Quantitative studies of bone with the use of 18F-fluoride and 99mTc-methylene diphosphonate

Quantitative Studies of Bone With the Use of 18F-Fluoride and 99mTc-Methylene Diphosphonate Glen M. Blake, So-Jin Park-Holohan, Gary J.R. Cook, and Ignac Fogelman This article discusses methods for quantifying bone turnover based on tracer kinetic studies of the shortlived radiopharmaceuticals s~'nTc-MDP and 18F-fluoride. Measurements of skeletal clearance obtained by using these tracers reflect the combined effects of skeletal blood flow and osteoblastic activity. The pharmacokinetics of each tracer is described, together with some of the quantitative tests of skeletal function that have been described in the literature. The physiologic interpretation of quantitative measurements of bone obtained

with the use of short half-life radionuclides is discussed, and the advantages and limitations of sgrnTc-MDP and 18F-fluoride are compared and contrasted. Currently, lSF-fluoride dynamic positron emission tomography (PET) is the technique of choice for physiologically precise quantitative studies of bone. However, comparable data could probably be obtained by using 99mTc-MDP if methods for single photon emission computed t o m o g raphy (SPECT) quantitation were improved. Copyright 9 2001 by W.B. Saunders Company

NATOMICALLY, BONE can be divided into 2 types: compact (cortical) bone and cancellous (trabecular) bone. Compact bone is found in the diaphyses of long bones and the surface of flat bones, whereas cancellous bone is found in the epiphyseal and metaphyseal regions of long bones and the interior of flat bones. 1 As with all living tissue, bone is continuously renewing itself through a process referred to as remodeling. 2 The turnover of the skeleton by remodeling is essentially a surface phenomenon. Thus, although cancellous bone represents only 20% of the skeleton by mass, the rodlike structure of trabeculae means that they account for 80% of the total surface area, and thus 80% of bone turnover takes place there. In contrast, cortical bone represents 80% of the skeletal mass but accounts for only 20% of turnover. The turnover of the skeleton is achieved through the activity of groups of cells called osteoclasts and osteoblasts, which, respectively, resorb the old bone and lay down new bone at sites of bone remodeling. 2 At any one time, up to 100 million of these sites are active throughout the skeleton. During childhood and especially puberty, there is a period of rapid growth as the skeleton achieves its adult form. 3,4 Subsequently, from the third decade onwards, the bone lost by resorption is not completely replaced by formation, and a gradual loss of bone tissue occurs. 5 In women, there is a period of faster loss of bone mass after menopause when, because of the loss of endogenous estrogen, bone turnover is increased and a more pronounced imbalance exists between bone resorption and bone formation. In approximately 30% of women, this leads to the development of osteoporosis, 6 which is a systemic disease of the skeleton characterized by low bone mass and increased risk of

fracture. 7 Focal abnormalities of bone turnover are found in conditions such as Paget's disease and metastatic bone disease. Many techniques are available for the assessment of bone turnover. Among the simplest and least invasive are biochemical markers of bone resorption and bone formation measured in serum or urine (Table 1). T M These markers have been developed and refined over the past decade, with their sensitivity and specificity having been improved for characterizing the state of bone turnover (Fig 1). Their principal limitation is their poor precision in individual patients because of day-today variations in the measurements? 2 Among the more complex and invasive methods of measuring bone turnover is histomorphometric analysis of bone biopsies, which allows direct evaluation of the integrity of trabecular bone, as well as dynamic measurements of the rates of change at bone surfaces by using the technique of tetracycline labeling. 13 Other methods include bone densitometry techniques such as dual x-ray absorptiometry, which allows the measurement of bone mineral density at sites including the spine, hip, or forearm. 14,a5 However, even for the most favorable site (ie, the lumbar spine) it may be several years before a statistically significant change can be measured in an individual patient. 16,~7 Of particular interest to nuclear medicine specialists is the application of radionuclide tech-

A

28

From the Department of Nuclear Medicine, Guy's Hospital, London, England. Address reprint requests to Glen M. Blake, PhD, Department of Nuclear Medicine, Guy's Hospital, St. Thomas Street, London, England, SE1 9RT Copyright 9 2001 by W.B. Saunders Company 0001-2998/01/3101-0005510.00/0 do#lO.lO53/snuc.2001.18742

Seminars in Nuclear Medicine, Vol XXXI, No 1 (January), 2001: pp 28-49

QUANTITATIVE STUDIES OF BONE USING 1OF AND ~gmTc-MDP Table 1. Currently Available Bone Biochemical Markers

Type of Marker

Units

Bone formation markers Serum Bone-specific alkaline phosphatase Osteocalcin Carboxy-terminal propeptide of type 1 collagen Amino-terminal propeptide of type 1 collagen Bone resorption markers Urine Free and total pyridinoline

ng/mL ng/mL ng/mL ng/mL

nmol/mmol creatinine nmol/mmol creatinine nmol/mmol creatinine nmol/mmol creatinine

Free and total deoxypyridinoline N-telopeptide of collagen cross-links C-telopeptide of collagen cross-links Serum Cross-linked C-telopeptide of type 1 collagen Tartrate-resistant acid phosphatase

Bone Resorption

PHARMACOKINETICS OF SHORT HALF-LIFE BONE TRACERS

Pharmacokinetics of 99mTc-MDP and Other Diphosphonates

ng/mL

Bone Formation . . _ _ ~ I --I A N'X P

2

ter tracers allow measurements of skeletal clearance that reflect a combination of skeletal blood flow and osteoblastic activity. 23 In this article, methods that apply these latter 2 tracers to the measurement of bone turnover are discussed, and the merits of the 2 radiopharmaceuticals are compared. The following sections describe (1) the pharmacokinetics of 99mTc-MDP and ]8F-fluoride, (2) the various quantitative tests of skeletal function that have been proposed that use these 2 short half-life tracers, (3) the physiologic basis for ascribing the quantitative measurements of these tracers to bone blood flow and osteoblastic activity, and (4) a comparison of the advantages and limitations of 99mTc-MDP and ]SF-fluoride.

ng/mL

niques. These include complex kinetic studies of bone turnover with the use of calcium radionuclides (45Ca, 47Ca)18.19 or more convenient analogues such as 85Sr,Z~as well as studies that use the short half-life tracers 99mTc-methylene diphosphonate (99mTc-MDp)21 and 18F-fluoride.22 These lat-

3

29

The 99mTc-labeled diphosphonate radiopharmaceuticals (Fig 2) are analogues of pyrophosphate in which the P - O - P bond is replaced by a P - C - P bond. 24,25 In applications other than nuclear medicine, these compounds are more correctly known as bisphosphonates. 24,26 However, in this article, the convention of referring to them as diphosphonates in the context of their use as radiopharmaceuticals will be maintained. 2~,-~7,28 The development of these compounds was based on studies by Fieisch et al, who showed that, like pyrophosphate, they bind strongly to calcium phosphate and are

0

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Methylene Diphosphonate (MDP)

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Months

Fig 1. Results from a study of bone resorption and bone formation that used the biochemical markers N-telopeptide of collagen cross-links and bone-specific alkaline phosphatase in 84 elderly women who received bisphosphonste treatment for osteoporosis. Results are expressed in standard deviation (SD) units (T-scores) with respect to the mean and population SD measured in premenopausal women. Note that the bone resorption marker responds within 1 month and the bone formation marker within 6 months of the commencement of treatment. (Data from Garnero et al. 11 )

O

OH

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tl

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CH3 OH

Ethane-l-Hydroxy-1, 1-Diphosphonate (EHDP)

HO-- P - - C - HO

H

P--OH

I

OH

Hydroxymethane Diphosphonate (HMDP)

Fig 2. Structural formula of pyrophosphate and 3 commercially available diphosphonates that have been used for bone quantitation studies.

