The early identification of graft failure would improve patient management. 18F-fluoride is a suitable tracer for quantifying bone metabolism. Performance of parametric images constructed by Patlak graphical analysis (PGA) with various time periods was evaluated in the analysis of dynamic 18F-fluoride PET studies of eight patients with fibula bone grafts after limb salvage surgery. The PGA parametric image approach tended to underestimate influx rate. The linear portion of PGA analysis was found to be from 10 to 50 min. It shows promise in providing a quantitative assessment of the viability of bone grafts.
Free vascularised fibula grafting is well described in limb salvage surgery after resection of bone tumours. Nonunion at the osteotomy site and fracture of the graft are recognised complications, which may be related to poor blood flow within the graft. Currently there is no diagnostic modality that can reliably assess graft viability. Graft viability is usually judged by evidence of bony bridging and graft hypertrophy on plain radiographs, but this is problematic and delayed union and infection cannot be reliably predicted. The early identification of graft failure would improve patient management, and a reliable assessment of graft viability would also help identify characteristics associated with successful grafts.
Functional imaging techniques, such as positron emission tomography (PET), can visualise subtle metabolic changes and have the potential for assessing graft viability. The PET tracer 18F-fluoride has been used to evaluate regional bone metabolism and skeletal kinetics [
Kinetic modelling of PET imaging usually involves obtaining a series of blood samples for the input function (IF), and a tissue time activity curve (TTAC), derived from dynamic imaging data as the output function. Rate constants are determined by parameter estimation methods, which fit the TTAC according to an underlying kinetic model. Traditionally, manually defined regions of interest (ROI) are used to derive average, but reduced noise, TTACs for the selected regions by deriving the mean activities for the defined ROI. Alternatively, parameter estimation can be conducted voxel by voxel to form a three-dimensional parametric image volume whose voxel values represent quantitative functional parameters. The parametric image approach reduces operator-dependant bias in the manual delineation of ROI and eliminates the need to know the spatial distribution of newly developed tracers [
The nonlinear least square (NLS) analysis, a standard parameter estimation method, provides estimates with optimum statistical accuracy in kinetic analysis by iteratively adjusting the kinetic parameters of the nonlinear model equations [
A number of investigators reported on the kinetic analysis of 18F-fluoride in the evaluation of vascularisation of allogenic bone grafts [
Our aim was to systematically investigate the performance of parametric images derived by the PGA method and evaluate the optimum linear portion of PGA using dynamic 18F-fluoride PET imaging. Eight patients with limb salvage surgery and bone grafting were included with volume of interest (VOI) defined on bone grafts and normal bone tissues. Quantitative rate constants and net influx rates were also derived for VOI-derived TTACs with NLS and PGA analysis for comparison.
A three-compartment and four-parameter model has been used in the kinetic analysis for fluoride bone metabolism (Figure
Three-compartment and four-parameter kinetic model for fluoride bone metabolism.
For the ROI-based approach, a fifth parameter of fractional blood volume (fBV) is often included in parameter estimation to address spillover from capillary blood activity within the tissue regions as shown in
The influx rate macroparameter,
The studies and protocols were approved by the Ethics Committee of the Central Sydney Area Health Service. Eight patients with previous limb salvage surgery and bone grafting were studied; there were 3 men and 5 women with age range of 20–53 years. The bone grafts were taken from the fibula. The time between the bone graft surgery and PET scans was ranging from 1.3 to 4.9 years. All imaging studies were carried out on an ECAT 951R whole body PET scanner (Siemens/CTI, Knoxville, Tenn, USA) in Royal Prince Alfred Hospital. The scanner acquired 31 planes simultaneously with a slice separation of 3.375 mm and axial field of view (FOV) of 10.8 cm.
