2015 Ph.D. Comprehensive Examination III. Radiological Sciences - Medical Physics

Transcription

1 January Ph.D. Comprehensive Examination III Radiological Sciences - Medical Physics In this three-hour exam, you are required to answer all of the questions in Part A and any two (2) out of the four (4) problems in Part B. Use one answer book for Part A and one answer book for each of the problems of Part B. Please make sure that your name is on the answer books, that each problem is clearly numbered, and that your final answers (with correct units and number of significant figures) are highlighted by framing or circling. Be certain that you have done all of the short answer questions in Part A, choosing only one answer for each question. Answer no more than two problems from part B (if you offer more than two problems from Part B, only the first two will be graded). Partial credit will be awarded for Part B, but only if you document your work on these two problems in a legible and logical manner (defining variables, declaring assumptions, consolidating units, etc.). The last page contains some useful constants and equations. 1 of 12

2 Part A: Short Answer Questions (Obligatory) 1. Which of the following statements is false regarding exposure and dose to air or soft tissue? a. The mass energy absorption coefficients (μ en /ρ) for air and soft tissue are approximately equal over a broad range of photon energies. b. The definition 1 R / !4 C kg!1 establishes an approximate equality between exposure in the unit of roentgen and dose to soft tissue under the condition of charged particle equilibrium and in units of rad or rem. c. Exposure in the unit of roentgen is a factor of 1.14 greater than the dose to air under the condition of charged particle equilibrium and in the unit of rad. d. The average energy required to produce one coulomb of charge in dry air is 33.7 J. e. Exposure is defined for any form of uncharged ionizing radiation that can produce ion pairs in air Na decays by beta plus decay and emits a positron with a maximum energy of 0.81 MeV and a gamma ray. 22 Na (BE = MeV) decays to 22 Ne (BE = MeV). What is the energy of the gamma ray? a MeV b MeV c MeV d MeV e MeV 3. For equal fluence rates incident on the human body, which of the following radiations will produce the largest dose rate to the skin? a. 2 MeV photons b. 1 MeV beta particles c. 5 MeV alpha particles d. Thermal neutrons e. 40 kev recoil nuclei 2 of 12

3 Part A: Short Answer Questions (Obligatory) 4. Which of the following statements is false regarding the penetration of broad, parallel beams of charged particles in soft tissue? a. Most of the dose for heavy charged particles is delivered near the end of their track. b. A plot of dose vs. depth for heavy charged particles will produce a Bragg Peak. c. The location of a Bragg Peak is useful for planning radiotherapy with proton beams. d. The Bragg peak for heavy charged particles can be broadened by inserting an absorbing material with various thicknesses between the particle beam and the soft tissue. e. A plot of dose vs. depth for electrons in general will be a maximum at the surface and decrease exponentially as depth increases. 5. When MTF of the focal and receptor blur are both equal to 0.1 (at 2 lp/mm), the imaging system MTF at this spatial frequency is most likely: a. 0.2 b. 0.1 c d e The actual anode focal area is 3 mm (length) and 2.5 mm (width) for 16 degree anode angle. The projected focal spot size (mm2) at the central axis is approximately a. 2 b. 3 c. 4 d. 5 e An ultrasound signal attenuated to 1% of its original intensity corresponds to attenuation (-db) of: a. 1 b. 5 c. 10 d. 20 e of 12

4 Part A: Short Answer Questions (Obligatory) 8. The most likely limitation of magnification is an increase in: a. Focal blur b. Scattered photons c. Absorbed photons d. Detector exposure e. Quantum mottle 9. Typical soft tissue differences (%) in spin density are most likely: a. Less than 1 b. 3 c. 10 d. 30 e An ionization chamber designed to satisfy the conditions of Bragg-Gray cavity theory for 662 kev photons contains 6 cm 3 of air at a density of !3 g cm!3. If the current produced by the chamber is 1.4 pa when exposed to a constant fluence rate of 662 kev photons, then what is the exposure rate at the location of the chamber? a. 2.7 R hr!1 b R hr!1 c R hr!1 d R hr!1 e R hr!1 11. A sample containing min 27 Mg with an initial activity of 1 μci was measured for 10 minutes using a detection system with a counting efficiency of 0.3 counts per decay for 27 Mg. What is the expected number of net counts recorded if the 27 Mg sample was measured for 10 minutes? a b c d e of 12

