Methodological considerations in quantification of oncological FDG PET studies

High blood glucose levels, due to a non-fasting state or diabetes mellitus, interfere with FDG uptake in malignant lesions. The transmembranous glucose transport facilitators (GLUT), albeit overexpressed in many cancers, can be saturated by an excess of unlabelled glucose. This diminishes FDG uptake as glucose and FDG both compete for the binding sites of transporters and enzymes, leading to zero-order kinetics. In patients without any known form of glucose intolerance it is shown in two consecutive scans that the SUV, using body weight as a measure of distribution volume, is significantly lower in the loaded state (serum glucose >8.0 mmol∙l⁻¹) in both head and neck cancer (SUV_BW = 6.9 vs 4.0, p < 0.02) [16] and bronchial carcinoma (SUV_BW = 5.07 vs 2.84, p < 0.001) [17] compared to the fasting state (<6.0 mmol∙l⁻¹). In contrast to the reduction of tumour uptake, skeletal muscle accumulates more FDG, resulting in blurring of tumour margins and less clear localization of lesions [16]. Also Patlak-based net influx rate constants (K_i) of the lesions decrease markedly in the glucose loaded state (mean −25%, p < 0.05), while MR_glc is on average 36% higher. This paradoxical increase in MR_glc might be due to the fact that the authors assumed the same value for the relative affinity of the biological system to FDG and glucose (‘lumped constant’, LC) in both states to compute MR_glc from K_i, which is likely untrue [18].

The effect of hyperglycaemia has clear impact on visual interpretation of FDG PET images as it results in a reduced detection rate of malignancies [19], but it also has a major effect on quantification. Therefore, hyperglycaemia should be a reason to reschedule the procedure. Correction of hyperglycaemia by insulin directly prior to the FDG injection is dissuaded, because hyperinsulinaemia increases the translocation of GLUT₄ thereby rapidly and efficiently shunting FDG to organs with a high density of insulin receptors (e.g. skeletal and cardiac muscles) [19]. When FDG injection is postponed to 1 h after insulin administration (up to a serum glucose below 8.0 mmol∙l⁻¹) in hyperglycaemic diabetic patients, no differences between normoglycaemic non-diabetics and hyperglycaemic (insulin-corrected) diabetics are found in SUV, using lean body mass as measure for distribution volume (SUV_LBM), in lungs, liver, muscles, myocardium or suspected pulmonary lesions [20]. However, recently a standardized protocol of intravenous insulin at least 1 h prior to FDG injection led to an unacceptable biodistribution in 25% of diabetic cancer patients (increased muscle uptake and decreased liver uptake). In these patients the interval between insulin and FDG injection was significantly shorter than in the patients with a normal biodistribution (65.7 vs 80.2 min, p < 0.01) [21]. Metformin strongly increases the SUV of the small and large intestines, potentially decreasing the detection sensitivity for malignant lesions, but the influence on lesion quantification is not described [22]. To prevent hyperglycaemia in non-diabetic patients, guidelines [12‐14] recommend that patients should have fasted at least 4 h, but preferably 6 h before administration of FDG. When blood glucose levels are well outside physiological ranges (e.g. >11 mmol∙l⁻¹ [14]) the scan should be postponed. We use a stricter cut-off for research purposes (8.0 mmol∙l⁻¹).

Typically, PET acquisition is performed 45–60 min after FDG injection, based on the fact that FDG activity concentrations become constant within the first hour after tracer injection in normal tissues. In malignancies, however, it has been shown that for some tumour types FDG concentration continues to increase up to 4–5 h after injection and that constant FDG activity concentrations are rarely reached within the first hour after injection. Between 60 and 90 min post-injection, it is not uncommon for a lesion to further increase SUV as much as one tenth of the value reached 10 h post-injection [23]. Since a further increase in FDG activity concentration 1 h after injection is rare in normal tissues [24], it has been hypothesized that dual-time-point imaging (45 and 90 min post-injection) might improve detection rates of lesions with high glucose metabolism by increasing tumour to background ratios. Therefore, for response monitoring studies using SUVs it is highly important to keep the uptake period of FDG within narrow limits (55–65 min) [13, 14].

