contributions from each point in the cubic grid. This calculation, called the uniformly active half ellipsoid (UAHE) approximation, assumes that the antibody is uniformly distributed throughout the tumor volume. Examinations of the grain density distribution in autoradiographs of thin tumor sections usually found greater antibody concentration near the tumor periphery relative to the tumor center (14, 15). To gain greater understanding of the experimental planar dose-rate distributions, planar dose-rate distribution (along with coefficients of variation and skewness, minimum dose-rate, etc.) was computed by summing the contributions from an inhomogenous activity distribution. In particular, an activity distribution was chosen in which the activity linearly diminished in the radial direction from its maximum on the ellipsoid surface to zero at the tumor center. This activity distribution qualitatively resembled early stages of the activity distribution, prior to evolution to more uniform distributions, and is subsequently abbreviated as RDAHE (radially distributed activity in the half ellipsoid). The RDAHE does not represent actual distributions. It is a functional form that gives more weight to the surface relative to interior pockets, presumably simulating wellvascularized regions. Various parameters that describe the dose-rate distribution were computed from the calculated and experimental dose-rate distributions. Dose-rate distribution delivered to the ellipsoid interior having total area AT,,,, were characterized through dose-rate histograms using dA/dD, which is the differential dose-rate area or area occupied by dose rates ranging from D, to D,+dD,. The average dose-rate, D,,,, the coefficient of variation (CV), and the coefficient of skewness (CS), are computed using conventional definitions (17) of these quantities and treating the planar dose-rate histograms like a probability distribution. In

A

I

1 cm

wYr90

6

I

Fig. 1. (a) Two dimensional relative dose-rate contour delivered antibody injected into nude mice. Dashed line denotes tumor outline. One hundred percent dose rate corresponds to 0.34 Gy/h. (b-d) Relative dose-rate contour plots for tumor sizes 0.085, 0.41, and 0.83 g, respectively. Figures la, b, and c were scanned at a resolution of 200 dpi but d was scanned at a resolution of 100 dpi. Isodose rate lines denote 10% of maximum dose rate, but only every 20% isodose rate line is explicitly indicated. One hundred percent dose rate corresponds to 0.24,0.27, and 0.15 Gyih, respectively. to tumor of size (0.043 g) for v-labeled

addition, Dti” and D,, , the minimum and maximum tumor dose rates, respectively, and fifth and 95th percentile dose rates (5 and 95% of all pixels found within the tissue plane outline have less than or equal to these dose rates, respectively), were generated from the planar doserate distribution. RESULTS Mono- or bispecific antibody systems treated 25 tumor halves. The planar dose-rate distributions were determined using the methodologies described earlier. Nine tumor halves with weights ranging from 0.045 to 0.83 g were examined from animals killed 3 days after injection of v-labeled hapten (bispecific antibody had been injected 1 day earlier). Figure 1 shows examples of twodimensional isodose rate contours treated with this regimen of the smallest tumor half (A) 0.045 g, two intermediate-sized tumor halves, (B) 0.085 g and (C) 0.41 g, and the largest tumor half (D) 0.83 g. The tumor outline is shown as a dashed line. Except for the largest tumor half (D), a single peak characterizes the dose-rate distribution within the tumor border generated from Y-labeled antibody. The minimum dose-rate regions were always located along the tumor half outline.

Concave

(convex)

curvature of the tissue boundary results in higher (lower) dose rates relative

to the average dose rate along the

Human tumor xenographs 0 R. MAYER et al.

151

system and excised on day 6 had a large positive skewness relative to tumors excised at earlier times. In contrast, time of killing had little affect on the coefficient of variation. The observed dose-rate distributions were compared to the UAHE approximation. As described in the Methods and Materials section, the UAHE approximation computes the dose-rate distribution for a uniformly active half ellipsoid having the same total activity, volume, and approximately the same shape as the actual tumor half. Figures 4a, b, and c plot the observed fifth percentile, mean, and 95th percentile dose rates, respectively, for 16 tumors excised 2 or 3 days after WY injection. These tumors were treated with two different antibody systems 0

