Statistical and Mathematical Techniques in Nuclear Medicine 9789350432792, 9789350243053

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STATlmeAl AND MATHEMATICAL. TECHNIQUES IN NUCLEAR MEDICINE

Editor

G.S. Pant Additional Professor (Medical Physics) Department of Nuclear Medicine All India Institute of Medical Sciences New Delhi - 110029 (India)

Hal GJiimalaya CPOOlishingGUouse MUMBAI • DELHI. NAGPUR • BANGALORE • HYDERABAD

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Contents Part A : STATISTICAL TECHNIQUES Types of Study Design .................................................... ......... 1-6 Basics principle of data analyses: An overview .................... 7-13 Counting Statistics and Basic Principle of ROC ................... 14-27 Non-parametric tests, Matchmaking and McNemar in the comparison of diagnostic modalities .......................... 28-37 Statistical Parametric Mapping (SPM) .................................. 38-43

Part B : MATHEMATICAL TECHNIQUES Basic Mathematical Concepts relevant to Nuclear Medicine ...................................................................... 44-63 Fourier Transform and its applications in Nuclear Medicine ...................................................................... 64-71 Back Projection SPECT and Filtration .................................. 72-83 Correction for Attenuation, Scatter and Partial Volume effect in SPECT - An Overview ................................ 84-91 Single Photon Emission Computed Tomography (SPECT)Iterative Reconstruction Incorporating Depth Dependent Resolution, Attenuation, and Scatter ..................................... 92-126 Basic Physics of Positron Emission Tomography (PET) ...... 127-130 Quantification in SPECT and PET ......................................... 131-141 Deconvolution Analysis and Renal Transit time Parameters ................................................................................. 142-158 Background Subtraction in Nuclear Medicine '" .................... 159-170

Role of Artificial Intelligence and Neural Networks in Nuclear Medicine ................................................................. 171·176 Radiotracer Kinetics: Basic Principles .................................. 177·188 Radiotracer Kinetics: Applications in Nuclear Medicine .... 189·205 Estimation of Left Ventricular Volume in Nuclear Cardiology ................................................................... 206·210

PART

C:

RADIATION SAFETY Principles of Radiation Protection .......................................... 211·219 Radiation Safety in Nuclear Medicine ................................... 220·225 Radiation Safety Aspects in Radioiodine Therapy ................ 226·234

List of Contributors C.S. Bal Dept. of Nuclear Medicine, AIIMS, New Delhi-ll0029 Bharathi J. Dasan Dept: of Nuclear Medicine, AIIMS, New Delhi-ll0029 Aseem Bhatnagar Dept. of Nuclear Medicine, INMAS, Lucknow Road, Delhi - 110054 AR. Bitarafun Dept. of Medical Physics, School of Medical Sciences, University of Tarbiat Modarres, Tehran, Iran S.N. Dwivedi Associate. of Biostatistics, AIIMS, New Delhi-ll0029

S. K Kataria Electronics Division, BARC, Trombay, Mumbai 400085 KS. Kini Radiologi.1>osed areas, moderately exposed area and severely exposed area. This may be noted that there is specific order amongst the categories but the difference between two consecutive categories cannot be quantjfied. (b) Quantitative Data: These data which are recorded in numeric form are generally collected in the form of ratio scale or interval scale. A variable is known to be recorded in the form of interval scale which does not have its well deflned '0' base, for example, temperature, date of birth etc. On the other hand, a variable is known to be recorded in the form of ratio scale when it has got well deflned '0' base, for example, height, weight etc. However, it may be noted that analysis of data collected on each of these scales of measurement are carried out in the similar way. Further, quantitative data may also be categorised as continuous and discrete data. A quantitative data recorded in the form of distinct integers is known as discrete variable. Otherwise, it is known as continuous variable. Understanding of Data We devote a lot of time and money in the data collection but we forget its importance at the time of data analysis. It is understood that appropriate data analysis very much depend on better understanding of data. For this, a series of exploratory

Basic Principles of Data Analysis: An Overview

9

analysis with special reference to univariate analysis have to be carried out. (a) Consideration of Variable: It is advisable that variables should not be categorized at the time of data collection. If necessary, categories need to be decided after some exploratory analysis which will help us to have the correct idea about frequency distribution in various categories of a particular variable. At the same time, modification of categories of a particular variable should be carried out taking into account theoretical aspects in addition to simple statistical considerations. This means that finalization of the categories of variables should not add to distortion of the meaning. Also, for easy understanding and interpretation, data collected on interval/ratio scale are also considered in form of the nominal/ ordinal scale. This exercise should also be done .carefully to have the meaningful understanding and interpretation. This may, however, be noted that whatever steps we take in transformation of data collected on interval/ratio scale in form of nominal/ordinal scale, we will be loosing some information because qf obvious reasons. (b) Tabular Presentation of Data: First step to describe the data is to present them in the form of tables. A table should have appropriate title along with necessary foot-notes as per the content to be included in the table. Tabular presentation of data should be done through proper considerations. For example, rows, columns, absolute frequency, relative percentage and so on. The ultimate goal of tabular presentation of data is to understand our data in a better way which can help us in deciding appropriate analysis. (c) Diagramatic Presentation of Data: The next step required in understanding of data is to describe them in the form of appropriate diagram. Most of the time, it is seen that we are fond of using diagrams without any specific purpose. This practice should be discouraged. The use of diagram should be considered to highlight some of the important findings. Also, to make understanding easier specifically in case of comparison between the groups, sometimes we may use appropriate diagrams. There are various of diagrams which are used in practice. The bar diagram, pie diagram etc. '8l'e used to describe generally qualitative data. On the other hand, a histodiagram, frequency polygon, frequency curve and cumulative frequency curve (Ogive) are used generally to describe quantitative data. Specific use of the diagram is decided based on the type of the data in hand as well as objective of using the diagram.

10

Statistical and Mathematical Techniques in Nuclear Medicine

(d) Univariate Analysis: In case of qualitative data, for comparison purpose, we generally use Chi-square Test. If assumptions of Chi-square Test are not fulfilled, we go for alternative methods known as Fisher's Exact Test. These tests are used in case we want to compare proportion of interesting events between two or more than two categories (groups). In contrary, if we have got quantitative parameters to be compared between two or more than two groups, there are specific procedures to be used based on certain assumptions. For example, if we want to compare means of a particular variable between two groups, we use Unpaired t-test under the assumptions that data is following normal distribution and variance of two groups are comparable. If these assumptions do rrot seen to be true in a given case, we have to change the method of data analysis. For example, if sample is relatively larger we can further explore the possibility to use Parametric Test like Unpaired t-test through transformation of the variables. As we know that the purpose of transformation of the data is three-fold-(£) to minimize the variance; (u) to normalize the data and (ih) to linearise the relationship with other variable. If assumptions are not fulfIlled, even after the transformation of the data and also sample size is relatively small, we do not have choice other than using Non-Parametric Test. For example, in case of two groups, we use Wilcoxan Rank Sum Test in place of Unpaired t-test Likewise, if we have got follow-up data on same group at 2 points of time, we use Paired t-test under certain assumptions. Otherwise, we go for Non-Parametric Test viz. Wilcoxan Sign Rank Test. This may be noted that while using Non-Parametric Test, we compare Medians instead of means. If we have more than two groups in case of comparing means, because of theoretical reasons, we have to go for analysis of variance instead of using Unpaired/Paired t-tests. Obviously, here also there is involvement of similar assumptions. Otherwise, we have to go for appropriate Non-Parametric Tests e.g. in case of three or more independent groups, we can use Cruskal Walli's Test, whereas, in case of repeated measures we can use Freedman Test. In case of signifIcant result under parametric/non-parametric analysis of variance, we have to go for appropriate Multiple Comparison Test. This is necessary to identify the pairs of data having signifIcantly different level of variables. The above described methods do not only help us to see the relationship between the variables/categories, they also help us to understand our data in better way and plan the future analysis appropriately.

Basic Principles of Data Analysis: .4n Oven'i~lc

11

(e) Statistical Significance: To compare proportions or means I:>etween the groups, we first of all define our null hypothesis which is nothing but equality of means/proportions. We test this null hypothesis for its possible rejection against an alternative hypothesis which is nothing but non-equality of means/propo:rtions. Generally this may be of two types, i.e. two sided test or one sided test. A test becomes one sided, once we define our alternative hypothesis in terms of less than or equal to/greater than or equal to. In reality, either null hypothesis will be true or it will be false. Hence, under testing of hypothesis, we may commit two types of errors. First one is known as type one error which is rejection of null hypothesis instead of the fact the null hypothesis is true in reality. Like-wise type two error is defined as accepting null hypothesis instead of the fact that null hypothesis is false in reality. Accordingly, probability (chance) of type one error is known as level of significance (p value). Similarly one minus probability of type two error is known as power of the study. Also one minus level of significance is known as level of confidence. As a usual convention, in statistics, level of significance is considered as 5%/1%/.1%. Under any test of hypothesis, we have to decide at which level of signifIcance the result will be considered as significant. Accordingly, if p value is less than, the considered level of significance, we considered the result as significant, i.e. means/proportions are not equal between the groups. These levels of significance are considered as a usual convention. However, one may change the level of significance, if necessary. But one should know that while increasing the level of significance, we agree to avoid higher level of error in drawing our conclusions. Moreover, we should not give excess importance to statistical significance instead of giving due consideration to clinical significance. Multivariate Analysis Most of the time it is noticed that we are tempted to carry out multivariate analysis without looking into our objectives, type of the data in our hand especially number of variables and sample size. It may be pointed out here that we should take due consideration of minimum sample size in view of number of variables while planning our study for multivariate analysis. As mentioned earlier, after series of exploratory analysis, we should fmalize the form of the variables to be consid3red in data analysi~ including multivariate analysis. While doing so we should explore the possibility that the relationship between the variables do not get distorted because of change in scale of measurement or categories of a variable.

12

Statistical and Mathematical Techniques ill Nuclear Medicine

Next important issue under multivariate analysis is 1.0 define our dependent variable clearly. In view of specific form of the dependent variable, we decide the method to be used in multivariate analysis. For example. if dependent variable is continuous, we generally explore the possibility to carry out linear regression analysis; if dependent variable is dichotomous (discase(V non-diseased), logistic regression analysis is used; and so on. Sometimes forms of independent variables also play role in deciding the method of data analysis. In summary, the method of data analysis should be decided taking into account all necessary i'isuesl assumptions. Once the method of data analysis is fmalized, next important question is to select sub-group of variables to be fmally included in multivariate analysis. Sometimes, people give excess importance to statistical significance and they take the sub-set of independent variables in multivariate analysis only if they are significantly related with dependent variable. However, to have the better strategy for multivariate modeling, one should also include those variables which are statistically insignificant but they are clinically important variables. Also, we should consider the known confounders (age and sex) irrespective of their significance. Moreover, for multivariate analysis, we should prefer to consider higher level of significance (preferably 25%) to have appropriate modding. There are various issues involved in multivariate analysis even after selection of sub-group of independent variables to be included in data analysis. We should rule-out the possibility of collinearity and interaction effects of the variables. Amongst various strategies, we may prefer to use the step-wise regression analysis approach to have comparable results in comparison to those obtained through all possible regression approach.

Interpretation of Results This issue is also equally important once we have computerized results in our hand. Needless to mention that we have to interpret results in view of our question, design of study, methodology used in data analysis, sample size and so on. In summary, we can conclude the results only if we have got data through well planned scientific study which takes into account question under investigation, defmed population, sample size, sampling method, method of data collection, design of study, accuracy of data and appropriate analysis. Statistical Packages There are a number of statistical packages available to be

Basic Prillcipies of Data Analysis: An Overview

13

used for carrying out multivariate analysis using a particular method. Sometimes different packages reveal different results related to a particular data analysis. We should try to understand the convention used in development of package regarding specific method to be used in multivariate analysis. This will help us to have appropriate understanding of results leading to accurate interpretation. By now, we may be wiser enough to remember that no statistical package will choose the appropriate method for analysis of a particular data. We have to decide and specify the methodology and instruct the computer accordingly to have appropriate analysis of the data. If we subject any data set with any methodology, the packages may produce out-puts having all the nonsense results. Therefore, we should take all due precautions while analyzing our precise data collected through rigorous approach. References 1.