To optimize the distribution of FDG throughout the body, international guidelines recommend prehydration (0.5 l) of the patient to ensure excretion of FDG from healthy background tissue, which may be further enhanced by furosemide-induced forced diuresis. This might be of special value when the pelvis or kidney regions are of interest [12‐14]. Median SUV values of tumours are lower if furosemide is used. However, the total fraction of excreted activity is not different if diuretics are used, but is significantly higher early after injection for the furosemide group leading to improved image quality and reducing patient radiation exposure [25]. Therefore, it seems important when comparing parameters for glucose metabolism that the use of (loop) diuretics should be taken into account. A practical disadvantage of using forced diuresis during dynamic acquisition is that measures should be taken to avoid premature termination of the acquisition due to urinary urgency.

Apart from exercise-induced increased muscle uptake during the uptake period, the effect of motion during acquisition has consequences for lesion localization (e.g. spatial mismatch around the diaphragm due to breathing) and causes smearing of the lesion activity concentration within the volume of movement. Consequently, the lesion metabolic volume is overestimated and the SUV is underestimated. Moreover, tissue inhomogeneity is similarly smeared, leading to loss of spatial heterogeneity. The magnitude of the decrease of recovered activity concentrations depends most markedly on lesion size and amplitude of motion and to a lesser extent on the motion frequency. Recovered activity concentrations can be increased by better lesion volume estimation by a motion correction algorithm. Verified in nine lung cancer patients, this algorithm reduces the estimated lesion volume by 15% leading to an increase of the mean SUV in the ROI (SUV_mean) by 5% [26]. Different other techniques may be applied to improve recovery of activity concentration in periodically moving lesions such as gated PET/CT (in which data are only acquired during a certain respiratory phase), respiratory correlated dynamic PET/CT (by summing the sinograms of images of a particular breathing phase selected using a point source) or deep inspiration breath-hold PET/CT [27].

During dynamic acquisition, non-periodic patient movement can have major influence on measured parameters, since the lesion can “move into” the ROI usually defined in the last time frame(s). Consequently, activity concentrations of the lesion are underestimated for the period before patient movement due to a mispositioned ROI. In the time frames in which the lesion of interest is visible the ROI can be realigned, but during the early time frames this is often impossible due to noisy images or insufficient tissue to blood contrast. Patient movement therefore should be prevented and monitored during acquisition, the original position should be restored as quickly as possible and any movement should be noted including time at which it occurred.

If CT-based attenuation correction (AC) is used, any spatial mismatch will lead to incorrect amplification of measured activity concentrations, leading to unreliable values for lesion quantification (differences of around 10% in SUV [28, 29] due to breathing, smallest for free breathing CT [28]).

Patient stress or cold during the distribution period increases uptake of FDG in muscle and brown adipose tissue (BAT) [30‐32]. This can lower detection sensitivity (by lowering contrast) and specificity (by increasing the number of false-positive lesions) of the images and might affect quantification [14, 33]. Factors known to increase FDG uptake in BAT such as exposure to cold [31, 32, 34‐36] should be prevented by exposing patients to thermoneutral conditions. Medication such as the beta-adrenergic blocking agent propranolol [31, 36‐39], reserpine [36] and the opiate fentanyl [40] all prevent FDG uptake in BAT, but the effect of benzodiazepines seems doubtful [35, 36, 40, 41]. The NEDPAS guidelines [14] suggest considering the use of benzodiazepines to reduce muscle uptake when tumours in the head and neck region are expected and state that there is no place for it to reduce uptake in BAT.

