National Academies Press: OpenBook

Medical Isotope Production Without Highly Enriched Uranium (2009)

Chapter: 6 Molybdenum-99/Technetium-99m Production Costs

« Previous: 5 Molybdenum-99/Technetium-99m Demand
Suggested Citation:"6 Molybdenum-99/Technetium-99m Production Costs." National Research Council. 2009. Medical Isotope Production Without Highly Enriched Uranium. Washington, DC: The National Academies Press. doi: 10.17226/12569.
×
Page 80
Suggested Citation:"6 Molybdenum-99/Technetium-99m Production Costs." National Research Council. 2009. Medical Isotope Production Without Highly Enriched Uranium. Washington, DC: The National Academies Press. doi: 10.17226/12569.
×
Page 81
Suggested Citation:"6 Molybdenum-99/Technetium-99m Production Costs." National Research Council. 2009. Medical Isotope Production Without Highly Enriched Uranium. Washington, DC: The National Academies Press. doi: 10.17226/12569.
×
Page 82
Suggested Citation:"6 Molybdenum-99/Technetium-99m Production Costs." National Research Council. 2009. Medical Isotope Production Without Highly Enriched Uranium. Washington, DC: The National Academies Press. doi: 10.17226/12569.
×
Page 83
Suggested Citation:"6 Molybdenum-99/Technetium-99m Production Costs." National Research Council. 2009. Medical Isotope Production Without Highly Enriched Uranium. Washington, DC: The National Academies Press. doi: 10.17226/12569.
×
Page 84
Suggested Citation:"6 Molybdenum-99/Technetium-99m Production Costs." National Research Council. 2009. Medical Isotope Production Without Highly Enriched Uranium. Washington, DC: The National Academies Press. doi: 10.17226/12569.
×
Page 85
Suggested Citation:"6 Molybdenum-99/Technetium-99m Production Costs." National Research Council. 2009. Medical Isotope Production Without Highly Enriched Uranium. Washington, DC: The National Academies Press. doi: 10.17226/12569.
×
Page 86
Suggested Citation:"6 Molybdenum-99/Technetium-99m Production Costs." National Research Council. 2009. Medical Isotope Production Without Highly Enriched Uranium. Washington, DC: The National Academies Press. doi: 10.17226/12569.
×
Page 87
Suggested Citation:"6 Molybdenum-99/Technetium-99m Production Costs." National Research Council. 2009. Medical Isotope Production Without Highly Enriched Uranium. Washington, DC: The National Academies Press. doi: 10.17226/12569.
×
Page 88
Suggested Citation:"6 Molybdenum-99/Technetium-99m Production Costs." National Research Council. 2009. Medical Isotope Production Without Highly Enriched Uranium. Washington, DC: The National Academies Press. doi: 10.17226/12569.
×
Page 89

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

6 Molybdenum-99/Technetium-99m Production Costs The focus of this chapter is on the cost of producing medical isotopes, specifically molybdenum-99 (Mo-99) and its decay product technetium- 99m (Tc-99m), from highly enriched uranium (HEU)-based production systems. This cost information is used in Chapter 10 to address the fourth charge of the study task (Sidebar 1.2), which calls for an assessment of the “potential cost differential in medical isotope production in the reactors and target processing facilities if the products were derived from production systems that do not involve fuels and targets with HEU.” The study charge does not specify the point in the medical isotope supply chain (Figure 3.5) at which this potential cost differential is to be estimated. The committee received a range of opinions about how such estimates should be made from participants at its information-gathering meetings. Representatives of some isotope production organizations sug- gested that the congressional language clearly called for this estimate to be made at the point of Mo-99 production. Other participants suggested that this estimate should be made at the point of Tc-99m use (i.e., at the patient) because Congress is most concerned about the patient impacts of any medical isotope cost increases that might result from conversion to low enriched uranium (LEU)-based production. At its first information-gathering meeting (see Appendix C), the com- mittee invited Dr. Peter Lyons to provide a background briefing on the   Dr. Lyons was on the staff of the Senate Energy and Natural Resources Committee and played a key staff role in developing the language for this study. Dr. Lyons is now a member of the Nuclear Regulatory Commission. 80