Statistical Methods in Medical Research By P. Armitage, Blackwell Cenotaphic Publications, UK (1973).

2.

Health Research Methodology (A Guide for Training in Research Methods); WHO (1992); Oxford University Press, Delhi, 1993.

3.

Sample Size Determination in Health Studies By S.K. Lwanga and S. Lemeshow (WHO, 1991).

4.

Epidemiology in Medicine, By C.H. Hennekens and J.E. Buring; 1987, Little Brown and Company.

5.

Case-Control Studies (Design, Conduct, Analysis) By J.J. Schlesselman (1982), Oxford University Press. Applied Regression Analysis and other Multivariable Methods, By D.G. Kleinbaum, L.L. Kupper and K.E. Muller, 1988, PWSKENT Publishing Company.

6.

7.

Statistical Models for Causal Analysis By R.D. Retherford and MK Choe, 1993, John Wiley & Sons, Inc.

COUNTING STATISTICS AND BASIC PRINCIPLE OF ROC A.K.Pandey and G.S. Pant Need of Counting Statistics Nuclear Medicine is used to investigate the functional status of body organs. For this purpose radiopharmaceuticals are admmistered to the patient and the body organs are imaged with the help of external detectors. These detectors pick up the emitted photons and convert them into electrical signals, which are processed for fmal display of the image. The process of gamma photon emission and its interaction with matter is random in nature. Therefore, all radiation measurements (in-vivo and invitro) are subject to random error. If the measurements are random in nature then few questions arise as to how confident we are of the accuracy of results so obtained, how sure we are that a patient's test value is different from the normal and how precise are the results? Counting statistics answers these questions and also checks the validity of results. Counting Statistics Let us start with a set of measurements on a thyroid probe peaked for Cs-137. A standard source of Cs-137 was counted for 5 and 20 seconds respectively. The measurements were repeated 20 times under identical conditions. The results are shown in figure la and lb. These measurements and their graphical display provides the following information:

Counting Statistics and Basic Principle of ROC

15

5 .ec count. form Cs-137 11200 11000 17100 17100 C 17400 :I 17200 0 Col 17000 , . .00

•

'1100 ,.400 ~

G

~

•

----_

~

D

•

~

Me.surement points

Figure-I. 20 sec d.t. from CS-137 71000 70100 70000

J!I ...00 c: :::I

0

..000

Col

..100 11000 .7100

I

I

-

•

Me.surement Points

Figure-Ib

Although measurements in a given set of experiment are taken for exactly the same time interval but counts observed in 20 . measurements are not exactly the same (random variation). Analysis of the results are given below: Mean count= 17520.55, standard deviation (s.d.)= 304.4202, Coefficient of variation (CoV)= 1.737503 were observed in the lit experiment as shown in Fig-1a (5 second duration), whereas Mean = 69846.2, s.d.= 512.6607, CoV= 0.733985 in the 2nd experiment shown in Fig-lb. The method of calculating mean, s.d. and COV has been described elsewehre (pandey and Pant, 2000). The COV merely shows how smallllarge the standard deviation is when compared with the mean value. Less CoY always indicates better precision in the measurements. To have better precision more and more counts should be acquired either by increasing the count rate or acquisition time.

16

Statistical and Mathematical Techniques in Nuclear Medicine

Following points are also applicable in radiation measurements/detection.

* *

The distribution of the number of particles detected during any interval depends only on the length of that interVal and not on the end points.

If the interval is sufficiently small, the probability of obtaining exactly one count during that interval is directly proportional to the length of the interval. The probability of obtaining two or more counts during a sufficiently small interval is negligible. In an infmitesimally small time interval, there are only two possibilities either we record the count or fail to record. The radioactive decay/detection is thus a binary process. [A binary process is a process in which a trial can only have two outcomes (success and failure)!. The probability of getting zero count in the zero time is 1. With the above observations if we take 'Y as the mean rate of detection of the photon then it can proved mathematically (Meyer, 1970) that the probability of detection of photon in time tis: P D(t) = exp(-A.t) (A.t)D / n! , n=0,1,2,3, .... Thus the number of photons detected during time interval [O,t) from a radioactive source follows Poisson distribution with parameter A.t.

*

*

Mean, s.d. and CoV of a single measurement The radioactive decay is a binary process and so is the detection process. Probability distribution function describes the probability of obtaining each outcome from a measurement. There are three probability distribution functions relevant to binary processes namely the binomial, the Poisson, and the Gaussian (Normal). The binomial probability distribution function, which exactly describes the probability of each outcome from a measurement of binary process is given as: ' X(1 - p )N-x N .p P() x =--":""---''---

x!(N-x)!

where N is the total number of trials in a measurement, p is the probability of success in a single trial, and x is the number of successes.

Counting Statistics and Basic Principle of ROC

17

It can be shown that the sum of the probabilities of all outcomes for the binomial probability distribution function is 1.0. The mean and standard deviation for such a distribution are: ... (1)

X=pN and

0

= ~pN(l- p)

If the probability of a success in a trial is much less than one (as is true for most radiation measurements), the standard deviation (s.d.) may be approximated by o =~pN(l-p)

[the term (l-p) is negligible]

o=JpN

o=JX

[from equation (1)]... (2)

Because of the factorials used in the binomial probability distribution function, it is inconvenient or even difficult to use the equation if either x or N is large. The Poisson and Gaussian probability distribution functions are approximations to the binomial p in such cases are approximations to the binomial probability distribution functions that we often used when x or N is large. The standard deviation can be estimated by making several measurements. However, it can also be estimated from a single measurement, if the process is binary. In counting measurements, the single measured value is probably close to the mean (see the results of experiment in Fig-I and the text). Since the s.d. is approximately the square root of mean, it is also approximately the square root of a single measurement.

=Jf5 COV = (o/C) * 100 = (Jf5IC) * 100 0c

and

= (1/J(5}*100 where C is the value of single measurement.

18

Statistical and Mathematical Techniques in Nuclear Me.dicine

Standard deviation is the uncertainty in measurement. CoY is also called percentage uncertainty in the measurement. Counting statistics (poisson) are also described by the Gaussian distribution SO long as the number of counts greater than about 30 (Bemier,I994). The Gaussian distribution has 68.3% of all results within the range mean (x) ± la, 95.4% of all results within x ± 20, and 99.7% of all results within x ± 30. Thus for a given some number of counts C, 68% of repeat measures wiU fall within c±l and 95% of repeat measures of the sample wiU faU within c±2..[C, and. so on. Example: How many counts are needed to be 99% sure that the true answer is within 1% of the measured value? Let C be the true sample count. Ninety nine percent times the repeat measurement would be in the range C ± 3..[C. The uncertainty in the measurement is In this example 1% of the measured value = uncertainty

rc

3rc.

lxC=3..[C 100

Thus C = 90,000. A simple formula for such a calculation can be given by: C = [(100 x n) I p]2 n can vary from 1 to 3 (for 68%, 95% and 9goA, confidence interval) In the above mentioned problem n = 3 and p = 1. Hence C = [(100 x 3 ) I 1]2 = 90,000. Types of error 1. Blunders 2. Systematic error 3. Random error In nuclear medicine normally random errors are encountered and we are confming here to random errors and their propagation. In most of the measurements, mathematical operations (such as addition, subtraction, multiplication and division) are carried out, which further propagate error in the fmal result. Table-l shows the equations that are to be used for estimating the s.d. in the fmal result.

Counting Statistics and Basic Principle of ROC

19

Table-I. Operation Multiplication

Standarddeviation

C*X Xl * X2

Division

Addition/Substraction

X/C

C*cr ((110"1)2 +(1I0"2n

cr/C

X11X2

((1/0"1)2 +(1I0"2n

Xl + X2

((0"1)2 + (0"2n

Xl - X2

((0"1)2 + (0"2n

C is a number without random error, cr is the standard deviation of X, cr1 is the standard deviation of Xl and cr2 is the standard deviation of X2. Background counts create problem in most of the counting measurements. It arises from natural terrestrial/cosmic sources of radioactivity and also from radioactive material in the vicinity, if any. The sample is usually counted in the presence of some background radiation, yielding a gross count for sample plus background. Background count is usually obtained by recording the count in the absence of sample. Example: A sample in presence of background yielded 2500 counts (A). Background alone (B) produced 900 counts. Calculate true (net) counts and standard deviation. Net count = A - B = 2500 -900 = 1600 counts crnet = ~(2500+900) = "3300 = 57 counts So the net counts can be expressed as 1600 ± 57 counts. Note that the presence of background increases the statistical uncertainty in the results. If there were no background, the sample count (net count =1600) would have produced 1600 ± "1600 = 1600 ± 40 counts. Uncertainty in count rate Count rate (C) = N/t Where N is the number of counts in time 't'

20

Statistical and Mathematical Techniqlles i/l Nllclear Medicine

Uncertainty in count rate will be = uncertainty in counts (N) I time(t)

= JNtt = 1I .Jt * ~(N It)

= ~(C/t) Uncertainty in sample count rate (Cg) will be O"g = ~(Cg / t g) Similarly uncertainty in the background count rate O"b

=

~(Cb / t b)

Difference in uncertainty between sample and background can be expressed as :

Percentage uncertainty in the difference

For a given time of measurent (tg + tJ, the maximum precision can be obtained with the following condition

Example: In an experiment the total time available for measurement is 5 minutes. Gross counts from the sample and background for 10 sec were 5000 and 250 respectively. Calculate the optimum time for the sample and background for maximum precision. Gross Count rate (C) = 5000/10 = 500 Background count rate (G) =250/10 = 25 tg 1 ~

= ~(Gg 1G b ) = ~(500/ 25)

Counting Statistics and Basic Principle of ROC

21

= 4.47 tg = 4.47 t" Given, tg + t" = 5 min 4.47 t" + t" = 5 5.47 tb = 5 tb = 0.91 therefore, t g = 4.47 * 0.91 = 4.09 If the percentage uncertainity in a given measuremeni is decided then the time of sample measurement can be obtained as follows Let Cs be the net sample count rate When t, = t" = t then

~(Cg+c;,)/t]*I00

% uncertainity in sample count rate (V) =

C _ c;, g

Squaring both side and re-arranging we get ... (3)

Example: In a given measurement, gross and background count rates are 1200 cpm and 150 cpm respectively_ What counting time is required to have 5% uncertainty in the result. Net sample count rate rate = 1200 - 150 = 1050 cpm Substituting the values in equation (3) above t= [1050+2*150]*(100)2 = 0.489 min (1050)2 *(5)2 Medical decision making and principle of ROC The ~ublic awareness in recent years has increased to an extent that they want the justification of the cost and possible risks of a diagnostic procedure. It is important to measure the quality of diagnostic information and diagnostic decisions. Here we will deal with the quality and diagnostic decision of a test. To compare two test modalities one has to choose a parameter/ index. The simplest parameter/index could be "accuracy". This is the fraction of cases for which test provides the correct result. We

22

Statistical and Mathematical Techniques in Nuclear Medicine

always require accuracy to be very high (near 100%). This parameter has to be used carefully as it may mislead in some situations. For example in screening relatively rare disease when the test can be very accurate, simply by ignoring all evidence and calling all cases negative. If only 5% of patients have the disease in question, a test, which always blindly states that the disease is absent. will be right (accurate) 95% of the time (Metz, 1978). Similar situation arises, when the disease is common (high prevelance). It is obvious from above example that disease prevalence affects the accuracy quite significantly. Even if disease prevalence is known and fixed, this index has limited role to play. For example, there may be two differ~nt tests with equal accuracy but different false positive and false negative decisions. One might provide almost all false negative decisions, while other nearly all false positive decisions. Thus the usefulness of these two tests for patient management could be quite different in different situations. To make the accuracy a meaningful index, prevalence of the disease, sensitivity and specificity should also be included in decision making. Sensitivity and specificity are defmed as follows: Sensitivity = Number of True Positive (TP) decisions / Number of actually positive cases (TP+FN) Specificity = Number of True Negative (TN) decisions / Number of actually negative cases (TN+FP) The "sensitivity" represent a kind of accuracy for actually positive cases while "specificity another kind of accuracy for actually negative cases. It is necessary to specify the basis of determining true positive/true negative (gold standard) while calculating sensitivity and specificity. Disease prevalence is defmed as: Prevalence = (TP+FN)/(TP+FN+TN+FP) Disease prevalence is the characteristic of the patient population group. Fig-2 (hypothetical curve) shows a distribution of normal and abnormal (ill) persons in the population. Y-axis represents the number of persons who are normal (left part of Fig-2) or abnormal (right part). Disease prevalence is the area under the distribution curve for diseased persons compared to the area under both the curves in Figure-2. If prevalence is high, the test with high sensitivity should be chosen while in case of low prevalence test with higher specificity should be preferred. Accuracy = (True positive (TP) +True negative (TN»/(Total cases (TP+TN+FP+FN)

Countillg Statistics and Basic Principle of ROC

23

Test Result --.