The choices of acquisition parameters are closely interrelated and are based on trade-offs between signal to noise ratio (SNR) and radiation safety, financial issues (e.g. patient throughput, costs of FDG), patient comfort and logistics. Increasing the sensitivity of the PET scanner by using 3-D acquisition (instead of 2-D acquisition using lead or tungsten septa between crystal rings), increasing scan duration, enlarging bed overlap and raising the administered FDG activity (below the amount that results in count rates exceeding the maximum count rate capabilities of the scanner) all improve SNR. Removing the interplane septa from the PET scanner (i.e. changing from 2-D to 3-D mode) typically leads to a four- to eightfold increase in sensitivity but also increases the number of detected scattered and random photons. Generally, the peak noise equivalent count rate (NEC) is obtained at a lower activity concentration in 3-D than in 2-D as expected from the behaviour of the (increased) true coincidence rate. As a result the SNR (for a uniform cylinder \( SNR \propto \sqrt {NEC} \) [43]) will be higher when operating in 3-D versus 2-D mode for the low activity concentration range. Recommendations for administered FDG activity therefore should be based on acquisition mode (2-D or 3-D), scan duration and bed overlap, rather than on pre-determined diagnostic reference levels [12]. The NCI guidelines recommend a total administered FDG activity of 5.18–7.77 MBq∙kg⁻¹ [13], and the NEDPAS recommendations advise 27.5 MBq∙min∙kg⁻¹ (for 2-D and ≤25% bed overlap), 13.8 MBq∙min∙kg⁻¹ (for 3-D and ≤25% bed overlap) or 6.9 MBq∙min∙kg⁻¹ (for 3-D and 50% bed overlap). For a 3-D acquisition of a 70-kg patient with 4 min per bed position (with 25% bed overlap), it recommends approximately 242 MBq (±10%) to be administered, which corresponds to an effective absorbed dose of 4.6 mSv of the FDG (0.019 mSv∙MBq⁻¹ [44]). Reducing scan duration therefore necessitates increased administered FDG activity to maintain SNR. Increasing acquisition time effectively maintains the quality (SNR) of FDG PET scans of heavier patients, agreeing with the hypothesis that increasing body weight increases the fractions of random and scatter coincidences [45, 46]. Increasing administered FDG activity does not improve SNR in a study, explained by the fact that it was likely to saturate count rates of the equipment [47].

For dynamic acquisition, activity concentration changes are largest during the first minutes of acquisition (bolus transit) but depend on the rate of FDG infusion, distribution and clearance. Therefore, when partitioning list-mode data or using pre-defined time frames, one should consider a high temporal resolution for this period, especially important for pharmacokinetic analysis of two-compartment models. Improvement of temporal resolution inherently decreases the count accuracy per time frame, since the (approximate) Poisson distribution of count statistics (for prompt coincidences) dictates a relative standard deviation dependent on the inverse square root of the observed counts. As the choice of framing and the duration of FDG infusion are related, it is impossible to give general recommendations. Generally, for scanners with low sensitivity, time frame durations should be longer and consequently the rate of FDG infusion slower. The choices of different groups using dynamic acquisition for oncological purposes can be found elsewhere [48‐50] (Fig. 1).

Correction for photon attenuation is necessary since positron annihilation photons interact with surrounding tissues (mainly Compton scattering, to a lesser extent photoelectric effect). Before the introduction of combined PET/CT, attenuation correction was applied by transmission imaging of the subject with an external rotating isotope source, either positron emitters (e.g. ⁶⁸Ga using its mother isotope ⁶⁸Ge) or single photon emitters (e.g. ⁵⁷Co or ^137mBa using its mother isotope ¹³⁷Cs). Since photon attenuation is dependent on the photon energy, the latter two require scaling to obtain transmission sinograms adapted to 511 keV photons. The attenuation sinogram, the ratio of a transmission scan and a scan without an object in the FOV (blank scan), is used to correct the emission sinogram, which is subsequently reconstructed to an image. Since the introduction of PET/CT, the spatial distribution of the linear attenuation coefficients can be obtained using the CT scanner. Advantages of CT AC are: reduction in total scan time, lower noise in the transmission sinograms and no replacement of isotope sources necessary due to decay. Finally, they can be acquired after tracer injection, choosing the energy window around the CT photon peak to exclude the 511 keV photons (radionuclide-based transmission scans suffer from contamination by emission photons unless the transmission data are acquired before the PET tracer is administered to the patient). CT AC however leads to extra challenges: the use of polyenergetic Bremsstrahlung photons with energy much lower than 511 keV (X-ray tube potential difference usually ∼130 kV leading to photon energy ranging from 40 to 130 keV, effective energy ∼70–80 keV), artefacts due to spatial mismatches with PET or metal objects, effects of CT-enhancing contrast and artefacts due to truncation and beam hardening [51].