30

potent inhibitors of both the crystallization of calcium phosphate and the dissolution of hydroxyapatite crystals. 29 For this reason, pyrophosphate, polyphosphates, and bisphosphonates are widely used as antiscaling additives in washing powders. However, the enzymatic hydrolysis of pyrophosphate was found to limit its clinical application. In contrast, the P - C - P bond in bisphosphonates is extremely stable, and these compounds are not significantly metabolized in vivo. 24 In addition to their use for radionuclide imaging of the skeleton, bisphosphonates have found important clinical applications in the treatment of Paget's disease 3~ and hypercalcaemia of malignancy, 31 in which their main effect is to inhibit bone resorption. Subsequently, newer and more potent bisphosphonates such as alendronate and risedronate have been found to prevent bone loss in postmenopausal women, 32,33 and patients with existing osteoporotic fractures were shown to reduce the incidence of further fractures by up to 50%. 34,35 More recently, they have been used as an adjunc tive therapy for the treatment and prevention of metastatic bone disease, including the palliation of bone pain. 36,37 In general, bisphosphonates are poorly absorbed from the gastrointestinal tract. 24 However, when available systemically, they disappear rapidly from plasma with (depending on the compound) between 20% and 60% cleared to the skeleton and the remainder excreted through the kidneys. Plasma protein binding can vary but is often a significant factor. For many compounds, renal clearance in humans is comparable with glomerular filtration rate (GFR). 24 Once a bisphosphonate is deposited in bone, a portion may remain in the skeleton until the bone is remodeled. 24 Thus, the terminal halflife may be very long, up to 10 years for some compounds. The favorable properties of 99mTc-MDP for radionuclide imaging include its rapid clearance from plasma and its high urinary excretion, which contribute to the high contrast between bone and soft tissue. 21 Immediately after intravenous injection, protein binding is 25% to 30%, increasing to 45% to 55% by 4 hours and 60% to 70% by 24 hours (Fig 3). 38 Hyldstrup et a138 compared the renal extraction efficiencies of free 99mTc-MDP and 51Cr-ethylenediaminetetraacetic acid (EDTA) in 5 patients with renal artery catheterization and found an average ratio (and standard deviation) of

BLAKE ET AL o_

ci

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"6 0.60.5U-

"~ 0.4.~ 0.30

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28

Time (hr) Fig 3. Time dependency of protein binding of 99mTc-MDP after intravenous injection. The binding is expressed as the fraction of the total activity in plasma. (Reprinted with permission,as)

0.95 (0.12), which showed that renal clearance of unbound 99mTc-MDP is essentially identical to GFR. Unlike lSF-fluoride, 99mTc-MDP renal clearance is independent of urine flow rate. Like 51CrEDTA, 99mTc-MDP is not taken up by erythrocytes, and the 2 compounds share a similar extravascular extracellular fluid (ECF) space, which makes 51Cr-EDTA particularly suitable as a cotracer. 39,4~ When both are injected simultaneously, the plasma concentration of free 99mTCMDP initially falls more rapidly than 51Cr-EDTA, reflecting the effect of the additional clearance to the skeleton. 38 In contrast to 51Cr-EDTA, the terminal exponent for 99mTc-MDP in plasma is not reached until at least 6 hours, and the subsequent half-life is significantly longer than EDTA, which probably reflects the slow release of bound tracer from the skeleton. 38

Pharmacokinetics of lSF-Fluoride Stable fluoride is a natural trace element, and at least 99% of whole-body fluoride is thought to be present in the skeleton, primarily as fluoroapatite. 41 Like 99mTc-MDP, the pharmacokinetics of 18Ffluoride is principally determined by its uptake in bone and its renal excretion. Apart from its behavior in bone, fluoride is an analogue of chloride and bromide. All 3 halides occupy an ECF space significantly larger than that of 51Cr-EDTA or 99mTc-MDP, partly because they equilibrate with the transcellular fluid spaces including the alimentary tract, and partly because they are not entirely extracellular ions. 42-44 The transmembrane migration of fluoride ions is believed to be mediated by

QUANTITATIVE STUDIES OF BONE USING 18F AND 99mTc-MDP

the chemical equilibrium with hydrogen fluoride, which has a permeability through lipid membranes more than a million times greater than fluoride ions. 4] In particular, all 3 halide ions are taken up by red blood cells. 45 Erythrocyte concentration of ~8F-fluoride is around 45% to 50% of plasma concentration, and the transport of tracer in red cells accounts for approximately 30% of the total flux in blood. 46 It is therefore important to consider the issue of the availability of red cell ]8F for clearance to bone. Measurements that show that the single-passage extraction of whole blood t8F by bone is close to 100% 47 suggest that red cell ]8F is largely available for clearance to bone. This conclusion is consistent with the rate constant of 0.3 s "] for the release of ]8F ions from erythrocytes measured by Tosteson. 45 The observed concentration of t8F-fluoride in red blood cells suggests there is probably uptake also by immature erythrocytes in bone marrow. More significantly, chloride is known to cross the cell membrane into leukocytes as well as erythrocytes, 42 suggesting that granulocytes, the principal cellular component of active marrow, also take up tSF. Such behavior is consistent with the significant bromide space (55 mL/100 g) reported in marrow in animal studies. 43 In contrast, bromide space in other adipose tissue is much lower (12 mL/100 g) and is compatible with the total H20 content. Given that around 85% of the volume of vertebral bodies is occupied by active marrow, these considerations suggest that ~8F in bone marrow may be a significant factor in positron emission tomography (PET) imaging studies of fluoride kinetics. 48 Under normal physiologic conditions, plasma protein binding of ~SF-fluoride is negligibly small, 49-5~ and fluoride ions are freely filtered by the glomerulus. As with other halides, fluoride renal clearance is modified by tubular reabsorption, although the fraction reabsorbed is much less than for chloride, bromide, or iodide. 4].49 Fluoride reabsorption in the nephron is mediated by hydrogen fluoride, ~2 and consequently, 18F renal clearance varies with pH. 52.53 Fluoride renal clearance is also modified by diet. -s4 However, it is the effect of urine flow rate that is of most practical importance for nuclear medicine studies that use 18F.46 At high urine flows (-->5 mL 9 min-]), fluoride renal clearance averages 60% to 90% of GFR (Fig 4). However, for flows < i m L . min 4, renal clearance

31

1.21.0-

18F.fluoride renal clearance Ratio to GFR n=45x4

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012

014

016

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1-hour Urine Volume (liters) Fig 4. Scatter plot of the ratio of the renal clearance of 18F-fluoride to the renal clearance of SlCr-EDTA plotted against urine volume. Data were obtained from hourly urine collections made between 0 and 4 hours in 45 postmenopausal women. A urine flow rate of 5 mL 9 rain "1 or higher is required to control whole-body fluoride kinetics. These data were obtained in a study in which care was taken to maintain good hydration in all patients. However, this was not successful in every case.

may be as low as 5% of GFR. 46 Therefore, establishing good hydration of the patient and maintaining urine flow rates in the range of 5 to 10 mL 9 min -t are important for the conduct of clinical studies if uncontrolled effects on whole-body fluoride kinetics are to be avoided. Fluoride has important clinical applications in the prevention of dental caries and the treatment of osteoporosis; more detailed descriptions of its pharmacokinetics can be found in reviews of its use in these contexts.4 ~.55

THE QUANTITATIVE INVESTIGATION OF BONE TRACER KINETICS Although discrete changes such as metastatic bone disease, fractures, or Paget's disease are readily identified on radionuclide bone scans, the diffuse changes associated with metabolic bone diseases, such as renal osteodystrophy, osteomalacia, primary hyperparathyroidism, or osteoporosis are more subtle, and the scan image often appears indistinguishable from normal. In such cases, quantitation of whole-body skeletal tracer kinetics may provide useful information relating to the state of bone turnover. The methods described in the literature for the quantitation of ]8F and 99mTcMDP kinetics are reviewed in the following 4 sections: (1) the 24-hour whole-body retention

32

BLAKE ET AL

Table 2. Methods for Quantitative Evaluation of Bone Tracer Kinetics Bone Kinetic Method

Radionuclide Tracer

References

Parameter*

24-h whole-body retention Compartmental modeling of plasma, clearance curve Ratio of plasma concentration of bone and renal tracers Continuous infusion of bone and renal tracers Deconvolution of whole-body retention curve Dynamic PET imaging Gamma camera global skeletal uptake Quantitative SPECT

99mTc-MDP 18F-fluoride or 99mTc-MDP

FogelmanS6-59 Charkes 76-so

Kbone/Krenall" Ktotat and Kbone

99mTc-MDP and 51Cr-EDTA

Nisbet 4~

~ K b o n e / K .... Ir

99mTc-MDP and alCr-EDTA ~8F-fluoride 18F-fluoride 99mTc-MD P 99mTc-MDP

Hyldstrup 39 Wootton 91 Hawkins ~ D'Addabb0105 Front110

Kbone Kbonew Ktotal and Kbone Kbone/Krena I KbonJKrenaI

* The methods have been interpreted according to whether they represent the bone tissue (Ktotal) or the net clearance to the bound bone compartment Table 6. $ By rearranging Equation 1, one obtains: Kbone/KrenaI = WBR/(1 - WBR). This is a rough approximation derived by substituting the 99mTc-MDP and a single-sample GFR and ignoring the issue of the protein binding of MDP. w If a single exponent is fitted to the slow component of the bone impulse