Figure-2

Accuracy of a test depends on disease prevalence for the same sensitivity and specificity. It is therefore quite possible that the accuracy for a given test at two centres may be different due to their different disease prevalence. Accuracy can also be expressed in terms of sensitivity, specificity and prevalence. Accuracy = sensitivity x prevalence + specificity x (l-prevalence) Positive predictive value (PPV) : This is a conditional probability of having disease when the test shows true positive result. PPV = TP/(TP+FP) Similarly negative predictive value (NPV) = TN/(TN+FN) Other parameters, which are mentioned at times in medical decision making are: True positive fraction (TPF = p( T+ / D+) is simply the same as sensitivity, and true negative fraction (TNF= p(T- / D-), is simply the same as specificity. False Positive fraction (FPF = p(T+ / D-) = No. of false positive decisions / No. of actually negative cases. False Negative fraction (FNF= p(T- I D+) = No. of false negative decisions I No. of actually positive cases. Example: Result of 10 volunteers (7 normal individuals and 3 ill patients) are given in the following table. The bold face letters indicate the normal individuals. Using a threshold value ~ 20 (as positive) label them as TP, FP, TN, FN.

24

Statistical and Mathematical Tech11iques in Nuclear Medicine

c

B 5

20

D 40

E 60

F

G.

9

70

B 5

C

10

20

FN

TN

TP

FP

H 50

I 80

D

E

F

G

40

60

9

H 50

I

J

70

80

15

FP

TN

TP

FP

FP

TN

Answer: A

Example: In 100 patients who underwent thyroid uptake measurement, the test results are: Negative Positive 60 (TN) 10 (FP) 5 (FN) 25 (TP) Sensitivity = 25/(25+5) = 83.3% Specificity = 60/(60+ 10) = 85.7% • Accuracy = (60+25)/100 = 85% Because of the variations in biological response, possible statistical noise in the data, and other technological deficiencies, a medical test some times produces identical results for abnormal (disease) and normal patients. Usually a normal range for normal . people is established and if the results fall outside this normal range they are termed as positive (ill). As is obvious from the figUre-3 th~ no single decision criterion can be found that separates the populations cleanly. Usually a threshold value is chosen arbitrarily, and different choices yield different frequencies for various kinds of correct and incorrect decisions. For example, if high value of results indicate the presence of a disease, then increasing the threshold value will make both false positive and true positive decisions less frequent, but will make both true negative and false negative decisions more frequent. A threshold should therefore be selected in a judicious manner, which can make a good balance between sensitivity and specificity. By changing the decision threshold several times, we will obtain several different pairs of TPF and FPF. These pairs can be plotted on a paper. Both the axes of this graph range from 0 to 1 because these are the limits of possible TPF and FPF values. Repeated change in the decision threshold provides more and more points (TPF, FPF), which can be plotted on a graph paper. The points representing all possible combinations of TPF and FPF must lie on a curve. This curve is called the receiver operating characteristic (ROC) curve for a given diagnostic test. ROC

25

Counting Statistics and Basic Principle of ROC

curve can also be obtained by plotting the sensitivity on y-axis and the specificity on x-axis. The value of x-axis decreases left to right from 100010 to 0% specificity. The ideal point for a test result would be the upper left comer of the ROC curve with sensitivity = 100 % and specificity =100%. The dotted lines (Fig-4) show a desired ROC curve for a given diagnostic test. Esample: 32 patients are subjected to a particular test A. The test results are given in the table given below. The data in the bold face indicate normal group as determined by gold standard. Draw ROC by changing the decision threshold. 68.63

Y Z

79.28

61.45

AA

0.44

P

91.99

AB

93.58

26.17

Q

95.69

AC

38.87

F

67.80

R

11.65

G

S

84:24

AD AE

46.04

82.27

H

28.78

T

8.29

I

18.75

U

29.11

J

71.04

V

63.64

K

29.68

W

51.74

L

44.86

X

11.68

A

8.16

M

8.77

B

71.59

N

C

55.28

0

D

61.33

E

6.78

6.81

Answer: Using the above data the TP,FP,TN FN has been calculated and is tabulated as follows and corresponding ROC curve is shown in Figure-3.

-

O.t 0.1 0.7 0.'

o..

IL t-

.-.....- ~

0.5

o.• 0.3 0.2 0.1 01

02

03

04

os

FPF

Figure-3

08

07

08

O'

26

Statistical and Mathematical Techniques in Nuclear Medicine

Threshold ~O ~ ~ ~

20 40 80

TN 0 3 7 7

FP 7 4 0 0

TP

FN

FPF

TPF

25 19 17 5

0 6 8 20

1 0.57 0 0

1 0.76 0.68 0.2

Example: A nuclear medicine image data is subjected to two test nlters (Test A and Test B). After processing the images were evaluated according to the following criteria: Condition Definitely no lesion Probably no lesion Possibly lesion is present Probably lesion is present Definitely lesion present

Score 1 2 3 4 ,;

TN, FP, FN, TP, FPF and TPF are given in the following Tables for Test A and Test B. The ROC for the for the Test A and Test B is given in Figure-t. Test A

Threshold 1 2 3 4 5

TN 0 4 12 18 27

FP 23 14 16 5 1

TP

FN

FPF

TPF

0 1 3 8 16

17 21 19 9 6

1 0.77 0.57 0.21 0.03

1 0.95 0.86 0.52 0.21-

Test B Threshold

TN

FP

TP

FN

FPF

TPF

1 2 3 4 5

0 3 14 17 24

20 15 14 6 4

0 1 3 9 15

20 21 19 8 7

1 0.83 0.50 0.26 0.14

1 0.95 0.86 0.47 0.31

Test A appears to be better than Test B as area under the ROC (Fig. 4) curve is more for the former than the latter on the basis of the data given in the example.

COllnting Statistics and Basic Principle of ROC

27

ROC of Two Test A and B (Hypothetical) 1

,

S 0.9

, ,

F7

'6 ~ 0.8 , 0.7 0.6 0.5

t lO.4

u. 0.3 ~ 0.2 0.1

,

~

, ,

77

//

,

,,

-

- -- ---------------77

I".!.~:I

/./

-, 7

17

V

00

0.2

0.4

0.6

0.8

FPF (False Po8IthIe Fraction) FilUre-4

References 1.

2. 3.

4.

Brown PH( 1997) Mathematics and Statistics In Nuclear Medicine : Technology and Techniques 4 th Edition ( Eds) Donald R Bernier, Paul E. Christian, Games K Langan pp 135 Mosby St. Louis. Metz CE (1978) Basic Principles of ROC analysis. Sem Nucl Med 8, 283-298. Pandey AK and Pant GS (2000) Counting statistics In Radiation Safety for Unsealed Sources pp 52-63 (ed) G.S. Pant, Himalaya Publishing House, Mumbai Paul L. Meyer (1970) The Poisson and Other Discrete Random Variables, Introductory Probability and Statistical Applications, Second Edition, Oxford & IBH Publishing Co. Pvt. Ltd., New Delhi. pp 159-181.

NON-PARAMETRIC TESTS, MATCHMAKING AND McNEMAR IN THE COMPARISON OF DIAGNOSTIC MODALITIES CS Sal If the data are clearly not Normally distributed, and there is no simple transformation to render it so, for example, if there are outliers in the data, then it is worth considering a nonparametric test. Most of the imaging research yields matched data- the result of the direct comparison of different diagnostic techniques performed on the same patients - the "paired X2 test" or popularly known as McNemar test and related statistics should be well understood by the investigators. The purpose of this paper is to illustrate and explain the application and principles of these statistical techniques and to provide a list of references for further reading.

Matched Data Comparative imaging studies commonly produce matched data (matched samples) since, all the examinations under comparison are performed on same subject. For example, infections were experimentally created in the legs of rabbits and every animal was imaged with both Ga-67 imaging and 99mTc-HIG. Matched data consist of matched pairs of results- in this case, the Ga-76 image and 99mTc-HIG scan for each experimental animal. Since the same lesion is imaged by means of both techniques, the data are matched by the characteristics that may influence the imaging results (i.e. lesion size, extent, and location).

Non-Parametric Tests, Matchmaking and McNemar...

29

(a) McNemar Test The McNemar test pertains to matched pairs of binary (dichotomous) test results. The results of each diagnostic test fall into two categories, positive or negative. The data are succinctly presented in a 2x2 array with the rows corresponding to the results of one diagnostic test and the columns to the results of the other. Each element of the array is the number of cases observed with the particular combination of test results. For example 32 rabbits were innoculated with Staph. aureous and developed osteomyelitis. They were imaged first with 99mTc-IDG and then with Ga-67. Table 1: The results are displayed in a 2x2 array Ga-67 Positive Negative Total

99mTc-HIG Positive 20(A)

10(B)

1(C)

1(D)

21

11

30 2 N=32

The sample (or observed) "sensitivity" or true-positive rate of each technique to the presence of the osteomyelitis is the number of cases with "positive" fmdings divided by the total number in the array; hence, the sample sensitivity of Ga-67 imaging = (A + B)/(A + B + C + D) = 30/32 = 0.94 and the sample sensitivity of 99mTc-fiG = (A + C)/(A+ B + C + D) = 21/32 = 0.66. By subtraction, the sample (or observed) difference in the sensitivities is the sensitivity of Ga-67 imaging minus the sensitivity of 99mTc-HIG ([B - C]/N = 9/32 = 0.28). The objective of the McNemar test is to assess the statistical significance of the observed differences in sensitivities between Ga-67 imaging and 99mTc-HIG scanning. Band C in the data array are "discordant" data (i.e, the Ga-67 imaging results differ from the 99mTc-fiG results). These discordant data are the basis of the McNemar analysis (Conver, 1980 and Fleiss, 1981). The more uneven the distribution of the discordant cases between the discordant cells-the more B differs from C-the greater the evidence that the sensitivity of 99mTc-HIG in the population differs from that of Ga-67 imaging. The McNemar test assesses the likelihood that the observed distribution of discordant cases between the two discordant cells could occur by chance if the diagnostic techniques being compared had equal sensitivities in the population. The significance level of the result of the McNemar test is the probability of the observed distribution or a more unequal distribution of the discordant data occurring if the diagnostic tests being compared had equal sensitivities.