Conversion of the X-ray to 511 keV linear attenuation coefficients can be performed by either segmentation, scaling or dual X-ray imaging. By segmentation, regions of different material types are identified for which linear attenuation coefficients for 511 keV photons are known. Linear scaling of X-ray linear attenuation coefficients can be performed as long as Compton scattering is the major determinant of attenuation. However, at CT photon energies the photoelectric effect plays a significant role for high atomic number elements (e.g. calcium in bone, iodine or barium in contrast agents with atomic numbers of 20, 53 and 56, respectively) in which case hybrid or bilinear scaling is appropriate [51]. Finally, linear attenuation coefficients can be measured at two tube potential differences, enabling the separation of attenuation due to the Compton scattering and the photoelectric effect. In practice, no significant difference in quantification of malignant lesions is found comparing CT-based attenuation correction with segmented AC (SAC) using transmission imaging [28] or between measured (MAC) and segmented (SAC) attenuation correction using transmission imaging [29].

CT artefacts due to metal objects and attenuation due to iodine-containing CT contrast agents might influence lesion quantification. Multiple studies have found a negligible change of the SUV in a variety of malignancies varying from +2.8% to +4% [52‐55]. This small effect surprisingly disappears after chemotherapy [52]. The SUV_mean significantly increases in the (normal) aorta (+15%), kidneys (+13%), liver (+11%), spleen (+10%) and inferior caval vein (+12%) [52]. This might be of relevance when the plasma time-activity concentration curve for pharmacokinetic analysis is image derived (IDIF): a positive bias in the input function leads to underestimation of MR_glc. Around metal prosthesis, CT AC leads to an underestimation of FDG activity concentration by <6% [28].

Finally, truncation artefacts, due to a smaller transaxial FOV of CT than that of PET, lead to incorrect attenuation correction if there are tissues outside the CT FOV. Therefore, it is recommended to scan a patient with arms up except for head and neck imaging. Usually the degree of truncation is small and therefore no major effects on quantification are expected. Lowering the arms also causes beam hardening (structures of higher density cause attenuation of low-energy photons of the polyenergetic X-ray bundle) and scatter-induced artefacts. These can influence quantification up to 11–15% [51].

Apart from attenuation correction, other corrections must be applied before an image can be quantified. These are: normalization, correction for random coincidences, correction for scattered radiation, correction for dead time and cross-calibration with a dose calibrator or well counter.

Remaining differences in detection sensitivity that have not been corrected in the setup procedure are corrected by normalization. During normalization all detectors are exposed to the same amount of radiation by a rotating source or a cylinder with a uniform activity concentration. The measured counts of each detector pair (line of response, LOR), which should all be equal, are corrected by normalization factors, which are used to scale the number of counts of each detector pair to correct the emission sinogram. Using 3-D acquisition poses a new challenge for this, since the number of LORs are high (order of 10⁸); therefore, to obtain enough counts per LOR long normalization procedures seem necessary. For this reason modified methods have been developed. Instead of using the acquired number of counts in each LOR separately, a factorization into different components is being made (component-based normalization). These components are the individual crystal detection efficiencies, geometrical factors which account for differences in the distance between detectors and their exposed face and the position of crystals in a detector block [56, 57].

Random coincidences arise when photons of two unrelated positron annihilations are detected within the coincidence timing window and are recorded as a single pair. This leads to incorrectly positioned LORs and thus adds a relatively uniform background to the reconstructed images. An estimate of the random coincidence rate can be obtained by delaying the coincidence timing window by an interval relatively large to its width. Delayed coincidences cannot be true or scattered events, since photons of the same positron annihilation will always be detected within a few nanoseconds of each other, but the rate of random coincidences will be the same in the delayed and the original window. This number can be subtracted in real time from the total number of coincidences for the detector pair to correct for randoms. This, however, will increase the statistical noise level of the corrected images, since the variance of the number of random counts is added to the variance of the uncorrected counts. Other methods use ‘smoothed delays’, in which the delayed coincidences are acquired in a separate and thereafter smoothed sinogram, or estimations based on singles rates [58].

One or both photons arising from one positron annihilation might be Compton scattered by the tissue within the gantry, leading to mispositioned LORs. This leads to a hazy background activity concentration, generally highest in the centre of the image. The percentage of scattered events detected in 3-D PET might approach 60–70% of all coincidences. The attenuation data can be used to estimate the number of scattered photons as for 511 keV photons virtually all attenuation is due to the Compton effect [51]. Another method is by extrapolation of the projection profiles immediately outside the object (determined from the attenuation data), which only represent scattered photons as almost no positron annihilations occur in air. This scatter distribution profile can be subtracted from the projections prior to image reconstruction [59]. A study of cerebral FDG PET describes that all the pharmacokinetic rate constants of glucose metabolism are overestimated due to photon scatter up to 10–30% (in decreasing magnitude: K₁, K_i, k₂, k₃ and k₄). MR_glc is 12–30% higher when no scatter correction is applied [60].