20

40

60

80

Relative

100

0

20

40

60

60

100

Dose-Rate

Fig. 2. (a-d) Area1 differential dose-ratehistogramof relative planardose-ratedistributionwithin tumor outline corresponding to Figs. la, b, c, and d for mouseinjected with y-labeled antibody. Figures la, b, and c were scanned with a resolution

of 200 dpi except for d, which was scanned with 100 dpi. One hundred percent dose rate corresponds to 0.34, 0.24, 0.27, and 0.15 Gy/h, respectively. outline. This type of distribution is attributable to the relatively long range of the beta particle (90% range = 0.5 cm shown in Fig. 1) compared to the curvature. A differential dose rate area histogram was computed for each planar isodose-rate contour. For example, the planar radiation dose-rate distributions within the tumor border shown in Fig. 1 were converted to differential dose rate area histograms and are shown in Fig. 2. The area occupied by tumor regions receiving relative dose rate was calcubetween D,/D,,,, and (D,+O.OSD,,,)/D,,, lated from the number of pixels and the known spatial scanning resolution. The fifth percentile relative doserate bins were chosen to achieve reasonable statistical accuracy, but also meaningful dose-rate resolution. The number of pixels within a dose-rate range are plotted against the relative dose rate in Fig. 2. For this series, and those to be described later, two numerical indicators were used to characterize the shape of the dose rate area distribution, namely, the coefficients of variation and skewness. These parameters describe the relative width of the dose-rate distribution and the dose-rate distribution asymmetry or relative size of “hot” and “cold” spots. The coefficients of skewness and variation of the doserate distributions are plotted as a function of tumor half weights for this series in Fig. 3. Also shown are values for bispecific antibody/labeled-hapten-treated animals killed 1 or 6 days after injection, or treated with a directly labeled IgG and killed 2 or 3 days after injection. All sets of antibody systems showed a trend towards positive coefficient of skewness and larger coefficient of variation with increasing tumor half size. The dose-rate distribution for the three largest tumors treated with the bispecific

indicated in Fig. 4 and are described in the Methods and Materials section. As no clear differences were observed in dose-rate distributions between the two systems, the following analysis groups results for both systems. It can be seen (from Fig. 4a, b, and c) that dose rates whose correlation coefficients and slopes lie closer to 1 are associated with increasing percentile dose rate. Because the higher percentile dose rate regions are near the center, the half ellipsoid approximation should provide a better dose-distribution estimate near the center than on the periphery, where activity heterogeneities and surface irregularities play a more important role in determining the dose rate. Many studies (3) of radioimmunotherapy (RIT) in animal tumors have used dose-rate and total dose-rate estimates based on the “uniform MIRD approximation.” This approximation assumes all the released energy is deposited uniformly within the tumor. The approximation does not account for regions of the tumor having lower dose rates simply due to proximity to the tumor surface and, therefore, are irradiated predominantly from activity originating from one side. Radioimmunotherapy delivers a wide range of doses to the tumor. Tumor cell survival probability is much higher in regions receiving the minimum dose rate relative to the survival probability for areas receiving the maximum dose rate. The overall tumor response that is correlated with tumor cell survival probability will, therefore, strongly depend on the size of the low dose-rate regions. Figure 5 is a plot of the observed fifth percentile dose rate vs. a dose-rate estimate based on the 0.95 x activity/g (or uniform MIRD dose/2; the factor 2 in the denominator results from the uniform activity being located on just one side of the plane). Rf is the fraction of the activity that decays while the tumor is in contact with the dosimetry medium (Eq. 2). The factor 0.95 (Gy/mCi) is half the mean energy emitted per unit cumulated activity (C). The slope of the best fit is 0.27 and the correlation coefficient is 0.78. The uniform half ellipsoid approximation overestimates the observed fifth percentile dose rate by a factor of 0.75, and the uniform MIRD approximation underestimates it by a factor 0.27.

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1.5 i

0.1

L

?I 0

I

0

0.2

I

I

I

0.4

I

0

I

0.6

t 0'

0.8

' 0

Weight of tumor half (gm) ZCEO25 1 day

1 day

A

I

I 0.2

I

I 0.4

,

, 0.6

1

, 0.8

,

Weight of tumor half (gm)

ECA 3 day 6 day q

I

Ed

ZCE025

ECA

1 day A

1 day (by

3 day

6 day

0

(8) Fig. 3. (a) Coefficients of skewness and (b) variance of planar dose-rate distributions injected with y-labeled antibody.

To further examine the observed dose-rate distribution and that calculated for the UAHE, is the coefficient of variation vs. coefficient of skewness for the planar dose rate for the uniformly active half ellipsoid approximation, and the experimentally observed distributions are plotted in Fig. 6. The coefficients of skewness and variation are global averages over the tumor plane and, therefore, are less dependent on the exact shape of the tumor. The calculated values for the coefficients of skewness and variation huddle around values of -0.4 (2 0.2) and 0.2 (2 O&I), respectively. The scattering of the observed values compared to the calculated values in Fig. 6 reflect the contribution of activity heterogeneity to the dose-rate distribution. Generally, the observed tumors (15 out of 16) have a broader dose-rate distribution or coefficient of variation

vs. tumor weight for mice

than the UAHE calculation. Similarly, the observed distributions are shifted to lower dose rates (13 out of 16 doserate distributions have more positive skewness) relative to the calculated UAHE dose-rate distribution. DISCUSSION This study experimentally determines the planar doserate distribution within a tumor. The measured dose-rate distributions results from a summation of contributions from activity distributed throughout the tumor at the time of animal killing. No direct information is obtained about the source of the dose, namely, the activity distribution itself. Such information can only be inferred by comparing the observed planar dose-rate distribution with com-