30

Statistiral and Mathematical Techniques in Nuclear Medicine

Binomial Distribution The statistics governing the distribution of discordant cases with equally sensitive techniques are identical to those of the flip of a coin. The binomial probability distribution gives the probability that a specific number of these events, x, will be positive as a function of nand p. Therefore, if the diagnostic tests compared are equally sensitive, the probability that B cases will be Ga-67 positive and 99mTc-HIG negative and C cases will be Ga-67 negative and 99mTc-HIG positive is determined by means of binomial distribution with p = .5, n = B + C, and x = B. Exact Form of the McNemar Test The binomial distribution is the basis of the exact form of the McNemar test. The objective of the test is to calculate the probability that the observed discrepancy between the numbers of discordant cases (one and 10) or an equally or more discrepant combination (ie, 10 and one, 11 and 0, 0 and 11) could occur by chance if Ga-67 imaging and 99mTc-HIG had equal sensitivities in the population. This probability is calculated by means of the binomial distribution and is the significance level, or· P value, of the test. The significance level forms the basis for rejection of the null hypothesis that the diagnostic tests being compared are equally sensitive; the smaller the P value, the stronger the evidence for rejection. The P value indicates the likelihood that the null hypothesis is being falsely rejected. The McNemar Statistic Approximation rather than an exact method are the basis of an alternative form of the McNemar test. This form is rooted in the fact that if the diagnostic tests being compared are equally sensitive, then I(B - C) - 1,. lIB + C) approximates r} distribution with 1 df (Rosner, 1982). The expression I(B - C) - 11l.f[B + C) is termed the McNemar statistic with continuity correction (drop the -1 within the brackets and it is the McNemar statistic). The greater the difference between Band C, the greater the value of the statistic and the stronger the evidence for rejecting the hypothesis that Ga-67 imaging and 99mTc-HIG have equal sensitivities. Since this form of the McNemar test is based on a "limit theorem" (ie, the approximation becomes exact only in the "limit" as the size of the sample becomes infmite), it should be applied only to large samples. There are guidelines for determining what constitutes a sufficient sample size such as B + C > 20. Some methods- extend the notion of the McNemar test to

Non-Parametric Tests, Matchmaking and McNemar...

31

matched data tables with more than two rows and columns suitable to the analysis of diagnostic tests with more than two out comes

(Siegel, 1988). Statistical versus Diagnostic Significance The diagnostic advantage of one modality over another depends on the magnitude of the differences in their sensitivities. One problem with the McNemar test- a trait shared with tests of significance in general- is that trivial differences in sensitivity, no matter how small, become statistically significant as the sample size increases. Hence, it is important to distinguish between statistical significance and diagnostic significance; assessment of the magnitude of the differences in sensitivities of the diagnostic tests is a necessary part of the comparative analysis (Berry, 1990). The McNemar analysis provides for estimation of the magnitude of the difference in the sensitivities, Specifically, the estimate of the sensitivities is (B - C)/N = (10 -1)/32 = 0.28 for the matched Ga-67 imaging-99mTc-HIG data array. Confidence Intervals (B - C)/N provides what is known as a "point" estimate; the estimate of the difference in sensitivities is given as a single value. The "confidence intervaf' is another type of estimate; it is given as a range of values rather than just a single value. With the confidence interval comes a "confidence level," which indicates the likelihood that the confidence interval derived from the data will include the true value of the parameter that is being estimated for the population from which the data are a sample. The greater the confidence level, the wider the interval (ie, the more certain the conclusion, the less precise the statement). The confidence interval of the difference in the sensitivities of two diagnostic tests may be approximated from the matched data array. With a confidence of 95%, it can be derived that the sensitivity of Ga-67 imaging in the population is between 7% and 49% greater than the sensitivity of 99mTc-IDG in the population; in other words Ga-67 imaging wQuld detect between 7% and 4SOAI more of the infections than 99mTcHIG would (Dwyer, 1991). The use of confidence intervals to summarize results should be encouraged for several reasons. They serve to diminish confusion between statistical significance and diagnostic significance by making explicit the magnitude of the differences in sensitivities. They reinforce the reality that the estimates are projections subject to uncertainty. The confidence interval provides a range of plausible

32

Statistical and Mathematical Techniques in Nuclear Medicine

values of what is to be estimated; the width of this range indicates the degree of this uncertainty. The extremities of the confidence interval give some indication of the limits of what is inferable from the data at hand. Complementarity of Results The comparison of two diagnostic modalities should include consideration of the complementarity of their results. How often does one modality depict an abnormality that was missed with the other? How many additional infections would be detected if 99mTcHIG were performed in addition to Ga-67 imaging? The matched data array provides answers to such questions. BI(B + D) gives the fraction of cases negative at 99mTc-HIG that were positive at Ga-67 imaging (10/ 11 in the table). Similarly, C/(C + D) gives the fraction of cases negative at Ga-67 imaging that were positive at 99mTc-HIG (1/ 2 in the Table). Take-home m~ssage Comparative studies of imaging techniques commonly yield matched data due to the ease and desirability of performing all cf the techniques on each of the patients. The 2x2 matched data array and the McNemar analysis provide a succinct format for the presentation and proper analysis of matched comparisons of binary (positive or negative) test results. When comparing two diagnostic tests, it is essential not to rely on just the statistical significance of the differences in sensitivities (or specificities); the magnitude of the differences must also be assessed. Confidence intervals provide a useful form of estimation by providing a range of plausible values and an indication of the precision of the estimate. The matched data array also indicates the complementarity of the diagnostic tests being compared. Other important non-parametric statistical methods Other important non-parametric statistical methods often used in imaging science are Wilcoxon signed-rank sum test, ChiSquared test for trend (2xC table) and Mann-Whitney U test etc. I shall discuss them in brief with one example in each case and how they influence the decision making process. (b) Wilcoxon signed-rank sum test

When the data are paired, for example in a matched casecontrol study, or a crossover trial, then the pairing should be taken into account in the analysis. The procedure is to subtract one member of the pair from the other, and rank the resulting

J\'on-Parametric Tests, Matchmaking and Mcl\'emar ...

differences, but ignoring the respect.ive plus or minus signs. Once the ranking is made, the signs are rest.ored, so that. t.he sum of the ranks associated wit.h the plus sign gives T. We t.hen compute z using the following formula (Campbell, 1990).

Z=

T-n(n+l)/4

J{ n{n + 1){2n + 1) 124} where n is the number of pairs and z is tabulat.ed from t.he Normal Table.

Example Consider a matched case - control study to reveal t.he association of of breast cancer with that of the oral contraceptive pill (OC) use. Ten women with breast cancer were matched with ten age, sex and social class controls, and the total duration of time they used the oral pill was noted. The results are given in the following Table Table 2: Duration of time using Oral Contraception (years) Pair Case Control Difference Ignoring Signs Rank Signed

1 2.0 1.5 0.5 0.5

2 10.0 9.1 0.9 0.9

3 7.1 8.1 -1.0 1.0

4 2.3 1.5 0.8 0.8

5 3.0 3.1 -0.1 0.1

6 4.1 5.2 -1.1 1.1

2 2

4.5 4.5

6 -6

3 3

1

7

-1

-7

789

10

10.0 1.0 9.0 9.0

10.5 9.6 0.9 0.9

12.1 7.6 4.5 4.5

15.0 9.0 6.0 6.0

10 10

45 4.5

8 8

9 9

Thus T = 2 + 4 . 5 + 3 + 10 + 4 . 5 + 8 + 9 = 41. From the above formula we get Z = (41 - 27.5)/9.8 = 1.4 From the standard table with z = 1.4, we get p = 0.16, statistically not significant. Thus one concludes that oral pill use has no bearing on breast cancer development. (c) Chi-Squared test for trend (2xC table) An important class are 2xC table, where the multi-level factor has ordered level. For example, patients might score their pain on an integer scale from 1 to 5 on one of two treatment. In this case the test is very inefficient, because it fails to take account of the ordermg. In this case one should use the 'X.2 test for trend. In this

"I:

34

Statistical and Mathematical Techlliques in Nuclear Medicille

test one must assign scores to ordered outcome. So long as the scores reflect the ordering, the actual values affect the result little. Consider the notation in Table 3, which gives the results of a parallel clinical trial with ordered outcomes. Table 3: Results of clinical trial of two treatments such as a.p and "~r to alleviate bone pain Wor.w

Same

Slightly Better

Moderately better

Much

Total

11

53

42

27

11

144

15

7

Total y R(S, 9), is defmed as the line integral along a straight line L, defmed by its distance S from the origin and its angle of inclination from the x-axis 9 (Fig.- 3).

J

R(s,e) = g(x, y)dL

... (1)

Each points along the line L satisfies the equation: x : sin (e) - y . cos (e) = S ...(2) Where S is the distance between the line p and the line L. The line p is the ·shortest line from the 0 (center of rotation) to the projection line. Therefore the equation can be written as:

JJg(x, y) . s(x.sin(e)- y.cos(e)-S~dxdy

R(S, e) =

(3)

Where the delta function defmes integration only over the line L. The range of e and S are limited to 0 ::: e < 1t and -00 < S < + EJk A, et al (1988) Assessment and comparison of three scatter correction techniques in single ph9ton emission computed tomography. J Nucl Med 29, 1971-197.9. Gullberg GT (1979) The attenuated Radon transform: Theory and applications in medicine and biology. PhD dissertation, University of California, Berkeley, CA. Hoffman EJ, Huang SoC, Phelps ME (1979) Quantitation in positron emission computed tomography: I.Effect of object size. J Com put Assist Tomogr 3, 299-308.

10.

11.

12.

Jaszczak RJ. Greer KL, Floyd CEo et al (1984) Improved SPECT

Correctioll for Attel1l1atioll, Scalier and Partial "ollime effect....

9]

quant.ification using compensat.lOn for scattered photons. J Nucl Med 25, 893-900. 13.

Jaszczak RJ, Floyd CEo Coleman RE (J 985) Scatter compensation t.echniques for SPECT. IEEE trans Nuclear Sci 32, 786-793.

14.

Koral KF, Wang X, Rogers WI, et al (1988) Compt.on scatt.ering correction by analysis of energy spectra. J Nucl Med 29. 195-202.

15.

Koral KF, Swailem FM, Buchbinder S, et al (1990) SPECT dual-energy window Compton correct.ion: Scatter multiplier required for correction. J Nucl Med 31, 90-98.

16.

Maiko JA, Van Heertum RL, Gullberg GT, Kowalsky WP (1986) SPECT liver imaging using an it{lrative attenuation correction algorithm and an external flood source. J Nucl Med 27, 701-705.

17.

Morozumi T, Akajima m, Ogawa K. Yukta S (1984) Attenuation correction methods using information of attenuation distribution for single photon emission CT. Med Imag Tech 2, 20-28.

18.

Msaki P, A.xelsson B, Larsson SA (1989) Some physical factors influencing the accuracy of convolution scatter correction in SPECT. Phys Med Bioi 35, 283-298.

19.

Ogawa K. Harata y, Ichihara T, et al (1991) A practical method for position dependent Compton scatter correction in SPECT. IEEE Trans Med Imag 10, 408-412.

20.

Sorenson JA (1974) Methods for quantitative measurement of radioactivity in vivo by whole body counting. In: Instrumentation in nuclear medicine, Vo1.2, Hine GJ(ed), Academic Press, New York, 311-348.

SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY (SPECT) : ITERATIVE RECONSTRUCTION INCORPORATING DEPTH DEPENDENT RESOLUTION, ATTENUATION AND SCATTER B. Singh and S.K. Kataria

Introduction Nuclear Medicine Imaging (Gelfand and Thomas, 1988, Sharp et al 1989) assesses the functional status of a region based on the distribution of the radioactive tracer. Static imaging studies involve only one time snap of the radioactivity distribution. Dynamic study data consists of a number of snapshots of the dynamic biologicalsystem taken at regular interval and hence is termed as dynamic imaging of the biological system. These planar imaging techniques utilize the projection images where a three-dimensional distribution is projected on to a two-dimensional space. The clinical diagnosis is based on the detection of focal defects in static imaging technique. The dynamic imaging studies utilize the transient behavior of the tracer to generate the parametric image. These parametric images are then analyzed to detect the presence of focal defects. The projection image looses the depth information and leads to reduction in the ability to detect the focal defect surrounded by normal tissues. PET and SPECT imaging devices attempt to reduce this limitation, by reconstructing three- dimensional object from a set of two-dimensional projections. This procedure is similar to the three-dimensional object generation in other branches of science - astronomy (Bracewell 1956,1967), optics (Berry & Gibs

Single Photon Emission Computed Tomograph)' (SPECT)....

