The Essential Role of Nuclear β-Catenin Translocation in the Osteoblastic Differentiation of GCTB: Prediction of Tumor Ossication After Denosumab Treatment

Denosumab is a game-changing drug for giant cell tumor of bone (GCTB); however, its clinical biomarker regarding tumor ossication of GCTB has not been elucidated. In this study, we investigated the relationship between Wnt/β-catenin signaling and the ossication of GCTB and evaluated whether endogenous nuclear β-catenin expression predicted denosumab-induced bone formation in GCTB. Genuine patient-derived primary GCTB tumor stromal cells exhibited osteoblastic characteristics. Identied osteoblastic markers and nuclear β-catenin translocation were signicantly upregulated via differentiation induction and were inhibited by treating with Wnt signaling inhibitor, GGTI-286, or selective Rac1-LEF inhibitor, NSC23766. Furthermore, we reviewed the endogenous ossication and nuclear β-catenin translocation of 86 GCTB clinical samples and elucidated that intra-tumoral ossication was signicantly associated with the nuclear translocation. Three-dimensional quantitative analyses (n = 13) of tumoral CT images have revealed that the nuclear β-catenin translocation of naïve GCTB samples was signicantly involved with the denosumab-induced tumor ossication. Our ndings suggest a close relationship between the nuclear β-catenin translocation and the osteoblastic differentiation of GCTB. Investigations of the nuclear β-catenin in naïve GCTB samples may provide a promising biomarker for predicting the ossication of GCTB following denosumab treatment. OGM analyzed in the and cytoplasmic fractions by western blotting. Experiments were repeated three times, and representative were shown. induction differentiation β-catenin

Denosumab inhibits RANKL, thereby preventing RANK-RANKL interactions, resulting in deletion of GCTB-OCs and decreasing tumor-induced osteolysis [15][16][17][18] . In addition, diffuse bone formation with the peripheral sclerotic rim is often observed after denosumab treatment 4 . These histological and clinical consequences can result in a more comfortable operative procedure and decrease surgical morbidity 4,15−17 . However, the underlying mechanism of that ossi cation was not known.
Although osteolysis is the characteristic feature of GCTB, intra-tumoral and peripheral bone develops in 30-50% of cases of GCTB 19,20 . Consistent with this observation, several previous studies reported that GCTB-SCs have the ability to undergo osteoblastic differentiation 1,7,8,13,21,22 . One essential requirement for osteoblastic differentiation could be the association between WNT/β-catenin signaling and its target gene, Runt-related transcription factor2 (RUNX2) [23][24][25] . Previous studies reported nuclear β-catenin translocation and expression of RUNX2 in GCTB-SCs 21,26 . These results suggest the involvement of the so-called "canonical" Wnt signaling pathway in the osteoblastic differentiation of GCTB-SCs. However, this hypothesis has remained unproven 7 , and no useful markers have been identi ed to predict bone formation in GCTB.
In this study, we investigated the relationship between the Wnt/β-catenin signaling, a critical pathway for osteogenic differentiation, and ossi cation of GCTB using patient-derived primary cultures. In addition, we investigated whether nuclear β-catenin translocation in GCTB-SCs predicted bone formation after denosumab treatment.

Denosumab induced bone formation in the patient with GCTB
In patients with GCTB, administration of denosumab often induced massive bone formation, as shown in Figures 1a and 1b. Histologically, we observed loss of GCTB-OCs with marked bone formation (Figures 1c   and 1d). Meanwhile, H3G34W-positive GCTB-SCs remained adjacent to or within the newly formed bone (Figures 1e and 1f), suggesting that GCTB-SCs were of the osteoblast lineage, as previously reported 1,5,27 .

