pet for bone imaging pet for bone imaging positron emission tomography for bone imaging, as an in vivo tracer technique, allows the measurement of the regional concentration of radioactivity proportional to the image pixel values averaged over a region of interest (roi) in bones. positron emission tomography is a functional imaging technique that uses naf radiotracer to visualise and quantify regional bone metabolism and blood flow. naf has been used for imaging bones for the last 60 years. this article focuses on the pharmacokinetics of naf in bones, and various semi-quantitative and quantitative methods for quantifying regional bone metabolism using naf pet images. use of naf pet the measurement of regional bone metabolism is critical to understand the pathophysiology of metabolic bone diseases. bone biopsy is considered the gold standard to quantify bone turnover; however, it is invasive, complex and costly to perform and subject to significant measurement errors. measurements of serum or urine biomarkers of bone turnover are simple, cheap, quick, and non-invasive in measuring changes in bone metabolism, but only provide information on the global skeleton. the functional imaging technique of dynamic naf pet scans can quantify regional bone turnover at specific sites of clinical importance such as the lumbar spine and hip and has been validated by comparison with the gold standard of bone biopsy. pharmacokinetics of naf the chemically stable anion of fluorine-18-fluoride is a bone-seeking radiotracer in skeletal imaging. naf has an affinity to deposit at areas where the bone is newly mineralizing. many studies have naf pet to measure bone metabolism at the hip, lumbar spine, and humerus. naf is taken-up in an exponential manner representing the equilibration of tracer with the extracellular and cellular fluid spaces with a half-life of 0.4 hours, and with kidneys with a half-life of 2.4 hours. the single passage extraction of naf in bone is 100%. after an hour, only 10% of the injected activity remains in the blood. 18f- ions are considered to occupy extracellular fluid spaces because, firstly, they equilibrate with transcellular fluid spaces and secondly, they are not entirely extracellular ions. fluoride undergoes equilibrium with hydrogen fluoride, which has a high permeability allowing fluoride to cross the plasma blood membrane. the fluoride circulation in red blood cells accounts for 30%. however, it is freely available to the bone surface for uptake because the equilibrium between erythrocytes and plasma is much faster than the capillary transit time. this is supported by studies reporting 100% single-passage extraction of whole-blood 18f- ion by bone and the rapid release of 18f- ions from erythrocytes with a rate constant of 0.3 per second. naf is also taken-up by immature erythrocytes in the bone marrow, which plays a role in fluoride kinetics. the plasma protein binding of naf is negligible. naf renal clearance is affected by diet and ph level, due to its re-absorption in the nephron, which is mediated by hydrogen fluoride. however, large differences in urine flow rate are avoided for controlled experiments by keeping patents well hydrated. the exchangeable pool and the size of the metabolically active surfaces in bones determines the amount of tracer accumulated or exchanged with bone extracellular fluid, chemisorption onto hydroxyapatite crystals to form fluorapatite, as shown in equation-1: c a 10 ( p o 4 ) 6 ( o h ) 2 + 2 f − => c a 10 ( p o 4 ) 6 f 2 + 2. o h − (po_)_(oh)_+2f-=>ca_(po_)_f_+2.oh-} equation-1 fluoride ions from the crystalline matrix of bone are released when the bone is remodelled, thus providing a measure of the rate of bone metabolism. measuring suv definition the two image in the top row (the image on the left hand side is plotted on log scale and on the right hand side is plotted on linear scale) show the output of the spectral analysis showing its frequencies components grouped around three clusters, referred to as high, intermediate and low frequencies, supporting the assumption of three compartments in the hawkins model corresponding to plasma, bone ecf and bone mineral compartment respectively. the image at the bottom row shows the irf plotted using the frequency components obtained previously.the standardized uptake value (suv) is defined as tissue concentration (kbq/ml) divided by activity injected normalized for body weight. appropriateness the suv measured from the large roi smooths out the noise and, therefore, more appropriate in naf bone studies as the radiotracer is fairly uniformly taken up throughout the bone. the measurement of suv is easy, cheap, and quicker to perform, making it more attractive for clinical use. it has been used in diagnosing and assessing the efficacy of therapy. suv can be measured at a single site, or the whole skeleton using a series of static scans and restricted by the small field-of-view of the pet scanner. known issues the suv has emerged as a clinically useful, albeit controversial, semi-quantitative tool in pet analysis. standardizing imaging protocols and measuring the suv at the same time post-injection of the radiotracer, is necessary to obtain a correct suv because imaging before the uptake plateau introduces unpredictable errors of up to 50% with suvs. noise, image resolution, and reconstruction do affect the accuracy of suvs, but correction with phantom can minimize these differences when comparing suvs for multi-centre clinical trials. suv may lack sensitivity in measuring response to treatment as it is a simple measure of tracer uptake in bone, which is affected by the tracer uptake in other competing tissues and organs in addition to the target roi. measuring ki the quantification of dynamic pet studies to measure ki requires the measurement of the skeletal time-activity curves (tac) from the region of interest (roi) and the arterial input function (aif), which can be measured in various different ways. however, the most common is to correct the image-based blood