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Estimation of organ depth by gamma ray spectral comparison

This content has been downloaded from IOPscience. Please scroll down to see the full text. 1977 Phys. Med. Biol. 22 988 (http://iopscience.iop.org/0031-9155/22/5/019) View the table of contents for this issue, or go to the journal homepage for more

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PHYS. MED. BIOL.,

1977, VOL. 22,

NO.

5, 988-993.

@ 1977

Scientific Note

Estimation of Organ Depth by Gamma Ray Spectral Comparison KENNETH F. KORAL,

P H . D . ~and

A. R. JOHNSTON,

PH.D.

Department of Pure and Applied Physics, The Queen's University of Belfast, Belfast BT7 lNN, Northern Ireland

Received 28 June 1976, infinal form 4 iMarch 1977

1. Introduction

I n order t o measure the amount of radioactive tracer taken up by anorgan in the human body, it is necessary to determine the depth of the organ in the body. Two techniques for determining organ depth employing a single gamma ray detector in afixed position have been published. The first methodinvolved analysis of the valley-to-peak ratio for the full-energy photopeak measured with an uncollimated detector (Mohindra and NcNeill 1965). The second method employed two isotopes with gamma rays of widely different energies, and 1251,and a collimated detector (Dolan and Tauxe 1968). The procedure presented here is similar to the valley-to-peak method but involves analysis of the entire pulse-height spectrum. Measurements are made single collimated detectorina fixed on l3II withawaterphantomanda position. A set of calibration spectra are taken for a source a t depths ranging fixed from 2 to 15 cm in 1 cm increments. Then test spectra are taken for times with sources placed at various depths. By comparing a test spectrum with the calibration spectra, it is possible t'o calculate the source depth. The method is checked for dependence of calculated depth on source thickness and on background concentration. 2.

Procedure

2.1. Experimental design

The methoddescribed above can, inprinciple, be applied to themeasurement of any gamma-emitting radioisotope with the accuracy likely to be greater the lower the energy of the principle photopeak. This dependence on energy is expected because of the increase in gamma ray scattering relative to transmission with a decrease in energy (Mohindra and McNeill 1965). Thisnote describes the result with the medium energy (364 keV) isotope, 13lI, which is

t Present address: R-3054Kresge 11,University of Michigan Medical Center, Ann Arbor, Michigan 48109, U.S.A.

Organ Depth by Spectral Comparison

989

used in Hippuran renograms. The geometry is also similar to that in renogram measurements except for the omission of the effects of a contralateral kidney. The source sizes were chosen to be similar to those in Dolan and Tauxe (1968) so that a direct comparison with their results could be made. 2.2. Apparatus

The experimental arrangement is shown in fig. 1. Four cylindrical sources, 4.9 cm in diameter, were constructed of Lucite and filled with 1311 solution.

Fig. 1. Diagram of the experimental apparatus. S = radioactive source. W = water phantom. Pb = lead collimator. C = scintillation crystal and P M = photomultiplier.

The sources were 1, 2, 3 and 4 cm long and could be positioned as desired in the water-filled Lucite tank. The lead collimator was cylindrical in shape, 19 cm in diameter with a 4.5 cm diameter bore. The detector was a shielded NaI(T1) crystal 5.08 cm in diameter and 7.62 cm long. Depths were measured from the face of the collimator to the centroid of the source. Data were recorded with a 256 channel pulse-height analyser. 2.3. Data

The calibration spectra were taken with the 1 cm long source placed on the detector axis a t depths ranging from 1.8 to 14.8 cm in 1 cm steps. The counting time was increased with depth so as to accumulateapproximately 600000 counts under the 364 keV photopeak at each source depth. Test spectra were obtained for each of the cylindrical sources a t positions on the detector axis at varying distances from the detector. The counting time was kept constant and was such as to accumulate 310 000 counts under the photopeak for a depth of 5.5 cm. This number is that expected in the clinical case of normal state-ofdehydration kidney patients counted for 30 minutes (Tauxe,Hunt andBurbank 1962: fig. 6.8 witha correction factor of 0.825 for difference in collimator acceptance angle). I n oneexperiment,a check forsensitivity to background was made by taking a set of spectra with iodine added to the water phantom. The background concentration was varied over a large range from 0 to 1.5 pCil-1 in 0.15 pCi 1-1 increments. Normal background encounteredin isotope renography is less than 0.3 FCi1-1 (Dolan and Tauxe 1968). The 4 cm source was placed a t a depth of 5.5 cm for the measurements.

990

Kenneth F . Koral and A . R. Johnston

3. Results

3.1. Spectral shifts

The calibration spectra showed shifts in the peaks along the pulse-height axis of up to one channel in 129 for the 364 keV peak for a change of 1 cm in depth. It was assumed that a small percentage of such shifts may have been real but that the rest was due to changes in the gain and zero level of the electronics. All spectra were therefore shifted by computer program (Helmer, Heath, Schmittroth, Jayne and Wagner 1967) to locate the 364 and 80 keV photopeaks in exactly the same channels. 3.2. Normalization

Two methods were employed to normalize the various spectra to each other. First, the 364 keV photopeak was fitted by a gaussian plus underlying cubic for allspectra.Then,eitherthetotalpeakheight or thearea under the gaussian was used to normalize the spectra.

c

36L keV

x103 50r LO

2 2010; 0 3

0

20

,

,

I

LO

60

80

,

100

,

I

120 1LO

-l

160

Channelnumber

Fig. 2. Calibration spectra with the 1 cm thick source at depths of 1.8, 7.8 and 13.8 cm. The spectra are normalized so that computer fits to the 364 keV photopeak have the same height.