MOLYBDENUM-99/TECHNETIUM-99m PRODUCTION COSTS 81 study task, and also to clarify whether Congress intended to specify the point in the supply chain where this cost differential was to be estimated. Dr. Lyons told the committee that Congress did not intend to specify a par- ticular point in the supply chain, and he recommended that the committee should use its best judgment in deciding how to develop these estimates. The committee recognizes that its report will have several audiences (e.g., the sponsor: Department of Energy-National Nuclear Security Admin­ istration [DOE-NNSA]), Congress, and medical isotope producers and u ­ sers) that will be interested in costs at different points in the supply chain. The committee also recognizes that its report could be used by Congress and NNSA to inform future policy decisions that could affect the avail- ability of HEU for medical isotope production. The committee judged that its report would be most useful to all of these audiences and purposes if it provided cost estimates at several points in the supply chain. The committee concluded that it could develop reasonably accurate cost estimates at the following three points in the supply chain: 1. Costs to medical isotope producers for making Mo-99; 2. Costs to radiopharmacies, hospitals, and clinics for purchasing technetium generators loaded with Mo-99; 3. Costs to patients (or their insurance companies) for purchasing Tc-99m doses obtained from these technetium generators. The next section of this chapter describes how the committee estimated costs at these three points in the Mo-99/Tc-99m supply chain. Subsequent sections present the cost estimates. The timeframes for the estimates are specified where they are presented. APPROACHES USED TO ESTIMATE COSTS It is important to recognize that the cost estimates developed by the committee do not need to be exact to meet the needs of this study. The National Academies were asked by Congress to estimate the potential cost differential for producing Mo-99 from HEU-based versus LEU-based pro- duction systems. As discussed in Chapter 10, the variability in costs identi- fied in this chapter, which are substantial and judged by the committee to be real, greatly simplifies the analysis. In conventional business terms, the cost of producing an article includes both the fixed costs associated with construction of the facilities used for production as well as the variable costs attributable to production and dis- tribution. When that article is sold, the price to the purchaser of that article reflects the producer’s cost for making it, plus a premium that reflects the

82 MEDICAL ISOTOPE PRODUCTION WITHOUT HIGHLY ENRICHED URANIUM value added by the production step, plus any product delivery costs. The premium represents the producer’s gross profit for selling the article. The committee initially set out to develop cost estimates using this busi- ness approach. Accordingly, costs for Mo-99/Tc-99m through the supply chain (Figure 3.5) were defined as follows: • Mo-99 producer. The cost of producing Mo-99 includes the fixed costs for constructing the Mo-99 production facility and that portion of the reactor that is attributable to production. The variable costs include both direct expenses for production (e.g., materials, labor, facilities, and services) and indirect expenses (e.g., facility maintenance, safety, and security) that are attributable to production. • Tc-99m generator producer. The cost of producing a Tc-99m gen- erator includes the gross cost of the Mo-99 (i.e., the price paid by the tech- netium generator producer for the Mo-99 plus any delivery charges) plus the fixed and variable costs associated with producing the generator. • Radiopharmacy, hospital, or clinic. The cost of producing a Tc-99m dose includes the net cost of the Tc-99m generator (i.e., the price paid by the radiopharmacy or hospital for the Tc-99m generator, plus any associ- ated delivery charges, minus any refunds received by the radiopharmacy or hospital when the generator is returned to the producer) plus the fixed and variable costs associated with producing the dose. • Patient. The cost for the Tc-99m dose used in the medical isotope procedure includes the cost of the Tc-99m dose to the hospital plus any hospital costs associated with preparing and administering the dose. As the study progressed it became clear to the committee that this approach was impractical for several reasons. First, the committee was not able to obtain detailed cost/price breakdowns for production because companies consider this information to be proprietary. Second, some of the fixed costs for producing Mo-99, especially the construction of reactors used to irradiate targets, were borne decades ago by state-owned entities. Reactor construction is expensive, and nobody knows what portions of these costs are attributable to Mo-99 production. Finally, and perhaps more important, the committee came to under- stand that there is no single cost or price for Mo-99/Tc-99m at any point in the supply chain. The costs to Mo-99 producers are different because they are located in different countries, operate under different currencies, and   Technetium generator producers may reuse the generator case and shielding.   The National Academies did receive proprietary information from some companies under nondisclosure agreements. However, these companies were unwilling to provide cost or price information.

