1. Introduction
There are now compelling evidences for the importance of hypoxia as an independent prognosticator of therapeutic outcome regardless of treatment modality [1-3]. A consequence of this has been a strong interest in methods to reliably quantify the distribution of tumor hypoxia and to potentially delineate radio-resistant hypoxic foci as intra-tumoral targets for intensity modulated radiation therapy (IMRT) [4-7]. Multiple methods were developed to detect hypoxia. These include direct measurements with interstitial PO2 probes [8,9], immunohistochemistry
[10], and in vivo imaging [11]. Of widest clinical applicability, however, is the imaging approach because of its noninvasive nature and potential to provide hypoxia images of the whole tumor, thereby avoiding “sampling” errors potentially associated with the first two methods. The most widely investigated ones for the non-invasive imaging approaches to detect tumor hypoxia are the nuclear methods using SPECT and PET. A number of hypoxia radiotracers have been developed and evaluated for this purpose. Those which have been used clinically include the single-photon emitter Iodine-124 labeled iodoazomycin arabinoside (124I-IAZA) [12] and the positron emitter Fluorine-18 labeled misonidazole (18F-FMISO) [13-15], Copper-60 and Copper-64 labeled Cu-diacetyl-bis(N4-methylthiosemicarbazone) (Cu-ATSM) [16], 18F-labeld fluoroerythronitroimidazole (18F-FETNIM) [17], 18F-labeled azomycin arabinoside (18F-FAZA) [18] and 18F-labeled 2-(2-nitro-(1)H-imidazol-1-yl)-N-(2,2,3,3,3- pentafluoropropyl)-acetamide (18F-EF5) [19].
18F-FMISO was among the first hypoxia radiotracers proposed [11] and has been the most extensively investigated one to date. 18F-FMISO is a 2-nitroimidazole that undergoes irreversible electron reduction and eventual metabolic trapping at low PO2, i.e., at radiobiologically significant oxygen tensions of 5 mm Hg or less. Under such conditions, the radiotracer becomes bound to proteins or other macromolecules. At higher oxygen concentrations, oxidation readily occurs and the 18F-FMISO reverts to its diffusible form and thus does not accumulate in normoxic tissues.
Because of its relatively short physical half-life of 110 min, PET scans of 18F-labeled radiotracers generally must be performed within about 3 hours of administration in order to obtain statistically reliable numbers of counts. Clinically, therefore, static PET scans of 18F labeled hypoxia tracers have most commonly been performed between 90 - 180 minutes post injection. The imaging time point represents a compromise among the available imaging signal (i.e., count statistics), which decreases with time, and the contrast between hypoxic and normoxic foci, which increases with time. The hypoxia-to-normoxia contrast increases over time because the amount of unfixed activity (i.e., activity not associated with hypoxia) decreases and therefore imaging at later times post-injection should more specifically identify hypoxic foci.
The practical advantages of single-time point imaging are the convenience and similarity to routine 18F-FDG PET. However, the identification of regions of hypoxia on single-time point images requires a criterion for 18FFMISO PET image segmentation. The group at the University of Washington, who pioneered 18F-FMISO PET imaging, has suggested that voxels whose intensities are 1.3 times higher than that of blood correspond to hypoxia [20]. This threshold value was based upon the finding that fewer than 5% of normal tissue voxels at late time point imaging exceeded this value. Thus contiguous intra-tumor 18F-FMISO PET voxel values greater than 1.3 may identify tumor hypoxia [21].
However, recent kinetic studies showed that the rate and amount of 18F-FMISO uptake may vary among tumors and therefore a single hypoxia segmentation criterion may not unambiguously identify tumor hypoxia [22]. To quantitatively differentiate hypoxic from non-hypoxic tissue in tumors, and to determine if late PET images reliably identify tumor hypoxia, we performed either 2-hour dynamic 18F-FMISO PET studies or 1-hour dynamic images followed by sequential 5-minute images at 90, 120, 150 and 180 minutes post-injection on rodent xenografts. A static “late” 18F-FMISO PET image could be considered as the last scan of the sequential post-injection scans which constructing a dynamic study. These dynamic data were analyzed by compartmental modeling on a voxel-by-voxel basis to derive parametric maps of the rate of 18F-FMISO trapping in tissue and these maps were compared to the static “late” 18F-FMISO PET images.
