FMISO PET/CT measurements design for Partial Volume Effects correctionDescription of the PET/CT device

The measurements for the RC calculation and validation, as well as all of the clinical PET/CT image acquisitions were done on a Philips Gemini TF BigBore 16 PET/CT (Eindhoven, The Netherlands) at the Nuclear Medicine department at Medical Centre University Freiburg. It is a full three-dimensional, time-of-flight capable whole-body PET scanner, combined with a 16-slice Brilliance CT scanner unit. The PET scanner is designed with a 90 cm scanner diameter and an 18 cm axial field of view. It uses flat modules of a 23 × 44 array of 4 × 4 × 22 mm3 discrete lutetium-yttrium oxyorthosilicate (LYSO) crystals in a pixelated Anger-logic detector design arrangement. The spatial resolution in both the transverse and the axial directions is 4.8 mm near the central axis [29]. The scanner uses an iterative reconstruction algorithm with spherical coordinates (BLOB-OS-TF), 3 iterations, 33 subsets and a relaxation parameter for smoothing of 0.35. The voxel size of the reconstruction is isotropic at 2 mm. Finally, correction for random- and scatter-coincidences and photon attenuation is provided, based on the combined CT scan [30].

Description of the phantomsPhantom-1

The phantom set-up used for the calculations of the RC curves (Fig. 1) was the PTW PET/SPECT-phantom, set T43004.1.008-0106 (PTW, Freiburg, Germany). The phantom body is cylindrical with an inner diameter of 200 mm and an outer diameter of 236 mm made of polymethylmethacrylate (PMMA) [31]. The phantom includes an insert, which has six hollow glass spheres with inner, active diameters of 10, 13, 17, 22, 28, and 37 mm.

Fig. 1

The cylindrical phantom used for the first stage of the development of the correction model from spherical lesions with homogeneous activity concentration. The six spheres are numbered from 1 to 6 with increasing volume

The aim was to have a set-up that resembles the conditions of the head and neck region of the human body during FMISO PET/CT acquisition in terms of activity and contrast of the HTV against its surrounding tissues (BG). We repeated the measurements for six contrasts (10.0:1, 7.6:1, 5.8:1, 4.0:1, 2.5:1, 2.0:1) of hot (high activity) spheres against warm (lower activity) BG and used water for the representation of the BG and the HTV because it resembles soft tissue density. For all image acquisitions, we used the same imaging protocol that was used in the clinical study.

Phantom-2

The phantom set-up that was used for the validation of the RC correction method (Fig. 2) has the same body as phantom-1 but instead of the glass spheres, we inserted custom-made cylinders of different volumes. For the construction of the cylinders, we used alginate, mixed with a solution of [18F]fluordesoxyglucose (FDG). Each cylinder contained alginate of two different activity concentrations with a contrast of 1.3:1, resembling the contrast SUVmean:SUVmax in the HTV of the FMISO patients of the study, and they were all submerged in water of lower activity [32]. The set up was scanned at three lesion-to-background contrasts, starting with the highest (7:1) and proceeding with introduction of extra activity to the background, to decrease the contrast twice (4:1 and 2:1).

Fig. 2

The cylindrical phantom used for the validation of the PVE correction model on non-spherical lesions with inhomogeneous activity distributions. There are ten blue cylinders, suspended in water with a net that is stabilised on the phantom’s walls with Velcro straps. The cylinders are numbered with increasing size and the seven largest (4–10) are used for the analysis

Calculation of recovery coefficient

In this study, the RC was used for the PVE correction. The PET scanner measures only a portion of the actual activity in small volumes, when they are located in a background of lower activity. This portion depends both on the size of the lesion and on the local contrast.

Considering the geometry in phantom-1 (Fig. 1), the contours of the spheres were delineated on the CT image from the phantom's PET/CT scan and then, they were transferred to the PET image. Due to the lower spatial resolution of the PET, in some cases, the contours of the smallest spheres were not accurately replicated on the PET image. Consequently, manual adjustments were performed to correct these inaccuracies in the contours on the PET image.

The RC for a specific sphere, filled with a tracer solution of known activity concentration, is defined by the following equation [17, 18]:

The dependence of RC on volume was measured using phantom-1 for the embedded six spheres of different sizes for a specific contrast level.