5 Part A: Short Answer Questions (Obligatory) 12. What net counting rate would be observed for a Geiger-Mueller (GM) detector when measuring a 1 mci point source of 137 Cs at 1 m from the detector face? The dead time for this detector is 0.5 ms, and the counting efficiency for this source and geometry and in the absence of dead time losses is !5 counts per decay of 137 Cs. a. 558 cps b. 632 cps c. 925 cps d. 1,033 cps e. 1,720 cps 13. Reference man takes in 3 L/day of water. The total body water in reference man is 42 L. For intakes of tritiated water, reference man is modeled as one compartment with instantaneous and uniform mixing of water intake and excretion. What is the biological half-life of tritiated water in reference man rounded to one significant digit? a days b. 1 day c. 10 days d. 14 days e. 10 years 14. The ratio of the activity of radioactive carbon (C-14, half-life = 5730 years) to stable carbon in living organisms is equal to 16 d/min per gram of carbon. This ratio decreases starting at the time the organism dies. If the ratio in a once living artifact is found to be 2.0 d/min per gram of carbon, how old is the artifact? a years b. 11,500 years c. 11,900 years d. 17,200 years e. 22,900 years 5 of 12

6 Part A: Short Answer Questions (Obligatory) 15. In 10CFR20, a Very High Radiation Area is defined as an area, accesible to individuals, in which radiation levels from radiation sources external to the body could result in an individual receiving an absorbed dose in excess of at a distance of 1 meter in one hour? a. 500 mrads b. 500 rads c. 1 mgy d. 0.5 Gy e. 1 Gy 16. In an experiment with an ion beam, 3 Gy of absorbed dose generates a measurable biological effect. It takes 12 Gy of 250 kvp X-ray radiation to produce the same biological effect. What is the relative biological effectiveness of the ion beam? a. 2.5 b. 3 c. 4 d The Fricke dosimeter provides an example for a. the oxygen effect b. scavenger reactions c. both A and B d. none of the above 18. Which of the following groups of cells are least radiosensitive? a. Adult nerve cells b. Nerve cells in the embryo c. Lymphocytes d. Immature spermatogonia 6 of 12

7 Part A: Short Answer Questions (Obligatory) 19. A tissue with cells of 15 µm in average size and 3.84x10-12 kg in mass is irradiated with 1.0 cgy dose. Assuming that an active event corresponds to 60 ev, the number of events in a cell will be: (a) 1000 (b) 2000 (c) 4000 (d) 8000 (1 J = x ev) 20. With respect to the law of Bergonie and Tribondeau, which of the following sentences would best complete the following statement? "The most pronounced radiation effects occur in cells having the." a. Least reproductive activity, shortest mitotic phases, and most maturity b. Greatest reproductive activity, shortest mitotic phases, and most maturity c. Greatest reproductive activity, longest mitotic phases, and least maturity d. Least reproductive activity, shortest mitotic phases, and least maturity. 7 of 12

8 Problem 1. Ph.D. Comprehensive Examination, January 2015 Part B: Problems (Do any two out of four) An imaged part of a patient's body consists of iodine (thickness x i ), bone (thickness x b ) and soft tissue (thickness x s ). We acquire two exposures at high and low energies, E H and E L, respectively. Derive the formula for the soft tissue cancelled image using the energy subtraction method. Assume that the respective attenuation coefficients for iodine ( i ), bone ( b ), and soft tissue ( s ) are known at both energies. 8 of 12