93

]970), electron micrography (De-Rosier & Moore 1970. De-Rosier & king 1970, Crowther & Amos 1971, Ramachandran & LRkshminarayanan 1971) fluoroscopy (Kak et a1. 1977) and radiology (Cormack 1963, 1964 & 197:3, Hunt 1970, EMI 1972, Ilounsfield 197:3, Mersereau 197:3, Brooks & DiChiro 1974). Generat.ion of images at different depths in nuclear medicine imaging (Hounsfieid 1976. Bellini et a1. 1979, Shepp 1974, Brooks 1976, Kuhl & Edwards 1963 & 1964, Anger et a1. 1967, Muehllehner 1968, Muehllehner& Wetzel 1971, Kuhl et a1. 1973, Patton et a1. 197:3, Oppenheim et a1. 1976, Keys 1976) was precursors to emission tomography (Jaszczak et a1. 1977 & 1981, Isenberg & Simon 1978, Fleming 1979, Budinger 1980, Cao & Tsui 1993, Amersham 1994) which essentially is based on the tomography developments in other sciences. In SPECT the estimate of the distribution of the radioactive tracer is affected by number of factors - contribution of the scatter, performance of collimator to partition the data in to transverse slices, depth dependent resolution of the collimator, methods for reconstruction, attenuation of the gamma rays in the tissue and the partial volume effects. This paper gives a tutorial on these topics. Statistical model Conventional single head rotating SPECT system maps the 3-D object radioactivity di::;tribution f(x, y, z) in a number (Na> of projections p~ (t, y) at different angle of rotation 8. Fig. 1 shows the schematic diagram. The axis of rotation is aligned with the yaxis of the 3-D object. The detector at angle of rotation (, generates a projection Pe(x, y) or p~ (t, y). This projection is obtained by summing the activity along the rays (parallel to s-axis) at different values of t. Chornoboy et al (1990) have described the aim and the statistical model for the SPECT imaging. Assuming that (a) Intensity of radioactive decays A.(x) is proportional to the concentration of tracer at point. For sake of brevity index x for A. spans all the possible values of indices x, y, z of the distribution f (x, y, z). (b) Single photons are emitted in isotropic manner. This disintegration is modeled as a space time process N (N emission) with intensity A.. • (c)

The projection data p~ (t, y), Ne in number measure the intensity A.(x) and generate a measurement point processes Nm , and are defined over the projection space p~ (t), 8 = 1.2 .... ,N e.

9-l

Statistical and J/(/Ihematical Techniqlle's in Suclear Medicine'

.... ",

2-D projectIOn p(x,y) at,." f~ay Sum \ angle e , ,. .' \

.'

Detector,

'.'

Z

... T

I I I

3-D Object f(x,Y,z)

Axis of rotation / /

/ /

Patient (Fixed) Coordinate system

- axes s, y, Z : 3-0 objett f(x, y, z) - Transverse slke f y-ycC:x,z)

Detector (Rotating) Coordinate system - au. s, z rotate to (t, s) and at an angle 9 transform('d toordinates are t = x t05(9) + y sin(9) s = - s 8in(9) + y t05(9) pg{t) Is a row in 2-D projection pg{x,y) of 3-0 obj.. ct f(s, y, z) at an angle 9.

Figure-I: Coordinate system in SPECT data acquisition. Fixed (patient) coordinates system is shown by dotted lines while the rotating (detector) coordinate system is shown by solid lines. Axis of rotation is aligned with y-axis. The depth dependent resolution is given by the length of solid thick arrow from the point in the attenuating medium to the detector. The attenuation length is the part of this arrow that is within the transverse slice.

The aim of the SPECT imaging is to estimate tracer concentration A.(X) , given the measurements N In ideal case. with the assumptions of perfect. collimator, no scatter and no attenuation. the projection data is the sum of the voxels along the ray. As the N. is a Poisson process the measurement process is also a Poisson process with intensity ~m for a 2-D projection Pe (t, y), defined as OI

~m =~m (t.e)= 1/21tf~·(x)dx

•

... (1)

Where the integration iR carried along the line perpendicular

Single Photon Emission Computed Tomography (SPECT)....

95

to the detector surface and contributes to the projection point (t) in the projection. Further only those photons that are directed towards the detector are considered. This equation implies the Radon transformation. Given the observation of Ilm inverse t.ransformation should be carried out to obtain the tracer concentration. It is common to interpret Nm as noise corrupted version of Ilm and apply back projection methods for reconstruction. However as the observations are on N m and not on Ilm • Former is a poor estimate of the later. The assumptions of ideal system are rarely met in practical SPECT imaging systems. Due to these factors the filtered back projection methods may not give the exact or accurate estimates of the tracer concentration. Chornoboy et a1 (1990) have modeled the relationship between the emitter'concentration and the counts obtained in the projection data. The known physical effects (scatter, attenuation, oyerlapping of rays because of point spread function) are not explicitly modeled. They have considered two separate phenomena that alter the relationship between photons emitted at site x and those counted at site (t, 9) in the projection. These are (a) The point-spread function along with the rartdom errors that corrupt the ideal measurement process. It is further assumed that translations (from x to site (t, 9» are independent of one an other. This assumption modify the equation 1 to Ilm = Ilm (t, 9) = 1I21t

f

Ps(t I x, 9) A(X) dx

... (2)

where Ps (t I x, 9) is the transition probability and it can be determined for imaging system with measurements of line source placed in the equivalent scattering medium. (b) Alterations in the counting of photons emitted at site x due to the photon attenuation and the detector efficiency. A mark Vi is assigned value of 1 if the event at x is recorded at (t, 9) else it is O. The conditional probability, Prob {Vi = 1 IN., Nm }, that an events is recorded given N. and Nm is ~(x, t, 9), and defmed as ~(x,

t, 9) = E (t, 9) e[·r .. (~d~

•••

(3)

where integration is carried out along the line from x to t for the projection at an angle 9. E (t, 9) is the efficiency of the detector at a point (t, 9) in the projection and can be measured by flood phantom. ex (1;.) is the attenuation density and is defined by the characteristics of the medium. With incorporation of these factors the equation (1) is modified to

96

Slal;sl;w! (llld lUalhe11lal;ca! Techniques ill Nue/ear Afedicille I-lm

= I-lm (t. =

8)

= 1I21t f

Ps(t I x. 8) ~(x. t. 8) j,(x) dx

f Ps(tlx, 8) E(t,8)e[-f a(;)d;]A,(x) dx

... (4)

This relation (4) shows that measured intensity I-lm intensity is given by an attenuated Radon transform of the emission intensity A,. The process N m represents a statistical model that is more appropriate for the acquisition of SPECT data. Reconstruction As mentioned in section 2, the aim of the SPECT imaging is to estimate the emission intensity from the measured intensity in the projection data. The projection data are Radon transform of the object. With the assumptions of ideal imaging system the back projection methods are used. Fourier slice theorem formed the basis of the earlier versions of obtaining the estim~tes of the 3-D object. It is shown by Hall (1979) and van Elmbt et a1 (1993) that Fourier transform Pe (l) of the projection row Pe (t) at y=yc leads to a slice of Fourier transform Fe (X.Y) of the unknown fe (x,y). In the following description, capital letters are the Fourier transform of the corresponding entities represented by small letters (i.e. F is Fourier transform of f array, T represent the spatial frequency corresponding to variable t and so forth)

f f(x,y ,z) e-' dt ds = 1I(4n2) f f f f F(x,y,z) e-' ( e-' dX dZ dt ds = 1/(4x2)f f f f F(x,y,z) e- x zyr ey dX dZ dt ds =f f F(x,y,z) ~(x - T cos(8), y - T sin(9» dX dZ

p~ (t,y)

=f

tT

x X + • Z)T

i

IX

+.

tT

i (x 000(8) +

oiD(e))tT

= Fe (T,Z) Implication is that by taking the Fourier transform of the projection data at different angles lead to estimation of the Fourier transform of the unknown image. The required interpolation can be used to obtain the values on a square grid. The inverse Fourier transform then leads to the estimation of the unknown image. Back projection: With the assumption of the ideal imaging system, the projection value represented by ray sum is uniformly distributed along the ray. Interpolation between the pixel is carried out to obtain good quality reconstruction. In the absence of interpolation the values are assigned to nearest pixel - leading to a fast but a little bit poor quality reconstruction. The reconstructed

Single Photon Emission Computed Tomography (SPECT)....

97

image has the gradual built up with the addition of the projections. This is demonstrated in Fig. 2 that shows t.he back projection of a point source data. Notice that the maximum counts in the reconstruct.ed image after each addit.ion of the projection increases from 82 for back project.ion of first projection t.o :3078 for back projection of all 32 projections. As the opposite projection are added before the back projection the number of total back projection steps are reduced from 64 to 32. There are reconstruction artifacts - st.ar effect is clearly seen in t.he initial st.ages of reconstruction it gradually disappears. Not.ice t.hat the resolution is poor.

111111111 'I \1 \1 \11 10
ON NET Z RES . REc.lUERV

0.7:5

0.:10 0 . 2:5

0 . 12

0.2:1

0.38

0 ._

.

1.39

IL

0.:10

..

0.38

15 ..I

i6: 0.2:1 0 . 3:5

o·'lf'.OG

0 . 12

0.12

0 . 2:1

0 . 38

0 ._

0.2:1

0.38

0._

Figure-3: Window and filter transfer functions used in the filtered back projection method of reconstruction. The cutoff frequency is 0.5. The order for the Butterworth filter is 7. The Metz filter is a resolution restoration filter, notice the increase in the window and transfer function around 0.1 frequency.

Iterative Reconstruction: Iterative reconstruction methods have two basic steps - 1) back projection and 2) re-projection from the reconstructed transverse slice data. The first procedure is for the generation of the image data from the observed projection. This has been already described in earlier section. The second step of re-projection i.e. generation of the projection data from the given slice has more significant contribution for obtaining better quality reconstruction. This step makes use of all the corrections

Singl.e Photon Emission Computed Tomography (SPECT)....

99

for attenuation , scatter and depth dependent resolution of the imaging system. The factors for SPECf projection generation have been demonstrated with SIMCAM a gamma camera simulation package. A point source was kept in an elliptical medium (major axis 15.7 cm . minor axis 13.3 cm) of attenuation coefficient of 0.12 per cm. The x·z coordinates in the transverse slice are x=31.0 and z=46.97 pixels. The computer program evaluated t.he attenuation path, depth of the point source, resolution of the collimator at that depth and the fraction of the activity after the attenuation. Fig. 5 shows the variations in the system FWHM for low energy general·purpose collimator.

1I1I1 \ I \ I \ I \,1\1 \11 101

7 101

zz

13 101

101

3O!tIC

3?!tIC

4:1 101

:IO!tIC

:I?

'\"), ." "",\", '\.,. , I

f'f~f~f~f~~;; f~· f!~ II· 101

1a6 11K

""

1. . 11K

134 !tIC

142 11K

1:10 I!IC

aoo

ao? 101

1:1' I!IC

168 11K

174 I!IC

lila

aa3 11K

a32""

238

I.~ I I" I·* I I ~ I"'If II .or

194 101

of

101

~ ••

101

CtftlUlTlIIE SIIi-SETS (Pftl).]ECTlOft . . . . u I ) o 1 2 3 4 :I 6 7 • ' I O U 12 13 14 1:1 16 17 18 "

ZO 21

aa

23

24aXa?28n30:U

Figure-4: Reconstruction based on filtered back projection using Metz filter with Fc=O.5. F~g. 7 shows the attenuated activity as a fraction of the nonattenu'ated value. Fig. 8 shows the effect of the attenuation and depth dependent resolution on point spread function . This figure also shows the sinogram (variations in x direction) and linogram (variations in y direction) data. These data are used for assessment of patient motion and correction. Fig. 9 shows the corresponding projection data for 64 projection. These figures show that it is a straightforward procedure for incorporating these factors while generating the projection data. These factors are also used for the re-projection of the reconstructed data in the iterations. It is a bit

100

Statistical and Mathematical Techniques ill Nuclear Medicine

tedious to incorporate these factors in back projection , as the projection data in any bin is the integral of the activity along the ray. The activity distribution along the ray can not be ascertained form this ray sum. "'SIMCAM

"qmt"." "',mt" IrHl",) 1II[iJE')

GAMMACAh4I-HASlloo4tJIAT10N(I-IJ'''IHFIG.