MOLYBDENUM-99/TECHNETIUM-99m PRODUCTION COSTS 83 have different cost structures for materials, labor, facilities, and services. Infor­mation obtained by the committee suggests that the costs for produc- ing this isotope probably vary by at least 35 to 40 percent across all large- scale producers. This variation is substantially larger than the 10 percent cost feasibility test established by Congress (Sidebar 1.2). The costs to a radiopharmacy or hospital for purchasing technetium generators are also highly variable. Tc-99m generator producers publish list prices for Tc-99m generators, but the committee was told by several companies that nobody pays list prices. Costs are negotiated with each purchaser and are affected by market mechanisms. These include producers’ pricing power due to normal supply/demand balances as well as the ability of purchasers to obtain discounts through long-term and bulk purchasing agreements. The cost to a patient for a Tc-99m radiopharmaceutical is controlled largely by the reimbursement policies of the Centers for Medicare & Medicaid Services and private health insurance. Reimbursement levels vary by insurer and by procedure. Some insurers bundle the reimburse- ment for Tc-99m with the reimbursement for the nuclear medicine proce- dure. Other insurers will only reimburse the hospital for the actual cost for the Tc-99m radiopharmaceutical; the hospital is not allowed to add on any additional overhead charges associated, for example, with assay- ing or admin­istering the radiopharmaceutical. This practice is expected to become universal in the United States in the years ahead as insurance companies seek to contain the costs for medical care. If that occurs, the cost to the patient for Tc-99m radiopharmaceuticals will be the same as the cost to hospitals or clinics. Third, it is clear to the committee that the producers’ costs for making Mo-99 defined above does not include all of the actual costs of produc- ing this isotope. All large-scale producers irradiate targets in multipurpose r ­ eactors that were constructed either partly or wholly with government funding. These reactors serve many other users, and it is not at all clear how costs are apportioned to these users for the services they receive. At best, users probably cover only a share of operational costs and may or may not cover part of the capital costs of the facilities.   Reimbursement rates for nuclear medicine procedures can typically range from hundreds to thousands of dollars. The cost of the Tc-99m dose used in the procedure is typically on the order of $10.   For example, Mallinckrodt and Institut National des Radioéléments (IRE) utilize ­government- owned reactors in Europe for irradiating targets; MDS Nordion obtains Mo-99 from Atomic Energy of Canada Ltd (AECL) in Chalk River, Canada. AECL is a Canadian Crown Corporation that is wholly owned by the Canadian government. See Chapter 2.   Comparable new multipurpose facilities (e.g., the Open Pool Australian Lightwater [OPAL] reactor; see Table 3.2) cost hundreds of millions of U.S. dollars to construct.

84 MEDICAL ISOTOPE PRODUCTION WITHOUT HIGHLY ENRICHED URANIUM Fourth, and finally, international exchange rates may also have a sub- stantial impact on market prices and costs. All of the Mo-99 consumed in the United States is produced in other countries. Producers’ costs are denominated in the currencies of host countries, but Mo-99 prices are set in U.S. dollars. Consequently, swings in exchange rates can substantially impact market costs and prices. Recent U.S. currency devaluations can have substantial impacts on medical isotope pricing and could in fact make it more difficult to bring new foreign supplies of Mo-99 into the U.S. market. The committee decided to use a variety of approaches for developing cost estimates for the three points in the supply chain (i.e., for Mo-99 pro- duction, technetium generators, and Tc-99m doses). The committee used actual cost information in some cases, and it was able to deduce costs by compiling available information in other cases. The committee attempted where possible to develop multiple cost estimates at each point in the supply chain, both to improve its confidence in the estimates and also to understand cost variability. However, in some specific cases it was difficult for the committee to differentiate between “costs” and “prices” based on available information. Some of the estimates provided in this chapter prob- ably represent a mix of both. The approaches for estimating costs are described in more detail in the following sections. In some cases the committee has been intentionally vague about sources of information used to estimate costs. This was done to protect proprietary information and to make it impossible to trace cost e ­ stimates back to particular companies. The committee has not divulged any proprietary information in this report. Finally, it is important to note that all of the cost estimates provided in this report are in U.S. dollars. Costs of Producing Mo-99 For the purpose of this report, the committee defines Mo-99 produc- tion costs as the costs to the producer for making a unit quantity of Mo-99 that can be sold to a technetium generator manufacturer. As noted in the preceding section, these costs do not necessarily include all of the costs for producing Mo-99 because producers probably do not pay the full costs for using reactor facilities. As discussed in Chapter 3, the quantity of Mo-99 available for sale from an irradiated target is much less than the total quantity of Mo-99 produced in the target because of radioactive decay and process losses. Standard industry practice is to sell bulk Mo-99 on a calibrated “6-day curie,” which is nominally the quantity of Mo-99 remaining 6 days after the Mo-99 leaves the producer’s facility (see Sidebar 3.1). The committee will express the cost of producing Mo-99 in terms of 6-day curies.

