Three anthropomorphic phantoms were created representing examples of bone anatomy of a normal patient and two patients positive for UCH, based on data from clinical CT studies (Fig. 1). Bone structures were segmented in 3D Slicer (v4.11.20210226; www.slicer.org). A shell of 2 mm thickness was created for the phantom using Meshmixer (Autodesk Inc., San Francisco, CA, USA) and divided into four parts for printing. Spherical inserts of different diameters (8 mm, 10 mm, 13 mm, and 15 mm) were placed in the phantoms using Inventor (v2021; Autodesk Inc., San Francisco, CA, USA) in the positions of the mandibular condyles. The spherical inserts are fillable through small access tubes.

(A) Segmentation of the bone structures of the skull. (B) Model of the corresponding anthropomorphic phantom. The red segmentation of the skull is the region representing the phantom. (C) Front view picture of the phantom with mounted access tubes for the condyle spheres and the background volume

A resin 3D printer (Form 3, FormLabs, Somerville, MA, USA) was used to print the phantoms in parts before final assembly. The quoted resolution of the printer (25 μm) far exceeded the ability to visually detect differences between prints of the same phantom. The accuracy of the phantom was determined by the Dice coefficient, comparing the volumes of the phantoms with the bone segmentations on their respective patient CT studies [22]. A more detailed analysis of the printing accuracy exceeds the scope of the current study.

The anthropomorphic phantoms were filled with a clinically relevant spheres-to-background ratio of 3:1 with concentrations of [99mTc]-pertechnetate of 120 kBq/mL in the spheres and 40 kBq/mL in the background similar as determined from patient scans. The spheres on both sides were injected with the same activity concentration to test the smallest meaningful difference for symmetric size condyles and the PVE on the asymmetric phantoms. The background volume was filled with an HK2O4P-containing solution to mimic the attenuation of trabecular bone (1.05 g HK2O4P / g water) [23].

Clinical datasets from consecutive patients referred to the nuclear medicine department of the Antwerp University Hospital from 2020 to 2022 to evaluate condylar growth were used if all pertinent data on administered activity and time were available. Patients were excluded if there was a history of craniofacial trauma or malignancy, or if the CT part of the study showed osteoarthritic changes in the temporomandibular joints. Clinical follow-up data was collected and used to determine the reference standard based on the composite of routine (post-operative) clinical follow-up. This study was approved by the ethics committee of the Antwerp University Hospital (N°: 5640).

All scans (patient and phantom) were performed on a GE Discovery 670 NM/CT 16 slice SPECT/CT camera with 3/8” NaI crystal (GE Healthcare, Haifa, Israel). LEHR collimators were used, and 120 projections were acquired. Each projection consisted of a 100-second (phantoms) or 25-second (patients) acquisition in a 128 × 128 matrix with 4.4 × 4.4 mm² pixels. Experiments were repeated using a matrix of 256 × 256 pixels, yielding identical findings (data not shown). Following the SPECT acquisition a CT image was acquired with tube voltage of 120 kV, tube current of 50 mA and slice thickness of 1.25 mm. The anthropomorphic phantoms were placed in a box to simulate clinical positioning and typical detector-to-patient distance in clinical scans.

The SPECT camera and radionuclide calibrator (VDC-405, Veenstra (Comecer), Castel Bolognese, Italy) are cross-calibrated using the planar sensitivity method according to the manufacturer’s recommendations. Afterward, the absolute quantification was verified using a large cylindrical phantom of 6,283 mL. The camera sensitivity was measured and confirmed at 78.97 cps/MBq.

All image reconstructions were based on the ordered-subsets expectation and maximization (OSEM) algorithm as implemented in MIM (7.2.3, MIM Software Inc, Cleveland, OH, USA) and optimized prior to the start of the experiments (data not shown): 5 iterations and 20 subsets had the best activity recovery while limiting noise. Three reconstructions were made: “NAC” an OSEM reconstruction without corrections (in counts), “ACSC” an OSEM reconstruction including AC and SC, and “ACSCRM” an OSEM reconstruction including AC, SC, and RM. No post-reconstruction filter was applied. The phantom measurements and patient data were reconstructed using identical settings. Image analyses of the phantom and patient data were subsequently performed in MIM. Numerical analyses were performed in MatLab (v2021a, The MathWorks Inc, Natick, MA, USA). Error estimation on the phantom data was done using the bootstrap method [24]. The phantom datasets were Poisson sampled for the error estimation using Xeleris IV (GE Healthcare, Haifa, Israel) to include 25% of the data so that the statistics would resemble the patient data. All cited error estimates represent a 95% confidence interval.