2. Material and Methods
2.1. Animal Handling
Nude rats were injected subcutaneously with 5 × 106 HT- 29 colorectal carcinoma cells to establish a tumor in the right hind limb. After 5 weeks, tumors reached a size of ≈2 cm in diameter. This site for the tumor xenograft was selected to minimize the effects of respiration and potential tumor motion during the dynamic scan. In addition, each anesthetized animals (with 1.5% isoflurane/ compressed air) were immobilized in a custom-fabricated rapid-setting foam mold [23]. These molds maintained the animal’s position for the duration of the microPET™ scan as well as to facilitate accurate repositioning in serial scans. This animal protocol was approved by the Institutional Animal Care and Use Committees (IACUC) of Memorial-Sloan Kettering Cancer Center (MSKCC).
2.2. MicroPET™ Imaging Protocol and Data Handling
The fluorine-18 radioisotopes were produced in MSKCC in-house cyclotron (EBCO Technologies, Inc., Vancouver, Canada) by irradiating an enriched 18O-water target inside a titanium chamber with accelerated proton beams. 18F-FMISO was synthesized accordingly as reported [24, 25].
A total of 7 nude rats were scanned on a Focus 120 microPET™ scanner (Concorde Microsystems, Knoxville, TN) following tail vein injection of ≈55.5 MBq 18F-FMISO. The animals were imaged using two differrent scanning protocols as depicted below.
Five animals were imaged continuously for 2 hours starting at the time of injection. The list-mode data was divided into 40 - 50 durations, of 12 - 15 seconds for the first-minutes, and 300 second subsequently. Two animals were continuously scanned for 1 hour, and then for 5-min at 90, 120, 150 and 180 min post-injection. After each scan, the animal was returned to its cage (animals will be in very bad condition during the 3-hour scan without recovery between scans) after removal of anesthetic. For every subsequent scan the animal was re-anesthetized and carefully repositioned in its custom mold before the scan. Similar to those 5 animals above, the 60-minute list-mode data was divided into 20 - 30 consecutive images of similar time durations, the 4 later scans were separated into 2 image frames, each of 300 seconds durations. The image sets for the later 90 - 180 minute time points were co-registered using external fiduciary marker-based registration. With each fiduciary rod occupying several voxels in an image, the uncertainty of registration is less than 1 voxel (data not shown). The co-registered scans were then combined to yield a temporal sequence of data spanning from the time of injection to 3 hours post-injection. Studies of the accuracy in repositioning animal into the foam mold have been reported by Zhang et al. [26].
The list-mode data were sorted into two-dimensional temporally sorted sonograms by Fourier re-binning and transverse images reconstructed in a 128 × 128 × 96 matrix (voxel size 0.87 × 0.87 × 0.80 mm3) by filtered backprojection (FBP) using a ramp filter with a cutoff frequency equal to the Nyquist frequency. Although no attenuation, scatter, or partial-volume correction was applied, the reconstructed images were expressed in quantitative terms (the activity per unit volume, Bq/ml, decay-corrected to the time of injection) using a system calibration factor measured by imaging a rat-size waterfilled cylinder containing a known concentration of 18F. However, absolute quantification of 18F-FMISO was not required for this study, but rather relative changes over time.
2.3. Compartmental Modeling
The idea of compartmental modeling was first proposed for epidemiology analysis by Kermack & McKendrick in 1937 [27], and was later applied to pharmacokinetics, including that in cancer studies [28]. Pharmacokinetic analysis of dynamic 18F-FMISO data was first performed using a simplified compartmental model by Casciari et al. in 1995 [29], and was adopted in this study (Figure 1).
The time-dependent activity concentration (Bq/ml) in a given region of interest (ROI) was extracted from the sequential image frames and used to generate a time activity curve (TAC). A volume of interest (VOI) was used
Figure 1. A conceptual 2-compartment model for 18FFMISO uptake in tumor hypoxia. In this model the transfer rate constant k4 from C2(t) →C1(t) is set to zero.
for the tumor and a region of interest (ROI) at the coronal section was used for the input function Cp(t). The vessel was readily discernible in the early frames (i.e. within the first minute post-injection) and its TAC exhibited a welldefined peak within the first one to two frames. The rate of metabolism (breakdown) of 18F-FMISO is slow in vivo (4% - 8% in 90 minutes [30]), and therefore metabolite correction of the input function was not considered in our analysis.