MOLYBDENUM-99/TECHNETIUM-99m PRODUCTION COSTS 85 The committee estimated the cost of producing a 6-day curie using two types of information. The committee was able to develop a cost estimate based on its understanding of the production process and its understanding of costs at some key parts of the process. The committee was able to verify that this estimate was reasonable by checking it against public sources of information about producers’ revenues and the quantities of these isotopes that these producers supply to the market. The committee’s best estimate of average production costs for a 6-day curie of Mo-99 is about $225. However, there is likely to be a wide varia- tion in production costs among producers because of the factors described previously in this chapter. The committee could not gather sufficient infor­ mation to develop a quantitative estimate of the distribution of costs. However, based on the information it received, the committee judges that a reasonable estimate in the variation in production costs is probably on the order of $100. In other words, the cost for producing Mo-99 probably range from about $125 to $325 per 6-day curie. The overall cost of produc- ing 12,000 6-day curies of Mo-99 per week to meet 2006 demand at $225 per 6-day curies is about $140 million. At the National Nuclear Security Administration (NNSA) and Austra- lian Nuclear Science and Technology Organisation (ANSTO) conference in Sydney in December 2007, a representative of ANSTO informed the par- ticipants that a gram of Mo-99 was “worth” (i.e., could be sold for) about $46 million. Assuming a specific activity for Mo-99 of 4.8 × 105 Ci/g, a curie of Mo-99 is worth about $96 and a 6-day curie is worth about $470. This selling price is just over twice the average cost of production that was estimated by the committee. Costs for Technetium Generators Technetium generators are also sold on the basis of a calibrated quan- tity of Mo-99. However, the calibration is not based on 6-day curies, but rather on the number of curies that are contained in the generator on the day of or day after its delivery to the radiopharmacy, hospital, or clinic. The committee will refer to this calibrated quantity as technetium genera- tor curies.  No producers provided cost estimates to the committee or were asked to confirm such estimates.  As shown in Table 3.4, technetium generator producers can deliver technetium generators to radiopharmacies, hospitals, and clinics a day or two after they receive Mo-99. Depend- ing on the timing of its delivery, the technetium generator can contain up to about twice the number of 6-day curies that were delivered to the technetium generator manufacturer by the Mo-99 producer.

86 MEDICAL ISOTOPE PRODUCTION WITHOUT HIGHLY ENRICHED URANIUM The generators contain less than a curie to about 20 curies of Mo-99. The cost of shipping the generator to the hospital, radiopharmacy, or clinic will generally depend on the shipping mode and distance. For the purposes of this discussion the committee will neglect the shipping cost in the estimate of technetium generator costs, which is likely to be small in comparison to the costs of the generator itself and because it will vary from place to place. Technetium generator manufacturers publish list prices that can be used as a first step in estimating costs. The 2008 price list for a technetium generator sold by the Australian company ANSTO Radiopharmaceuticals and Industrials (ARI),10 for example, is plotted in Figure 6.1. There are two notable features about the data in this plot. First, list prices for 120 GBq (about 3.25 curies) and smaller generators define two linear trends that can be represented by the equation P = a GA + FP, (6.1) where P is the generator price in Australian dollars, GA is the quantity of technetium generator curies, and FP is the fixed price. The slope of the line, a, is the incremental price per GBq11 of Mo-99. The intercept of the line with the y-axis, b, represents the fixed part of the price for the techne- tium generator. Part of this price is presumably refunded if the generator is r ­ eturned to the producer. The two data trends shown in the figure represent two different calibra- tion days. The right-most (lower) data trend shows the prices for genera- tors calibrated for Thursday delivery but actually delivered on Wednesday; the left-most (upper) data trend shows the prices for generators calibrated on Monday but actually delivered the previous Friday. The price differ- ences (i.e., difference in the slopes) between the data trends can be almost exactly explained by the extra 2 days of radioactive decay for generators on the ­ upper curve. Also note that the intercepts of the two curves are a ­ pproximately equal, providing some confidence that they represent the fixed portion of the generator price. The second notable feature of this plot is the list price for 370 GBq (10 Ci) technetium generators: The list price is identical for both calibration days but falls along the data trend for Thursday calibration. Generators of this size are more typical of those sold in the United States, as will be discussed later in this section.   Asnoted in Chapter 3, Department of Transportation regulations allow technetium genera- tors to be shipped by Federal Express if they contain less than 20 curies. 10  ARI is a wholly owned subsidiary of ANSTO. 11  The price per curie can be obtained by multiplying this price per GBq by 37.