Although, PVE depends on the dimensions and not directly on the volume of the region of interest (ROI) [13, 14], in our experimental set-up with spherical ROIs both volume and radius/diameter dependence of RC were equivalent. Using the semi-logarithmic representation of the RC values in relation to volume, data could be modeled for each contrast level [27]:

$$RC = a \times ln\left( V \right) + b$$

(2)

The linear regression fit was done using MATLAB (R2020b, Update 2, Natick, Massachusetts: The MathWorks Inc.).

The above model demonstrated equivalent performance in fitting our experimental data at different contrast levels with the also investigated two-parameter logistic function, as presented by Gear et al. [18], when focusing in the range of volume and contrast that were used in our investigation. The semi-logarithmic model was finally preferred since it could be easily expanded to describe the contrast dependence of RC.

Contrast dependence of RC

In published investigations, the dependence of RC on contrast for a specific volume was addressed by, either a nearest neighbour [27] or a look-up-table-based [28] correction approach. In the present work and based on our measurements using the phantom-1 at six different contrast levels, we considered explicitly both volume and contrast dependence of RC. For that purpose and based on Eq. 2, RC can be written as a function of both volume (V) and contrast (C):

$$RC\left( \right) = a\left( C \right) \times ln\left( V \right) + b\left( C \right)$$

(3)

The dependence of both a(C) and b(C) coefficients on contrast was determined by fitting Eq. 2 to the experimental RC data for the six different contrast levels used in our experiments.

Validation with inhomogeneous activity volumes

The introduced correction method is validated in a more complex and realistic set-up using the phantom-2 (Fig. 2) with inhomogeneous activity concentrations. The generalised RC model (Eq. 3) was applied on the measured activity values of the seven cylinders in phantom-2 by multiplying the measured activity with the inverse of RC [16].

Two different methods were considered to define the appropriate RC value for each of the seven cylinders: (a) The volume of each cylinder is directly used in Eq. 3 (volume-method) and (b) the diameter of the cylinder, that is the smallest dimension of the ROI, is used to calculate the volume of a corresponding sphere to be used in Eq. 3 (diameter-method).

Application of PVE correction to patient dataPatient cohort

Our cohort consisted of forty-nine HNSCC patients treated with definitive chemoradiation treatment (CRT) at the University Medical Centre Freiburg within a prospective imaging trial. The trial received approval by the Independent Ethics Committee of the University of Freiburg (reference no. 479/12) and was performed according to the Declaration of Helsinki (revised version of 2008). It is registered at the German Clinical trials Register (DRKS00003830). CRT was administered for 7 weeks in daily fractions of 2 Gy to a total dose of 70 Gy to the primary tumour and macroscopic lymph node metastases and 50 Gy to the elective lymphatic drainage [33]. The Sequential Boost and Simultaneous Integrated Boost (SIB) technique were used on 33 and 16 cases respectively, for treatment planning. Replanning took place in seven cases. All patients underwent FMISO PET/CT examinations before the start of radiotherapy (W0), and two consecutive FMISO examinations at the second (W2) and fifth week (W5) after the start of treatment. In detail, at W0 and W2, all patients (49) underwent FMISO examination, while 41 patients received a FMISO PET/CT scan at W5. The image acquisitions were planned at 160 min after the injection of 4 MBq per kg of body weight tracer, and for a duration of 10 min. The FMISO images were imported in our treatment planning system, Eclipse® version 15.6 (Varian Medical Systems, Inc., Palo Alto, USA), for subsequent analyses.

GTVs were delineated by board-certified radiation oncologists on the planning CT, based on FDG PET/CT and multi-parametric MRI (mpMRI) [34]. The expansion to clinical target volume (CTV) and planning target volume (PTV) was performed based on the standard operating procedure (SOP). The acquisition of both FDG and mpMRI took place before the start of chemoradiation.

The GTV, defined on the planning CT, represents the initial GTV before therapy. Subsequently, this initial GTV was transferred from the planning CT to W0-, W2- and W5-FMISO PET/CT imaging using deformable image registration of the corresponding CT volumes. This process was performed on Eclipse® Image Registration v15.5.

In our investigation, we focus on the hypoxic volume at W0, W2 and W5. The propagation of the initial GTV to W2 and W5, through deformable image registration, improved its allocation within the anatomical boundaries in W2 and W5 and accounted for anatomical changes due to differences in positioning, occurred tissue (tumour) shrinkage or weight loss.