(WBR) test, (2) compartmental modeling of whole-body tracer kinetics, (3) model-independent approaches to skeletal tracer kinetics, and (4) imaging approaches to studying regional tracer kinetics with the use of PET, single photon emission computed tomography (SPECT), or wholebody bone scans. A list of the methods discussed is given in Table 2. In the following sections, kinetic variables representing measurements of plasma or whole blood clearance rates (units: milliliters per minute) are denoted by an upper case K, and variables representing intercompartmental rate constants (units: minutes -1) are denoted by a lower case k. T h e 2 4 - H o u r WBR T e s t The 24-hour 99mTc-diphosphonate WBR test was developed by Fogelman et al as a method of extending the diagnostic potential of radionuclide bone scans in the investigation of metabolic bone disease. 56-59 The basis of the 24-hour WBR investigation can be explained in terms of the simplified compartmental model shown in Fig 5. 60 After administration, the tracer equilibrates with the ECF space and is cleared either to the bound bone compartment or out of the body through the kidneys. Although there is a slow release of tracer from bone represented by the rate constant k 4, the effect of this on the 24-hour WBR is probably negligibly small. 21,61 As discussed previously, most diphosphonates show significant protein binding, but it is likely that the fraction of tracer available for uptake in the skeleton is the same as

measurements of the total clearance to the whole of alone (Kbone). The distinction is explained further in

S~Cr-EDTA plasma concentrations in the equation for function, the intercept is Kbone.

that available for renal clearance. With this assumption, and ignoring the effect of k4, then after 24 hours the WBR approximates to the value determined by the partitioning of tracer between bone and kidneys: 24-hour W B R

=

gbone/(Kbone-t-g....

l)

(1)

where Kbone and Krenat denote the whole skeleton and renal plasma clearances, respectively. Two approaches have been adopted to measure 99mTc-diphosphonate WBR. Fogelman et al used whole-body counting at 24 hours with either a shadow-shield whole-body counter (requiring 2-MBq tracer) 56'62 or a gamma camera. 63 Other studies require the patient to perform a 24-hour urine collection; the calculation of the WBR comes from the following equation64-66: 24-hour W B R = l - 24-hour UE

(2)

where 24-hour UE is the fraction of tracer recovered in the urine collection calculated from a

ECF

Plasma

Mineral

Krenal Fig 5. The compartmental model used to explain the 24-hour sSmTc-MDP WBR investigation. After intravenous injection into the plasma compartment, tracer equilibrates with the extravascular ECF compartment, and it is cleared from plasma through the kidneys and to the bound bone compartment with the plasma clearance rates KrenaI and Kbono, respectively.

QUANTITATIVE STUDIES OF BONE USING ~SF AND 9amTc-MDP

measurement of urine volume and counting an aliquot of urine in a gamma counter with a standard. With either approach, making the measurement at 24 hours ensures that errors caused by incomplete emptying of the bladder or continuing retention of tracer in soft tissue are minimized. With both methods, careful attention to technique is required to reduce errors. 62,64,65 To ensure a high radiochemical purity ( > 99%), the 99mTcdiphosphonate should be freshly prepared with the appropriate activity and not obtained by dilution from a high specific activity bone imaging vial. The most significant source of error in the urine collection method is the completeness of the collection. Patients must be physically able to collect the 24-hour urine, but motivation to ensure that the collection is complete is also essential. If necessary, the completeness of the 24-hour urine collection can be checked by using a small dose (0.3 MBq) of 5tCr-EDTA given at the same time as the bone tracer. Recovery of the EDTA in urine at 24 hours should be greater than 95%, and a lower figure in a patient with normal renal function indicates an incomplete collection. Although the whole-body counting method avoids the uncertainties of a urine collection, care is still needed to achieve accurate results. 62.67 The baseline whole-body count is begun 5 minutes after injection and then repeated at 24 hours. After correction for background and radioactive decay, the ratio between the 24-hour and 5-minute counts is used to calculate the WBR. Additional considerations to ensure accuracy include careful control and monitoring of the scanning speed, care with repositioning the patient, daily counting of a standard to check sensitivity, and care with injection technique to avoid extravasation of tracer. It is clear that the assumption that all of the tracer in soft tissue will be eliminated by 24 hours is unlikely to be correct. From follow-up imaging studies of patients having radionuclide bone scans, Smith et ai estimated that approximately 30% of 99mTc-hydroxyethylidene diphosphonate (HEDP) retained at 24 hours was localized in soft tissue. 68 However, no correction was made in this estimate for the inclusion of Compton scattered photons from bone in the soft tissue counts, which are likely to be a significant source of error. The interpretation of the 24-hour WBR is based on the assumption that the rate of release of tracer from the bound bone compartment (k4 in Fig 5) is

33

negligibly small. Fogelman et al reported daily measurements of WBR of 99mTc-HEDP from 24 to 96 hours in 10 patients after radionuclide scans. 6~ The mean release of tracer was 20% per day in 4 patients with normal scans (mean 24-hour WBR = 16.3%) and 10% per day in 6 patients with abnormal scans (mean 24-hour WBR = 33.9%). Expressed in more conventional units, these figures correspond to values of k 4 of 1.5 • 10-4 and 0.7 • 10 -4 min -], respectively. Subramanian et al reported a similar rate constant of 1.0 • 10-4 min -~ derived from the slope of the terminal exponent measured over 35 days by using 95mTc-MDP in beagle dogs. 2~ However, it is unclear from either of these studies whether the labeled tracer leaked from the bone surface and was available for recirculation, or whether there was dissociation of the technetium label from the diphosphonate. 69,7~

Clinical Studies of Whole-Body 9~ Retention Fogelman et al reported values of 24-hour WBR of 99mTc-HEDP in healthy patients and in groups of patients with renal osteodystrophy, Paget's disease, osteomalacia, primary hyperparathyroidism, and osteoporosis. 56-58 Values ranged from 19.2% --1.7% in healthy patients to 88.6% _+ 10.6% in patients with renal osteodystrophy (Fig 6). The 24-hour WBR figure varied with the diphosphonate used. Results for ~gmTc-HEDP, 99mTc-MDP and 99'"Tchydroxymethane diphosphonate (HMDP) in the same 20 healthy patients gave mean values of 1O0

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Fig 6. Results of measurements of 24-hour sgmTc-HEDP WBR in patients with metabolic bone disease. (Reprinted with permission of the Society of Nuclear Medicine from Fogelman I, et sl: The use of WBR of Tc-99m disphosphonate in the diagnosis of metabolic bone disease. J Nucl Med 1978;19:270275.)

34

BLAKE ET AL

inine clearance. 66 In 21 women with osteoporosis who were treated with calcium and vitamin D, the mean 24-hour WBR fell from 48.1% to 37.9%. It is clear from Equation 1 that 24-hour WBR values reflect not only bone clearance of tracer but also renal clearance, which for 99mTc-MDP can be assumed to equal GFR. On this basis, Hyldstrup et al proposed a GFR-corrected 24-hour WBR index in which the renal clearance term in Equation 1 was adjusted to a standard creatinine clearance of 100 mL 9 min-l. 73 Mosekilde et al examined the dependence of 24-hour WBR on bone mineralization rate, measured by using a 7-day 47Cakinetic study, creatinine clearance, and forearm bone mineral content; the forearm bone mineral content was measured by photon absorptiometry. 74 Multiple regression analysis of data from a group of patients with metabolic bone disease showed that 24-hour WBR was correlated with all 3 variables. However, in a second group of patients with osteoporotic vertebral fractures, only the correlation with creatinine clearance was statistically significant. Further information about the 24-hour WBR test can be found in Hyldstrup's review. 75