The simplified 3-compartment 2-tissue model [29] can be described by the following partial differential equations:
(1)
Here η is the fraction of the tissue volume occupied by extracellular space. The observed activity concentration for a given ROI is a linear combination of Cp(t), C1(t) and C2(t):
(2)
in which V is the observed volume and β fractional blood volume. By solving (1), Cobs(t) can be rewritten as a convolution of input function Cp(t):
(3)
in which:
(4)
(5)
The first term of Equation (3), representing the “trapped contribution”, models the progressive hypoxia-related accumulation of tracer over time, the second represents the “diffusible contribution” for normoxic tumor tissue, and the third the vascular contribution, with the trapped component presumably reflecting the degree of hypoxia.
We define the flux Ki as follows:
(6)
Ki represents the flux, or overall “trapping rate,” of 18F-FMISO in hypoxic tissue. Both Ki and k3 are indicators of hypoxia, where Ki ≈
when 
The extra-cellular fraction h and V were kept fixed at typical values reported in the literature (h = 0.5, V = 1) [29], and the optimization scheme fitted the free parameters of the model namely, k1, k2, k3 and b.
2.4. Parametric Images Verse Late-Time Image for Tumor Hypoxia
As results of pharmacokinetic analysis, parametric images (Ki and k3) are deemed more convincing hypoxia indicators in theory than late-time 18F-FMISO microPET images [29]. To conduct compartmental modeling for microPET images, sequential scans are taken at different time spots within 2 - 3 hrs post-injection period in order to acquire differential uptake information of 18F-FMISO in hypoxia, thus the “late” 18F-FMISO microPET scan is actually the last scan of the entire dynamic sequential scans. Consequently, parametric images Ki and k3 are based on much more imaging information and hence more reliable than the late-time image.
The 18F-FMISO uptake in the “late” scan is the outcome of the entire post-injection 18F-FMISO uptake history. In addition to hypoxia uptake, late-time microPET images may reveal 18F-FMISO concentration caused by other factors, such as temporary high-blood flow, or necrosis trapping 18F-FMISO in the early time that has much longer residual time. Parametric images Ki or k3, however, may filter out those “noises” against hypoxia uptake with compartmental modeling.
2.5. The BioGuide( Software Toolkit
Kinetic analysis was performed using the proprietary BioGuideÔ software package (Philips Healthcare) which provides the capability of performing compartmental modeling on a voxel-by-voxel basis as well as for conven tional ROIs. The BioGuideÔ software package is part of the research version of Pinnacle3Ô, the radiotherapy treatment planning program marketed by Philips Healthcare.
After fitting a TAC to blood time-activity data (derived by dynamic imaging or radio-assay of serial blood samples) the software optimizes the model parameters defined above in order to minimize the summed χ2 be tween the model fit and the measured data on a voxel by voxel basis. The Levenberg-Marquardt algorithm is used for the optimization. The results are generated as a set of voxel-by-voxel parameter maps.
2.6. Regions of Interest Definition for Arterial Input Function
The artery was contoured using a summed image of the first minute of acquisition post injection (Figure 2). To define the contours for tumor regions, the last 10 minutes of the acquisition (120 min post-injection) was used. Since 18F-FMISO targets hypoxic tissues, there is no clear contrast between normoxic tissues in tumor and surrounding normal tissue in 18F-FMISO PET images, thus regions of higher uptake in the late-time images were contoured as they were assumed to correspond to hypoxic foci. In addition, a much larger box containing the hypoxic foci in the 3D-image was also extracted as the volumes of interest (VOIs). These regions were then copied to the individual image time frames in order to generate the TAC data. Compartmental modeling was then applied to all voxels within an ROI corresponding to the whole tumor for each animal constrained within the physiological boundary conditions. The goodness of fit was evaluated using the χ2 test.
3. Results and Discussions
3.1. Validation of BioGuide( Software
The precision and accuracy for BioGuideÔ software which implements the irreversible one-plasma two-tissue compartmental model on simulated dynamic PET scans for hypoxic and normal tissue regions were validated to provide “ground truth” k1, k2 and k3 parameter constants and tissue activity curves i.e. input function. The initial dynamic dataset was produced without noise to determine the accuracy of parameter estimation. The addition of Gaussian noise to this data was used to test the precision of BioGuideÔ under realistic PET noise levels. Furthermore, the impact of the sharpness, amplitude and bias of the arterial input function peak on the kinetic parameter estimation was also studied.