3.3. Calibration spectra

Height-normalized calibration spectra for several source depths are shown in fig. 2. There is a significant increase in the number of counts in the low energy section of the spectrum with increasing depth as seen by Mohindra and McNeill (1965) for an uncollimated detector. 3.4. Depth determination

A given spectra was compared to the calibration spectra by computing a set of differences, A@,) :

by Xpectral Comparison

Organ Depth

99 1

Here, q.is the number of counts in t h e j t h channel of the test spectrum: Cj(xi) is the number of counts in the same channel for the calibration spectrum corresponding to depthxi,and theweighting factor oiis the expected combined statistical error. Then parabolic interpolation was used among the smallest three values of A(xJ to int'erpolate to the value of the depth x which produced the minimum difference. The depths calculated using heightnormalizationareplottedagainst the actual depths in fig. 3. The calculated points fall close to the 45" line which marks exact agreement. There is a slight tendency for the points to diverge from t'he line on the low side as the depth increases. With area normalization there was better estimation in the medium depths but more divergence from the line at the larger depths.

LA

1L- Sourcethlckness

Icm 2cm - 3cm -&cm

o-

12-

-

xD

5 10-

I

5a

8-

W U

r0

I

0

2

L

0 /

'

O

I

I

I

I

6

8 1 0 1 2 1 L Depth [cm 1

Fig. 3. Calculated depth versus actual depth for test spectra from sources of a number of thicknesses. The 48" line marks exact agreement. Calibration spectra were made with a 1 cm thick source.

Table 1 summarizes the differencesbetween actual and calculated source depths as a function of source length and method of spectrum normalization. The average absolute valueof the deviation for all sourcesis 3.9 mm for height normalizationand 3.7 mm for areanormalization.The rate of change of calculated depth with source length is - 3.2 mmjcm with height normalization and - 2 - 5 mmjcm with area normalization. This is comparable to the rate of + 2.5 mm/cm for the double-isotope technique (table 1 of Dolan and Tauxe (1968) with depths recalculated to the source centroid). The results of the measurements with iodine addedto the water phantom are shown in fig. 4. In the case tested, the background produces a linear distortion of the calculateddepth. For the backgroundconcentrationexpectedin renograms, the distortionwould be approximately 1 cm, assuming no correction was made. Since the backgroundspectrum is linearlyadded to the source spectrum the slope of the line in fig. 4 indicates that the effective centroid of the background is a t a depth greater than 5 cm for this geometry and isotope.

Kenneth F. Koral and A . R. Johnston

992

Table 1. Deviation between calculated source depth and true source depth as a function of source length and of normalization Height normalization Area normalization

(cm)

Source length (cm)

Number of

1 2

10

12

3

12

12

4

(cm)

points

1-4

Average Average absolute deviation deviation deviation deviation

+ 0.34

Average absolute

+ 0.18

- 0.61

0.40 0.13 0.41 0.61

- 0.41 - 0.56

0.25 0.26 0.41 0.57

- 0.23

0.39

- 0.23

0.37

- 0.13 - 0.41

46

Average

- 0.08

L c m source

I 0

I

0.3

I

0.6

I

0.9

I

I

1.2

1.5

l 1.8

Concentratlon (1 C / ["I

Fig. 4. Effect on the calculated depth of a background conmntration of uniformly throughout the water phantom.

1311

distributed

Discussion The results indicatethat in the limit of very high source-to-backgroundratio the depth in a water phantom of a kidney-sized source containing 1311 can be determined to within 4 mm without appreciable dependence on source length. Thisaccuracy is comparable tothat inphantom measurementswith the double-isotope technique (Dolan and Tauxe 1968). is presentoutside the source, the calculated Whenbackgroundactivity depth is distorted in the spectral comparison method. With the double-isotope technique, phantom tests for a single geometry indicated an insensitivity to background (Dolan and Tauxe 1968), but recent measurements of kidney depth in patients reveal an average distortion towards greater depth of 11% due to background(Ostrowski and Tothill 1975). Themethod used to correctfor blood-pool activity by Ostrowski and Tothill (1975) involves apreliminary injection of 131I-labelled human serum albumin whereby a ratio for the count rate in the kidney detector to that in a heart monitor is established. In the 4.

Organ Depth by Spectral Comparison

993

subsequent measurement with I3lI-Hippuran, this ratio and the heartmonitor count rate determine the background count rate within the field of view of the kidney detector. Such a calibration and heart monitor count rate could similarly be related to a depth correction in the spectral comparison method, assuming is a good that a uniform backgrounddistributioninthewaterphantom approximation to the actual distribution in thebody. No determination of the effect upon the depth calculation in the spectral comparison method was made for a second, off-axis source (simulating a contralateral kidney) or for a change in source diameter or water phantom tank size. We would like to acknowledge the very helpful advice of Dr. T. K. Bell of the Royal Victoria Hospital, Belfast, andthe technical assistance of W. P. Raa of our staff. This work was supported by a grant from the Medical Research Council, London. REFERENCES DOLAN,C. T., and TAUXE,W. N., 1968, Am. J . Clin. Path. 50, 83. HELMER, R. G., HEATH, L. A., SCHMITTROTH, L. A., JAYXE, G. A., and WAGNER,L. M., 1967, Nucl. Instrum. LMeth., 47, 305. MOHISDRA,V. K., and MCNEILL,K. G., 1965, J . Il;ucZ. Med., 6 , 747. OSTROWSKI,S. T., and TOTHILL,P., 1975, BT.J . RadioZ., 48, 291. M. K., 1962, Am. J . Clin. Path., 37, 567. TAUXE,W. N . , HUNT, J., and BURBAKK,