18.4% _+ 2.9%, 30.3% -+ 4.2% and 36.6% -+ 5.0%, respectively. 71 Figures for the 3 tracers in individual subjects were highly correlated. Studies that used 99mTc-HEDP in 250 healthy patients showed that 24-hour WBR values fell from age 20 to 35 and thereafter slowly increased with age. 59 The latter effect is at least partly because of the decline in renal function with age. However, in women there was a marked rise in 24-hour WBR at menopause, which reflects the increased state of bone turnover in postmenopausal women: This effect was confirmed by Thomsen et al, who showed differences in 24-hour WBR values between 2 groups of age-matched pre- and postmenopausal women in age groups of 45 to 49 years and 50 to 54 years; the differences in 24-hour WBR values were similar to the differences in biochemical markers of bone turnover (Fig 7). 72 This finding is consistent with the report of Fogelman et al of a group of 37 women who underwent oophorectomy who enrolled in a trial of estrogen therapy for the prevention of bone loss. 57 The 24-hour WBR values were significantly lower in patients taking estrogen compared with placebo, were inversely related to daily estrogen dosage, and correlated positively with the rate of bone loss measured by photon absorptiometry. Davie et al also studied 99mTc-MDP 24-hour WBR in healthy and osteoporotic postmenopansal women and reported increased values in patients with osteoporosis over and above that expected from their reduced creat-

Compartmental Modeling of Whole-Body Tracer Kinetics Two potential disadvantages of the 99mTc-MDP 24-hour WBR method are that the values reflect renal clearance of tracer as well as bone clearance, and that no allowance is made for the release of

A 24-h Whole Body Retention of B Serum Bone Gla Protein (ng/ml)C Fasting Urinary Hydroxyproline 99mTc-diphosphonate (%)

9

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Premenopausal women

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Age 45-49

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Age 45-49

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50-54 yr

Age 45-49

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50-54 yr

Fig 7. Comparison of measurements of 24-hour WBR, serum bone Gla protein (a bone formation marker), and fasting urinary hydroxyproline (a bone resorption marker) in pre- and postmenopausal women aged 45 to 49 years or 50 to 54 years. All 3 markers of bone turnover are responding to the patients' menopausal status rather than their age. (Data from Thomsen et al. 72 )

QUANTITATIVE STUDIES OF BONE USING 18F AND 99r~Fc-MDP

bound tracer from the skeleton. An alternative index of skeletal status is provided by the direct measurement of Kbo,,e (see Fig 5), which represents the skeletal clearance of tracer to the bound bone compartment analogous to the use of 51Cr-EDTA plasma clearance to measure GFR. This latter approach to quantifying bone tracer kinetics was examined by Charkes et al in a series of papers that interpreted whole blood clearance curves by using the 5-compartment model shown in Fig 8. 76-80 Compared with the simple model used to explain the 24-hour WBR investigation, the Charkes model introduced 2 additional compartments: a renal tubular urine compartment to correct for the tubular reabsorption of 18F-fluoride, and a bone-ECF compartment to mediate the transfer of tracer from the bone capillary bed to the sites of mineralizing bone. Bone ECF is an important element in the description of tracer deposition in bone mineral. 8t For example, in studies in canine tibia, Hooper et al reported a fractional ECF volume of 0.10-in tibial cortical bone and 0.22-in tibial marrow space. 82 The solution of the Charkes model for a bolus injection in the vascular compartment is a blood curve represented by the sum of 4 exponents, of which the terminal exponent reflects the slow release of bound tracer from bone. Because the curve is normalized by summing the coefficients of the 4 exponents to unity, there is a total of 7 unknown constants to solve in the model. Charkes and Siegel recently presented an analytical solution allowing the rate constants to be calculated directly from the coefficients and exponents of the sum-ofexponents fit to the blood curve. 83 However, the Non-Bone ECF 4 k41 I

[ k14

35 Table 3. Rate Constants for 5-Compartment Model of Whole-Body ~SF-Fluoride Kinetics in Man

Compartment

Parameter*

Vascular Nonbone-ECF Bone-ECF Bone Tubular urine

k4t k14 k21 kl 2 k32 k2a ks1 k15 ko5

Value (and Standard Error) (min -1)

Volumet (L)

1,191 (0.059) 0.567 (0.027) 0.246 (0.011) 0.908 (0.42) 0.602 (0.030) 0.020 (0.004) 0.0245 0.388 0.612 (0.052)

i,-32[k32 Bone ECF ~ Bone Minera~ 2 ~ 3

Tubular Urine 5

l k0s Fig 8. The 5-compartment modal used by Charkes et al to study the whole-body kinetics of ~SF-fluoride and 99mTC" MDp.7s-s0

1.3 40 0.3

NOTE. Data from Charkes et al. 76 * Parameters listed are identified in Fig 8. t Notional volume of compartment for a 70-kg patient. 5 Assumes GFR is 120 mL 9 rain 1.

solution is not unique, and in general there are 3 sets of solutions that must be evaluated to establish the one with physiologically appropriate values. Table 3 lists values of the rate constants for t8F-fluoride in humans published by Charkes et al. 76 Notional volumes for each compartment relative to blood volume can be calculated from the ratio of the 2 rate constants that connect it with the vascular compartment. In the Charkes model, the total clearance to the skeleton is represented by the rate constant k21 (Fig 8). However, this reflects the clearance to the bone-ECF rather than the bound bone compartment. To estimate the net clearance to bone mineral, as represented by the K~,,..... term in Fig 5, the net transfer of tracer through the bone-ECF compartment for deposition on bone surfaces must be calculated by allowing for the fraction returned to the vascular compartment, as in the following equation:

Kho,,,, = Vh,,,,,,," k2, " (k.,2/[k,2 + k,2]) k21

4.9 10,3

(3)

where the blood volume Vhmoa has been introduced to convert the figures into a clearance measurement. When interpreted with the data in Table 3, Equation 3 shows that approximately 40% of tracer entering the bone-ECF compartment is transferred to the bone mineral compartment. There is a similar effect on tracer that is released from bone mineral and flows back to the blood compartment in which the rate constant k2s is modified by the fraction of tracer returned to bone to give a net transfer to the vascular compartment, represented by the following equation:

k,~ = kz," (k,ff[k,2 + k32])

(4)

36

T h e 5-compartment model was used by Charkes et al to quantify the effects on bone scan images of changes in cardiac output, increased bone avidity for tracer, edema and renal failure, and to investigate the optimal timing of skeletal imaging. 79,84 However, there are a number of obstacles to the use of the model to evaluate skeletal clearance in individual patients. First, adequate sampling of the blood curve is essential with at least 3 data points for each exponent, and sampling must continue for a period long enough to ensure the accuracy of the slope and intercept of the terminal exponent. 83 In this respect, the short half-life of 18F (T1/2 = 110 minutes) is a significant limitation because it is not feasible even with the use of PET imaging activities to obtain data on the time scale (12 to 24 hours) that may be required. A second difficulty that can arise in compartmental modeling is the high correlation between the errors in the coefficients and rate constants in the multiexponential curve fit, which leads to associated large errors in the intercompartmental rate constants inferred from the model. The correlation between the errors in Kbo~ and k 4 is a particular problem in this instance. Finally, the representation of nonbone-ECF by a single compartment is an oversimplification. In practice, ECF space is multicompartmental, with a variety of different spaces that equilibrate with the vascular compartment at different rates. 42 The effect of this can be seen in studies of renal tracers, such as 99mTc-DTPA and inulin, in which plasma clearance curves depart from the biexponential equations predicted by models with a single ECF space. 85 Additionally, if blood sampling finishes too early to properly characterize the terminal exponent, then the wrong exponents will be identified with the movement of tracer in and out of bone, and the rate constants inferred may be erroneous.

Model-Independent Approaches to Skeletal Tracer Kinetics The compartmental analysis method discussed previously is dependent on assumptions about the number and arrangement of the compartments encountered by the tracer. Some of the inherent uncertainties can be avoided with the use of noncompartmental methods to derive indices of skeletal tracer kinetics based on plasma clearance data. A number of model-independent approaches to the

BLAKE ET AL

analysis of blood sampling data for short half-life bone tracers have been described and are discussed in the following sections. The Nisbet Method