At high count rates effects of system recovery after detection of a photon are piled up leading to dead time. Systems can either be non-paralysable (i.e. any event within the dead time will not be counted) or paralysable (i.e. this event will furthermore restart the dead time). Empirical dead time models can be used in which the observed count rate as a function of radioactivity concentration is measured for a range of object sizes at different energy window widths, but other methods are under investigation [61].

If all previously mentioned corrections are applied, the number of counts per voxel in the reconstructed images is directly proportional to the activity concentration of that voxel. Calibration to absolute concentrations can be performed by scanning e.g. a cylinder containing a uniform solution of known activity concentration. The obtained calibration factor can be used for absolute quantification of the images.

It can be concluded that standardization of PET acquisition is highly important. Images should be acquired in a normoglycaemic (fasting) state. When using insulin to reverse hyperglycaemia, this should be injected at least but preferably longer than 1 h before the FDG. The distribution period should be held within narrow limits (55–65 min). The effect of prehydration and diuretics led to recommendations advocating standardization. For dynamic acquisition, however, the practicability of forced diuresis should be considered. Patient motion leads to underestimation in the measured SUV or MR_glc and should therefore be prevented. To prevent muscle uptake and uptake in BAT, the waiting room should be kept warm and the patient should be instructed to minimize exercise. The effect of benzodiazepines is doubtful and recent literature suggests the use of beta-blocking agents when uptake in BAT is interfering interpretation of the images.

The administered FDG activity should be standardized, dependent on acquisition method and patient body weight and kept within narrow limits (<10%). When using CT attenuation correction, quantification in areas around (metal) artefacts should not be performed. Likewise, quantification of lesions in cases of spatial mismatch between PET and CT should not be performed. Even though the effect of contrast agents on SUV may be small, the bias introduced in the blood pool used for pharmacokinetic modelling is large and therefore its use is discouraged. Whenever possible, acquisition should be performed with the arms outside the FOV to prevent effects of truncation, beam hardening and increased photon scattering. For reliable quantification, the scanner should be normalized, (cross-) calibrated and corrections for photon attenuation, randoms, scatter and dead time should be performed.

Dynamic PET studies provide the opportunity to perform pharmacokinetic analysis of two-compartment models of glucose metabolism. In addition to the PET signal [C _PET (t)], the tracer concentration in the arterial blood plasma should also be measured [C _plasma (t)], which is a drawback compared to static methods in which only the SUV is of interest. Another drawback of dynamic acquisition is that only one FOV (typically ∼15–20 cm) can be taken into account; therefore, in metastasized disease not all lesions can be quantified simultaneously.

Since deoxyglucose-6-PO₄, in contrast to glucose-6-PO₄, cannot be catabolized further and does not diffuse across cell membranes, metabolism can be simplified to a two-compartment model (Fig. 2) with four rate constants. Tracer kinetic modelling is based on several key assumptions including the tracer principle (i.e. negligible concentration of the tracer), steady-state assumption (i.e. metabolic processes are at steady state during measurement), tissue homogeneity and instantaneous mixing assumption (i.e. homogeneous tracer distribution within each compartment), linearity assumption (i.e. rate constants are independent of tracer concentration: first-order kinetics) and the tracer dynamic assumption (i.e. the tracer behaves similarly to the substance under investigation) [77]. Moreover, it is assumed that the extraction of FDG from the plasma normally is low enough for the delivery of FDG to be independent of blood flow.