MOLYBDENUM-99/TECHNETIUM-99m PRODUCTION COSTS 87 6000 Monday Calibration 5000 Thursday Calibration 4000 Price (A$) 3000 2000 1000 0 0 100 200 300 400 Generator Activity (GBq) FIGURE 6.1  List prices in 2008 for ARI technetium generators sold in Australia on two different calibration days. NOTES: 100 GBq = 2.7 Ci. These data should not be used for estimating actual costs for the6-1 reasons explained in the text. Source: Data from ANSTO/ARI. As noted previously in this chapter, almost nobody pays list prices for technetium generators. Consequently, the prices shown in Figure 6.1 should not be used for cost estimation purposes. It is also important to recognize that these generators are sold in a different market (Australia and Pacific countries) in a different currency and do not necessarily reflect U.S. market prices. In contrast to the United States, Australian and Pacific markets place different social values on health care and have different structures for pric- ing and reimbursing medical treatments. The committee obtained a proprietary generator list price for another technetium generator producer that supplies the U.S. market. It shows the same slope and intercept behavior as Figure 6.1, especially for smaller gen- erators, but the slopes and intercept values are substantially different. Never­ the­less, Figure 6.1 is useful because it illustrates an important fact about

88 MEDICAL ISOTOPE PRODUCTION WITHOUT HIGHLY ENRICHED URANIUM technetium generator pricing: For a given generator producer, the incre- mental cost of a technetium generator curie of Mo-99 is approximately the same regardless of the size of the generator, and there is also a fixed-price component that is independent of generator size. This observation led the committee to conclude that it should develop estimates for the technetium generators rather than the Mo-99 that is contained within them. The committee used two sources of information to estimate technetium generator prices. First, Bio-Tech Systems (2006) reported that average prices for Mallinckrodt and BMS (now Lantheus) generators in 2005 were $1,400 and $2,080, respectively. Bio-Tech Systems (2006) also reported that the average Mallinckrodt generator size was 10 Ci, and the average BMS generator size was 16 Ci (see Table 3.3).12 Second, the committee obtained the radiopharmaceutical price list for Fraser Health, a large health authority in British Columbia, which contains technetium generator prices for two companies.13 This price list was negoti- ated in 2005, the same year covered by the Bio-Tech Systems report ­described previously, and is valid for purchases during the period 2005–2008. The prices were quoted in Canadian dollars (C$). In 2005, a ­ Canadian dollar was worth about US$0.83.14 The low and high prices for each generator size are C$1,800 (US$1,490 in 2005) and C$2,300 (US$1,910 in 2005), respec- tively, for a 7.5 Ci generator and C$2,300 (US$1,910 in 2005) and C$2,800 (US$2,320 in 2005), respectively, for a 10 Ci generator. The price variations reflect different bundles for different numbers of generator purchases. The cost variation for technetium generators sold to Fraser Health is about 12 percent for the 7.5 Ci generator and 10 percent for the 10 Ci generator. It is interesting to note the prices for 10 Ci generators sold to Fraser Health generator are much higher than the average price of a BMS generator. Of course, the latter price is an average and the former represents prospective prices for generators to be sold over a 3-year period. This data- set is too sparse to develop quantitative distributions of generator costs. Costs for Tc-99m Tc-99m is produced from technetium generators as a sodium pertech­ netate solution (NaTcO4); the quantity of Tc-99m contained in the solution 12  As noted in Table 3.3 the sizes of Mallinckrodt and BMS generators are incorrectly trans- posed in the Bio-Tech Systems (2006) report. 13  Fraser Health requested that the committee not name the companies. Fraser Health is a large health care company that can obtain competitive prices based on the numbers of genera- tors it purchases. 14  This exchange rate is based on the average daily interbank exchange rate for 2005 listed on the Bank of Canada website. As of December 2008, C$1.00 was approximately equal to US$0.80.