This study (Wang et al. [31]) showed that at a 15% image noise level, the standard deviation in the voxel based 18F-FMISO-trapping rate constant k3 was 13.5%, but only about 5% for the influx rate constant Ki. The peak-to-tail affect the estimation precision of k3 and Ki. Simulation of high (18:1) and low (4.5:1) peak-to-tail input function
Figure 2. A sagittal microPET image of an animal summed over the first minute post injection with 18F-FMISO. The hottest voxels, corresponding to linear structure within the circle is the artery. The arterial TAC derived from the counts within this region serves as the reference input of compartmental modeling.
resulted in a change in the percent standard deviation from 9% to 20% for k3. The error for the more robust parameter Ki increased from 6% to 9% between the high and low peaked input functions.
3.2. Tissue Activity Concentration Profiles and Parametric Maps of Tumor Hypoxia
A good arterial TAC, Cp(t), is characterized by a sharp bolus injection peak followed by rapid wash out clearance. The TAC, Cobs(t), for an intra-tumor region of high “late” uptake, presumably corresponding to an hypoxic focus, is characterized by an initial rapid uptake over the several minutes followed by a more gradual but progressive accumulation. In contrast, normoxic tumor areas exhibit an initial rapid uptake corresponding to the initial arterial bolus and diffusion into well-perfused tissue followed by a gradual clearance. Sample TACs corresponding to artery and a hypoxic tumor area are displayed in Figures 3(a) and (b).
By optimizing the model parameters k1, k2, k3 and β, BioGuide™ fits the model to the observed TAC, Cobs(t), resulting in voxelwise k3 and Ki maps. These maps may be displayed as parametric images in which each pixel or voxel intensity represents the magnitude of the respective rate constant. This analysis was conducted for 4 microPET tumor slices, selected from the regions of highest 18F-FMISO uptake, for 7 tumor bearing rats.
Images resulting from the analysis of the first rat (ID#1) are shown in Figure 4. This figure contains 4 different panels of the same transaxial image plane: 1) the reconstructed microPET™ image of 18F-FMISO at 1 minute post-injection; 2) the reconstructed microPET™ image at 3 hour post injection; 3) the k3 parametric image depicting the rate tracer entrapment; and 4) the parametric image of the flux parameter Ki.
The microPET™ 3-hour post injection image (deemed to represent tumor hypoxia) is complementary to the 1- minute post-injection image which depicts initial 18FFMISO transport into tissue from the vasculature. Both k3 and in particular Ki correspond closely with the distribution of 18F-FMISO in the late 3-hour image for this particular animal tumor. Thus for this tumor, the late 18F-FMISO image provides a good representation of the location of tumor hypoxia relative to the model based parameters k3 and Ki. This is further analyzed in the form of scatter plots (Figure 5) in which the late-time pixel intensity is plotted on the originate verse the estimated k3 and Ki value plotted on the abscissa. Voxel intensities of the late-time image correlate well to both Ki and k3 with a Pearson correlation coefficient rp(k3) = 0.960 and rp(Ki) = 0.971. The Pearson correlation coefficients are above 0.9 for all 4 tumor-slices analyzed (Table 1).
For the second tumor bearing rat (ID#2), there was also close agreement between the late microPET™ images of 18F-FMISO distribution with rp(k3) and rp(Ki) > 0.9 for all central tumor slices. For this tumor the hottest k3 and Ki voxel intensities corresponded to the 18F-FMISO voxels of highest signal.
Figure 6 shows a corresponding 4 panel image display for tumor for rat (ID#3) to that shown in Figure 4 for rat (ID#1). For this tumor neither of the parametric images of Ki nor k3 is similar to the late 3-hour post-injection microPET™ image. In this case, the rate of tracer entrapment determined from the compartmental model is lower, suggestive of a lower level of hypoxia. The appearance of the voxel-wise scatter plots between the parametric rate parameters k3 and Ki and the late time point 18F-FMISO microPET™ image intensities for this tumor are shown in Figure 7. This scatter plot contains a broader dispersion of the data and poorer correlation coefficients ranging for rp(k3) from 0.507 to 0.714 and for rp(Ki) from 0.732 to 0.875 (Table 1). The study of the