#set document(title: "32.1 Diagnostics and Medical Imaging", author: "OpenStax / XYZ Homework") #set page(width: 8.5in, height: auto, margin: 1in) #import "@preview/cetz:0.5.2" #set text(font: ("STIX Two Text", "Libertinus Serif", "New Computer Modern"), size: 10.5pt, lang: "en") #show math.equation: set text(font: ("STIX Two Math", "New Computer Modern Math")) #set par(justify: true, leading: 0.62em, spacing: 0.9em) #set enum(spacing: 1.1em) // room between list items so tall inline fractions don't collide #set list(spacing: 1.1em) #set table(stroke: 0.5pt + rgb("#c7ccd3")) #let BLUE = rgb("#183B6F") // brand navy — section bars + example/solution labels (white on navy 11.09:1) #let ORANGE = rgb("#A94509") // brand primary-700 — AA-safe deep orange for TEXT (5.93:1 on white; raw brand #F37021 is 2.94:1 and must never carry text) #let RED = rgb("#DC2626") // brand error-600 #let GREEN = rgb("#059669") // brand success-600 (decoration only; small green text uses green-text #007942) #show heading.where(level: 1): it => block(width: 100%, above: 0pt, below: 16pt, fill: gradient.linear(BLUE, rgb("#2C5AA0")), inset: (x: 14pt, y: 12pt), radius: 3pt, text(fill: white, weight: "bold", size: 19pt, it.body)) #show heading.where(level: 2): it => block(width: 100%, above: 18pt, below: 10pt, fill: BLUE, inset: (x: 10pt, y: 6pt), radius: 2pt, text(fill: white, weight: "bold", size: 12pt, it.body)) #show heading.where(level: 3): it => text(fill: ORANGE, weight: "bold", size: 12.5pt, it.body) #show heading.where(level: 4): it => text(fill: BLUE, weight: "bold", size: 10.5pt, it.body) #let examplebox(label, title, body) = block(width: 100%, breakable: true, fill: rgb("#EFF1F5"), stroke: 0.5pt + rgb("#CFDDF0"), radius: 4pt, inset: 10pt, above: 12pt, below: 12pt)[ #block(below: 6pt)[#box(fill: BLUE, inset: (x: 6pt, y: 2pt), radius: 2pt, text(fill: white, weight: "bold", size: 8.5pt, label)) #h(0.4em) #strong[#title]] #body] // rail = decorative left rule (raw brand token); labelcolor = AA-safe label text shade #let notebox(label, rail, labelcolor, tint, body) = block(width: 100%, breakable: true, fill: tint, stroke: (left: 3pt + rail), inset: (left: 10pt, rest: 8pt), radius: (right: 4pt), above: 11pt, below: 11pt)[ #text(fill: labelcolor, weight: "bold", size: 7.5pt, tracking: 0.5pt)[#upper(label)] #linebreak() #body] #let solutionbox(body) = block(above: 4pt, below: 8pt)[ #text(fill: BLUE, weight: "bold", size: 8.5pt)[Solution] #linebreak() #body] #let figph(msg) = block(width: 100%, height: 60pt, fill: rgb("#f6f7f9"), stroke: (paint: rgb("#c7ccd3"), dash: "dashed"), radius: 4pt, inset: 10pt)[ #align(center + horizon, text(fill: rgb("#889"), style: "italic", size: 9pt, msg))] // Standardize inlined figure sizes: measure the natural CeTZ canvas, then scale to a // consistent envelope (aspect-aware; see build_typst.py FIG_* constants). Unlike the // print preamble, dimensions are FLOORED: in an editor a user can trim a figure to a // degenerate 1-D shape (a bare line), and w/h or tw/w would then divide by zero. #let _STD_W = 3.5 #let _WIDE_W = 5.6 #let _MAX_H = 3.4 #let _ASPECT_WIDE = 2.2 #let _UPSCALE_MAX = 1.15 #let stdfig(body) = context { let m = measure(body) let w = calc.max(m.width / 1in, 0.01) let h = calc.max(m.height / 1in, 0.01) let tw = if w / h > _ASPECT_WIDE { _WIDE_W } else { _STD_W } let s = calc.min(tw / w, _MAX_H / h, _UPSCALE_MAX) align(center, box(scale(x: s * 100%, y: s * 100%, reflow: true, body))) } #show figure: set block(breakable: false) #set figure(gap: 8pt) #show figure.caption: set text(size: 8.5pt, fill: rgb("#555")) == 32.1#h(0.6em)Diagnostics and Medical Imaging === Learning Objectives By the end of this section, you will be able to: - Explain the working principle behind an anger camera. - Describe the SPECT and PET imaging techniques. Most medical and related applications of nuclear physics are driven, at their core, by the difference between a radioactive substance and a non-radioactive substance. One of the first such methods is the precision measurement and detection method known as radioimmunoassay (RIA). Developed by Rosalyn Sussman Yalow and Solomon Berson in the late 1950s, RIA relies on the principle of competitive binding. For the particular substance being measured, a sample containing a radioactive isotope is prepared. A known quantity of antibodies is then introduced. By measuring the amount of "unbound" antibodies after the reaction, technicians