Radioactivity and Nuclear Transformation

Roentgen had discovered x-rays in early November 1895. Even in the absence of the virtually instantaneous worldwide communication networks known today, this discovery spread very quickly and ignited the imagination of scientists and the general public alike. One of those scientists was Henri Becquerel who was studying the phenomenon of phosphorescence following the absorption of light by different minerals. Becquerel was intrigued by Roentgen’s discovery and wondered if any of the minerals in his collection might emit a similar type of ray that could penetrate visually opaque objects when exposed to strong sunlight. The experiment he planned was simple. He wrapped an unexposed photographic plate in black paper, placed the mineral to be tested on the top of the paper, and left it out in strong sunlight to see if this would “activate” the mineral to produce x-rays and produce a darkening of the photographic plate when it was developed. The experiment with the mineral uranium was set up but delayed due to cloudy skies and placed in a desk drawer. Later, and by accident, one of Becquerel’s assistants developed the plate. To their surprise, the uranium sulfate had left a faint impression of its granules on the plate. Becquerel soon discovered that the properties of this mineral (uranium) were quite unique and that the type of radiation was being emitted spontaneously without the uranium salts having to be illuminated by the sun. He also showed that the “rays” emitted, which for many years were named after their discoverer, differed from x-rays in that they could be deflected by electric or magnetic fields. In 1975 the General Conference on Weights and Measures decided to honor Henri Becquerel by accepting a proposal from the International Commission for Radiation Units and Measurements (ICRU) to adopt the special name of becquerel (Bq) as the official SI derived unit of activity (the quantity of radioactive material). Prior to 1975, the unit of activity was the Curie (Ci) named in honor of Marie Curie, one of the most accomplished women in the history of science.

Becquerel’s discovery inspired Marie and her husband Pierre Curie to further investigate this phenomenon. They examined many substances and minerals for signs of radioactivity. They found that the mineral pitchblende was more radioactive than uranium and concluded that it must contain other radioactive substances. From it, they managed to extract two previously unknown elements, polonium (Po) and radium (Ra). Marie Curie named polonium in honor of her homeland, Poland, and radium (a rare, brilliant white, luminescent, and highly radioactive metallic element) whose name is derived from the Latin word radius, meaning “ray.” Noting that the number of radiated emissions per unit time per unit mass from both Ra and Po was much more frequent than with uranium Marie Curie coined the term “radioactivity.”

Marie Curie was a woman of many “firsts” and her research paved the way for numerous remarkable applications of radiation in science, technology, and medicine. In 1903, she was the first woman in the world to earn a Doctor of Science degree. That same year she was the first woman to be awarded a Nobel Prize in Physics and in 1911 she was the only women to be awarded a second Nobel Prize, this time in Chemistry. She was also the first woman Professor and Chair of physical sciences at the Sorbonne. In 1935, the Curies’ daughter, Irene Joliot-Curie and her husband
Frederic Joliot won the Nobel Prize for Chemistry, making them the only mother and daughter to share this honor.

Marie Curie’s relentless resolve and insatiable curiosity made her an icon in the world of modern science. She championed the use of radiation in medicine and fundamentally changed our understanding of radioactivity. Today many people fear anything to do with the word radiation or radioactivity. In the following pages, we will discuss the types of radioactive transformations common to the radionuclides used in medical imaging. It would be prudent to remember the words of Dr. Curie at this juncture who said:

“Nothing in life is to be feared, it is only to be understood. Now is the time to understand more, so that we may fear less”

15.1 RADIONUCLIDE DECAY TERMS AND RELATIONSHIPS

15.1.1 Activity

The quantity of radioactive material, expressed as the number of radioactive atoms undergoing nuclear transformation per unit time (t), is called activity (A). Described mathematically, activity is equal to the change (dN) in the total number of radioactive atoms (N) in a given period of time (dt), or

The minus sign indicates that the number of radioactive atoms decreases with time. Activity has traditionally been expressed in units of curies (Ci). One Ci is defined as 3.70 × 10¹⁰ disintegrations per second (dps), which is roughly equal to the rate of disintegrations from 1 g of radium-226 (Ra-226). A curie is a large amount of radioactivity. In nuclear medicine, activities from 0.1 to 30 mCi of a variety of radionuclides are typically used for imaging studies, and up to 300 mCi of iodine-131 is used for therapy. Although the curie is still the most common unit of radioactivity in the United States, the majority of the world’s scientific literature uses the SI unit for radioactivity, the becquerel, defined as 1 dps. One millicurie (mCi) is equal to 37 megabecquerels (1 mCi = 37 MBq). Table 15-1 lists the units and prefixes describing various amounts of radioactivity.

TABLE 15-1 UNITS AND PREFIXES ASSOCIATED WITH VARIOUS QUANTITIES OF RADIOACTIVITY

QUANTITY	SYMBOL	DPS	DPM
Gigabecquerel	GBq	1 × 10⁹	6 × 10¹⁰
Megabecquerel	MBq	1 × 10⁶	6 × 10⁷
Kilobecquerel	kBq	1 × 10³	6 × 10⁴
Curie	Ci	3.7 × 10¹⁰	2.22 × 10¹²
Millicurie	µCi (10^-3 Ci)	3.7 × 10⁷	2.22 × 10⁹
Microcurie	µCi (10^-6 Ci)	3.7 × 10⁴	2.22 × 10⁶
Nanocurie	nCi (10^-9 Ci)	3.7 × 10¹	2.22 × 10³
Picocurie	pCi (10^-12 Ci)	3.7 × 10^-2	2.22
Multiply mCi by 37 to obtain MBq or divide MBq by 37 to obtain mCi (e.g., 1 mCi = 37 MBq).