Fig. 4. (a) Experimentally observed fifth percentile planar dose rate vs. fifth percentile planar dose rate for uniformly active ellipsoid fitted to tumor outline for mouse injected with WY. Straight lines in a-c are a linear least square fit to the data. The fitted line in a has a slope of 0.75 and a correlation coefficient of 0.65. (b) Similar to 4a except experimentally observed average planar dose rate vs. average planar dose rate for uniformly active ellipsoid. The fitted line has a slope of 0.84 and correlation coefficient of 0.73. (c) Similar to 4a except experimentally observed 95th percentile planar dose rate vs. 95th percentile planar dose rate for uniformly active ellipsoid. The straight line has slope 0.9 and correlation coefficient 0.75.

153

Human tumor xenographs 0 R. MAYER et al.

5 Percentile

Dose-Rate

Mean Dose-Rate

Comparison

Comparison

Y-90

Y-90 Observed

Observed Dose-Rate (Gy/hour) 0.2

Dose-Rate (GyMour)

o.3 I

0.15

0.1

0.05

O-

l&iform

0.1

0.05

0.15

0

0.2

ECA 0

0.05

0.1

0.15

ECA 0

ZCE025 A

ZCE025 A

(a)

(b)

95 Percentile

Dose-Rate

Comparison

Y-90 95 Percentile Observed Dose-Rate (Gy/Hour)

0.25

95 Percentile Calculated Dose-Rate (Gy/Hour) ECA q

0.2

0.25

0.3

Uniform Half Ellipsoid Dose-Rate (Gy/Hour)

Half Ellipsoid Dose-Rate (Gy/Hour)

ZCE025 A (c)

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puter simulations of various activity distributions within the tumor (see ensuing discussion). Nevertheless, because of the ability to examine several tumors under each treatment condition, this study finds some general trends concerning the dose-rate distribution in tumors and their dependence on size and time intervals between injection and killing. The increase in coefficients of variation and skewness with tumor size and time predominately results from the size of the 9oY beta particle penetration range that either exceeds or is comparable to the tumor dimensions. For these small tumors, activity distribution has less influence on the dose-rate distribution.

Volume 32, Number 1, 1995

Skewness

vs. Coefficient

of Variation

Y-SO 0.4

,

I

Tumor Size Affect on Planar Histograms and CoefJicients of Variation and Skewness

The coefficients of variation and skewness of the doserate distribution generally increase and become more positive as the tumor size increases (Fig. 3a and b). This is specifically shown for tumor halves B and C in Figs. 1 and 2. For tumor half B, a large part of the interior region received relatively large dose rates, with substantially lower doses delivered to smaller areas near the outline. Therefore, a large fraction of the area apparently receives irradiation from all parts in the smaller tumors. This results in a dose-rate distribution with a narrow dose-rate distribution, with a small coefficient of variation and large

Observed

5 Percentile vs. .95*A

(1) 1 0.1

I 0.2

1

I

0.3

0.4

, 0.5

I 0.6

Coefficient of Variation Day

2 (ZCE025)

CAL.

Day

3 (ZCE0251 r,

CAL.

Day

3 (ECA) .!J

CAL.

Day

2 lZCEO25) l

OBS.

Day 3 iZCE0251 B

OBS.

Day

3 (ECA) A

OBS.

Fig. 6. Plot of coefficient of variancevs. coefficientof skewness for experimentally observedplanar dose-ratedistribution and uniformly active ellipsoid for mice injected with goY-labeled ZCE025 and hapten.Calculatedand observedparametersfor individual tumorsare connectedby a line.

Y-90 Observed

5 Percentile Dose-Rate (Gy/Hr)

negative coefficient of skewness. For the larger tumor half (C), the area associated with dose rates close to the maximum dose rate is relatively small, resulting in a more positive coefficient of skewness. We attribute the relatively small maximum dose-rate region to greater attenuation within the larger tissue from dose-rate contributions of distant regions of the tumor. For the larger tumor halves, such as C, only the central region received significant irradiation in all directions from all parts of the tumor. Exception to the trend for the coefficient of skewness to increase with size was observed when the dose-rate maxima lie physically close to the tumor periphery. Such

0.2

(Slope=.27[

q

.