According to the Michaelis-Menten hypothesis, an intermediate complex is formed between the substrate (S) and the transporter or enzyme, which is then converted to the chemical product (P) with release of the transporter or enzyme. The reaction rates of these processes are described by \( {k_{S \to P}} = {V_{\max }} \cdot \left[ S \right] \cdot {\left( {\left[ S \right] + {K_m}} \right)^{ - 1}} \) in which V _max is the maximum rate of the reaction and K _m (the Michaelis constant) is that concentration of the substrate ([S]) which leads to 0.5∙V_max. This is clearly a non-linear relation, but it is still possible to use linear tracer compartment models if an alternative substrate (S^*) is competing for the transporter/enzyme, the concentration of which is of a much lower value than of S [78, 79]. In this case, the reaction rate of the original substrate is (approximately) unaltered and the reaction rate of the tracer can be described as: \( {k_{S* \to P*}} \cong V_{\max }^* \cdot \left[ {{S^*}} \right] \cdot {K_m} \cdot {\left( {K_m^* \cdot \left( {\left[ S \right] + {K_m}} \right)} \right)^{ - 1}} \) which is a linear function of [S^*] as long as \( \left[ {S*} \right] << \left[ S \right] \). Therefore, the two-compartment model with four pharmacokinetic rate constants (Phelps 4K model) can be expressed by the following differential equations [80]:

Where ‘\( \otimes \)’ stands for the operation of convolution and \( {\alpha_{1,2}} = \frac{1}{2} \cdot \left[ {{k_2} + {k_3} + {k_4} \mp \sqrt {{{\left( {{k_2} + {k_3} + {k_4}} \right)}^2} - 4 \cdot {k_2} \cdot {k_4}} } \right] \).

The sum of the activity concentrations in both compartments plus a fraction of the plasma activity concentration [V _b  · C _plasma (t), with V_b the blood volume fraction] are measured within the ROI by the dynamic PET acquisition:

Therefore, when the plasma input function is known, all five free parameters of FDG metabolism (K₁, k₂, k₃, k₄ and V_b) can be estimated using non-linear least squares fitting of C _PET (t).

The original irreversible model (Sokoloff 3K model) did not incorporate k₄ [81] since the rate of hydrolysis of FDG-6-PO₄ by glucose-6-phosphatase activity is negligible in mammalian tissues, except for liver tissue [82]. This is verified in further studies [83], which compare the residual sum of squares of fits with and without k₄ by the Akaike Information Criterion [84] and Schwarz Criterion [85]. These statistics reward goodness of fit but depreciate the number of free parameters of the model (the lowest value denotes the model that best explains the data with a minimum of free parameters). Moreover, simulation studies caution that a k₄ might result from tissue heterogeneity rather than real dephosphorylation [86]. Therefore, currently most studies use the simplified three-rate constant (Sokoloff 3K) model. With k₄ = 0, Eqs. 1 and 2 simplify to:

The ratio of the phosphorylation rates of FDG (MR_FDG) and glucose (MR_glc) equals both the ratio of fluxes between the compartments of free and bound substrates (Eq. 5) and the ratio of the V_max, K_m and concentration of both the intracellular free tracer and the natural substrate:

In contrast to analogue tracers (such as FDG) when direct isotopic substitution labelling of glucose is used (e.g. [¹¹C]-glucose), the V_max and K_m for both substrates are essentially the same and Eq. 6 would reduce to a simple ratio of concentrations of FDG and glucose. In the condition where C _plasma (t) of glucose and FDG is constant, Eq. 6 can be written as:

In which F is the blood flow and λ are the partition coefficients \( \left( {{C_{free}} \cdot {C_{plasma}}^{ - 1}} \right) \) of both the substrates. This ratio is called the lumped constant of FDG (LC_FDG), or the steady-state ratio of the net extraction of FDG to that of glucose at constant plasma levels of both substrates [81]. The full operational equation is often written as: \( L{C_{FDG}} = {V_{\max, FDG}} \cdot {K_{m,glc}} \cdot \lambda \cdot {\left( {{V_{\max, glc}} \cdot {K_{m,FDG}} \cdot \varphi } \right)^{ - 1}} \). In this λ denotes the ratio of partition coefficients and ϕ is the fraction of glucose-6-PO₄ that continues down the Embden-Meyerhof pathway (i.e. regular glycolysis), which is normally quite close to 1.0. The value of the LC_FDG can be determined by simultaneous measurement of MR_glc (e.g. by [¹¹C]-1-glucose) and MR_FDG [87], independent determination of all six parameters of the LC or by the ratio of fractional arteriovenous differences for the two substrates [81, 88].