12 arterialised-venous blood samples [
Transmission images were reconstructed by an ordered-subset median-root-prior (OS-MRP) iterative reconstruction algorithm with 2 iterations and 16 subsets, which were then segmented into lung, bone, and soft tissue. The dynamic emission images were reconstructed into
The images from the last six frames, ranging from 30 to 60 min, were averaged to aid definition of VOI, which were defined using the PMOD package (version 3.1, PMOD Technologies Ltd., Zurich, Switzerland) by manually delineating ROIs on voxels with similar values across a sequence of image planes shown in Figure
Example of one transaxial plane from the average images of the last six frames. The arrows indicate manually drawn ROI.
Mean value and standard deviation (SD) value were then derived for each VOI on each frame of reconstructed images to form TTAC and SD curve. Figure
(a) PTAC and TTACs for graft and ilium. (b) Standard deviation curves.
The Patlak graphical analysis (PGA) assumes a three-compartment and three-parameter model, where the release of fluoride from the bony matrix is considered negligible, that is,
When equilibrium has been reached after a sufficient time
PGA was used to derive the parametric images of
For comparison, the derived VOIs in Section
The weights used in NLS analysis were defined by the inverse of the VOI-derived SD curve. The range of parameter variation was set from 0 to 1 for fBV,
For the equivalent comparison with the PGA method, NLS analysis was also applied to fit the VOI-derived TTAC with fBV and
Figure
Plots of values of
Comparably, low values of SD were observed in all the regions for parametric image of
Summary of standard deviation (mean ± SD) in all the regions for parametric images of
Linear Period | 4–60 min | 10–50 min | 20–50 min | 20–60 min |
---|---|---|---|---|
Mean ± SD |
Figure
Parametric images of
Table
Kinetic parameters for bone metabolism.
No. | fBV | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Graft | 1 | 0.000 | 0.037 | 0.118 | 0.091 | 0.016 | 0.016 | 0.002# | 0.014 | 0.016 | 0.016 | 0.012 |
2 | 0.000 | 0.051 | 0.389 | 0.120 | 0.000 | 0.012 | 0.012 | 0.013 | 0.013 | 0.013 | 0.012 | |
3 | 0.000 | 0.018 | 0.060 | 0.098 | 0.000 | 0.011 | 0.012 | 0.012 | 0.011 | 0.011 | 0.012 | |
4 | 0.084 | 0.013 | 0.000# | 0.453 | 0.006 | 0.013 | 0.012 | 0.012 | 0.012 | 0.012 | 0.011 | |
5 | 0.042 | 0.016 | 0.000# | 1.000# | 0.100 | 0.016 | 0.016 | 0.016 | 0.016 | 0.017 | 0.018 | |
6 | 0.000 | 0.044 | 0.064 | 0.048 | 0.000 | 0.019 | 0.020 | 0.022 | 0.021 | 0.022 | 0.021 | |
7 | 0.000 | 0.012 | 0.000# | 0.000# | 0.000# | 0.000# | 0.011 | 0.011 | 0.012 | 0.012 | 0.010 | |
8 | 0.000 | 0.057 | 0.030 | 0.001 | 0.000 | 0.002# | 0.027 | 0.029 | 0.026 | 0.026 | 0.027 | |
9 | 0.000 | 0.007 | 0.000# | 0.910 | 0.090 | 0.007# | 0.007# | 0.022 | 0.023 | 0.022 | 0.015 | |