Isolation of GCTB-SCs and induction of bone differentiation
To assess the osteogenic potential of GCTB-SCs, we harvested primary cultures from freshly sorted samples (pGCTB-SCs). As shown in Figure 1g, almost all pGCTB-SCs were positive for H3G34W, demonstrating that the cultures were pure. Next, we grew pGCTB-SCs in the presence or absence of OGM. The presence of OGM strongly stimulated ALP expression in pGCTB-SCs in a time-dependent manner (Figures 1h and S1a). This induction of ALP expression was not abolished by the removal of OGM, indicating that the osteoblastic differentiation was irreversible ( Figure S1b). In addition, the mRNA levels for representative osteoblast genes ALP, COL1A1, IBSP (bone sialoprotein), RUNX2, and BGLAP (osteocalcin) were signi cantly increased by the presence of OGM (Figure 1i) in a time-dependent manner ( Figure S1c). Fluorescence immunocytochemical analysis revealed that H3G34W-positive pGCTB-SCs expressed high levels of ALP after OGM treatment (Figure 1j). Based on these ndings, we con rmed that H3G34W-positive pGCTB-SCs had the capacity to differentiate into bone-forming osteoblasts.
Effect of the activation of Wnt/β-catenin signaling on osteoblastic differentiation of pGCTB-SCs The osteoblastic differentiation from mesenchymal precursors is regulated by the Wnt and BMP signaling pathways 23,[28][29][30] . In addition, previous studies reported nuclear β-catenin translocation in GCTB-SCs 31 . Hence, we hypothesized that the canonical Wnt pathway regulates the osteoblastic differentiation of pGCTB-SCs. Accordingly, we grew pGCTB-SCs in OGM, lysed the cells, and puri ed cytoplasmic and nuclear protein fractions. By western blotting, we con rmed that the nuclear β-catenin translocation was upregulated within 12 hours after OGM treatment, although cytoplasmic β-catenin remained unchanged (Figures 2a and 2b). To further determine whether the nuclear β-catenin translocation was due to activation of the canonical Wnt pathway, we treated pGCTB-SCs with LiCl or the anti-sclerostin antibody romosozumab, both of which activate canonical Wnt signaling 7 . Interestingly, treatment with those Wnt pathway agonists did not induce ALP expression in pGCTB-SCs (LiCl; Inhibition of the nuclear β-catenin translocation by geranylgeranyltransferase inhibitor abolished osteoblastic differentiation of pGCTB-SCs Next, we studied the effect of GGTI-286 (GGTI), a recently identi ed Wnt/β-catenin pathway inhibitor 32 , on the osteoblastic differentiation of pGCTB-SCs. GGTI dramatically decreased OGM-induced ALP expression in pGCTB-SCs in a dose-dependent manner (Figures 3a and 3b). GGTI also signi cantly abolished the osteoblastic makers' expression (ALP, COL1A1, IBSP, and RUNX2; Figure 3c). We also con rmed that GGTI inhibited the OGM-induced nuclear β-catenin translocation in a dose-dependent manner ( Figure 3d). The immunocytochemical analysis also revealed that GGTI abrogated the OGMinduced nuclear β-catenin translocation in pGCTB-SCs (Figure 3e). These results suggested that the nuclear β-catenin translocation was indispensable for osteoblastic differentiation of pGCTB-SCs.