15.1.2 Decay Constant

Radioactive decay is a random process. From moment to moment, it is not possible to predict which radioactive atoms in a sample will decay. However, observation of a larger number of radioactive atoms over a period of time allows the average rate of nuclear transformation (decay) to be established. The number of atoms decaying per unit time (dN/dt) is proportional to the number of unstable atoms (N) that are present at any given time:

A proportionality can be transformed into an equality by introducing a constant. This constant is called the decay constant (λ).

The minus sign indicates that the number of radioactive atoms decaying per unit time (the decay rate or activity of the sample) decreases with time. The decay constant is equal to the fraction of the number of radioactive atoms remaining in a sample that decay per unit time. The relationship between activity A and the decay constant λ can be seen by considering Equation 15-1 and substituting A for -dN/dt in Equation 15-3:

The decay constant is characteristic of each radionuclide. For example, the decay constants for technetium-99m (Tc-99m) and molybdenum-99 (Mo-99) are 0.1151 h^-1 and 0.252 day^-1, respectively.

15.1.3 Physical Half-Life

A useful parameter related to the decay constant is the physical half-life (T½ or T_p½). The half-life is defined as the time required for the number of radioactive atoms in a sample to decrease by one half. The number of radioactive atoms remaining in a sample and the number of elapsed half-lives are related by the following equation:

where N is the number of radioactive atoms remaining, N₀ is the initial number of radioactive atoms, and n is the number of half-lives that have elapsed. The relationship between time and the number of radioactive atoms remaining in a sample is demonstrated with Tc-99m (T_p½ ≈ 6 h) in Table 15-2.

After 10 half-lives, the number of radioactive atoms in a sample is reduced by approximately a factor of a thousand. After 20 half-lives, the number of radioactive atoms is reduced to approximately one millionth of the initial number.

The decay constant and the physical half-life are related as follows:

where ln 2 denotes the natural logarithm of 2. Note that the derivation of this relationship is identical to that between the half-value layer (HVL) and the linear attenuation coefficient (µ) in Chapter 3 (Eq. 3-9).

The physical half-life and the decay constant are physical quantities that are inversely related and unique for each radionuclide. Half-lives of radioactive materials range from billions of years to a fraction of a second. Radionuclides used in nuclear medicine typically have half-lives on the order of hours or days. Examples of T_p½ and λ for radionuclides commonly used in nuclear medicine are listed in Table 15-3.

TABLE 15-2 RADIOACTIVE DECAY FOR Tc-99m^a

TIME (DAY)	NO. OF PHYSICAL HALF-LIVES	EXPRESSION	N	(N/N₀) × 100 = % REMAINING
0	0	N₀/2⁰	10⁶	100%
0.25	1	N₀/2¹	5 × 10⁵	50%
0.5	2	N₀/2²	2.5 × 10⁵	25%
0.75	3	N₀/2³	1.25 × 10⁵	12.5%
1	4	N₀/2⁴	6.25 × 10⁴	6.25%
2.5	10	N₀/2¹⁰	≈ 10³	≈ 0.1% (1/1,000) N₀
5	20	N₀/2²⁰	≈ 1	≈ 0.000001% (1/1,000,000) N₀
^a The influence of radioactive decay on the number of radioactive atoms in a sample is illustrated with technetium-99m, which has a physical half-life of 6 h (0.25 day). The sample initially contains one million (10⁶) radioactive atoms (N).

15.1.4 Fundamental Decay Equation

By applying the integral calculus to Equation 15-3, a useful relationship is established between the number of radioactive atoms remaining in a sample and time—the fundamental decay equation:

where N_t is the number of radioactive atoms at time t, A_t is the activity at time t, N₀ is the initial number of radioactive atoms, A₀ is the initial activity, e is the base of natural logarithm = 2.718 …, λ is the decay constant = ln 2/T_p½ = 0.693/T_p½, and t is the elapsed time.

TABLE 15-3 PHYSICAL HALF-LIFE (T_p½) AND DECAY CONSTANT (λ) FOR RADIONUCLIDES COMMONLY USED IN NUCLEAR MEDICINE

RADIONUCLIDE	T_P½	λ
Rubidium-82 (⁸²Rb)	75 s	0.0092 s^-1
Fluorine-18 (¹⁸F)	110 min	0.0063 min^-1
Technetium-99m (^99mTc)	6.02 h	0.1151 h^-1
Iodine-123 (¹²³I)	13.27 h	0.0522 h^-1
Samarium-153 (¹⁵³Sm)	1.93 d	0.3591 d^-1
Yttrium-90 (⁹⁰Y)	2.69 d	0.2575 d^-1
Molybdenum-99 (⁹⁹Mo)	2.75 d	0.2522 d^-1
Indium-111 (¹¹¹In)	2.81 d	0.2466 d^-1
Thallium-201 (²⁰¹Tl)	3.04 d	0.2281 d^-1
Gallium-67 (⁶⁷Ga)	3.26 d	0.2126 d^-1
Xenon-133 (¹³³Xe)	5.24 d	0.1323 d^-1
Lutetium-177 (¹⁷⁷Lu)	6.7 d	0.1034 d^-1
Iodine-131 (¹³¹I)	8.02 d	0.0864 d^-1
Ra-223 (²²³Ra)	11.4 d	0.0608 d^-1
Strontium-82 (⁸²Sr)	25.60 d	0.0271 d^-1
Cobalt-57 (⁵⁷Co)	271.79 d	0.0117 d^-1