10 | 0.000 | 0.014 | 0.000# | 0.000# | 0.000 | 0.006# | 0.013# | 0.023 | 0.022 | 0.020 | 0.018 | |
11 | 0.000 | 0.070 | 0.844 | 0.136 | 0.006 | 0.010 | 0.008 | 0.008 | 0.009 | 0.010 | 0.008 | |
12 | 0.009 | 0.120 | 0.444 | 0.044 | 0.008 | 0.011 | 0.009 | 0.008 | 0.008 | 0.009 | 0.007 | |
13 | 0.000 | 0.032 | 0.054 | 0.037 | 0.004 | 0.013 | 0.012 | 0.015 | 0.015 | 0.015 | 0.014 | |
Ilium | 14 | 0.000 | 0.172 | 0.486 | 0.135 | 0.007 | 0.037 | 0.033 | 0.033 | 0.032 | 0.030 | 0.030 |
15 | 0.000 | 0.125 | 0.229 | 0.078 | 0.004 | 0.032 | 0.030 | 0.033 | 0.033 | 0.034 | 0.031 | |
16 | 0.000 | 0.248 | 0.302 | 0.062 | 0.006 | 0.042 | 0.038 | 0.045 | 0.044 | 0.041 | 0.037 | |
17 | 0.000 | 0.408 | 0.895 | 0.122 | 0.004 | 0.049 | 0.044 | 0.045 | 0.048 | 0.047 | 0.041 | |
18 | 0.000 | 0.180 | 0.220 | 0.074 | 0.007 | 0.046 | 0.040 | 0.044 | 0.042 | 0.040 | 0.039 | |
19 | 0.000 | 0.234 | 0.592 | 0.170 | 0.014 | 0.052 | 0.039 | 0.040 | 0.041 | 0.034 | 0.029 | |
20 | 0.048 | 0.067 | 0.079 | 0.126 | 0.015 | 0.042 | 0.035 | 0.035 | 0.035 | 0.034 | 0.032 | |
21 | 0.000 | 0.145 | 0.212 | 0.131 | 0.006 | 0.055 | 0.050 | 0.052 | 0.049 | 0.048 | 0.049 | |
22 | 0.002 | 0.136 | 0.484 | 0.165 | 0.003 | 0.034 | 0.032 | 0.032 | 0.032 | 0.032 | 0.032 | |
23 | 0.063 | 0.110 | 0.069 | 0.074 | 0.008 | 0.057 | 0.052 | 0.052 | 0.050 | 0.048 | 0.047 | |
24 | 0.000 | 0.012 | 0.000# | 0.999 | 0.000 | 0.012# | 0.011# | 0.020 | 0.018 | 0.018 | 0.020 | |
25 | 0.024 | 0.067 | 1.000# | 0.609 | 0.009 | 0.025 | 0.022 | 0.020 | 0.020 | 0.018 | 0.018 | |
26 | 0.000 | 0.075 | 0.197 | 0.216 | 0.013 | 0.039 | 0.029 | 0.033 | 0.035 | 0.035 | 0.030 | |
27 | 0.000 | 0.024 | 0.016 | 0.023 | 0.000 | 0.014 | 0.014 | 0.017 | 0.017 | 0.017 | 0.016 | |
28 | 0.000 | 0.036 | 0.312 | 0.098 | 0.004 | 0.009 | 0.008 | 0.008 | 0.008 | 0.008 | 0.008 | |
29 | 0.000 | 0.039 | 0.337 | 0.170 | 0.013 | 0.013 | 0.010 | 0.011 | 0.010 | 0.009 | 0.010 | |
30 | 0.000 | 0.058 | 0.801 | 0.167 | 0.008 | 0.010 | 0.008 | 0.009 | 0.008 | 0.008 | 0.008 | |
31 | 0.000 | 0.035 | 0.326 | 0.178 | 0.011 | 0.012 | 0.010 | 0.011 | 0.010 | 0.010 | 0.010 | |
32 | 0.000 | 0.108 | 0.171 | 0.070 | 0.000 | 0.031 | 0.032 | 0.034 | 0.032 | 0.032 | 0.032 | |
33 | 0.000 | 0.024 | 0.000# | 0.090 | 0.090 | 0.024# | 0.014# | 0.035 | 0.038 | 0.038 | 0.032 | |
Lumbar vertebra | 34 | 0.065 | 0.090 | 0.106 | 0.048 | 0.000 | 0.028 | 0.027 | 0.029 | 0.023 | 0.021 | 0.026 |
35 | 0.003 | 0.163 | 0.226 | 0.121 | 0.011 | 0.057 | 0.046 | 0.048 | 0.046 | 0.043 | 0.043 | |
36 | 0.000 | 0.146 | 0.175 | 0.090 | 0.005 | 0.049 | 0.042 | 0.050 | 0.047 | 0.045 | 0.047 | |
37 | 0.000 | 0.103 | 0.283 | 0.163 | 0.010 | 0.038 | 0.031 | 0.031 | 0.032 | 0.033 | 0.028 | |
38 | 0.000 | 0.037 | 0.513 | 0.201 | 0.014 | 0.010 | 0.008 | 0.008 | 0.008 | 0.007 | 0.007 | |
39 | 0.000 | 0.040 | 0.491 | 0.201 | 0.013 | 0.012 | 0.009 | 0.009 | 0.009 | 0.008 | 0.008 |
#Unsuccessful fit.