Activation of Rac1 was required for osteoblastic differentiation of pGCTB-SCs
We then investigated the underlying mechanism by which GGTI inhibited the OGM-induced nuclear βcatenin translocation. A previous study claimed that GGTI binds a geranylgeranyl group on the C terminus of Rho family small GTPases, including Rac1 33 . Furthermore, Rac1 promotes the nuclear βcatenin translocation through phosphorylation at Ser191 by a downstream effector kinase, JNK 34 . Hence, we analyzed the effect of a selective Rac1-GEF inhibitor, NSC23766 (NSC), on OGM-induced osteoblastic differentiation of pGCTB-SCs. Like GGTI, NSC also decreased the expression levels of ALP and other osteoblastic markers in pGCTB-SCs following OGM treatment (Figures 4a-c). NSC also diminished nuclear β-catenin translocation following OGM treatment (Figures 4d and S1d). Together, these ndings indicate that activation of Rac1 is required for the nuclear β-catenin translocation and subsequent osteoblastic differentiation of pGCTB-SCs.
Nuclear β-catenin translocation in GCTB-SCs of patients with GCTB and its association with intra-tumoral ossi cation of GCTB Some cases of GCTB exhibit spontaneous intra-tumoral ossi cation, whereas others do not 20,35 . Based on our in vitro results, we hypothesized that in cases in which endogenous nuclear β-catenin translocation occurs in GCTB-SCs, the tumor cells might be more likely to differentiate into osteoblasts.
To test this notion, we rst assessed the distribution of NLBI in GCTB-SCs using 91 clinical samples of GCTB. Of those samples, three cases were excluded due to overlap, one was removed due to low sample quantity, and another was excluded because the associated patient data were not available. Ultimately, a total of 86 tumor sections were retrospectively reviewed. The background data on these sections are presented in Supplemental Table 1. A retrospective evaluation revealed that the distribution of NBLI in GCTB-SCs was variable, ranging from 0% to 76.4% (median: 13.5%, Figure 5a). In addition, the histogram of NBLI in GCTB-SCs exhibited a non-normal distribution (Figure 5b). We set the median as the cut-off value of the NBLI and subdivided the cases of GCTB into two groups as follows: positive (NBLI > 13.5%, positive group, n = 43) and negative for nuclear β-catenin translocation (NBLI ≤ 13.5%, negative group, n = 43). Retrospective evaluation of NBLI signi cantly coincided among reviewers (R 2 = 0.877 by Pearson product-moment correlation coe cient; P < 0.0001, Figure S2). When we examined the prevalence of intra-tumoral ossi cation of GCTB, we found that 42 out of 86 samples (48.8%) developed intra-tumoral ossi cation (Figures 5c and 5d), consistent with a previous report 20 . Remarkably, the positive group exhibited a signi cantly higher rate of intra-tumoral ossi cation (Figure 5e) than the negative group (Figure 5f), as shown in Figure 5g (P < 0.0001, Fisher's exact test).
The number of GCTB-SCs with nuclear β-catenin translocation in biopsy samples was correlated with the degree of bone formation after denosumab treatment The diversity of endogenous nuclear β-catenin translocation in GCTB-SCs may explain differences in bone formation after denosumab treatment. To address this issue, we studied 14 consecutive cases of GCTB that received denosumab. One case was excluded due to a problem with the specimen; the remaining 13 tumor samples were reviewed. Detailed information on individual cases is summarised in Table 1.
We rst investigated the NBLI in GCTB-SCs of the cases and found seven positive and six negative. Case #5, a positive group representative, exhibited massive bone formation after denosumab treatment, as revealed in CT images (Figures 6a and 6b). Histologically, deletion of osteoclastic giant cells and prominent bone formation was observed (Figures 6c and 6d). However, H3G34W-positive GCTB-SCs were still present in the specimen (Figures 6e and 6f). Biopsy samples acquired before denosumab treatment revealed that multiple GCTB-SCs were positive for nuclear β-catenin translocation (NBLI = 23.9, Figure  6g). Meanwhile, in case #10, a typical case of the negative group, bone formation after denosumab treatment was scarce (Figures 6h and 6i). Additionally, the surgically resected samples exhibited loss of osteoclast-like giant cells but not bone formation (Figures 6j and 6k). However, stromal cells were positive for H3G34W, as were the biopsy samples (Figures 6l and 6m). Importantly, before denosumab treatment, only a few GCTB-SCs were positive for nuclear β-catenin translocation (NBLI = 8.5, Figure 6n).
We next quanti ed denosumab-induced bone formation using CT images, as described previously 36 . In the window setting where the tumor margins were discernible, ROIs for histogram analyses were semiautomatically delineated by tracing the tumors' outer margins before (Figures 7a-7g) and after (Figures 7i-7o) denosumab treatment. The entire, peripheral, and intra-tumor Agatston scores of the GCTBs were obtained by histogram analyses using SYNAPSE VINCENT (Figures 7h and 7p). Notably, after denosumab administration, the positive group exhibited signi cantly higher ossi cation than the negative group (Figures 7q-7s). Therefore, the positive group would have more chances to undergo denosumabinduced bone formation. Thus, the NBLI in GCTB-SCs in biopsy samples represents a reasonable and straightforward biomarker for predicting the degree of bone formation after denosumab treatment.