Nisbet4~ described a simple method of quantifying 99mTc-MDP kinetics during routine radionuclide bone scanning by using the relative plasma clearances of 99mTc-MDP and 51Cr-EDTA. 51CrEDTA was used as a cotracer to correct for the renal clearance of 99mTc-MDP by glomerular illtration and because, as noted previously, the 2 tracers occupy ECF spaces with similar volumes of distribution. Initially, a method was developed based on multiple blood sampling from 5 minutes to 2 hours, with the results expressed in terms of the ratios of the areas under the 2 plasma concentration curves. 86 Subsequently, a simpler but essentially equivalent method was described based on the ratio of the plasma concentrations of 5XCr-EDTA and 99mTc-MDP at 4 hours. 4~ In healthy patients, this ratio was shown to be almost constant between 30 minutes and 7 hours with a mean ratio (and standard deviation [SD]) at 4 hours of 1.19 (0.12). However, no correction was made for the plasma protein binding of MDP, and the parallel plasma clearance curves of the 2 tracers are fortuitous, reflecting the offset of the more rapid fall of the free 99mTc'MDP curve, which is caused by the additional clearance to bone, by the increasing fraction of uncleared protein-bound MDP. The Nisbet index was elevated in patients with renal osteodystrophy, Paget's disease, osteomalacia, and hypercalcemia, reflecting the increased skeletal clearance of 99mTc-MDP in these diseases. 4~ The advantage of the Nisbet method is its simplicity, because it can be used as an adjunct to the routine bone scan to provide a quantitative index of total skeletal function, and it does not require either special equipment such as a whole-body counter; it also does not require the patient to make 2 separate visits. The method is semiquantitative in the sense that the value of the Nisbet index does not relate directly to the skeletal clearance Kbo,, e. As noted previously, one limitation is the absence of a protein-binding correction, which can vary significantly among patients. The method is best understood by comparing it with the single-sample methods for estimating GFR, which exploit the inverse rela-

QUANTITATIVE STUDIES OF BONE USING lSF AND 99mTc-MDP

tionship between GFR and 51Cr-EDTA plasma concentration measured at a set time point. 87,88 In this sense, the Nisbet index can be interpreted as an estimate of the ratio of the total body (renal plus skeletal) clearance of MDP to the GFR. As in the 24-hour WBR method, Kbo,e is expressed in terms of its ratio to GFR (Table 2). The Nisbet method was applied by Hosking et al in studies of the treatment of Paget's disease. 89,9~The ratio of the S]Cr-EDTA and 99mTcHMDP plasma concentration was interpreted as a measure of diphosphonate space, which was shown to correlate with the volume of bone involvement estimated from the radionuclide bone scan as well as with biochemical markers of bone resorption and bone formation. 89 In a separate study, the pretreatment diphosphonate space was shown to be a good predictor of the amount of pamidronate treatment required before biochemical markers fell back to within the normal range. 9~

The Hyldstrup Method Hyldstrup et al described a model-independent method of deriving the skeletal plasma clearance of 99rnTc-MDP (Kh....... Fig 5) by using the continuous infusion of MDP with 5JCr-EDTA as a cotracer. 39 Using the Fick principle, one can calculate the total body plasma clearance of a tracer as the infusion rate (Jin) divided by the steady state plasma concentration (Cpt[~]):

K,,,,,t body = Jitr/Cpl(00)

(5)

The total body clearance of 99mTc-MDP is the sum of the skeletal and renal components, and the latter can be estimated from the 51Cr-EDTA clearance. Thus, 99mTc-MDP skeletal clearance can be calculated from the following equation: K,,,,,,,. = K,,,,,,, b,,ay -- X ...... ,=

(J,,/C,,,[oO])MDP

- (J,,/Cp,[~

(6)

Hyldstrup et al showed that with a constant infusion after a bolus injection as a priming dose, a steady state plasma concentration was reached at 3.5 hours with no further changes observed at 5 hours (Fig 9). 39 It is important to measure free 99mTc-MDP because the bound fraction is not available for clearance by either the skeleton or the kidneys. During the steady state represented by the Fick equation, it is the net clearance to the skeleton

37

_14t 1.2

r-

9

.~

1 .o

o

0.8

tO

o

E r E

0.6

~

~

o

o

C

o

e~

r-EDTA 0.4-

t

6'0

120

180

....

Tc.MDP i

2,~0

360

Time (min) Fig 9. Plasma activity curves for sSmTc-MDP and SlCrEDTA after bolus injection and constant infusion of the 2 tracers. The activity is given as percent per milliliter of the infusion rate, (Reprinted with permission, as)

that is being measured (ie, the difference between the inflow and outflow of tracer from bone). In this instance, it is assumed that the release of bound tracer from bone is negligible and does not significantly perturb the equilibrium state represented in Equation 6.

The Wootton Method: Analysis of Skeletal Tracer Kinetics by Deconvolution Deconvolution is one of the most versatile model-independent numerical techniques used in the analysis of nuclear medicine data and was applied by Wootton and Reeve to the measurement of the skeletal clearance of ~SF-fluoride.9' Reeve et a19294 also applied similar principles to the analysis of the skeletal kinetics of 47Ca and 85Sr. In the Wootton method, 9j the WBR function R(t) after a bolus injection of tracer is calculated by subtracting from the initial dose the fraction excreted (this is simplified for ~SF because all excretion can be assumed to be through the kidneys) and the fraction in the vascular compartment:

R(t)= 1-

V p I " P ( t ) - K ..... t"

;o

P(t)dt

(7)

where P(t) is the plasma concentration, V.,t is the 125 t plasma volume (measured with I-human serum albumin [HSA]), and K .... t is the renal clearance of 18F (measured by a urine collection). The function R(t) is deconvoluted with P(t) to derive

38

BLAKE ET AL 10000

i

[ "~

~",k'tl

*

Bone

/ .....

Soft Ti . . . .

I---=--t-_

Total Body

_ _

1000

g

"".~ 9 '~-"'~--~'--'~-'-s - ~ ............. ,

ii -5 t~

100

_E 10

2'0

4'0

6'0

8'0

1 O0

120

Time (min) Fig 10. Derivation of the whole skeleton bone impulse function by deconvolution by using the method of W o o t t o n et alp 1 The plasma clearance curve of lSF-fluoride is used to derive the total body (bone plus soft tissue) impulse function. Plasma clearance curves of SlCr-EDTA or S2Br are used to estimate and subtract the soft tissue component. The bone impulse function is fitted w i t h a single exponent, whose intercept gives the net plasma clearance to bone mineral (Kbone, Table 5) and the slope of the rate constant for the reverse transport from bone (k4, Fig 5).

the whole-body impulse response function H(t) defined by the integral equation:

R(t) =

f0

H('r)" P(t - ~')d'r.

the rapid fall in plasma concentration in the first few minutes and the much slower changes that occur after several hours. Even before performing the deconvolution analysis, one may have problems trying to fit the rapid fall in the blood curve data during the first few minutes from interpolation of only 1 or 2 data points, and issues may arise from the incomplete mixing of tracer in the vascular compartment in this time period. Other difficulties include the systematic differences between arterial and venous curves 95 and the wider issue of whether venous sampling of 18F from the forearm is representative of the arterial input to core organs, including the kidneys and skeleton, especially during the first 5 or 10 minutes after bolus injection. Regardless of these criticisms, the deconvolution method is a powerful model-independent tool for studying skeletal tracer kinetics. It was subsequently shown by Reeve et al96 that measurements of Kbone that used the deconvolution approach correlated with histomorphometric measurements of osteoblastic work rate and also with 85Sr measurements of Ca 2+ infux into bone. The method is also of interest in the evaluation of radionuclide therapy of bone metastases, in which it can be used to study how the tumor dose is modified by the total burden of metastatic bone disease in the skeleton. 97

(8)

The function H(t) describes the WBR of tracer after a spike injection (discounting all effects of recirculation), and it is the sum of separate components due to bone and soft tissue (Fig 10). The skeletal component is readily identified by its dominant flat exponent that describes the slow release of tracer from bone, whereas the soft tissue component decreases very rapidly with time. Wootton et al used simultaneous tracer doses of 51Cr-EDTA and 82Br-bromide to quantify and subtract away the soft tissue component. 9t Once the bone impulse function is identified, the skeletal clearance Kbo,e is found from the intercept of the fit to the slow exponent, whereas the rate constant kg is found from the slope. As with all applications of deconvolution, care is needed to ensure that systematic errors in the evaluation of the impulse function are avoided. In this instance, the difficulties include the wide range of frequencies present in the fourier transform of the blood curve, which must accommodate both

Imaging Studies of Regional Skeletal Tracer Kinetics Dynamic PET Imaging With 18F-Fluoride The application of dynamic PET imaging of bone with the use of lSF-fluoride has attracted considerable interest over the last decade,48,98-]o2; these advances are discussed in an article by Cook in this issue. ~~ For this reason, the technique is reviewed only briefly here. However, the PET method is of interest because of the insight it gives into the physiologic basis of bone tracer kinetic studies. The most widely adopted approach to data analysis in 18F-fluoride dynamic PET is the 3-compartment model developed by Hawkins et al in analogy with the compartmental analysis of lSFfluorodeoxyglucose studies (Fig l 1). 48 The accurate and complete sampling of both the blood input curve and the bone uptake curve made possible by PET methods makes data analysis more robust than the compartmental modeling approach to whole- body lSF kinetics discussed previously. Table 4 lists values of the rate constants inferred by

QUANTITATIVE STUDIES OF BONE USING +SF AND 99mTc-MDP

Fig 11. The compartmental model used by Hawkins et aP e to analyze dynamic PET studies of lSF-fluoride in bone. (RBC, red blood cells.)