0.15

0.1

dose-rate distributions are due to the absenceof significant contributions of activity from the entire tumor. This

0.05

noncentrally located dose-rate distribution can prevail under at least two conditions. First, the tumor half size-dependent trend proves in0 0.1

0.2

0.3

0.4

0.5

0.6

.95*A ZCE025 q

ECA +

Fig. 5. Observedfifth percentileplanar doserate vs. 0.95 X (activity normalizedby tumor weight).

valid when the dose-rate distribution contains a “hot spot” near the edge of the tumor half. In such cases, the maximum dose-rate region originates from the high local activity rather than activity in the rest of the tumor. Such a tumor half would have a small high dose-rate region, and a larger low dose-rate region; the hot spot would tend to produce a positive coefficient of skewness. The two

Human

tumor

xenographs

smallest tumor halves, including A, had the high doserate peak near one side and, therefore, had more positive coefficient of skewness distributions. Second, tumors considerably larger than the particle range also deviate from this trend. In such cases, no area is significantly irradiated from all parts of the tumor. The dose-rate distribution will then reflect local (within the range of the radiation) activity differences in the different parts of the tumor. The largest tumor half (D) had a large negative coefficient of skewness. Figure 1D shows dimensions for this tumor considerably larger than the WY particle range. The dose-rate distribution suggests two hot spots located on opposite sides. Irradiation of the area between these two peaks from two sides would result in a large area receiving relatively large dose rates, producing a negative coefficient of skewness. As the tumor size increases, the data (Fig. 3a and b) show that the coefficients of skewness and variation generally become more positive and increases in magnitude, respectively, with increasing tumor size. Using either the UAHE or the RDAHE approximations, broader dose-rate distribution (larger coefficient of variation) is computed if the activity distribution is fixed and the ellipsoid size is enlarged (with constant eccentricity). Similar calculations for the coefficient of skewness are more ambiguous, being dependent on tumor size and shape. Tumor Size/Shape EJyects on Fifth Percentile, Average, and Maximun Dose Rates Minimum dose rates based on the UAHE approximation, which incorporates the average activity per volume and general size and shape of the tumor, agrees better with the observed minimum dose rate than predictions using the uniform MIRD approximation. The latter incorporates only the average activity per volume. Nevertheless (Fig. 4a), the UAHE approximation still overestimates the observed fifth percentile dose rate for many tumors. It was previously (12) noted that isodose rate contours do not follow the tumor outline in regions of high curvature relative to the particle range. Of the six (out of 16) tumors whose ratio of observed-to-calculated fifth percentile dose rates were less than 0.5, three tumors were judged to have the most irregular outline (least like an ellipse). Further, disparity in the predicted dose rate with the observed fifth percentile was correlated with overall spatial position of the dose-rate peak with respect to the tumor outline. For example, four out of the five tumors with maximum peak dose rate most displaced from the center of the tumor outline, including the tumor in Fig. lD, had ratios for their observed-to-calculated fifth percentile dose rates less than 0.5. We do not have a record of the three-dimensional shape of the tumor halves, and, therefore, do not know if asymmetric peaks are due to the tumors being thicker on one side or, alternatively, attributable to heterogenous activity distributions. It should be noted that the planar dose-rate distribution

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(compared to dose-volume distributions) underemphasizes the edges (generally low dose-rate regions) relative to the center. The observed dose rates agree with the calculated (from the UAHE approximation) dose rates for middle and upper range tumor dose rates. There is less agreement for a similar comparison involving the lower range dose rates. The slopes of the fits of the observed vs. calculated dose rates for the 5%, mean, and 95% dose rates (Fig. 4a, b, and c, respectively) indicate gradually increasing slope (0.75, 0.84, and 0.90, respectively) for the fitted line for increasing relative dose rate. For these tumor halves (< 0.83 cm”), the dose rate distribution for y has a single peak in the tumor interior (Figs. 1 and 2), and the minimum dose rate occurs near the tumor edge. Therefore, the fifth percentile dose rate is found near the tumor border and is determined by the convex curvature of the tumor. The half ellipse calculation assumes smooth curvature of an ellipse, and, therefore, the calculation systematically overestimates the fifth percentile dose rate. As the relative dose rate increases (and the dose rate point moves toward the center of the tumor for 9v), better agreement should be attained between the calculated and the observed values, as evidenced by the increasing slopes in Fig. 4a, b, and c. The lower correlation coefficients for the fifth percentile dose rate (0.65) relative to the mean and 95th percentile dose rate (0.73, 0.75) provide further evidence for the presence of an affect on the fifth percentile dose rate of the highly variable tumor shape. Efsects of Changes in Activity Distribution With Time on Coeficients of Variation and Skewness Figure 3a shows that the coefficient of skewness for tumors excised on day 6 is more positive than the values for tumors excised at day 1 and day 3. Similar data (Fig. 3b) for the coefficients of variation show little dependence on time of excision. Comparing the calculated dose-rate distributions derived from UAHE with RDAHE approximations suggest that a change of activity concentrated on the periphery to a more homogenous distribution also tends to result in a more positive coefficient of skewness. Therefore, the large positive coefficient of skewness shown by the larger day 6 tumor halves is consistent with the activity becoming more uniform with increasing time after injection. Comparison With Earlier Studies A number of dose-rate volume distributions have been previously published for tumors treated with RIT. Roberson et al. (14- 16, 24) treated LS 174T tumors with 13’1labeled murine monoclonal 17-1A antibody. They found the tumor dose-rate volume and activity distributions from mice killed after 1 and 4 days. The observed doserate distributions showed the effects of changes in activity distribution from a distribution initially concentrated on the tumor periphery to a more uniform distribution during