!~::

rl t\V

~

' .90

,,'IS

~'IO

~'" ,,. 0.&-4

: QC Um-cN .U_m>cN

Figure-5: The depth dependent resolution of the SPECT system demonstrated by SIMCAM a gamma camera simulation package. Notice that the FWHM varies from 0.64 to 1.11 cm. :i1t.4;:.;.AM GAMMACAhtI:HA~IMULAT1UN(I:I~1..1IU"".;t; U.v,... ,un HAHe

,I

i_' .. '

Twmbuy ~u,"bw Imj,u)

RIiJEJ

DET.CONFlGI CAMERACt£CKUP AOOIJIAfDATA CI'Wl O= -1, it follows that 11(i-l) (x) >= -1, thus ensuring that ').."'(x) satisfies a non-negativity constraint for all i and each x E E (E is the efficiency of the detector, its variations are estimated from flood field phantom). The advantages 01 EM derived algorithm are (1) L (')..,,(.» >= L (')..,,(1-1» - log likelihood values increases with each iteration. (2) ').."(1) (x) >= 0 for each x - the intensity of radioactive decay is always positive for each pixel in the images space. (3) ')..,,(.) tends towards a quantitative predictor of the total emitted photons. Ordered subset Expectation maximization: Expectation Maximization algorithm is an iterative procedure where one iteration consists of two steps - (1) projection and (2) back projection of the errors. Iterations are repeated until the convergence is achieved. In Ordered Subset Expectation Maximization (OSEM),

Single PhOtOl! Emission Computed Tomography (SPECT). ...

lO5

projection data are grouped (Hudson & Larkin 1994) in to a number of subsets. Standard EM procedure is applied to each one of these subsets. Hudsen et 01 (1994) have defined the OS level as the number of these subsets. Iteration of OS-EM is defined as a single pass using all the specified subsets. Further iterations may be performed by passing through the same ordered subsets, using as a starting point the reconstruction provided by the prevlOUS iteration. The algorithm by Hudsen et 01 (1994) is described below Let Pe(t) represent the counts in projection at index t, xI expected number of photons from pixel j X image vector {Xl: j=l, .... ,J) j the index for individual pixel t index in the projection data Pe (t) a tl probability of emission at pixel j being recorded at t (Matrix A is the projection generation matrix or the point spread function incorporating scatter, attenuation and depth dependent resolution effects) lJ.(t) = E (Pe (t» = Ax, the matrix product Ax gives the detector counts that are Poisson distributed. x"o be the prescribed starting image that is assumed to be uniform in the beginning. xl\JD be the estimate of the image x after m iterations. S. i= 1,2,3, ... n denote the chosen detector subsets in the order selected. The Ordered Subset Expectation Maximization (OSEM) algorithm of Hudsen et al (1994) is as follows (1) m = 0, xl\JD initialized and is positive (2) Repeat until convergence of x"'" (a) x

= x"m,

m

=m +

1

(b) for subsets i= 1,2,3, ... ,n

• Project:Calculate expected values cumulative counts Pe(t) as

for detectors (projection ray index) t E S. (i.e. t included in the subset S) • Back project: Calculate the image data.

106

Statistical a1ld Mathematical Tech1liques ;11 Sue/ear Medic;ne

X~+l = X~ItES jPe(t.)atj / Jli(t)]jItESI atj for pixels j = 1,2,3, ..... , J If the divisor is zero then (c) x·'·m

=

1+1 •)\ )

= ,.1 ".1

XD + 1

The selection of subsets can be (1) Non-overlapping subsets: With n subset.s of each T detectors (conventionally called number of ray sums in project.ion Pe(t) the index t = 1,2,3, ... ,1') per project.ion set.s are SI = {I, 2, 3,. ., T} S2 = {T+I, T+2, ..... , 2T} S3 = {2T+I, 2T+2, ..... , 3T} Sn = {(n-l)T+I, (n-I)T+2, ..... , nT} Algorithm continues to cycle through each of t.hese subsets. Data used in each sub-iteration consists of all t.he photonf; observed in projection included in the subset.. The rest.orat.ion at (i-I) is modified to incorporate data acquired on project.ion i. (2) Cumulat.ive subsets: The subset Si has the data of earlier subsets i.e. for i=I,2,3, ... (i-I) SI = {I, 2, 3, ..... , T} S2 = {I, 2, 3, ..... , 2T} S3 = {I, 2, 3, ..... , 3T} Sn = {I, 2, 3, ..... , nT} Back projected data from all projections already processed is combined to form current restoration of the image. (3) Standard EM: The single subset consists of all the projections in the study. SI = {I, 2, 3, ..... , nT} Conventional filtered back projection method uses the projections in a sequential order i.e. ascending order of e, the angle of rotation. Fig. 2 (for a simple back projection) and Fig. 4 (for filtered back projection) shows the generation of the data with this sequential order. Fig. 10 shows the back projection process when the projection are used in ordered sequence. In this ordered

Single Photon Emission Computed Tomography (SPECT).. ..

107

sequence - a pair of the projections at 90 degree apart (zero and ninety aegree to begin with) are considered for back projection. This selection leads to maximum error correction in the reconstructed slice based on a sub set of two projections. Projections mid way bet.ween these two i.e. at 45 degree and at 135 degree form the next projection pair. This process is repeated till all the possible pairs in the sub set of projections have been used. Fig. 10 shows this order of sequence for 32 projections along with the reconstructed slice after back projection of each one projection. From the comparison of Fig. 4 and Fig. 10 it is evident that the first and the last estimate (i.e. frame 1 top left and frame 32bottom row right column) are same. Implication is that when all the data are used in back projection, the result is independent of the sequence in which the projection data are added. In ordered subset a part of the data are used for reconstruction . The . reconstructed data obtained by this is used in re-projection and obtain the estimate of the remaining projections. These are then

CUl'l&A.lll!TIVE ."-IE'. (rNJ.JEOTICM . . . . . . , 016 aM 4 . . 1 2 _ 218 £_10261.430 1 1" , ZI II a1 J.3 a9 3.19 ., a3 .11 Z7 J.S 3.1

...'1..... _, ~~JPT

10

:

~ DATEi:l1aOT~

iM:iiurTY

>CICfCIA

0.1 >0.15

0.5

NA

>0.4

NA denotes Not Applicable. Since the threshold on dose rate rather than on total dose.

Table 2. Recommended dose limits1by IRCP 60 (1990) Application Effective Dose

Annual equivalent dose in the lens of the eye the skin4 the hands and feet

Occupational

Public

20 mSv per year, averaged over defUned periods of 5 years 2

1 mSv in a year3

150 mSv

15 mSv

500 mSv

50mSV

1The limits apply to the sum of the relevant doses from external exposure in the specified period and the 50-year committed dose (to age 70 years for children) from intakes in the same period. 2With the further provision that the effective dose should not exceed 50 mSv in any single year (AERB has set the limit of 30 mSv/yr in place of 50 mSvl yr). Additional restrictions apply to the occupational exposure of pregnant women. 3In special circumstances a higher value of effective dose could be allowed in a single year, provided that the average over 5 years does not exceed 1 mSv per year. 4The limitation on the effective dose provides sufficient protection for the skin against stochastic effects. An additional limit is needed for localised exposures in order to prevent deterministic effects.

Principles of Radiation Protection

219

It is not the zero dose which is the aim of radiation protection but a dose which results in acceptable level of risk. The principles of radiation protection, as has been clarified in this chapter have evolved though many decades of observation and are fairly sound having stood the test of time in light of existing knowledge which is more than for many other agents to which we are exposed to. References 1.

2. 3. 4. 5. 6.

ICRP 60, 1990 Recommendations of the International Commission on Radiological Protection, Pergamon Press. ICRP 85 (2001) Avoidance of radiation injuries from medical interventional procedures. Pergamon. Mould RF (1993). A century of X·rays and radioactivity in medicine. Inst. of Phys. Publ., Bristol. Rehani MM, Oovinda Rajan KN (1997) Eds. Radiation protection for doctors, Association of Medical Physicists of India. Rehani MM. (1992) ed. Radiation Safety in Medical Practice, Oalgotia Publishers, New Delhi. ehani MM (2000). Basis and principles of radiation protection In: Radiation Safety for unsealed sources, OS Pant (Ed), Himalaya Book Depot· Mumbai pp 121·128.

RADIATION SAFETY IN NUCLEAR MEDICINE K.S. Kini

Introd uction Nuclear Medicine is concerned with the applications of unsealed, short-lived radioisotopes in medical diagnosis and therapy. Diagnostic nuclear medicine studies can be classified into three categories viz. (a) In-vitro tests, (b) In-vivo non-imaging procedures and (c) In-vivo imaging procedures, depending on the type of work carried and information obtained. Because of the ionising property of radiations emitted by radioisotopes, their use is associated with potential radiation hazards to the persons handling them, the patients to whom they are administered and the environment to which a part of the used activity is released. However, these hazards can be quantified and minimised so that they can be effectively used in the human health care programme. In this article radiation safety requirements in a diagnostic nuclear medicine laboratory are dealt with. Principles of radiation protection The philosophy of radiation protection is described by International Commission on Radiological Protection (ICRP) in three basic principles, viz. Justification, Optimisation and Dose limitation. The risks involved in the administration of radioactive material in nuclear medicine must be weighted against the benefits which the patient seems likely to gain from it in terms of health and well-being. In relation to radiation exposure from a particular practice, except for therapeutic medical exposure, protection and

Radiation Safety in Nuclear Medicine

221

safety shall be optimised so that the magnitude of individual doses, the number of people exposed and the likely-hood of incurring exposures be kept as low as reasonably achievable, economic and social factors being taken into account. The dose to individuals shall not exceed the limit prescribed by the/national regulatory authority of the respective country. However, no limits have been prescribed for medical exposure. In India, the regulatory powers rest with the Atomic Energy Regulatory Board. Based on the principles stated in the 1990 ICRP recommendations, the International Atomic Energy Agency (lAEA) has brought out a Safety Series(No.115) on Basic Safety Standards(BSS) for protection against ionising radiation and for the safety of radiation sources. The BSS has dealt in detail with many aspects of use of ionising radiation, such as occupational exposure, medical exposure, public exposure, potential exposure (safety of sources), emergency exposure situations and chronic exposure situations. To ensure radiation safety, the BSS has stated the responsibilities at various levels, viz. the Regulatory Authority to enforce certain standards, the Licensee to implement these standards at each level of the practice with the help of Radiation Safety Officer and other staff involved. The BSS stresses the need to develop a safety culture among the employees so that radiation workers, the patients and the public are effectively protected from hazards of radiation, and the safety of radiation sources is ensured. Nuclear medicine laboratory requirement For safe handling of radioactive materials and performing nuclear medicine procedures efficiently and properly, a planned laboratory with all facilities is essential. It is the responsibility of the institution to give due consideration to this aspect to ensure that the layout plan of the laboratory is approved by the Competent Authority and constructed as per the approved plan. The AERB Safety Code (SC/Med-4) provides all the necessary information for establishing a nuclear medicine laboratory. To ensure that the general public are not affected adversely by the use of radioactive materials, it is desirable that the nuclear medicine laboratory is located away from residential premises, preferably in a corner of a hospital block. Separate rooms should be provided for each of the operations with radioactive materials, such as radioisotope storage, radiopharmacy, decontamination, radioactive wp.Gte storage, dose administration, imaging rooms, etc. In addition, separate waiting area for non-active and active patients with separate toilet facilities, rooms for staff, reception and records, should also be provided in the laboratory. Appropriate area should