I

R B C

Plasma

Kt~ _

F

39

_J -

k2

Hawkins et a148 and in a number of other studies of patients with metabolic bone disease and postoperative bone grafts. 98-1~ As with all such analyses, the appropriateness of the compartmental model is a key issue in evaluating the solutions obtained. Whereas the Hawkins model correctly includes a bone-ECF compartment (Fig 11), it is likely, in view of the intracellular uptake of ~SF in bone marrow discussed previously, that much of the bone-ECF compartment measured in PET studies of the vertebral bodies represents tracer uptake in bone marrow. This view is supported by the relatively large notional volume for bone-ECF ( K , , , J k 2 ~- 0.40) inferred from the rate constants in Table 4, as well as the comparable figure for bromide space in bone marrow reported in animal studies. 43 It is therefore unlikely that the bone-ECF compartment in Fig i I represents a single well-mixed compartment, with the attendant uncertainties in how this will affect the inferred values of the rate constants in the

[ BoneECF

I

k3

_

F

_J -

k4

Bone Mineral

t

model. However, in support of the Hawkins model, it is important to consider the evidence for the postmortem migration of 18F tracer reported by Tothill in animal studies. ~~ The rapid diffusion of fluoride indicated by these studies implies that 18F in bone marrow is fully available for uptake in the bound bone compartment, even if on a somewhat longer time scale than for true bone-ECF. G a m m a C a m e r a Studies With

99mTc-MDP

As well as PET imaging with ~8F-fluoride, interest in quantitative radionuclide studies of bone in recent years has centered on whole-body and SPECT gamma camera imaging with the use of 99mTc-MDP. Tracer uptake on dualhead gamma camera whole-body bone scans has been quantified to emulate the 24-hour WBR tracer investigation, j~176 In the method originally described by D'Addabbo et al, ")5 a region of interest (ROI) is drawn around the skeleton on a 4-hour total body scan to avoid the bladder,

Table 4. Published Values of Quantitative Parameters From 18F-Fluoride PET Studies in Healthy Patients, Patients With Metabolic Bone Disease, and Patients Studied After Maxillofeciel Bone Grafts* Bone Disease (Measurement Site) Healthy men (vertebra)

n 11

Paget's disease (pelvis)

21.

Primary hyperparathyroidism (vertebra)

21"

Osteoporosis (vertebra)

4

Secondary hyperparathyroidism (vertebra)

8

Bone graft study (normal cervical vertebra)

11

Bone graft study (maxillofacial bone grafts)

11

eostmenopausal women (vertebra)

26

Postmenopausal women (humerus)

26

Ktotal mL 9min 1 . mL 1

Kbone mL, rain 1 . mL +

k2 min 1

k3 min 1

ka rain 1

0.106 (0.054) 0.205 (0.009) 0.101 (0.003) 0.058 (0.020) 0.13 (0.06) 0.116 (0.040) 0.218r (0.016) 0.108 (0.029) 0.039 (0.024)

0.036 (0.006) 0.114 (0.008) 0.034 (0.004) 0.022 (0.014) 0.08 (0.03) 0.051 (0,019) 0.100t (0.021) 0.035 (0.008) 0.016 (0.007)

0.258 (0.158) 0.252 (0.074) 0.312 (0.012) 0.231 (0.108) 0.15 (0,26) 0.070 (0.035) -$

0.132 (0.030) 0.329 (0.007) 0.153 (0.015) 0.129 (0.056) 0,24 (0,16) 0.053 (0.019) -r

0.002 (0.001) 0.005 (0.004) 0,012 (0,003) 0.005 (0.005) 0,00 (0,01) 0.005 (0.075) -

0.260 (0.130) 0.208 (0.165)

0.116 (0.028) 0.130 (0.120)

0.009 (0.002) 0.011 (0.010)

NOTE. All studies were analyzed by using the 3-compartment model of Hawkins et al. 48 Numbers in brackets are the SD. * Results collated from Hawkins et al as and other studies. 98"1~ 1" SD results should be interpreted with care in view of the small number of patients. r Results for KtotaI and Kbon+ derived assuming k4 = 0. Results for k 2 and k3 not given.

40

BLAKE ET AL

Fig 12. (A) Anterior and posterior views of 99mTc-MDP bone scans at 4 hours after injection show the whole skeleton ROI used by D'Addabbo et al 1~ to quantify the global skeletal uptake of tracer. (Reprinted with permission from D'Addabbo et al: A new method of assessing Tc-99m-MDP bone uptake from a bone scan image: Quantitative measurement of radioactivity in global skeletal region of interest. Nucl Med Commun 13:55-60, 1992.1~ (B) Anterior and posterior views *SmTc-HMDP bone scans at 3 hours after injection show the ROI covering the adductor muscles used by Brenner et al l~ to correct the whole-body counts for the soft tissue retention of tracer. (Reprinted with permission. 1~

kidneys, and as much soft tissue uptake as possible (Fig 12A). The counts are normalized to the 5-minute whole-body count to derive a measure of global skeletal uptake. In a study of 40 healthy female patients, Carnevale et al reported that the 4-hour 99mTc-MDP global skeletal uptake showed highly significant correlations with age, creatinine clearance, and biochemical markers of bone turnover.l~ Subsequently, Brenner et al described an improved method of correcting for the soft tissue retention of tracer by drawing an ROI over the adductor muscles of both thighs 1~ (Fig 12B). Counts in this ROI were assumed to scale with the total body retention of tracer in soft tissue. By assuming that during the 3-minute scan, 100% of injected tracer is in soft tissue, one can estimate the soft tissue retention on later scans and subtract it from the whole-body counts to

derive the bone uptake. Brenner et al showed that both the soft tissue and the bone retentions reach a plateau by 6 hours, when they were essentially identical to the 24-hour values. The advantage of the whole-body gamma camera method is that an index equivalent to the 24-hour WBR can be derived from a routine whole-body bone scan. An alternative approach to quantifying gamma camera 99mTc-MDP scans is based on quantitative measures of regional volumetric bone uptake of tracer derived from SPECT studies. A method for achieving this was described by Front et al. 110,111 Subsequently, the Haifa group described results for volumetric bone uptake for different regions of the skeleton in patients with metabolic bone disease and osteoporosis. 112,113 However, the method used did not incorporate any attenuation correction. 111 It is likely that quantitative SPECT studies of bone

QUANTITATIVE STUDIES OF BONE USING 18F AND 99mTc-MDP

have substantial scope for technical improvement based on recent developments in techniques for attenuation correction. ~4,~ ~5 WHAT DO STUDIES OF BONE TRACER KINETICS MEASURE?

This section reviews the question of what physiologic information about bone tissue is actually provided by studies that use short half-life tracers, such as 18F and 99mTc-MDP. The variety of quantitative indices devised for expressing skeletal function described previously reflects a number of factors that, acting together, collectively determine the uptake of a bone-seeking radiopharmaceutical in the bound bone compartment. These factors include (1) bone blood flow, (2) the surface area of capillaries and their permeability to the diffusion of tracer molecules from plasma into bone ECF, (3) the transfer of tracer through bone ECF to the sites of mineralization, and (4) the rate of release of bound tracer from bone and its diffusion back into plasma. It requires sophisticated tracer studies such as the PET studies of Hawkins as and Piert ~~ with )SF-fluoride, or the animal studies of McCarthy & Hughes with 99mTc-MDpSI to quantitatively evaluate these different factors. Blood Flow, Clearance, or Uptake ?

Quantitative measurements of bone tracer kinetics are often presented as measurements of bone blood flow, especially when the tracer used is 18F-fluoride. However, this identification depends on the assumption that the single-passage extraction efficiency of the tracer E ~ !. 47 In practice, this is an oversimplification because E is known to vary with both bone blood flow itself and capillary permeability.,O~.t ~6-~9 For this reason, the results of skeletal tracer studies are more accurately regarded as measurements of plasma (or whole blood) clearance. Clearance is a versatile, modelindependent parameter that expresses the radionuclide uptake to bone in terms of the volume of plasma (or whole blood) cleared of tracer in unit time (units: milliliters per minute). For PET or SPECT studies, the measurements can by expressed as the clearance per voxel (units: mL min -I mL -l) averaged over a selected ROI. Compared with uptakes or retentions expressed as a percentage of injected dose (eg, the 24-hour WBR), clearance data has the advantage of eliminating the dependence on incidental factors that may affect

41

the plasma input curve. These factors include renal function and, in the case of regional bone studies, the effect of the burden of disease (Paget's disease, bone metastases) in other areas of the skeleton on the partitioning of the available tracer. As indicated previously, the total clearance to the whole of the bone tissue (K,,ta t ) and the blood flow (Q) are related through the single-passage extraction efficiency of the tracer (E) through the following relationship: Whole blood clearance: K,,,,t = Q" E.