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I. J. Radiation Oncology 0 Biology 0 Physics

the time interval between antibody injection and animal killing. The dose-rate distributions appeared to be more heterogenous than those observed in the present study, presumably due to the shorter particle range of the IL3’ relative to Y90 (4,9). Such results demonstrate how tumor size and range of radiation can strongly affect the doserate distribution. Longer range particles tend to “smear out” the heterogenous activity distribution. The effects on the dose-rate distribution from long-range particles (relative to the tumor size) are not directly displayed in the isodose rate distributions but, instead, are manifested more subtlely through the coefficients of variation and skewness. The labor-intensive and computationally intensive procedures (14- 16) required for generating dose-rate volume distributions from serial autoradiographs restricted the examination to a small number of tumors treated with the labeled antibodies. Results for 12 tumors have been reported. The serial autoradiographs showed a wide variation in activity distribution. It is, therefore, essential to observe the behavior of a large number of tumors to determine the essential factors that determine the tumor doserate distribution. Roberson et al. (14) compared the uniform MIRD dose rate delivered by i3’I-labeled antibodies to the calculated dose-rate distributions. As would be expected for a shortrange beta emitter (relative to the dimensions of the tumors) in which almost all the energy is deposited within the tumor, the mean dose rate appeared to qualitatively agree with the uniform MIRD dose rate. In both studies, however, the distribution minimum was at least four times less than the calculated MIRD dose. Implantation of micro-TLDs (3,24), is another method for measuring tumor doses delivered by RIT. Micro-TLDs measure a dose that is spatially averaged over the length of the TLD (0.5 cm). This technique integrates (over time) the dose rate from insertion up to time of excision. Examination of the plots in Fig. I suggest that a 0.5 cm microTLD would sample a wide range of doses even when

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placed in the dose maximum region. Comparison of the calculated MIRD doses with the measured micro-TLD measurements and dose distributions from our studies confirms the effect of large dose variation over the microTLD. The MIRD formulation (uncorrected for the tissue boundary) assumes that all the energy is deposited within the tissue, a situation that does not prevail with these tumors treated with the long-range beta emitters. In two studies of YW-RIT, the ratio of the observed micro-TLD dose to the calculated MIRD dose was 0.459 and 0.53 (20, 22). In our study of tumor halves, tbe ratio of the maximum dose to (MIRD dose/2) was 0.79 + 0.16. CONCLUSION These studies suggest that at least three factors are important in determining the tumor dose-rate distribution delivered by radioimmunotherapy: shape and size of the tumor, range of the emitted radiation, and radioimmunoconjugate activity distribution within the tumor. The new methodology is simple and readily usable for evaluating a number of tumors treated with a variety of RIT regimens. This technique directly determines the planar doserate distribution. Tumor size (O.l- 1.0 cm3) plays an important role in determining the radiation dose-rate distribution delivered by beta emission from Y90. Changes in the dose-rate distribution for tumors from animals killed at early times and those killed later (day 6) are consistent with the activity distribution becoming more uniform with time. The uniformly active half ellipsoid calculates the effect of tumor size and shape on the dose-rate distribution. This approximation, however, may not be valid near surface irregularities. The low tumor dose-rate range is more sensitive than middle and high tumor dose-rate ranges to the tumor surface configuration for these xenografts treated with 9oY. Although dose-rate histograms can be useful, further understanding of tumor response to RIT will require knowledge of how the dose-rate distribution relates to the dissemination of viable cells within the tumor.

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