can detect and measure the precise amount of the target substance. Radioimmunoassay is essential in cancer screening, hepatitis diagnosis, narcotics investigation, and other analyses. A host of medical imaging techniques employ nuclear radiation. What makes nuclear radiation so useful? First, #math.equation(block: false, alt: "γ")[$γ$] radiation can easily penetrate tissue; hence, it is a useful probe to monitor conditions inside the body. Second, nuclear radiation depends on the nuclide and not on the chemical compound it is in, so that a radioactive nuclide can be put into a compound designed for specific purposes. The compound is said to be #strong[tagged]. A tagged compound used for medical purposes is called a #strong[radiopharmaceutical]. Radiation detectors external to the body can determine the location and concentration of a radiopharmaceutical to yield medically useful information. For example, certain drugs are concentrated in inflamed regions of the body, and this information can aid diagnosis and treatment as seen in . Another application utilizes a radiopharmaceutical which the body sends to bone cells, particularly those that are most active, to detect cancerous tumors or healing points. Images can then be produced of such bone scans. Radioisotopes are also used to determine the functioning of body organs, such as blood flow, heart muscle activity, and iodine uptake in the thyroid gland. #figure(figph[A brain scan. Different regions of the brain are shown in different colors.], alt: "A brain scan. Different regions of the brain are shown in different colors.", caption: [A radiopharmaceutical is used to produce this brain image of a patient with Alzheimer’s disease. Certain features are computer enhanced.]) === Medical Application lists certain medical diagnostic uses of radiopharmaceuticals, including isotopes and activities that are typically administered. Many organs can be imaged with a variety of nuclear isotopes replacing a stable element by a radioactive isotope. One common diagnostic employs iodine to image the thyroid, since iodine is concentrated in that organ. The most active thyroid cells, including cancerous cells, concentrate the most iodine and, therefore, emit the most radiation. Conversely, hypothyroidism is indicated by lack of iodine uptake. Note that there is more than one isotope that can be used for several types of scans. Another common nuclear diagnostic is the thallium scan for the cardiovascular system, particularly used to evaluate blockages in the coronary arteries and examine heart activity. The salt TlCl can be used, because it acts like NaCl and follows the blood. Gallium-67 accumulates where there is rapid cell growth, such as in tumors and sites of infection. Hence, it is useful in cancer imaging. Usually, the patient receives the injection one day and has a whole body scan 3 or 4 days later because it can take several days for the gallium to build up. #figure(table( columns: 2, align: left, inset: 6pt, [#strong[Procedure, isotope]], [Typical activity (mCi), where #linebreak() #math.equation(block: false, alt: "1 mCi equals 3.7 times 10 to the power 7 Bq")[$1 "mCi" = 3.7 × "10"^(7) #h(0.25em) "Bq"$]], [#emph[#strong[#emph[Brain scan]]]], [], [#math.equation(block: false, alt: "to the power 99m Tc")[$"99m" "Tc"$]], [7.5], [#math.equation(block: false, alt: "to the power 113m In")[$"113m" "In"$]], [7.5], [#math.equation(block: false, alt: "to the power 11 C (PET)")[$"11" "C (PET)"$]], [20], [#math.equation(block: false, alt: "to the power 13 N (PET)")[$"13" "N (PET)"$]], [20], [#math.equation(block: false, alt: "to the power 15 O (PET)")[$"15" "O (PET)"$]], [50], [#math.equation(block: false, alt: "to the power 18 F (PET)")[$"18" "F (PET)"$]], [10], [#strong[#emph[Lung scan]]], [], [#math.equation(block: false, alt: "to the power 99m Tc")[$"99m" "Tc"$]], [2], [#math.equation(block: false, alt: "to the power 133 Xe")[$"133" "Xe"$]], [7.5], [#strong[#emph[Cardiovascular blood pool]]], [], [#math.equation(block: false, alt: "to the power 131 I")[$"131" "I"$]], [0.2], [#math.equation(block: false, alt: "to the power 99m Tc")[$"99m" "Tc"$]], [2], [#strong[#emph[Cardiovascular arterial flow]]], [], [#math.equation(block: false, alt: "to the power 201 Tl")[$"201" "Tl"$]], [3], [#math.equation(block: false, alt: "to the power 24 Na")[$"24" "Na"$]], [7.5], [#strong[#emph[Thyroid scan]]], [], [#math.equation(block: false, alt: "to the power 