(9A)

Or, if plasma clearance is preferred instead: Plasma clearance: K,o,,, = Q" (! - P C V ) 9 E (9B) where P C V is the packed cell volume. Because of the differential concentration of tracers in plasma and red cells, it is important there is no ambiguity regarding whether clearance measurements reported in the literature refer to plasma or whole blood. Both conventions have been used by different authors in the past. 48'9t Capillary. Permeabili~ and the Renkin-Crone Equation

The dependence of the single-passage extraction efficiency E on blood flow and capillary permeability is described by the Renkin-Crone equation,,,.t ~7 ~2o which models the situation in which the passage of tracer from the intravascular space to tissue is rate-limited by the free diffusion of the molecules. A theoretic analysis of this was published by Renkin, ~2~ who showed the following: Cv = CA exp -- ( P S / Q )

(10)

where CA and C v are the tracer concentrations in arterial and venous blood, Q is the blood flow, and PS is the permeability-surface area product of the capillaries flow (both Q and PS have units of mL 9 min ~ 9 mL-t). The following is true by definition: E = (CA -- Cv)/CA.

(1 1)

After substituting from Equations 9A and 10, one obtains the following relationship: K,,,,,, = O" (1 - exp - [ P S / a ] ) .

(12)

Plots of K~ot,~l and E as a function of the ratio Q/PS are shown in Fig 13. At low flow rates, E is constant and the clearance rate reflects blood

42

B L A K E ET A L

A

B

,oj

Ktotal/PS 1.0 0.8

0.8 i

0.6

0.6 J

0.4

0.4-

o2-

0.2-

o.o

l

2

3

Q/PS

4

0.0-

1

2

3

4

5

Q/PS

Fig 13. Schematic diagram shows the dependence of firstpassage extraction efficiency E and total plasma clearance Ktot,, t on blood flow Q according to the Renkin-Crone relation (Equation 12). PS is the permeability-surface area product of the capillary bed.

flow. 118 However, at higher flow rates, there is insufficient time for the tracer to equilibrate with surrounding tissues, the extraction efficiency is reduced, and Ktotaz is no longer proportional to Q. At the highest flow rates, the clearance rate tends asymptotically to a maximum value of PS (Fig 13B). Data presented by Hughes and Kelly for a number of bone tracers show a linear relationship between PS and the free diffusion coefficient of the molecule. ~21 Because the latter is approximately proportional to the inverse one-third power of the molecular weight, u7,1~9 the large mass difference between 18F-fluoride and 99mTc-MDP means that they operate at significantly different points on the Q/PS plot.

Measurements of the Single-Pass Extraction of Skeletal Tracers The measurement of the single-pass extraction efficiencies of skeletal radionuclide tracers is a controversial subject. 47,104,122,123 For many studies, insufficient information is available to evaluate at what point on the Q/PS plot the data refer. Wootton reported measurements of E for 18F-fluoride in rabbit bone based on the indicator-fractionation technique, in which a simultaneous injection of labeled microspheres is used as a reference tracer. 124 Mean values of 1.02 in the femur and 1.19 in the tibia were found. However, the method was criticized by Tothill, who identified a number of effects leading to the overestimation of E, including the postmortem migration of tracer from soft tissue to bone m4 and the removal of some microspheres in preosseous capillary beds? 22 Subsequently, Wootton repeated the study and re-

ported revised values of E of 0.88 in the femur and 1.02 in the tibia. 47 Other reported measurements of E for 18Ffluoride and 99mTc-MDP have been based on the indicator-dilution method, in which extraction efficiency is determined by the recovery of tracer from the venous drainage of a bone after injection into the nutrient artery. Using this technique, Lemon et al reported values of E ~ 0.7 for 18F-fluoride in dog tibia, a25 The same figure was obtained whether the tracer was injected in saline or was pre-equilibrated with red cells, a result that suggests that red cell fluoride was fully available for clearance to bone. McCarthy and Hughes used the same animal model to study the extraction of 99mTc-MDP at a number of different flow rates. 1~8,a26 At the lowest flows studied, E was 0.42, whereas values at higher flows were lower in accordance with the Renkin-Crone equation. A disadvantage of these data and those of Wootton 47A24 is that they apply to areas of mainly cortical bone with relatively low blood flow and may not be representative of other areas of the skeleton. Recently, Piert et al reported PET measurements of bone blood flow by using 150-labeled water and 18F-fluoride in pig vertebrae and found a range of values of E in agreement with the RenkinCrone equation, ml

Mechanisms of Tracer Localization in Bone Mineral Once bone tracers such as 99mTc-MDP and lSF-fluoride diffuse through capillaries into bone ECF, the evidence strongly suggests they become bound by chemisorption at the surface of bone crystals, preferentially at sites of newly mineralizing bone. 25,69,7~ This view is supported by microautoradiography studies that show accumulation of 99mTc-diphosphonates at the mineralization front between osteoid and mature bone. 7~ Autoradiographic studies of whole animal bones confirm that uptake is mainly confined to sites of newly forming bone, whereas in growing animals, a high, localized concentration appears at the metaphyseal ends of the long bones immediately adjacent to the epiphyseal cartilage, a3~ In general, these distributions reflect both bone blood flow and osteoblastic activity, with the rate of skeletal mineralization having an important influence on the quantitative uptake of tracer. 25,7~ Studies of 99mTc-EHDP show that the reduction

QUANTITATIVESTUDIESOF BONE USING 18F AND 99mTc-MDP

43

ions with the hydroxyl groups in hydroxyapatite according to the following equation22'27'137:

A (Whole complex directly to surface)

r~

~

/

/

~ ~Bone su/~ace

B

Mechanism 2 (Complex breaks at surface)

~

Bone Surface

Fig 14. Two possible mechanisms discussed by Francis 7~ for the reaction of SSmTc-diphosphonate complexes at bone surfaces. (A) in mechanism 1, the complex adsorbs to the bone surface intact. (B) In mechanism 2, the complex breaks, and the diphosphonate ligand and the released 99mTc(IV)ion bind separately to the bone surface. (Reprinted with permis-

sionY~

of pertechnetate ions by stannous tin chelated in the presence of excess diphosphonate is essential for tracer localization in bone tissue. J34.135 Studies of technetium chemistry suggest that the Tc(VII) state must be reduced to Tc(IV) before the atoms will coordinate with the ligand to form a stable complex. 136 Once it reaches the surface of the newly forming hydroxyapatite crystals, the 99mTc may bind to bone because the diphosphonate moiety of the complex becomes adsorbed to the hydroxyapatite (Fig 14A). Alternatively, the technetium complex may dissociate when the diphosphonate molecule is adsorbed, leaving the 99mTc atom to attach to bone separately (Fig 14B). Francis has presented some evidence in favor of the latter hypothesis, although the exact mechanism remains unclear. 7~ In the case of ISF-fluoride, stable fluoride is known to be present in the skeleton as fluoroapatite, which is formed by the exchange of fluoride

2 F - + Ca,0(PO4)6(on)2 = Cat0(PO4)6F2 + 2 O H - . Because of the short half-life of 18F, it is not possible to perform autoradiography studies of fluoride distribution in bone similar to those described for 99mTc-MDP. However, Bang and Baud have described electron probe x-ray fluorescence studies of an iliac bone biopsy in a patient receiving 3 months treatment with sodium fluoride for osteoporosis.~38 The results show a distribution of fluoride in newly mineralizing bone similar to that found for the 99mTc-diphosphonates. It is unclear how far the exchange reaction in hydroxyapatite proceeds during the much shorter time scale set by the 1 10-minute half-life of 18F. Neuman proposed that the uptake of fluoride in bone occurs in stages. ~39 In the first stage, fluoride ions migrate into the hydration shells of bone crystallites. These ion-rich aqueous shells are continuous with the bone ECF space, so fluoride ions in this pool are rapidly exchangeable. Later stages involve incorporation onto the crystal surface and finally fixation in the hydroxyapatite lattice itself, from which the fluoride ions are only released when the bone is remodeled. Such considerations suggest that for both ]SF and 99mTc-MDP there are probably different degrees of binding in bone that may be associated with different rates of release back into the circulation. What Do Bone Tracer Studies Measure?