time-activity curves using several venous blood samples taken at discrete time points while the patient is scanned. the calculation of rate constants or ki requires three steps: measurement of the arterial input function (aif), which acts as the first input to the mathematical model of tracer distribution. measurement of the time-activity curve (tac) within the skeletal region of interest, which acts as the second input to the mathematical model of tracer distribution. kinetic modelling of aif and tac using mathematical modelling to obtain net plasma clearance (ki) to the bone mineral. a bone tac is modelled as a convolution of measured arterial input function with irf. the estimates for irf are obtained iteratively to minimise the differences between the bone curve and the convolution of estimated irf with input function curve. the curve in green shows the initial estimates of the irf and the blue curve is the final irf which minimises the differences between the estimated bone curve and the true bone curve. ki is obtained from the intercept of the linear fit to the slow component of this exponential curve which is considered the plasma clearance to the bone mineral, i.e. were the red line cuts the y axis. spectral method the method was first described by cunningham & jones in 1993 for the analysis of dynamic pet data obtained in the brain. it assumes that the tissue impulse response function (irf) can be described as a combination of many exponentials. since a tissue tac can be expressed as a convolution of measured arterial input function with irf, cbone(t) can be expressed as: c b o n e ( t ) = ∑ k = 1 n α i . ( c p l a s m a ( t ) ⊗ e x p ( − β i . t ) ) (t)=\sum _^\alpha _.c_(t)\otimes exp(-\beta _.t) where, ⊗ is a convolution operator, cbone(t) is the bone tissue activity concentration of tracer (in units: mbq/ml) over a period of time t, cplasma(t) is the plasma concentration of tracer (in units: mbq/ml) over a period of time t, irf(t) is equal to the sum of exponentials, β values are fixed between 0.0001 sec−1 and 0.1 sec−1 in intervals of 0.0001, n is the number of α components that resulted from the analysis and β1, β2,..., βn corresponds to the respective α1, α2,..., αn components from the resulted spectrum. the values of α are then estimated from the analysis by fitting multi-exponential to the irf. the intercept of the linear fit to the slow component of this exponential curve is considered the plasma clearance (ki) to the bone mineral. deconvolution method the method was first described by williams et al. in the clinical context. the method was used by numerous other studies. this is perhaps the simplest of all the mathematical methods for the calculation of ki but the one most sensitive to noise present in the data. a tissue tac is modelled as a convolution of measured arterial input function with irf, the estimates for irf are obtained iteratively to minimise the differences between the left- and right-hand side of the following equation: c b o n e ( t ) = c p l a s m a ( t ) ⊗ i r f ( t ) (t)=c_(t)\otimes irf(t)} where, ⊗ is a convolution operator, cbone(t) is the bone tissue activity concentration of tracer (in units: mbq/ml) over a period of time t, cplasma(t) is the plasma concentration of tracer (in units: mbq/ml) over a period of time t, and irf(t) is the impulse response of the system (i.e., a tissue in this case). the ki is obtained from the irf in a similar fashion to that obtained for the spectral analysis, as shown in the figure. hawkins model a diagrammatic view of the process of kinetic modelling using hawkins model used to calculate the rate of bone metabolism at a skeletal site. cp refers to the plasma concentration of the tracer, ce refers to the tracer concentration in ecf compartment, cb refers to the concentration of tracer in bone mineral compartment, m1 refers to mass of tracer in the ce compartment, m2 refers to the mass of tracer in the cb compartment, ct is the total mass in the ce+cb, pve refers to the partial volume correction, fa refers to the femoral artery, roi refers to region of the interest, b-exp refers to the bi-exponential, .the measurement of ki from dynamic pet scans require tracer kinetic modelling to obtain the model parameters describing the biological processes in bone, as described by hawkins et al. since this model has two tissue compartments, it is sometimes called a two-tissue compartmental model. various different versions of this model exist; however, the most fundamental approach is considered here with two tissue compartments and four tracer-exchange parameters. the whole kinetic modelling process using hawkins model can be summed up in a single image as seen on the right-hand-side. the following differential equations are solved to obtain the rate constants: d c e ( t ) d t = k 1 ∗ c p ( t ) − ( k 2 + k 3 ) ∗ c e ( t ) + k 4 ∗ c b ( t ) \!c_(t) \over \operatorname \!t}=k_*c_(t)-(k_+k_)*c_(t)+k_*c_(t)} d c b ( t ) d t = k 3 ∗ c e ( t ) − k 4 ∗ c b ( t ) \!c_(t) \over \operatorname \!t}=k_*c_(t)-k_*c_(t)} the rate constant k1 (in units: ml/min/ml) describes the unidirectional clearance of fluoride from plasma to the whole of the bone tissue, k2 (in units: min−1) describes the reverse transport of fluoride from the ecf compartment to plasma, k3 and k4 (in units min−1) describe the forward and backward transportation of fluoride from the bone mineral compartment. ki represents the net plasma clearance to bone mineral only. ki is a function of both k1, reflecting bone blood flow, and the fraction of the tracer that undergoes specific binding to the bone mineral k3 / (k2 + k3). therefore, k i = ( k 1 ∗ k 3 k 2 + k 3 ) =\left(*k_+k_\right)} hawkins et al. found that the inclusion of an additional parameter called fractional blood volume (bv), representing the vascular tissue spaces within the roi, improved the data fitting problem, although this improvement was not statistically significant. patlak method patlak method is based on the assumption that the backflow of tracer from bone mineral to bone ecf