131 I")[$"131" "I"$]], [0.05], [#math.equation(block: false, alt: "to the power 123 I")[$"123" "I"$]], [0.07], [#strong[#emph[Liver scan]]], [], [#math.equation(block: false, alt: "to the power 198 Au")[$"198" "Au"$] (colloid)], [0.1], [#math.equation(block: false, alt: "to the power 99m Tc")[$"99m" "Tc"$] (colloid)], [2], [#strong[#emph[Bone scan]]], [], [#math.equation(block: false, alt: "to the power 85 Sr")[$"85" "Sr"$]], [0.1], [#math.equation(block: false, alt: "to the power 99m Tc")[$"99m" "Tc"$]], [10], [#strong[#emph[Kidney scan]]], [], [#math.equation(block: false, alt: "to the power 197 Hg")[$"197" "Hg"$]], [0.1], [#math.equation(block: false, alt: "to the power 99m Tc")[$"99m" "Tc"$]], [1.5], )) Note that lists many diagnostic uses for #math.equation(block: false, alt: "to the power 99m Tc")[$"99m" "Tc"$], where “m” stands for a metastable state of the technetium nucleus. Perhaps 80 percent of all radiopharmaceutical procedures employ #math.equation(block: false, alt: "to the power 99m Tc")[$"99m" "Tc"$] because of its many advantages. One is that the decay of its metastable state produces a single, easily identified 0.142-MeV #math.equation(block: false, alt: "γ")[$γ$] ray. Additionally, the radiation dose to the patient is limited by the short 6.0-h half-life of #math.equation(block: false, alt: "to the power 99m Tc")[$"99m" "Tc"$]. And, although its half-life is short, it is easily and continuously produced on site. The basic process for production is neutron activation of molybdenum, which quickly #math.equation(block: false, alt: "β")[$β$] decays into #math.equation(block: false, alt: "to the power 99m Tc")[$"99m" "Tc"$]. Technetium-99m can be attached to many compounds to allow the imaging of the skeleton, heart, lungs, kidneys, etc. shows one of the simpler methods of imaging the concentration of nuclear activity, employing a device called an #strong[Anger camera] or #strong[gamma camera]. A piece of lead with holes bored through it collimates #math.equation(block: false, alt: "γ")[$γ$] rays emerging from the patient, allowing detectors to receive #math.equation(block: false, alt: "γ")[$γ$] rays from specific directions only. The computer analysis of detector signals produces an image. One of the disadvantages of this detection method is that there is no depth information (i.e., it provides a two-dimensional view of the tumor as opposed to a three-dimensional view), because radiation from any location under that detector produces a signal. #figure(figph[The image shows the head of a man scanned by an Anger camera. The camera consists of a lead collimator and array of detectors. Gamma rays emerging from the man’s head pass through the lead collimator and produce light flashes in the scintillators. The photomultiplier tubes convert the light output to electrical signals for computer image generation.], alt: "The image shows the head of a man scanned by an Anger camera. The camera consists of a lead collimator and array of detectors. Gamma rays emerging from the man’s head pass through the lead collimator and produce light flashes in the scintillators. The photomultiplier tubes convert the light output to electrical signals for computer image generation.", caption: [An Anger or gamma camera consists of a lead collimator and an array of detectors. Gamma rays produce light flashes in the scintillators. The light output is converted to an electrical signal by the photomultipliers. A computer constructs an image from the detector output.]) Imaging techniques much like those in x-ray computed tomography (CT) scans use nuclear activity in patients to form three-dimensional images. shows a patient in a circular array of detectors that may be stationary or rotated, with detector output used by a computer to construct a detailed image. This technique is called #strong[single-photon-emission computed tomography(SPECT)] or sometimes simply SPET. The spatial resolution of this technique is poor, about 1 cm, but the contrast (i.e. the difference in visual properties that makes an object distinguishable from other objects and the background) is good. #figure(figph[A man lying down, going through a cylindrical scanning machine.], alt: "A man lying down, going through a cylindrical scanning machine.", caption: [SPECT uses a geometry similar to a CT scanner to form an image of the concentration of a radiopharmaceutical compound.]) Images produced by #math.equation(block: false, alt: "β to the power plus")[$β^(+)$] emitters have become important in recent years. When the emitted positron ( #math.equation(block: false, alt: "β to the power plus")[$β^(+)$]) encounters an electron, mutual annihilation occurs, producing two #math.equation(block: false, alt: "γ")[$γ$] rays. These #math.equation(block: false, alt: "γ")[$γ$] rays have identical 0.511-MeV energies (the energy comes from the destruction of an electron or positron mass) and they move directly away from one another, allowing detectors to determine their point of origin accurately, as shown. The system is called #strong[positron emission tomography (PET)]. It requires detectors on opposite sides to simultaneously (i.e., at the same time) detect photons of 0.511-MeV energy and utilizes computer imaging techniques similar to those in SPECT and CT scans. Examples of #math.equation(block: false, alt: "β to the power plus")[$β^(+)$] -emitting isotopes used in PET are #math.equation(block: false, alt: "to the power 11 C")[$"11" "C"$], #math.equation(block: false, alt: "to the power 13 N")[$"13" "N"$], #math.equation(block: false, alt: "to the power 15 O")[$"15" "O"$], and #math.equation(block: false, alt: "to the power 18 F")[$"18" "F"$], as seen in . This list includes C, N, and O, and so they have the advantage of being able to function as tags for natural body compounds. Its resolution of 0.5 cm is better than that of SPECT; the accuracy and sensitivity of PET scans make them useful for examining the brain’s anatomy and function. The brain’s use of oxygen and water can be monitored with #math.equation(block: false, alt: "to the power 15 O")[$"15" "O"$]. PET is used extensively for diagnosing brain disorders. It can note decreased metabolism in certain regions prior to a confirmation of Alzheimer’s disease. PET can locate regions in the brain that become active when a person carries out specific activities, such as speaking, closing their eyes, and so on. #figure(figph[The figure shows a patient undergoing a scan in a cylindrical device. The P E T system uses two gamma ray photons produced by positron electron annihilation. These gamma rays are emitted in opposite directions.], alt: "The figure shows a patient undergoing a scan in a cylindrical device. The P E T system uses two gamma ray photons produced by positron electron annihilation. These gamma rays are emitted in opposite directions.", caption: [A PET system takes advantage of the two identical #math.equation(block: false, alt: "γ")[$γ$]-ray photons produced by positron-electron annihilation. These #math.equation(block: false, alt: "γ")[$γ$] rays are emitted in opposite directions, so that the line along which each pair is emitted is determined. Various events detected by several pairs of detectors are then analyzed by the computer to form an accurate image.]) #notebox("Note", rgb("#8a94a6"), rgb("#556666"), rgb("#f7f8fa"))[ #emph[Simplified MRI] Is it a tumor? Magnetic Resonance Imaging (MRI) can tell. Your head is full of tiny radio transmitters (the nuclear spins of the hydrogen nuclei of your water molecules). In an MRI unit, these little radios can be made to broadcast their positions, giving a detailed picture of the inside of your head. #link("https://openstax.org/l/02simplemri")[Click to view content]. ] === Section Summary - Radiopharmaceuticals are compounds that are used for medical imaging and therapeutics. - The process of attaching a radioactive substance is called tagging. - lists certain diagnostic uses of radiopharmaceuticals including the isotope and activity typically used in diagnostics. - One common imaging device is the Anger camera, which consists of a lead collimator, radiation detectors, and an analysis computer. - Tomography performed with #strong[#math.equation(block: false, alt: "γ")[$γ$]]-emitting radiopharmaceuticals is called SPECT and has the advantages of x-ray CT scans coupled with organ- and function-specific drugs. - PET is a similar technique that uses #strong[#math.equation(block: false, alt: "β to the power plus")[$β^(+)$]] emitters and detects the two annihilation #strong[#math.equation(block: false, alt: "γ")[$γ$]] rays, which aid to localize the source. === Conceptual Questions In terms of radiation dose, what is the major difference between medical diagnostic uses of radiation and medical therapeutic uses? One of the methods used to limit radiation dose to the patient in medical imaging is