Question 1

The gamma camera seems to be producing erratic results. A ⁵⁷Co flood source is counted 10 times, producing the following count values: 1000, 975, 1032, 1096, 982, 997, 1012, 1090, 994, 977. What is the chi-square value for these counts?

Accepted Answer

Too little or too much variation in repeat measurements indicates equipment may not be functioning properly. The chi-square test is used to determine an acceptable range of variability in the repeat measurements. The mean 11eb66b8_6383_0ae3_b33b_e96c86484820_TB8318_00 of the 10 measurements is determined (11eb66b8_6383_0ae2_b33b_c5d5c1151216_TB8318_00 = $\Sigma$C/n), and chi-square is calculated as:
11eb66b8_6383_31f4_b33b_3513a743cb9e_TB8318_00

Question 2

How many counts should be acquired into each pixel of a nuclear medicine flood image if it is desired to be 95% confident that the true count in each pixel is within 1% of the measured counts in each pixel?

Accepted Answer

Counting statistics, besides being Poisson, are also described by a Gaussian distribution as long as the number of counts is greater than about 30. Hence, given some number of counts C, the standard deviation is automatically known. It is also known that 68% of repeat measures of the sample fall within C ± 11ecdbf6_8faa_415e_9c9e_798b89e62bda_TB8318_11 and 95% of repeat measures of the sample fall within C ± 11eb66b8_6382_bcbb_b33b_b11e69c6ff92_TB8318_00 and so on (95% confidence = C ± 2$\sigma$_c = C ± 11eb66b8_6382_bcba_b33b_8f5547c23ef1_TB8318_00 Sometimes this type of problem is expressed by saying that a certain number of counts are needed to be 95% confident that the true count is within 2% of the measured value. The presence of two different percentage values can seem confusing. The 95% confidence interval on 10,000 counts is ±200 counts, and this figure of 200 counts represents 2% of 10,000 counts. The general formula expressing the number of counts needed to be "n$\sigma$" sure that the true answer is within some percent (p) of the measured counts is given by: 11eb66b8_6382_bcbc_b33b_8b044ea36864_TB8318_00 In this formula, n is replaced with a 1 for 68% confidence, a 2 for 95% confidence, and a 3 for 99% confidence.

Question 3

A patient was injected with ¹³¹I on Monday at 10:00 AM. On Tuesday at 10:00 AM, the thyroid probe was placed over the thyroid and produced 100,000 counts. On Thursday at 10:00 AM, the probe showed 25,000 counts. What is the effective half-life in this patient's thyroid?

Accepted Answer

Typically the patient's organ excretes the radiopharmaceutical with some biologic half-life t_B while the radioactivity also decays physically with a physical half-life that is denoted as t_P.The counts observed by the gamma camera follow an exponential decay law based on the effective half-life t_E, where:11ecdbf5_f04c_116d_9c9e_5f3f02cb4c28_TB8318_11 or, in a format that is much easier for calculation purposes, 11eb66b8_6382_2075_b33b_f9aaf3bf41bf_TB8318_00. The effective half-life is always less than or equal to the smaller of t_P or t_B.

Question 4

A ⁹⁹Mo-^99mTc generator is eluted Monday at 7:00 AM, producing 1.8 Ci of ^99mTc in the eluate vial, in 20 ml saline. What volume of eluate should be withdrawn from the eluate vial into a syringe in order to inject a patient with 20 mCi of ^99mTc at 3:00 PM? (Given the half-life of ^99mTc is 6.02 hours.)

Accepted Answer

The radioactive decay law can be algebraically rearranged (dividing both sides of the decay equation by A₀) as: 11eb66b8_6382_4786_b33b_1db392b78732_TB8318_00. After solving for the half-life, the concentration (radioactivity per volume) in the eluate vial is then determined and the volume needed to be withdrawn into the syringe can be calculated from the equation activity = concentration * volume: A = C * V.

Question 5

Which expression describes the operation of the gamma camera in question 16?

Accepted Answer

The definition of acceptable chi-square is given by looking up the probability (P) of this chi-square value for the n repeated measures in a table. Too little variation is shown by a chi-square smaller than the P = 0.9 value; an amount of variation exactly as expected from the statistical nature of the decay process would yield P = 0.50; and an unacceptably large chi-square would yield a P value greater than 0.10. So, P = 0.90-0.10 range is acceptable.