222

Statistical and Mathematical Techniques in Nuclear Medicine

be provided for each of these rooms, so that the handling of radioactive materials is done with due care and comport from radiation safety point of view. For a nuclear medicine laboratory, having all diagnostic facilities, the total area recommended is about 200 square metres. The nuclear medicine laboratory should have separate drainage system. For easy decontamination of surfaces, the walls and doors in the laboratory should be painted with hard, washable paint, the floor covered with smooth, non-absorbent material such as linoleum and the work surfaces covered with smooth, nonabsorbent material such as sunmica or stainless steel. The laboratory should be properly illuminated, and the ventilation system should be such that the air flow is from low to high activity areas. If air-conditioning is provided in the laboratory, re-circulation of air should be avoided. Furniture should be kept to the minimum in the laboratory. Normally, in a diagnostic nuclear medicine laboratory there is no necessity of additional structural shielding except where large activities are handled or patients with large activities are made to wait. In such cases, concrete walls of adequate thickness may have'to be constructed in place of brick walls, particularly around the Gamma Camera room. Alternatively, lead sheets of adequate thickness may be used in place of suggested concrete wall to b•.'ing down the radiation levels to within the permissible limits. Protection of staff members From radiation protection point of view of staff members, the nuclear medicine laboratory should have adequate facilities, such as remote handling devices, adequate shielding, fume hood for handling gaseous products or radioactive materials which will give rise to vapourous activity, etc. All members of the staff working in the nuclear medicine laboratory should have personnel monitoring badges. Radiation survey meters and contamination monitors for routine monitoring of work areas and personnel contamination, should always be available in the laboratory. These instruments should be periodically checked for calibration, and their records should be maintained. Decontamination kit containing various items, .such as detergents, EDTA, polythene bags, absorbent papers, tongs, gloves, etc. should be readily available in the department to meet any emergencies involving spillage and contamination. Work practice It is well known that in the use of unsealed sources the

Radiation Safety in Nuclear Medicine

223

potential of internal contamination is more than the external exposure to the personnel working in the department. External exposure can be minimised by adopting appropriate safety measures, such as Time, Distance and Shielding. However, internal contamination, in spite of having adequate handling facilities, is possible if the work practice of the radiation workers is not satisfactory. Good work practice with adequate handling facilities go a long way in keeping the personnel,exposure to much below the limits prescribed by the Competent Authority. Some of the important rules, from radiation safety point view, to be observed in nuclear medicine laboratory are produced below: • Operations with radioactive materials should be carried out in the appropriately designated rooms of the approved nuclear medicine laboratory. • When not in use, radioactive materials should be kept in adequately shielded place of storage assigned exclusively for this purpose. Radiation symbols with appropriate warning inscriptions must be displayed conspicuously outside the nuclear medicine laboratory. • Good housekeeping procedures should be maintained in the laboratory. Special care should be taken to keep the radiopharmaceutical preparation area very clean and in aseptic condition. • All manipulations involving radioactive materials should be conducted in a suitable double tray provided with disposable lining such as polythene. In addition, adequate absorbent material should cover the disposable lining to soak up any possible spill. The absorbent material and the lining should then be treated as radioactive waste. • All radiation workers associated with radioactive materials should wear protective clothing such as laboratory or surgical coats and these coats should not be used outside the radioisotope laboratory, and for this purpose they must be identifiable. • Surgical gloves should be worn while working with radioactive materials. Disposable gloves are preferred for use in a nuclear medicine laboratory. • Pipetting by mouth should never be done in a radioisotope laboratory. • Smoking, eating or winking should not be permitted inside a nuclear medicine laboratory.

224

Statistical and Mathematical Techniques in Nuclear Medicine

Protection of patients Though nuclear medicine procedures are beneficial to patients from medical diagnosis point of view, it is the responsibility of the staff involved in the procedures to ensure that the concerned patient is not subjected to undue radiation dose. Misadministration of radioactivity can cause undue radiation dose to the patient. Misadministration can occu~ in different ways as detailed below: (a) Administration of radiopharmaceutical to a wrong patient (b) Administration of wrong activity (c) Administration of a wrong radiopharmaceutical and (d) Administration through wrong route. To prevent any misadministration, following safety measures are to be taken before the radioactive material is administered: (a) Identify the patient, asking hislher name and history. (b) Measure the activity in a properly calibrated isotope calibrator. (c) Provide proper tags or labels to vials containing the radioactive material and ensure that the correct radiopharmaceutical is drawn in the syringe for administration. . (d) Refer to the case paper of the patient carefully and ascertain the route of administration. In the case of female patients in the reproductive age group, it is necessary to ascertain that the patient is not pregnant. If pregnancy is confirmed, it is desirable to advice alternate diagnostic procedure, if available, or postpone the test until the end of pregnancy, unless immediately necessary from clinical stand point. In the case of a breast-feeding mother, it is necessary to stop breast-feeding for certain period which depends on the radioisotope used, activity administered and the type of procedures carried out. Normally, in the case of diagnostic procedures using 99mTc radiopharmaceuticals, period of interruption of breast-feeding is in the range 0-36 hours. When radionuclide investigations are carried out on children, consideration should be given to reduce the activity depending on the weight of the child. General Medical applications of radionuclides generate certain amount of radioactive waste, in liquid, solid or gaseous form. The major contributors to the radioactive waste are: radioactive material

Radiation Safety in Nuclear Medicine

225

supply vials, disposable syringes and gloves, paper cups, unused radioactive materials, etc. The disposal of radioactive waste so generated should be done as pel' the guidelines given in the Atomic Energy (Safe Disposal of Radioactive Waste) 1987 in which different limits for disposal of radioactive waste in liquid and solid form are prescribed. It is necessary to maintain proper log book containing complete details of radioactive materials received, used and disposed in the waste. Records of area monitoring and any accidents or incidents involving radioactive contamination of surfaces, personnel, etc. and action taken in these cases, should be maintained properly. These records should be presented to the officers from the Regulatory Body as and when they visit the institution for an inspection or radiation protection audit. From the safety point of view of the environment and general public, it is the responsibility of the institution to ensure that safe methods and limits of disposal of radioactive waste are adopted. In order to ensure proper use of radioactive material for the benefit of the patient without any prejudice to the staff and the environment, it is necessary to have a Safety Committee in every institution. This Committee should consist of the Administrator, Nuclear Medicine Physician, Radiation Safety Officer and other persons who are directly or indirectly involved in the use of radioactive materials. Finally, it is the safety culture in the workers and good work practice adopted by them, which will make the use of radioactive material for human health care programme a great success.

References 1.

International Commission on Radiological Protection (lCRP)1990 Recommendations of the International Commission on Radiological Protection- Publication 60.(pergamon Press, New York), (1990)

2.

International Atomic Energy Agency(IAEA)- International Basic Safety Standards for Protection against Ionising Radiation and for the Safety of Radiation Sources- IAEA Safety Series No.115 (1996) Atomic Energy Regulatory Board(AERB), India - AERB Safety Code on Nuclear Medicine Laboratories, SClMed-4.«1989)

3. 4.

K.S.Kini, Planning of Nuclear Medicine Laboratories for Diagnostic and Therapeutic Procedures- Indian Journal of Nuclear Medicine, Vol. 13, No.4(1998)

5.

P.K.Gaur, Radiation Safety of Staff and Public- Indian Journal of Nuclear Medicine, Vol. 13, No.4(1998).

6.

Government of India Gazette Notification - Atomic Energy (Safe Disposal of Radioactive Wastes) Rules, 1987 (1987)

RADIATION SAFETY ASPECTS IN RADIOIODINE THERAPY B. Rajashekhan;ao Radioiodine (1811) is the radionuclide of choice for both diagnosis and therapy in patients with thyroid abnormalities. !~ Nuclear Medicine, it is always essential to be conversant of any forbidden radiation health safety practices and this need is amplified while dealing with therapeutic quantities of radionuclides. Of all the therapeutic procedures dealing with the use of radionuclides, it is easiest to think of 1811, since this is the most widely used unsealed source of radionuclide for treatment of thyroid cancer and hyperthyroidism and carries with it most of the problems associated with therapy applications. During handling of 1811 for therapy, in addition to external irradiation, the risk of internal contamination is also considerably high. Radiation protection in radioiodine therapy therefore requires control of both external exposure and contamination of the medical and paramedical staff, laboratory personnel, family members, visitors and general public. An approved nuclear medicine department, a qualified nuclear medicine physician and a Radiation Safety Officer (RSO) are the prerequisites for,any radioiodine therapy program. Pre-therapy safety considerations Radioiodine (1311) is generally administered orally to the patient. Ideally, the patient should be on an empty stomach at least 1 to 2 hours before and after therapy. This results in an enhanced absorption of 1311 from the stomach due to which the radiation dose to the stomach can be Ihinimized and it also reduces

Radiation Safety Aspects in Radioiodine Therapy

227

the volume ofvomit.us should the patient develop nausea. Prior t.o therapy, the patient should be asked to remove any denture appliances such as removable bridges and dentures. Radioiodine that may adhere to these denture appliances, on removal by the patient. can result in transfer of contamination to surfaces and personnel's. Patients in a non-ambulatory or bed-ridden condition may also be referred for treatment. The radiation safety procedures to be followed in such situations are much more stringent and elaborate. The patient should be catheterized at least 24-48 hours before therapy so that any complication resulting due to the catheter will be observed during this period and it also allows time for the patient to get adjusted to the catheter. If the catheter is introduced just before therapy, then any complications due to it following therapy will result in significant radiation exposure to the physician and nursing staff attending to the patient inside the isolation room. In addition, the patient should be put on liquid or semi-solid diet, at least 24-48 hours before therapy to reduce the bowel activities during the period of isolation, which otherwise can be a source of contamination and exposure. During treatment of neural crest tumors with 13II_MIBG, the patency of the i.v.line should be ascertained before injecting the radiopharmaceutical into the dextrose saline bag. If female patients of thyroid carcinoma in the reproductive age group are undergoing therapy, the details of menstrual history should be obtained to rule out pregnancy. Pregnancy is a contraindication for radioiodjne therapy. Radioiodine administration Radioiodine solutions being highly volatile, require special handling. Administration of 37 KBq (1 !lei) of 1311 results in a radiation dose of about 1.3 cGy (1.3 rad) to the thyroid, based on a 30% thyroid uptake and thyroid mass of 20 gms. While handling large therapeutic quantities of 131I, in addition to the external radiation hazard, the risk of internal contamination is also magnified and thus stringent precautions should be taken to avoid this type of contamination. Nuclear medicine physician and other personnel involved in administration of the activity should wear disposable rubber gloves and protective clothing. Because of the hazards associated with liquid form of 1311, the vial containing 1311 should be always handled inside a well-ventilated fume hood. The identity of the patient requiring therapy and the therapeutic

228

Statistical and Mathematical Techniques in Nuclear Medicine

dosage, should be ascertained at the time of therapy. The three cardinal principles of time, dist.ance and shielding should be effectively implemented to keep the personnel exposure as low as reasonably achievable. To restrict spread of contamination, one should place absorbent papers on the edge of the fume hood and on the floor with a PVC sheet beneath, prior to starting of the treatment procedure. The patient should be instructed about the precautions to be taken while drinking the radioactivity. The vial containing the 1311 solution should be placed inside a lead pig and decapped within the fume hood. The vial after decapping should be diluted with water so that in case the patient accidentally coughs or spills 1311 while drinking, the droplets will not be too concentrated. The patient should never be allowed to handle the vial containing 1311. After patient has taken 1311, water should once again be added to the vial to ensure that all the 1311 is administered. This to certain extent decontaminates the vial and straw. Following this, the patient should be given water in a disposable paper cup to wash down the oral activity into the stomach. If the treatment has to be given inside the patients isolation room, as done in case of non-ambulatory patients, care must be taken in transporting the radionuclide to the room to prevent spillage and exposure to the personnel involved. After completion of treatment procedure, all personnels involved should be monitored for contamination. The treatment form must be completed and an entry made in the patient's case me by the nuclear medicine physician. The RSO should maintain a record of exposure-rate readings after treatment. Post-therapy safety considerations A patient who has been administered more than 1.1 GBq (30 mCi) of 1311 is generally hospitalized in an isolation room. There are two main reasons for isolating the patient. Firstly, the patient is a source of significant radiation exposure to the occupational staff, family members and visitors. Secondly, there is a major risk of contamination from urine, saliva and perspiration especially in the first 24-48 hours (Ibis et a!. 1992, Nishikawa et a!. 1980, Jacobson et a!. 1978). Also, there are added complications like patient feeling nauseated and vomiting, which are best dealt with under supervision, during the period of isolation. If a patient is receiving radioiodine therapy for the first time, the term 'isolation' should be carefully explained to the patient. To the patient, it may mean that there will be no communication between him/her and hospital personnel or family members during