Some unsuccessful fits were observed by NLS analysis such as when
Table
Mean and standard deviation (mean ± SD) of derived rate constants for successful NLS analysis.
fBV | Flux- | |||||
---|---|---|---|---|---|---|
Graft | ||||||
Ilium | ||||||
Lumbar vertebra |
Linear regression analysis was applied to compare the accuracy of the net influx rate derived by PGA compared with NLS for the three-compartment and five-parameter model with unsuccessful fits excluded. Table
Linear regression between NLS and PGA for parametric images.
Linear portion | 4–60 min | 10–50 min | 20–50 min | 20–60 min |
---|---|---|---|---|
0.979 | 0.983 | 0.970 | 0.961 | |
Linear regression analysis between NLS for VOI-based TTAC and PGA for parametric image with linear period of 20 to 60 min. Black line: the plot of obtained linear regression; grey line: theoretical ideal linear regression.
A high linear correlation was observed for
The potential for underestimating
18F-fluoride PET with quantitative kinetic analysis has allowed the quantitative assessment of regional lesions and treatment response in metabolic bone disease and also enabled early identification of bone viability and discriminated uneventful and impaired healing processes of fractures, bone grafts, and osteonecrosis [
The Gaussian noise model is usually assumed in the NLS fitting with the weights defined according to the activity of TTAC and the duration of imaging frame. In this study, the weight is defined by the inverse of the VOI-derived standard deviation instead, which provides an approximate estimation of noise distribution for the VOI-derived TTAC. However, due to the low signal-to-noise ratio in early, short imaging frames, the iterative reconstruction caused the values of voxels with low activity to be estimated to be zero and explains why the values of SD are shown to be zero for the early frames in Figure
The estimation of
The late time period inherently used for the PGA fit avoids the problem of the low count early frames for the PGA method. We observed high reliability for the studied PGA with four linear periods in the generated parametric images of
Hybrid PET/CT scanner has now become widespread with improved image quality and shorter imaging time with coregistered CT images. Combining with the detailed anatomical information readily available from CT images, the state-of-the-art PET/CT imaging may lead to more accurate assessment of graft viability. This requires in-depth investigation on improving the accuracy of CT-based attenuation correction for PET scans, especially for bone and graft tissues, to take advantage of the benefits offered by the hybrid scanners.
Dynamic 18F-fluoride PET imaging studies in patients with limb salvage surgery and fibula bone grafts were analysed using NLS and PGA methods to derive TTACs and parametric images. 39 regions were analysed respectively for the bone graft, ilium, and lumbar vertebrae. The results show that parametric images derived by PGA are consistent with VOI-based parameter estimation by PGA with high reliability. The PGA approach tended to underestimate influx rate because the assumption that
This work was supported in part by ARC, PolyU, ISL/Australia-China Special Fund, Shanghai Leading Academic Discipline Project (no. S30203), National Natural Science Foundation of China (no. 30830038), Shanghai Science and Technology Commission of International Cooperation Project Fund (nos. 08410702000, 07JC14039), and the Grant (nos. PY07002, 09XJ21032, and SS08031).