Question 6

A new gamma camera/computer system that uses a new method of calculating cardiac ejection fraction (EF) is installed in a nuclear medicine department. The department decides to calculate EF for the next 25 patients on both the old gamma camera and the new gamma camera before discontinuing the use of the old camera. In the future, if it is desirable to convert the new EF value to that which would have been obtained on the old gamma camera (e.g., to assess if the patient's EF had changed), the mathematical analysis to be used is called a(n)

Accepted Answer

The least squares method, or linear regression, calculates the best-fit values for y-intercept (a) and slope (b) in the best-fit straight line: y = a + bx. The line of identity is often drawn on regression graphs when the same parameter, here the ejection fraction, is being plotted on both the x and y axes. The line of identity facilitates an evaluation of whether the two methods (the x and y axes) are predicting the same result for ejection fraction. If the two methods produce the same value for ejection fraction, then the regression line should be the same as the line of identity.

Question 7

If the HVL for some radionuclide in lead is 0.30 mm, what thickness of lead shielding is necessary to reduce the radiation exposure from 8 mR/hr to 1 mR/hr?

Accepted Answer

It is common to follow the method used in radioactive decay and define a half-value layer (HVL) as that thickness of material that absorbs 50% of the photons. The HVL is the analog of t_/2in radioactive decay. One HVL transmits 50% of the photons. The equation of photon attenuation then can be expressed as: I = I₀e^- ^$\mu$ ^x = I₀e^-0.693 ^* ^(x/HVL) and a relationship exists between $\mu$and HVL, given by $\mu$ = 0.693/HVL. Remember the units of x and HVL must be the same, and remember that this equation calculates the transmitted intensity.

Question 8

The linear attenuation coefficient in lead for ^99mTc gamma rays (140 keV) is 23 cm^-1. What percentage of these gamma rays will be absorbed by a lead apron that contains 0.60 mm of lead?

Accepted Answer

The intensity of the transmitted radiation is given by: I = I₀e^- ^$\mu$ ^x where $\mu$is the linear attenuation coefficient, or the fraction of the beam absorbed in some (very small) thickness x. The linear attenuation coefficient $\mu$ is the analog of the decay constant $\lambda$ in radioactive decay. The linear attenuation coefficient $\mu$ depends on the type of absorbing material and the energy of the photons.

Question 9

A ⁹⁹Mo-^99mTc generator is calibrated for 1.00 Ci of ⁹⁹Mo at 7:00 AM Monday. The generator is eluted daily Monday through Friday at 8:00 AM, but the workload is especially heavy on Friday so the generator is eluted again at 3:00 PM to obtain more ^99mTc. Assuming 100% elution efficiency, how many mCi of ^99mTc will be eluted at 3:00 PM Friday?

Accepted Answer

The ^99mTc radioactivity expected to be eluted from the generator can be calculated by knowing three values: (1) the activity of ⁹⁹Mo in the generator, (2) the time since the last elution of the generator, and (3) the ratio of ^99mTc to ⁹⁹Mo in the generator. Using the equation, A = Ci *e ^-0.693 ^- ^{(t/65.9 hr)}, enter in the known values and solve for the unknown.

Question 10

The radiation intensity from a point source of ^99mTc is 9 mR/hr at 3 m from the source. If the distance is changed to 9 m, what is the new radiation intensity?

Accepted Answer

The inverse square law results in the radiation intensity quadrupling if the distance from the source is halved, or it results in the radiation intensity decreasing to one fourth of its value if the distance is doubled.

Question 11

20 mCi is equal to how many becquerels?

Accepted Answer

1 curie = 3.7 * 10¹⁰ disintegrations per second [dps], and in SI units 1 Bq = 1 dps; therefore, 1 Ci = 37 GBq and 1 mCi = 37 MBq. In this problem, activity in Bq = 11eb66b8_6381_f961_b33b_45b917abafca_TB8318_00

Question 12

The dose equivalent for occupational whole-body exposure is commonly limited to 50 mSv. How many rem is this?