Given the small structures involved spill-over will be apparent and partial volume correction (PVC) is required to achieve quantitative accurate results. While several approaches have been proposed [25] and developed for PET/CT [26], only resolution modeling is currently commercially available. A commonly used method is the application of empirically determined recovery coefficients from a NEMA IQ phantom [11]. The NEMA phantom was filled with the same activities and activity ratio as the anthropomorphic phantom (120 kBq/mL:40 kBq/mL) and scanned for two different configurations of the spheres, which differed by turning the insert 180° for the second acquisition. The acquisition was lengthened to have similar statistics for the second acquisition.

The RCs applied in the PVC are the result of a fit using a two-parameter logistic function of the sphere volume v [27]:

$$\:RC\left(v\right)=1-\:\frac\right)}^}.$$

(1)

The recovery curves from the NEMA phantom, and separately, using the asymmetric anthropomorphic phantoms were used for PVC. The PVC recovery curves were validated on the symmetric phantom for the ACSC and the ACSCRM reconstruction sets. All phantom experiments were repeated twice.

Only the quantitative reconstructions are considered for the phantom scans: “ACSC” and “ACSCRM”. The tracer uptake was quantified using spherical volumes of interest (VOI). For the spherical inserts, the diameter of the VOI was the same as that of the insert. VOIs of 8 mm (symmetric phantom) and 10 mm (asymmetric phantoms) were selected for the clivus as they were the largest that could be included while allowing some distance to the phantom edges. Recovery Coefficients (RC) were obtained for each sphere by drawing a spherical VOI:

where ASPECT is the mean activity concentration measured in the VOI and Ainj the activity concentration injected based on the radionuclide calibrator.

The ratio of tracer uptake in the left sphere was defined as:

with AL and AR the activity concentration measured in the left and right condyles, respectively.

The ratio of tracer activity concentration of the condyle versus clivus was defined as:

All three reconstructions (“NAC”, “ACSC”, and “ACSCRM”) were made for each scan to assess the potential impact on UCH classification of the applied reconstruction methods and the correction techniques. Although the NAC reconstruction is not quantitative, it may more closely reflect the SPECT only reconstructions previously reported in literature as information on reconstruction algorithm and settings were not always provided [4]. The clinical reference method of analysis consists of calculating the ratio of mean uptake in circular ROIs of the same size for both condyles on the NAC reconstruction. A scan is considered positive for UCH when the difference in uptake ratios between the pathological and the normal condyle exceeds 10% (55%:45%) [4]. Alternatively, thresholds of 12% and 8% are also considered [10]. Similarly, the mean condylar uptake was compared with the clivus using Eq. (4).

It is considered to represent residual condylar growth when the difference in ratios exceeds 10% [5]. Surgical intervention is typically postponed in the presence of either finding, and patients are followed longitudinally until normalization of uptake.

For PVC, the radius of the mandibular condyles was estimated using the measured anteroposterior and mid-lateral condylar lengths [28]. Although the mandibular condyles are not spherical, they can be approximated by an ellipsoid for which it has been demonstrated that the RCs are similar to those of a sphere with the same volume [20]. The radius of the equivalent sphere was defined using the measured lengths:

where a and b are the length of the anteroposterior and mid-lateral lengths. The RCs from the anthropomorphic phantoms were applied for the equivalent spheres on both the ACSC and ACSCRM reconstructions. Identical contours were drawn on the ACSC and ACSCRM reconstructions. The Bland-Altman method was used to assess agreement in ratios between methods and the reference method [24].

The reclassification rate was calculated for the diagnosis of UCH using the different quantitative methods compared to the reference method (NAC). The McNemar test was used to assess significant differences compared to the reference method in the subsets of patients considered to be positive and negative for asymmetric or residual growth according to the clinical reference standard, respectively [29]. As no recovery coefficients were available for the clivus, only the asymmetric growth status using the 55%:45% threshold was considered in the PVC datasets.