In the steady-state condition of the compartment of free intracellular FDG, the flux into this compartment is balanced by the flux out \( \left( {{{\left( {d{C_{free}}(t) \cdot d{t^{ - 1}}} \right)}_{FDG}} = 0} \right) \), the MR_glc can be estimated from Eqs. 5 and 7: In a study with 20 patients with non-small cell lung carcinoma using the Sokoloff (3K) model, it was shown that parameter estimation by non-linear least squares fitting of 30-min dynamic data yielded essentially the same results for K₁, k₂, k₃ and K_i, (R ² = 0.918, 0.937, 0.785 and 0.924, respectively, with mean relative differences varying 9–25%) compared to a 60-min protocol [89].

Primary, glucose metabolism (and thus the LC_FDG) are determined in the normal (rat) brain [18, 78, 87]. In this field it has been shown that the use of a single LC_FDG suits only considering the conditions during which it was determined. The LC_FDG is dependent on the time between tracer injection and measurement, surely changes in any disease with an enzymatic component and probably varies with regional glucose concentrations and in conditions of ischaemia, hypoglycaemia, the method of anaesthesia, age (adult or developing) and species of the subject under investigation. Due to the heterogeneity of neoplasia, these limitations are far greater and for many tumours the LC_FDG is not known. As perfectly summarized elsewhere, calculations of MR_FDG can be used if one is interested in comparative measurements (e.g. metabolic changes over time, during treatment, between a diseased or normal tissue or between different physiological states), assuming the LC_FDG of the tissue under investigation remains unchanged. In cases in which the true MR_glc needs to be determined from FDG results, then one must measure the LC_FDG in the particular experimental setup [18]. Studies of the LC_FDG in oncology are very limited and reports of determination of the LC_FDG of non-glioma malignant tissues are lacking to this date.

Variations to the previously mentioned pharmacokinetic models have been reported frequently [92‐98]. A variation to the Sokoloff 3K model with six parameters uses a reference region outside the tumour to account for the normal tissue within the tumour ROI (2 ROIs 6P model). In simulation studies it was found to adequately describe tumour pharmacokinetic rate constants of two-compartment models regardless of the amount of normal tissue within the ROI. A drawback of the technique is that reference tissue must be available [92].

Many variations to the Patlak graphical method are reported [93‐98]. Wong et al. [93] describe a technique in which they create three sequential images (each 15 min duration) starting 10 min after FDG injection combined with three arterialized venous samples taken at the mid-time of each scan. This method pre-empts the need for continued sampling and showed K_i to be within 3–4% of the values obtained by regular Patlak analysis. Another variation computes lesion K_i from the mean of the per voxel K_i for which the correlation coefficient of the Patlak plot is above a threshold [94]. This technique was further adapted by defining a 2-D ROI on a summed image of all correlation coefficient-constrained planes containing the lesion. This ROI was propagated over the planes containing the lesion in which the parameters of interest were determined. The authors conclude that this technique (total lesion evaluation method, TLE) is less ROI dependent and also incorporates therapy-related volume changes and is especially suitable for therapy response monitoring [95]. A simplified kinetic method (SKM) is advocated [96], assuming a uniform input function, based on fitting the input function of control patients with a triexponential decay function. The SKM allows MR_glc to be calculated from a static image and one late venous blood sample. It was shown in lung cancer patients that the SKM was an improvement over the SUV and approaches the MR_glc, calculated by non-linear least squares. A hybrid method of Patlak and SKM shows less bias and variability than either technique alone. For this method six time frames (each 5 min, 25–55 min post-injection) are acquired. By using every other time frame (3 data points) or every third time frame (2 data points) this method can be used to up to three fields of view [97]. The last method mentioned is based on the relation between K_i and SUV, average plasma clearance rate and the initial distribution volume of FDG (Sadato method). Estimated K_i and SUV are compared with Patlak K_i, leading to the conclusion that the estimated, non-invasively determined K_i is a better indicator of tumour uptake than the SUV [98].