Accepted Answer

To convert the dose equivalent in the new SI units of 1 cSv into the old unit of rem:
Dose equivalent = 11eb66b8_6381_f962_b33b_572edc373f19_TB8318_00

Question 13

A patient's thyroid is counted with the thyroid probe and produces 8000 counts. Then the patient is removed and background is found to be 2000 counts. The (net counts) ± (standard deviation in the net counts) in this patient is

Accepted Answer

Background counts are a problem in most measurements of counts from a radioactive sample. Background arises from natural terrestrial and cosmic sources of radioactivity or from other nearby sources of radioactive material. The sample is usually counted in the presence of some background radiation, yielding a gross count for sample plus background, denoted by the letter C. The sample is then removed from the counter, and the background B is counted. The net, or true counts, which represents the sample only, is denoted by N and given by:
N = C - B
The standard deviation of the net counts is given by:
 11eb66b8_6382_e3cd_b33b_0762b1169e39_TB8318_00 This is an example of the rules for combinations of errors, which states that for addition or subtraction, errors add in quadrature within the square root:
 11eb66b8_6382_e3ce_b33b_3b8293e4321f_TB8318_00 Additionally, since
11eb66b8_6382_e3cf_b33b_0ddef0b5fca0_TB8318_00 and 11eb66b8_6382_e3d0_b33b_6787a7a69303_TB8318_00 we obtain
 11eb66b8_6382_e3d1_b33b_e12f8d9ffb17_TB8318_00

Question 14

What is the coefficient of variation of 40,000 counts?

Accepted Answer

The standard deviation can be expressed as a percentage of the mean value, which is frequently called the percent standard deviation, or coefficient of variation (CV):
 11eb66b8_6382_95a8_b33b_657240e74292_TB8318_00 In this problem, the counts would be substituted for the mean in the equation.

Question 15

A source of  is delivered to the nuclear medicine department calibrated for 100 mCi at 8:00 AM on Monday. If this radioactivity is injected into a patient at noon on Tuesday, what radioactivity will the patient receive?

Accepted Answer

Solving the differential equation yields the radioactive decay law: A = A₀e^- ^$\lambda$ ^t where A = activity at time t, A₀ = activity at starting time, $\lambda$ = decay constant, t = time since starting time. The decay constant $\lambda$ is the fraction of atoms that decay per (small) time interval, and has units of 1 over time (e.g., 1/hr) or inverse time (hr^-1). The typical radioactive decay calculation required in nuclear medicine specifies three of the four variables (A, A₀, $\lambda$, t) in the decay equation, requiring that the fourth unknown variable be solved for.

Question 16

A nuclear medicine test produces a positive test result in only 80 of the 100 patients known to be ill. Similarly, the test produces a negative test result in only 190 of the 200 patients known to be not ill. Which is correct?

Accepted Answer

The sensitivity, or true positive fraction (TPF), is the percentage or fraction of ill patients who have a positive test:
 11eb66b8_6383_5906_b33b_39af286addb1_TB8318_00 The specificity, or true negative fraction (TNF), is the percentage or fraction of well patients who have a negative test:
 11eb66b8_6383_5907_b33b_d5b614c26e5b_TB8318_00 The prevalence is the fraction or percentage of ill persons in the study population:
 11eb66b8_6383_5908_b33b_4b1cf4a9861c_TB8318_00

Question 17

One group of 20 patients is given a drug that is thought to have an effect on kidney function, and another group of 20 patients is given a placebo (i.e., sugar pill, which is known not to have an effect on kidney function). The nuclear medicine gamma camera is used to calculate the glomerular filtration rate (GFR) in these two groups of patients. What would be the proper statistical test to use to test the hypothesis that no difference in GFR exists between these two groups of patients?

Accepted Answer

The t-test is used to test for differences between mean values. The two forms of the t-test are for independent samples and paired samples. For independent t-tests, two independent groups of data are used. The two groups are completely independent. No relationship or correlation exists between the two groups, typically because the groups represent different patients. The two groups have mean and standard deviations denoted by 11ecdbf6_ed79_e92f_9c9e_6bac6534d8c3_TB8318_11, SD₁,11ecdbf6_fb5f_7e60_9c9e_056f132f3ade_TB8318_11 , and SD₂. 11eb66b8_6383_31f5_b33b_3f83ecbc14bf_TB8318_00

Question 18

One radiologist is known to be a lax reader compared with another radiologist who is known to be a strict reader. In comparing these radiologists, how would one expect their sensitivity and specificity to compare?