The projected initial GTV on FMISO PET/CT in W2 and W5 does not accurately represent the true GTV at those time points. In our patient cohort, FDG PET/CT was available only at W0 and mpMRI was not available for all patients at W2 and W5. Consequently, delineating the “true” GTV at W2 and W5 was not feasible. These projected initial GTV volumes were utilised as a confining region for analysing SUV and HTV topography before and after the PVE correction.

The mean volume of the GTV across the entire patient cohort was 42.0 ± 42.9 ml (range 1.6–205.1 ml). The age of the group was 60 years on average, ranging from 34 to 78 years. Relevant details for our patient cohort are listed in Table 1.

Table 1 Characteristics of the patients included in our cohortApplication of the RC-based PVE correction on clinical data

The PVE correction was applied in a stepwise manner (see Fig. 3), targeting regions with specific SUV ranges by SUV-thresholding. At each step, a threshold generates a region of voxels or object. Since the specific RC for this object derives from Eq. 3, a volume for this object is required. To account for the irregular geometry of the object, a generalised volume V* was defined. The generalised volume is given by [17]:

$$V^ = 36\pi \frac^ }}^ }}$$

(4)

where Sobject and Vobject are the surface area and volume of the object.

Fig. 3

The flowchart describes the algorithmic process that was implemented to apply the RC-based PVE-correction method on the clinical data and to define the HTV based on corrected SUVs

To set the starting threshold, a well-oxygenated volume (WOV) was initially defined. Typically, the aorta or a muscle tissue is used for this purpose. Since, in our PET/CT data, the aorta was outside the scanned region, muscle tissue was chosen as WOV [35]. Specifically, a portion of the sternocleidomastoid muscle, on the opposite side of the location of the GTV, was delineated as WOV by board-certified radiation oncologists, and the mean SUV (\(\overline }}\)) was calculated.

A threshold of \(\overline }} \times 1.4\) is commonly used for defining HTV [19,20,21, 35]. A higher multiplication factor than 1.4 would generate more sub-regions within GTV. For our data and when applying thresholds above \(\overline }} \times 1.5\), V* was lower than the minimum volume (V ≥ 0.6 ml), used for fitting of the RC equations (Eq. 2). Therefore, the starting threshold (threshold-1) was set to \(\overline }} \times 1.5\). The voxels within the GTV, whose SUV superseded this threshold, defined region-1.

The RC(V*,C) for region-1 is given by Eq. 3, where V* is the generalised volume of region-1 and C is the contrast given by:

$$C = \frac1}} }} }} }} }}$$

(5)

The SUVs of the voxels in region-1 were then corrected by dividing their original SUV by the calculated RC.

The next region, region-2, was generated by decreasing the multiplication factor by 0.01 to define threshold-2. Region-2 consisted of voxels with original SUV in the range between threshold-1 and threshold-2. The RC for region-2 is given by Eq. 3, with V* being the generalised volume of region-1 and region-2 combined and the corresponding C, defined according to:

$$C = \frac1 + region2}} }} }} \right)}} }} }}$$

(6)

The SUV for all voxels in region-2 was corrected by dividing their original SUV by the RC of region-2. This was repeated until the multiplication factor reached 1.0 and thus the threshold became \(\overline }} \times 1.0\). Finally, using the corrected SUVs inside GTV, the HTV was defined based on the threshold \(\overline }} \times 1.4\).

Evaluation of clinical data after PVE correction

A SUV analysis for GTV and HTV and a topographical comparison of HTV was performed for the PET/CT volumes before and after the PVE correction. The HTV was in each case generated based on the SUV threshold of \(\overline }} \times 1.4\). For the SUV analysis, the mean SUV in the GTV (\(\overline }}\)) and HTV (\(\overline }}\)) was used. In addition, the hypoxic fraction (HF) defined as the percentage of the GTV that is characterised as hypoxic:

$$HF = \frac} \times 100 \%$$

(7)

was used to describe the extension of hypoxia and to compare the results before and after PVE-correction. The HF, by definition, can be calculated only in W0, since the actual GTV was not available at W2 and W5. For the topographical comparison of the generated HTVs, the volume, the DICE coefficient, the shift of centre of gravity (COG) and the Hausdorff distance were the used metrics.

Test selection for statistical comparisons

The statistical comparison of two groups, before and after the PVE correction, was made with a paired, two-sided Wilcoxon signed-rank test since our data were not normally distributed. The significance level was set at 0.05.