to employ isotopes with short half-lives. How would this limit the dose? === Problems & Exercises A neutron generator uses an #math.equation(block: false, alt: "α")[$α$] source, such as radium, to bombard beryllium, inducing the reaction #math.equation(block: false, alt: "to the power 4 He plus to the power 9 Be → to the power 12 C plus n")[$4 "He" + 9 "Be" → "12" "C" + n$]. Such neutron sources are called RaBe sources, or PuBe sources if they use plutonium to get the #math.equation(block: false, alt: "α")[$α$] s. Calculate the energy output of the reaction in MeV. #solutionbox[ 5.701 MeV ] Neutrons from a source (perhaps the one discussed in the preceding problem) bombard natural molybdenum, which is 24 percent #math.equation(block: false, alt: "to the power 98 Mo")[$"98" "Mo"$]. What is the energy output of the reaction #math.equation(block: false, alt: "to the power 98 Mo plus n → to the power 99 Mo plus γ")[$"98" "Mo" + n → "99" "Mo" + γ$] ? The mass of #math.equation(block: false, alt: "to the power 98 Mo")[$"98" "Mo"$] is given in Appendix A: Atomic Masses, and that of #math.equation(block: false, alt: "to the power 99 Mo")[$"99" "Mo"$] is 98.907711 u. The purpose of producing #math.equation(block: false, alt: "to the power 99 Mo")[$"99" "Mo"$] (usually by neutron activation of natural molybdenum, as in the preceding problem) is to produce #math.equation(block: false, alt: "to the power 99m Tc.")[$"99m" "Tc."$] Using the rules, verify that the #math.equation(block: false, alt: "β to the power minus")[$β^(−)$] decay of #math.equation(block: false, alt: "to the power 99 Mo")[$"99" "Mo"$] produces #math.equation(block: false, alt: "to the power 99m Tc")[$"99m" "Tc"$]. (Most #math.equation(block: false, alt: "to the power 99m Tc")[$"99m" "Tc"$] nuclei produced in this decay are left in a metastable excited state denoted #math.equation(block: false, alt: "to the power 99m Tc")[$"99m" "Tc"$].) #solutionbox[ #math.equation(block: true, alt: "42 99 Mo sub 57 → 43 99 Tc sub 56 plus β to the power minus plus v ¯ sub e")[$"42" "99" "Mo"_("57") → "43" "99" "Tc"_("56") + β^(−) + overline(v)_(e)$] ] (a) Two annihilation #math.equation(block: false, alt: "γ")[$γ$] rays in a PET scan originate at the same point and travel to detectors on either side of the patient. If the point of origin is 9.00 cm closer to one of the detectors, what is the difference in arrival times of the photons? (This could be used to give position information, but the time difference is small enough to make it difficult.) (b) How accurately would you need to be able to measure arrival time differences to get a position resolution of 1.00 mm? indicates that 7.50 mCi of #math.equation(block: false, alt: "to the power 99m Tc")[$"99m" "Tc"$] is used in a brain scan. What is the mass of technetium? #solutionbox[ #math.equation(block: true, alt: "1 . 43 times 10 to the power minus 9 g")[$1 "." "43" × "10"^(− 9) #h(0.25em) "g"$] ] The activities of #math.equation(block: false, alt: "to the power 131 I")[$"131" "I"$] and #math.equation(block: false, alt: "to the power 123 I")[$"123" "I"$] used in thyroid scans are given in to be 50 and #math.equation(block: false, alt: "70 μ Ci")[$"70 μ" "Ci"$], respectively. Find and compare the masses of #math.equation(block: false, alt: "to the power 131 I")[$"131" "I"$] and #math.equation(block: false, alt: "to the power 123 I")[$"123" "I"$] in such scans, given their respective half-lives are 8.04 d and 13.2 h. The masses are so small that the radioiodine is usually mixed with stable iodine as a carrier to ensure normal chemistry and distribution in the body. (a) Neutron activation of sodium, which is 100%#math.equation(block: false, alt: "to the power 23 Na")[$"23" "Na"$], produces #math.equation(block: false, alt: "to the power 24 Na")[$"24" "Na"$], which is used in some heart scans, as seen in . The equation for the reaction is #math.equation(block: false, alt: "to the power 23 Na plus n → to the power 24 Na plus γ")[$"23" "Na" + n → "24" "Na" + γ$]. Find its energy output, given the mass of #math.equation(block: false, alt: "to the power 24 Na")[$"24" "Na"$] is 23.990962 u. (b) What mass of #math.equation(block: false, alt: "to the power 24 Na")[$"24" "Na"$] produces the needed 5.0-mCi activity, given its half-life is 15.0 h? #solutionbox[ (a) 6.958 MeV (b) #math.equation(block: false, alt: "5 . 7 times 10 to the power minus 10 g")[$5 "." 7 × "10"^(− "10") #h(0.25em) "g"$] ]