Based on the previous discussion of the mechanisms for the transfer of tracer from plasma to the bound bone compartment, Table 5 summarizes the parameters involved in the quantitative modeling of bone tracer kinetics. Numeric values for most of these parameters based on 18F-fluoride PET studies are listed in Table 4. Bone blood flow Q and the capillary permeability-surface area product P S are the principal factors in determining the total clearance, K , , , , I, which represents clearance to the whole of the bone tissue. In contrast, K h..... represents the net clearance to the bound bone compartment alone, and in the context of the Hawkins' model, it is related to Krot, t through the rate constants k 2 and k3: Kb .... = K,ot~t" k3/(k2 + k3),

(13)

BLAKE ET AL

44

Table 5. Parameters for Quantitative Evaluation of Skeletal Tracer Kinetics With PET or SPECT Symbol

Parameter

Units

Comments

Q

Bone blood f l o w

mL 9 min 1 . mL 1

Requires a freely diffusible tracer such as 1SO-water

PS

Permeability-surface area product

rnL 9 rain -~ 9 mL -1

Limits the single-passage extraction efficiency of tracer in diffusion limited regime

E

Single-passage extraction efficiency

Ktota I

Plasma (or w h o l e blood) clearance to total bone tissue

m L . min -1 9 mL 1

Kbone

Net plasma (or w h o l e blood) clearance to bone mineral alone

mL 9 min -1 9 mL

Kbone = Ktota I 9 k3/(k2 + k 3)

k2

Coefficient for reverse transport f r o m bone ECF to intravascular space

min -1

The most statistically robust parameter. Can be estimated f r o m slope of Patlak plot if k4 is negligible. Probability per unit time of tracer molecule passing f r o m bone ECF or bone m a r r o w to intravascular space. The ratio Ktotal/k 2 gives the notional v o l u m e of the bone ECF compartment.

k3

Coefficient f o r transport f r o m bone ECF to bone mineral Coefficient f o r reverse transport f r o m bone mineral to bone ECF

min -1

k4

E ~ 1 - exp - (PS/Q) A p p r o x i m a t e s to bone blood f l o w f o r more diffusible tracers at l o w e r flows. Otherwise will underestimate true blood f l o w

Probability per unit time of tracer molecule passing f r o m bone ECF to bone mineral. Probability per unit time o f tracer molecule passing bone mineral to bone ECF. Net transport to intravascular space = k4 9 k2/(k2 + k 3)

min -1

which determine the fraction of tracer cleared to bone ECF that becomes bound in mineralizing bone rather than diffusing back into plasma. The level of osteoblastic activity in bone influences Kbo,, e principally through its effect on k3, but also because there is a general relationship between osteoblastic activity and bone blood flow, which influences the value of K t o t a l. Just as care is required in evaluating bone tracer studies to check whether the measurements relate to whole blood or plasma clearance, similar care is needed to determine whether the data presented relate to Ktota ~ or Kbone. The distinction between these 2 parameters is that a measurement of Ktota 1 approximates to bone blood flow, whereas Kbone reflects the fraction of the cleared tracer retained in bone with a long biologic half-life. The relationship to Ktota l or Kbon~ of each method is summarized in Table 2. Of the methods discussed above, only dynamic PET imaging and the Charkes model provide measurements of Ktota t. The 24-hour 99mTc-MDP WBR investigation is equivalent to a measurement of the ratio Kbo~JK . . . . l (see Table 2). The Nisbet ratio of the plasma concentrations of 51Cr-EDTA and 99mTc-MDP is also broadly equivalent to a measurement of KbonJK . . . . l, provided that the issues of the protein binding of MDP and the approximations involved in single-sample GFR techniques are ignored. Finally, because the clearance measurement is derived from a single exponent fitted to the long biologic half-life component of the bone impulse function, the Wootton decon-

volution method represents a measurement of

gbone" COMPARISON OF 18F-FLUORIDE AND 99rnTC-MDPAS SKELETAL TRACERS During the past decade, interest in quantitative studies of bone tracer kinetics has mainly centered on imaging that uses either tSF-fluoride dynamic PET or quantitative gamma camera studies with 99mTc-MDP. The relative advantages and disadvantages of the 2 tracers are summarized in Table 6. The superior performance of PET systems with bismuth germanium oxide detectors is based on their higher spatial resolution and more accurate attenuation correction methods compared with gamma camera SPECT.140 However, PET remains an expensive technology, and supplies of cyclotron-produced I8F are not widely available. In contrast, gamma camera imaging that uses 99mTcMDP is ubiquitous throughout departments providing a clinical nuclear medicine service. After recent developments in transmission sources introduced for cardiac SPECT imaging, and with improved scatter correction algorithms for image reconstruction, there is scope for a substantial improvement in the accuracy of bone quantitation with gamma camera SPECT systems. Apart from issues of the relative performance of the different imaging technologies, the advantages of 18F-fluoride over 99mTc-MDP for bone quantitation include the absence of protein binding and the higher capillary permeability of the fluoride

QUANTITATIVE STUDIES OF BONE USING 18F AND 99mTc-MDP

45

Table 6. Relative Advantages of 18F-Fluoride and S~r"Tc-MDP for Quantitative Evaluation of Skeletal Tracer Kinetics With PET or SPECT

18F-Fluoride

99mTc-MDP

Higher spatial resolution of BGO-based PET scanner gives superior quantitation Accurate attenuation correction transmission routinely available on PET systems Arterial blood sampling frequently performed in PET investigations Small axial field of view of PET scanner limits area of skeleton studied Highly diffusible tracer. Clearance measurements approximate to bone blood flow at lower flow rates Short half-life (110 rain) limits study duration 18F-fluoride kinetics not affected by plasma protein binding 18F-fluoride renal tubular reabsorption sensitive to urine flow rate. Good hydration of subject (->5 mL - min 1) required to ensure steady state conditions Significant percentage (-30%) of tracer transported in red blood cells ~SF recirculates from bone compartment as fluoride

Gamma camera SPECT systems have poorer spatial resolution Attenuation correction using sources less developed for SPECT Venous blood sampling likely to be preferred as less invasive Larger area of skeleton included in SPECT field of view Less diffusible tracer. Clearance values lower than for 18F-fluoride due to smaller PS product Longer half-life (6 h) 99mTc-MDP protein binding varies from - 2 5 % at injection to - 5 0 % at 4 h. Individual measurements of free MDP required in each subject 99mTc-MDP renal clearance not affected by urine flow rate. Renal clearance of free MDP approximates to GFR Negligible tracer uptake in red cells

99mTc and ligand may separate at bone surfaces affecting recirculation of tracer

Abbreviation: BGO, bismuth germanium oxide.

ion. The latter means that fluoride clearance measurements of K , , , , I approximate to bone blood flow at flow rates up to and including those found in normal vertebrae. However, at the higher blood flows found for pagetic bone and sites of bone grafts (see Table 4), the relationship between fluoride clearance and blood flow becomes nonlinear, with tSF measurements substantially underestimating true blood flow. )~ Potential disadvantages of ~8F-fluoride include the variable renal clearance that is sensitive to urine flow rate. This may affect studies that use deconvolution or simplified approaches to data analysis based on limited blood sampling, if these depend on the assumption of steady state conditions. Controlling lSF-fluoride renal clearance requires good hydration of patients, with the urine flow rate maintained at 5 mL 9 min ~ or higher. It is an advantage for studies with '~SmTc-MDP

that renal clearance is independent of urine flow rate and that the renal clearance of free MDP can be approximated by the GFR. However, plasma protein binding is an important aspect of 99mTCMDP kinetics that varies from around 25% immediately after tracer administration to 70% after 12 hours. For accurate tracer studies, it is imperative that measurements are made of free MDP. The large molecular weight of 9'~mTc-MDP compared with the ~8F ion leads to a lower capillary permeability and lower single-passage extraction efficiency compared with tSF-fluoride, so that the clearance measurements obtained are significantly lower. At present, lSF-fluoride PET is probably the technique of choice for accurate quantitative studies of bone. However, if SPECT quantitation of 99mTc-MDP kinetics can be improved, at least to the extent of making possible accurate measurements of K h ...... then this conclusion might change.

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