Hoekstra et al. reviewed [99] and compared [83] 34 variations of previously mentioned methods to obtain glucose consumption (2 T/N, 12 SUV, 2 Sadato, 2 SKM, 5 Patlak, 10 TLE and one “2 ROI, 6P” variations) on 30 randomly selected dynamic FDG PET scans in 19 lung cancer patients. Since incorporation of k₄ did not improve fits, the Sokoloff 3K model was used as gold standard. The reliability of the gold standard was considered high since the test-retest variability (ICC = 0.95) and intra- and interobserver variability (ICC = 0.98 for both) were small. Of the 34 models tested, 10 met the required minimal correlation with the gold standard (R ² > 0.95). They concluded that the best simplified options are SUV_BSA+glucose (40–60 min or 50–60 min post-injection), Sadato method based on BSA and Patlak graphical analysis (10–60 min post-injection). Similarly, Lammertsma et al. [100] pooled the results of three studies comparing methodological aspects of response monitoring in lung [83], breast [101] and gastro-oesophageal [102] cancer (in total 170 FDG PET studies) and show excellent correlation with the Sokoloff 3K model of Patlak MR_glc (ICC = 0.98), SKM (ICC = 0.94), SUV_BSA+glucose (ICC = 0.91) and SUV_BSA (ICC = 0.91). They conclude that although Patlak MR_glc has the best correlation with the gold standard, it remains to be proved that these findings are of clinical relevance. Changes found by SUV estimation may still represent a relevant response [103, 104].

For all previously described fully quantitative measures of glucose metabolism, the arterial plasma input function [IF or C _plasma (t)] of the tumour should be known. Different approaches to obtain this IF have been described in the literature. Since it is impossible to sample the artery directly vascularizing the tumour, the gold standard is serial arterial sampling of a superficial artery (e.g. the radial artery) after which the activity concentration of the plasma derived by centrifugation can be determined [105]. Alternatives to serial arterial sampling with less complications [106] or less radiation burden to the personnel are: (arterialized) venous blood sampling [107], use of an IDIF [48, 108], modelling of a population-based IF [109‐111] or extraction of IF using mathematical segmentation methods [112].

To overcome the time-dependent ratio of arterial and venous blood activity concentration, the heated hand procedure, which shunts the arterial blood to the venous system, can be performed [107]. In Patlak analysis, the use of arterialized venous blood shows a net effect of ∼10% overestimation of K_i and ∼5% overestimation of MR_glc compared to the gold standard of arterial sampling. IDIFs of the ascending (ICC = 0.98) or abdominal (ICC = 0.96) aorta show better Patlak MR_glc correlation than IDIFs of the left ventricle (ICC = 0.94) [48, 108], but due to the PVE the recovery of activity concentrations in the aorta is less than one, causing an underestimation of the FDG activity concentration. A left ventricle IDIF shows positive bias, since the PVE caused a hot myocardium to spill-in activity in later time frames [48] leading to an underestimation of MR_glc of 16.2–17.5% [113]. Another drawback of the IDIF is that it is a measure of whole blood activity concentration, which is known to be lower than in plasma and not constant over time [107]. Population-based curves reduce the need for blood sampling and moreover can be used in body areas where IDIFs are not feasible. They can be based on averaging normalized blood curves or on fitting to a proposed equation [109, 110]. Patlak-based MR_glc obtained by population-based curves overall show high correlation with the gold standard (R ² > 0.984) [109]. Usage of mathematical tissue segmentation results in whole blood activity concentrations as well [112, 114], but it leads to an image-derived whole blood IF with similar drawbacks as an IDIF.

For estimation of pharmacokinetic rate constants of two-compartment models, the exact timing (time delay) and shape (dispersion) of the IF are needed. When it is measured by sampling [82], this does not necessarily reflect the supply of the tracer to the lesion. The time delay can be corrected for, but the dispersion of the IF results from the impulse response characteristics of the distributing system of the patient and is therefore difficult to predict [79]. These factors complicate the use of pharmacokinetic analysis of two-compartment models and therefore frequently IDIFs of a large blood pool close to the tumour are used [49, 50]. The effect of time delay and dispersion is of negligible relevance for Patlak MR_glc estimation, since the C _plasma (t) in the Patlak equation is relatively constant in the period of linear regression and the integral of C _plasma (t) is almost not affected.

Concluding, for clinical practice and most research into the value of quantification of FDG PET, the SUV_max and SUVs of isocontour-based ROIs are most relevant. They can be performed whole body, pre-empt the need of an IF and can be obtained from static images. In special situations FDG metabolism can be quantified using dynamic acquisition, preferably using IDIFs of the ascending aorta. Even though these result in absolute quantification of FDG influx, they are limited in calculation of ‘real’ MR_glc due to the indefinite value of the LC_FDG.