MOLYBDENUM-99/TECHNETIUM-99m PRODUCTION COSTS 89 is expressed in terms of activity, usually in units of millicuries (mCi). Tc-99m sodium pertechnetate is sold as individual doses for single ­diagnostic imag- ing procedures, typically ranging from about 20 mCi to 35 mCi. It is also sold in bulk quantities up to several hundred millicuries, which would be used for multiple procedures.15 The committee obtained information on Tc-99m sodium pertechnetate prices from several sources. The Bio-Tech Systems (2006) report provides average prices per dose of Tc-99m sodium pertechnetate from hospital and radiopharmacy sales in 2005. It reports that average prices range from $8.20 for hospital/clinic sales and $7.20 for radiopharmacy sales. The dose size is not specified. The committee obtained 2008 data on actual prices for Tc-99m ­sodium pertechnetate sold by several radiopharmacies. These prices were obtained from three large U.S. health care organizations that purchase Tc-99m s ­ odium pertechnetate from these radiopharmacies. Price quotes are pro- vided for individual Tc-99m pertechnetate doses and for bulk Tc-99m sodium pertechnetate. Most of the prices fall in the range from $0.28 to $0.45 per mCi, but two prices were much higher, about $0.90 per mCi.16 The committee estimated the cost for a dose of Tc-99m sodium pertech- netate by taking the middle of the price range noted above, neglecting the highest two prices, and multiplying by a dose size of 30 mCi. The result is about $11.00. The cost range, again neglecting the highest two estimates, is greater than ± 20 percent. The committee did not obtain enough data to develop quantitative distributions of technetium dose costs. DISCUSSION AND FINDINGS The committee estimates the following costs/prices for medical isotopes at three points in the Mo-99/Tc-99m supply chain. • Cost for Mo-99 production in 2008: about $225 per 6-day curie with a cost variation of about ± 40 percent. • Price for technetium generators in 2005: The “average” cost of a 10 Ci generator is about $1,900 with a variation of about ± 25 percent. • Price for a Tc-99m dose in 2008: about $11.00 per dose of Tc-99m sodium pertechnetate, with a price variation of over ± 20 percent based on the information that was available to the committee. 15  The amount of Tc-99m used in a single medical isotope procedure depends on the proce- dure itself and the body mass of the patient. 16  The $0.90/mCi prices were not for standard dose quantities and may reflect higher labor costs associated with preparation and assaying.

Next: 7 Conversion to LEU-Based Production of Molybdenum-99: Technical Considerations »
Medical Isotope Production Without Highly Enriched Uranium Get This Book
×
 Medical Isotope Production Without Highly Enriched Uranium
Buy Paperback | $65.00 Buy Ebook | $54.99
MyNAP members save 10% online.
Login or Register to save!
Download Free PDF

This book is the product of a congressionally mandated study to examine the feasibility of eliminating the use of highly enriched uranium (HEU2) in reactor fuel, reactor targets, and medical isotope production facilities. The book focuses primarily on the use of HEU for the production of the medical isotope molybdenum-99 (Mo-99), whose decay product, technetium-99m3 (Tc-99m), is used in the majority of medical diagnostic imaging procedures in the United States, and secondarily on the use of HEU for research and test reactor fuel.

The supply of Mo-99 in the U.S. is likely to be unreliable until newer production sources come online. The reliability of the current supply system is an important medical isotope concern; this book concludes that achieving a cost difference of less than 10 percent in facilities that will need to convert from HEU- to LEU-based Mo-99 production is much less important than is reliability of supply.

READ FREE ONLINE

  1. ×

    Welcome to OpenBook!

    You're looking at OpenBook, NAP.edu's online reading room since 1999. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

    Do you want to take a quick tour of the OpenBook's features?

    No Thanks Take a Tour »
  2. ×

    Show this book's table of contents, where you can jump to any chapter by name.

    « Back Next »
  3. ×

    ...or use these buttons to go back to the previous chapter or skip to the next one.

    « Back Next »
  4. ×

    Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

    « Back Next »
  5. ×

    To search the entire text of this book, type in your search term here and press Enter.

    « Back Next »
  6. ×

    Share a link to this book page on your preferred social network or via email.

    « Back Next »
  7. ×

    View our suggested citation for this chapter.

    « Back Next »
  8. ×

    Ready to take your reading offline? Click here to buy this book in print or download it as a free PDF, if available.

    « Back Next »
Stay Connected!