Radiation Safety Aspects in Radioiodine Therapy

229

the period of isolation. The patient should be reassured that both nuclear medicine physician and nursing staff will be communicating as and when required. The patient should be advised that. routine nursing care would be kept to a minimum essential. However. it is appropriate to reassure the patient that any neceSt-iary medical or nursing care during the isolation period will be provided. The patient may sense a feeling of abandonment or rejection during the isolation period. These feelings may get compounded. as the visiting of the family members. relatives and friends also must be restricted. Ideally, the patient should be informed about what is e:ll.-pected of him/her during the isolation period. Patient co-operation is very much essential if radioactive contamination and external radiation exposure to the medical, paramedical, nursing st.aff and visitors are to be minimized. Nursing care All nursing staff should be familiar with various radiation safety procedures involved during treatment procedures. They should be provided with personnel monitoring badges. Pregnant nurses should not be allowed to work in a therapy ward. Any medication, food etc. provided to the patient is across the shoe barrier. However, the staff should be instructed to spend minimum time in direct contact with the patient. During the period of isolation, routine blood or urine sampling in the first 48 hours after therapy should be strictly avoided, to prevent contamination of the laboratory. If it is essential for these samples to be tested, they may be performed in consultation with RSO. In case of any medical and/or radiation related emergency, the nursing staff should have list of names and addresses with telephone numbers (both home and workplace) of the nuclear medicine physician and RSO, and should contact them immediately in such situations. Visitors The visitors must follow instructions of the nursing staff as per the RSO or nuclear medicine physicians orders as to duration of visit and restrictions on distance from the patient. It is understood here that the visitor will not be entering the isolation room and will abstain from physical contact with the patient. Children and pregnant women should not be allowed to visit the patient. Patient Monitoring and Discharge Criteria At Radiation Medicine Centre, we routinely measure the exposure-rate over the surface of the neck, metastatic site, stomach,

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thigh and at I-meter distance from the patient, using an ionization chamber type of radiation survey meter.. Surface exposure rate measurement enables one to know whether there is a desired concentration of 1311 in the tissues or not. A record ~f exposurerate measurements made at different time periods, especially the I-meter reading, will be useful in determining the date and conditions of discharge. The limit at which the patient can be discharged varies from country to country. As per the lAEA Basic Safety Standards, an activity of 1.1 GBq (30 mCi) of 1311 is specified as the discharge limit (lAEA, 1996). In India, the patient is released from the hospital, when the whole body 1311 activity is less than or equal to 555 MBq (15 mCi), a limit stipulated by AERB (1989). For an adult patient, 1.1 GBq (30 mCi) of 1311 retained in the body corresponds to an exposure-rate of about 50-60 (Sv/h (5-6 mRlh) at a distance of I-metre. At the time of discharge, the patient should be given instructions on radiation safety and hygiene. The patient should be advised to keep safe distances from pregnant women and small children. The objective of retaining the patient in the hospital till the activity has fallen below the recommended level is to minimize the radiation risk to the general public and family members (Rajashekharrao and Samuel 1999). Nursing mothers should strictly avoid breast-feeding the child for a time period (at least 4 weeks) suggested by the nuclear medicine physician. Optimisation of radiation dose to non-target tissues Radiation dose to the stomach can be minimized, by treating the patient on an empty stomach. As indicated earlier, it not only enhances absorption of 1311, but also considerably reduces the dose to the stomach. Salivary gland concentrates 1311 and sialedinitis is one of the acute complications resulting from therapy. Patients' during the first two days of therapy should be asked to chew lemon or any agent that increases salivation. Excessive salivation results in accelerated clearance of 1311 from salivary tissue, thus minimizing the radiation dose to the tissue. Radioiodine is primarily excreted through urine and therefore the kidneys, bladder and gonads are likely to get significant radiation dose. The patient should be asked to drink plenty of fluids and void as frequently as possible. Frequent hydration and voiding will minimize the radiation dose delivered to the kidneys, bladder and more importantly the gonads. Lactating breast concentrates 1S11 and therefore to minimize

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the dose to the breast tissue, the patient should be encouraged to suck (l11t the milk either manually or using a breast pump. It is the responsibility of the physician to advocate measures to be taken by the patients so that the exposures to the non-target tissues are kept as low as reasonably achievable. Radioactive waste management Radioactive wastes generated during radioiodine therapy generally are in the form of solid or liquid and mainly result from remains of administered radioactivity, patient's excretions, vomitus, contaminated laundry, contaminated syringes, needles, vials, gloves, contaminated accessories etc. The three main practices of radioactive waste disposal are (£) delay and decay (ii) dilution and dispersion and (ii£) concentration and containment. Liquid waste Disposal of radioactive waste in public domain shall be undertaken only in accordance with Atomic Energy Rules (Safe Disposal of Radioactive Wastes) 1987. The radioactive effiuents must be soluble or dispersible in water and the concentration and total quantity of the liquid radioactive wastes disposed should not exceed the limits specified by AERB (1989). In patients of thyroid carcinoma given 1311 therapy, the major route of excretion of 1311 is through urine. Depending on the uptake of 1311 in the remnant thyroid and/or metastatic tissue, the amount of 1311 excreted will vary. Significantly large amount of 1311 (70-80%) is excreted in the urine in the fIrst 48 hours following therapy. Hence the patient should be instructed to flush the toilet three or four times after use to ensure removal of radioactivity. The effiuents originating from the isolation room should not be released directly into the public sewerage as the activity concentration in the effiuent will be very high and there is always a possibility of contamination or exposure to the public resulting from such releases. Ideally all effiuents from 1311 treated patients should be collected in a purposebuilt delay tank. The entire drainage system of the isolation room should be directly connected to the delay tank. The plumbing lines should have minimum number of bends and should be connected to the tank by shortest possible stretch. The plumbing lines should be of a non-corrosive material like PVC. The delay tank should have sufficient shielding and fencing and should be absolutely leak proof in order to avoid con:.amination of the Sf'i! and ground water. Inside the tank, the effiuents in addition to dilution also radioactive decay and it is finally released into the public sewerage only when the activity concentration is less than the limit specified by AERB (1989).

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Solid Waste Solid radioactive wastes that are generated may be buried in pits locally. An exclusive burial ground for the solid radioactive waste should be located in an isolated area, which is duly fenced off. The site of such a burial ground would be governed such as nature of environment and the assessed anticipated risk of accidental dispersal of the waste back into the environment. Disposal limits for ground burial of solid wastes should not exceed that specified by AERB (1989). Because of presence of radioactivity in the salivary secretions, eating utensils may get contaminated during use by the patient. The patient should preferably use disposable type of utensils. If not, then they should be instructed to wash the utensils thoroughly with soap and water after every meal. However, such utensils should be monitored and decontaminated before any reuse. In addition to the routes viz. urine and saliva, 1311 is also excreted in sweat. As a result, the patients clothing, bed linen etc. get heavily contaminated and such contaminated laundry should not be released for washing. It should be collected as radioactive waste. In a center like ours where several patients are being treated routinely, it may not be feasible to dispose of contaminated clothings. Instead the procedure adopted is packing such contaminated laundry in a polythene bag and storing it in a radbactive waste storage room for a period of up to 3 months by which time almost 10 half-lives are over and radioactivity has decayed to negligible levels. After confIrming by contamination monitoring that there is no radioactivity present, these clothings then are released for washing. Radiation Emergencies and Accidents In any radionuclide therapy procedure, there is always a possibility of some radiation related emergency or accident occurring. To handle such situations, an emergency preparedness program should be available in the institute. The emergencies that one may foresee during 1311 treatment of thyroid carcinoma are spillage, misadministration and death of the patient. A decontamination kit should always be available in the treatment room in order to deal with the contamination resulting from spillage. All efforts should be made to restrict spread of contamination. Misadministration is considered to have occurred if any of the following has taken place;

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(a) Administration of a radionuclide other than the one intended (b) Administration of a radionuclide to the wrong patient (c) Administrat.ion of a radionuclide by the wrong rout.e (d) Administration of an amount of therapeutic activity far in excess of that desired. These situations can be avoided by properly ensuring the identity of the radionuclide, the patient. the route of administration and performance of the isotope calibrator. Death of a patient after treatment is also a radiation emergency. However, meticulous pre-planning for this eventuality is important. The regulation governing the disposal of cadavers containing radioactivity varies from country to country. In our country, guidelines provided by AERB on safe disposal of cadavers are applicable (AERB, 1989). No special precautions are normally necessary for cremation, burial or post-mortem/embalming, if the corpse contains 131 1 activity less than 400 MBq, 400 MBq and 10 MBq respectively (AERB, 1989). However, if the dead body contains activity higher than this, then depending upon whether cremation, burial, autopsy or an embalming procedure is to be carried out, the precautions and restrictions undertaken will vary. During cremation, prior authorisation and specific safety precautions to be followed must be obtained from RSO. In case of burial, relatives should be prevented from coming in contact with the cadaver and people must be at a distance from the coff'm. The RSO shall recommend methods on dose reduction to the personnel involved in washing, preparing and transporting the body to the burial ground. The cadaver should be handled with disposable gloves and kept on plastic sheets to control spread of contamination. If an autopsy is being performed, the RSO should supervise the proceedings. It is important that the autopsy physician know that he is dealing with a cadaver containing radioactivity and therefore body fluids should be treated as cQntaminated and perhaps 1311 concentrating tissues be removed during the autopsy to avoid unnecessary radiation exposure. During post-mortem or embalming all contaminati,9ll control measures should be adopted under the guidance and supervision of the RSO.

Thyroid monitoring and Bioassay procedures The potential hazard for 1311 intake by the occupational radiation workers in a nuclear medicine department has been very well recognised and appreciated. Evaluation of 1811 intake by

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a nuclear medicine personnel is performed either by thyroid counting or bioassay procedure. These procedures should be periodically carried out as they demonstrate the complian~e of the radiation worker with various safety regulations, and confIrms the containment of 1311 during treatment procedures and most importantly assures the radiation worker that they are receiving adequate protection.

Conclusions In any radionuclide therapy program, by implementing proper radiation safety measures, the radiation exposure to the patient, nuclear medicine physician, nurses, staff and public can be kept as low as reasonably achievable. References 1.

2.

3.

4.

5.

6.

Atomic Energy Regulatory Board (1989) AERB Safety Code for Nuclear Medicine Laboratories (AERB Code No. SCIMED-4). Ibis E, Wilson CR, Collier BD, Akansel G, Isitman AT, Voss RG (1992) Iodine-131 contamination from thyroid cancer patients. J Nucl Med 33, 2110-2115. International Atomic Energy Agency (IAEA) (1996) International basic safety standards for protection against ionising radiation and for the safety of radiation sources. Safety Series No. 115. Jacobsen AP, Plato PA, Toeroek D (1978) Contamination of the home and environment by patients treated with iodine131: initial results. Am J Public Health 68, 225-230. Nishisawa K, Ohara K, Ohshima M, t,iaekoshi H, Orito T (1980) Monitoring of iodine excretion ~nd used materials of patients treated with 1-131. Health Phys 38, 467-481. Rajashekharrao B., Samuel AM (1999) Radiation safety procedures in radioiodine therapy for thyroid cancer. In: Thyroid cancer: An Indian perspective, Shah DH, Samuel AM & Rao RS (eds.), Radiation Medicine Centre & Quest Publications, Mumbai, Chapter 20, pp 297-306.

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