Accepted Answer

The sensitivity, or true positive fraction (TPF), is the percentage or fraction of ill patients who have a positive test:
 11eb66b8_6383_8019_b33b_03cb92db7b0e_TB8318_00 The specificity, or true negative fraction (TNF), is the percentage or fraction of well patients who have a negative test:
 11eb66b8_6383_801a_b33b_2378fb0901af_TB8318_00 For an example, data that show a sensitivity of 78%, less than the specificity of 95%, mean that this test does a better job at correctly diagnosing well people than it does at correctly diagnosing ill people. High sensitivity = correctly finding ill people; high specificity = correctly finding well people.

Question 19

What is the standard deviation of 40,000 counts?

Accepted Answer

Counting statistics, meaning the number of counts expected from a sample, follow the Poisson distribution. In the Poisson distribution, the standard deviation ($\sigma$_C) for any number of counts (C) is fixed at the square root of C: 11eb66b8_6382_95a7_b33b_9fd2763a3577_TB8318_00 This fixed definition of standard deviation does not exist in Gaussian distributions; essentially only counting statistics are Poisson.

Question 20

A radioactive source of ¹³⁷Cs (t_1/2= 30 y) was calibrated on October 23, 2000, to contain 10 $\mu$Ci. This is used as a daily accuracy check source in the dose calibrator. Presuming the dose calibrator is working properly, what activity should the dose calibrator show on April 23, 2006?

Accepted Answer

The radioactive decay law can be algebraically rearranged (dividing both sides of the decay equation by A₀) as A/A₀ = e^-0.693 ^* ⁽^t/t_1/2⁾.

Quiz 1: Mathematics and Statistics

The gamma camera seems to be producing erratic results. A ⁵⁷Co flood source is counted 10 times, producing the following count values: 1000, 975, 1032, 1096, 982, 997, 1012, 1090, 994, 977. What is the chi-square value for these counts?

How many counts should be acquired into each pixel of a nuclear medicine flood image if it is desired to be 95% confident that the true count in each pixel is within 1% of the measured counts in each pixel?

A patient was injected with ¹³¹I on Monday at 10:00 AM. On Tuesday at 10:00 AM, the thyroid probe was placed over the thyroid and produced 100,000 counts. On Thursday at 10:00 AM, the probe showed 25,000 counts. What is the effective half-life in this patient's thyroid?

Which expression describes the operation of the gamma camera in question 16?

If the HVL for some radionuclide in lead is 0.30 mm, what thickness of lead shielding is necessary to reduce the radiation exposure from 8 mR/hr to 1 mR/hr?

The linear attenuation coefficient in lead for ^99mTc gamma rays (140 keV) is 23 cm^-1. What percentage of these gamma rays will be absorbed by a lead apron that contains 0.60 mm of lead?

The radiation intensity from a point source of ^99mTc is 9 mR/hr at 3 m from the source. If the distance is changed to 9 m, what is the new radiation intensity?

20 mCi is equal to how many becquerels?

The dose equivalent for occupational whole-body exposure is commonly limited to 50 mSv. How many rem is this?

A patient's thyroid is counted with the thyroid probe and produces 8000 counts. Then the patient is removed and background is found to be 2000 counts. The (net counts) ± (standard deviation in the net counts) in this patient is

What is the coefficient of variation of 40,000 counts?

A source of is delivered to the nuclear medicine department calibrated for 100 mCi at 8:00 AM on Monday. If this radioactivity is injected into a patient at noon on Tuesday, what radioactivity will the patient receive?

A nuclear medicine test produces a positive test result in only 80 of the 100 patients known to be ill. Similarly, the test produces a negative test result in only 190 of the 200 patients known to be not ill. Which is correct?