9 Problem 2. Ph.D. Comprehensive Examination, January 2015 Part B: Problems (Do any two out of four) A beam of 8 MeV electrons with a current equal to 5 milliamperes is incident on a 0.5 mm thick sheet of lead (density = g cm -3 ). The stopping power values for 8 MeV electrons are: Collision (electronic) Mass Stopping Power = (- dt / dx) col = (S / ) col = MeV cm 2 g -1 Radiation (nuclear) Mass Stopping Power = (- dt / dx) rad = (S / ) rad = MeV cm 2 g -1 Total Mass Stopping Power = (- dt / dx) tot = (S / ) tot = MeV cm 2 g -1 Assume that the sheet is thin enough that the stopping power values are constant at all points along the electron s track through the sheet. a. Estimate the energy of the electrons after they penetrate this sheet. Assume that they travel in a straight line perpendicular to the lead sheet. b. Estimate how much bremmstrahlung energy each electron produces. c. What is the average specific ionization for these electrons in this particular sheet of lead if the W value is 25 ev/ion pair? d. What is the fluence rate, in electrons cm -2 sec -1, at the surface of the sheet if the electron beam has a cross sectional area of 5 cm²? e. What is the absorbed dose rate, in rads/h, at the surface of the lead sheet? 9 of 12

10 Problem 3. Ph.D. Comprehensive Examination, January 2015 Part B: Problems (Do any two out of four) Most instruments for detecting radiation involve the ionization of atoms and then the harvesting of that charge, by one means or another, to produce an observable output signal. a. All real detector materials have many ways of absorbing energy, and only some are ionizing. Thus, the concept of an "effective" ionization potential, W, which is bigger than the true ionization potential, usually about double. If for some material, and some radiation, W = 20 ev, how many charge carriers, N, would radiation of 1 MeV cause? b. If N followed Poisson statistics, and remembering the variance, 2 = N, what would you expect the energy resolution of such a detector to be? c. In real life, for real materials, the correlations between ionizing and non-ionizing processes mean the energy resolution is better than the expectation from a Poisson distribution and 2 = F N with 0 < F < 1. What is this factor, F? Is F = 1 better than F = 0? d. For semiconductor detectors like silicon and germanium spectrometers (which for most radiation detectors is the optimum material for energy resolution) name TWO reasons why the energy resolution is far superior to most other materials. 10 of 12

11 Problem 4. Ph.D. Comprehensive Examination, January 2015 Part B: Problems (Do any two out of four) In an experiment using HeLa cells under oxygenated and anoxic conditions, the following survival curve was determined. The LQ model was found a good fit to these survival curves with the following parameters: For the oxygenated case, = 3.0E-1 and = 7.0E-2. For the anoxic case, = 1.0E-1 and = 4.0E-2. a. Determine the oxygen enhancement ratio at SF=0.1 and at SF=0.01. b. For each case, determine the dose where the linear contribution to cell killing equals the quadratic contribution. c. What oxygen enhancement ratio would you anticipate at SF=0.001 based on the above data? Justify your answer. 11 of 12

12 Part B: Problems (Do any two out of four) Useful Constants and Equations X = (μ en /ρ) air Φ T (e/w) D cpe = (μ en /ρ) Φ T K = (μ tr /ρ) Φ T D = (S col /ρ) Φ X = A Γ / r² X = 6 C E D = 300 A H = D Q X disc = π A a Γ ln[1 + (R/x)² ] X line = (A l Γ/x) tan -1 (L/x) = (A l Γ/x) Σ = σ ρ atom ρ atom = ρ N A / W R = Σ Φ = μ Φ Φ = S / 4 π r² Ω = A / R² Ω = 2 π (1 - x / R ) f = Ω / 4 Q = T = BE + Q nt = - m 0 c 2 N(t) = (P t) [ (1 - e -k t ) / k t ] P = U R F / λ P = σ Φ 0 N target A = λ N C = E D R = E A S = A Y D(T) = N (1 - e -λt ) e -x = 1 - x + x 2 /2! - x 3 /3! +... A air = A tissue = 12.8 A water = 13.4 W = 33.7 ev/ion pair e = 1.602x10-19 C N A = 6.022x10 23 c 2 = Mev/amu R = 2.58x10-4 C/kg Gy = 100 rad = 1 J/kg rad = 6.242x10 7 MeV/g amp = C/s ev = 1.602x10-19 J Ci = 3.7x10 10 Bq = 3.7x10 10 d/s barn = cm 2 watt = J/s 12 of 12