One radiologist is known to be a lax reader compared with another radiologist who is known to be a strict reader. In comparing these radiologists, how would one expect their sensitivity and specificity to compare?

What is the standard deviation of 40,000 counts?

A radioactive source of ¹³⁷Cs (t_1/2= 30 y) was calibrated on October 23, 2000, to contain 10 $\mu$ Ci. This is used as a daily accuracy check source in the dose calibrator. Presuming the dose calibrator is working properly, what activity should the dose calibrator show on April 23, 2006?

Quiz 1: Mathematics and Statistics

The gamma camera seems to be producing erratic results. A 57Co flood source is counted 10 times, producing the following count values: 1000, 975, 1032, 1096, 982, 997, 1012, 1090, 994, 977. What is the chi-square value for these counts?

How many counts should be acquired into each pixel of a nuclear medicine flood image if it is desired to be 95% confident that the true count in each pixel is within 1% of the measured counts in each pixel?

A patient was injected with 131I on Monday at 10:00 AM. On Tuesday at 10:00 AM, the thyroid probe was placed over the thyroid and produced 100,000 counts. On Thursday at 10:00 AM, the probe showed 25,000 counts. What is the effective half-life in this patient's thyroid?

Which expression describes the operation of the gamma camera in question 16?

If the HVL for some radionuclide in lead is 0.30 mm, what thickness of lead shielding is necessary to reduce the radiation exposure from 8 mR/hr to 1 mR/hr?

The linear attenuation coefficient in lead for 99mTc gamma rays (140 keV) is 23 cm-1. What percentage of these gamma rays will be absorbed by a lead apron that contains 0.60 mm of lead?

The radiation intensity from a point source of 99mTc is 9 mR/hr at 3 m from the source. If the distance is changed to 9 m, what is the new radiation intensity?

20 mCi is equal to how many becquerels?

The dose equivalent for occupational whole-body exposure is commonly limited to 50 mSv. How many rem is this?

A patient's thyroid is counted with the thyroid probe and produces 8000 counts. Then the patient is removed and background is found to be 2000 counts. The (net counts) ± (standard deviation in the net counts) in this patient is

What is the coefficient of variation of 40,000 counts?

A source of is delivered to the nuclear medicine department calibrated for 100 mCi at 8:00 AM on Monday. If this radioactivity is injected into a patient at noon on Tuesday, what radioactivity will the patient receive?

A nuclear medicine test produces a positive test result in only 80 of the 100 patients known to be ill. Similarly, the test produces a negative test result in only 190 of the 200 patients known to be not ill. Which is correct?

One radiologist is known to be a lax reader compared with another radiologist who is known to be a strict reader. In comparing these radiologists, how would one expect their sensitivity and specificity to compare?

What is the standard deviation of 40,000 counts?

A radioactive source of 137Cs (t1/2= 30 y) was calibrated on October 23, 2000, to contain 10 μ\muμ Ci. This is used as a daily accuracy check source in the dose calibrator. Presuming the dose calibrator is working properly, what activity should the dose calibrator show on April 23, 2006?

The gamma camera seems to be producing erratic results. A ⁵⁷Co flood source is counted 10 times, producing the following count values: 1000, 975, 1032, 1096, 982, 997, 1012, 1090, 994, 977. What is the chi-square value for these counts?

A patient was injected with ¹³¹I on Monday at 10:00 AM. On Tuesday at 10:00 AM, the thyroid probe was placed over the thyroid and produced 100,000 counts. On Thursday at 10:00 AM, the probe showed 25,000 counts. What is the effective half-life in this patient's thyroid?

The linear attenuation coefficient in lead for ^99mTc gamma rays (140 keV) is 23 cm^-1. What percentage of these gamma rays will be absorbed by a lead apron that contains 0.60 mm of lead?

The radiation intensity from a point source of ^99mTc is 9 mR/hr at 3 m from the source. If the distance is changed to 9 m, what is the new radiation intensity?

A radioactive source of ¹³⁷Cs (t_1/2= 30 y) was calibrated on October 23, 2000, to contain 10 $\mu$ Ci. This is used as a daily accuracy check source in the dose calibrator. Presuming the dose calibrator is working properly, what activity should the dose calibrator show on April 23, 2006?