Discussion
The introduction of denosumab has attracted attention as a novel therapy of GCTB. Several clinical studies have con rmed that denosumab administration prevents osteolysis, concomitant with the deletion of GCTB-OCs 15,16,18,37 . It may also cause additional histological consequences, including central sclerosis with peripheral bone formation, enabling surgical downstaging. However, the degree of bone formation is case-dependent, and we experienced some cases with little bone formation despite the treatment. Therefore, we assumed that predicting subsequent bone formation after denosumab administration would have clinical bene ts for decision making, enabling clinicians to achieve optimal treatment for GCTB.
We rst focused on the mechanism of osteoblastic differentiation of GCTB-SCs. H3G34W-positive GCTB-SCs had the ability to differentiate into osteoblasts but not chondrocytes or adipocytes (data not shown), indicating that GCTB-SCs did not retain pluripotency. During osteoblastic differentiation, the canonical Wnt/β-catenin signaling is the dominant pathway 26 . However, in our study, forced activation of LRP-and GSK3β-mediated canonical Wnt/β-catenin signaling did not cause differentiation. By contrast, our results showed that the apparent nuclear β-catenin translocation was associated with the osteoblastic differentiation of GCTB-SCs and that a recently identi ed inhibitor of the canonical Wnt signaling, GGTI, effectively inhibited it.
GGTI inhibits protein prenylation, and this process is essential for the correct localization and functions of GTPases, including Rac1 32 . In addition, Rac1 stimulates nuclear β-catenin translocation through phosphorylation at Ser191 by a downstream effector kinase, JNK 27 . Consistent with these previous results, we found that Rac1 inhibition suppressed nuclear β-catenin translocation and osteoblastic differentiation of GCTB-SCs. Therefore, we considered that denosumab administration caused activation of Rac1 and triggered the nuclear localization of β-catenin, followed by osteoblastic differentiation of GCTB-SCs, ultimately resulting in the cessation of tumor activity. If this is the case, forced activation of Rac1 in GCTB-SCs by a potent Rac1-agonist, such as the recently discovered natural polyketide deacetylmycoepoxydiene 38 , may stimulate the osteoblastic differentiation of GCTB-SCs, and combination treatment with denosumab and Rac1-agonist could be an effective strategy for the treatment of GCTB.
We detected baseline nuclear β-catenin translocation in pGCTB-SCs, indicating intrinsic activation of canonical Wnt/β-catenin signaling. Interestingly, a previous study showed that miR-125a stimulates the translocation of β-catenin in GCTB-SCs through GSK3β-mediated canonical signaling, resulting in cell proliferation and tumorigenicity 39 . However, extrinsic inhibition of GSK3β by LiCl did not play signi cant roles in osteoblastic differentiation of GCTB-SCs, as shown in Figures 2C and 2D. Together, we speculated that in GCTB of naïve status, there was a baseline activation of canonical Wnt signaling that regulates the proliferation of GCTB-SCs. Meanwhile, denosumab administration may cause Rac1associated activation of the canonical Wnt/β-catenin pathway by unknown factors.
Several stimuli can elicit Rac1 activation. For example, both Wnt-5a (a Wnt family member) and Ror2 (receptor tyrosine kinase-like orphan receptor2, a dominant receptor of Wnt-5a) activate Rac1 and induce differentiation of human mesenchymal stem cells into osteoblasts 38, 40 . Expression of the Wnt inhibitor secreted frizzled-related protein (sFRP) in GCTB-OCs has been con rmed by comprehensive mRNA pro ling of GCTB-SCs 41 . More importantly, we observed expression of Wnt-5a in GCTB-SCs (data not shown). Based on these ndings, we hypothesized that deletion of GCTB-OCs by denosumab might decrease the level of sFRP in tumor tissues, activate a cascade of Wnt-5a/Ror2/Rac1 signaling, and nally cause the osteoblastic differentiation of GCTB-SCs.
As another essential feature of this study, we found that endogenous nuclear β-catenin translocation was associated with osteoblastic differentiation of GCTB-SCs via denosumab treatment. Besides, upregulated NBLI was correlated with endogenous intra-tumoral bone formation in GCTB. Notably, a recent epigenetic analysis showed that GCTB-SCs could be classi ed into three groups, S1 to S3. S1 cells are characterized by the expression of osteoblast-associated genes such as osteopontin, whereas S3 cells have markers of the myo broblastic lineage, e.g., alpha-smooth muscle actin. S2 cells have features intermediate between those of S1 and S3 cells 42 . Therefore, we speculated that GCTB-SCs with nuclear β-catenin translocation would correspond to S1 cells and be partly committed to differentiation into osteoblasts. Therefore, as discussed in a previous paragraph, the deletion of GCTB-OCs by denosumab triggered the cells' nal osteoblastic differentiation. However, this notion should be further investigated.
This study had several limitations. First, the precise mechanism by which Rac1 activation occurs in GCT-SCs following denosumab treatment was not fully elucidated. More detailed in vitro experiments, including co-cultures of GCTB-SCs and GCTB-OCs, are needed to clarify this issue. Secondly, it is problematic to investigate the small number of cases that received denosumab in a retrospective analysis. To further validate the ability of the NBLI in GCTB-SCs to predict bone formation after denosumab treatment, we plan to conduct more extensive prospective studies in the future.

Conclusion
In summary, our ndings suggest a close relationship between the nuclear β-catenin translocation via Rac1 activation and the osteoblastic differentiation of GCTB. Investigations of NBLI in naïve GCTB samples will provide a promising biomarker for predicting the degree of bone formation after denosumab treatment.

Preparing cell brocks and immunocytochemistry of GCTSCs
To determine the purity of primary cultures, we prepared cell blocks and performed immunostaining with anti-H3G34W. Con uent suspensions of pGCTB-SCs were harvested, and cell pellets were prepared by centrifugation for 5 minutes at 1,500 rpm. The pellets were incubated overnight at 37°C in DMEM, and then xed for 3 hours at room temperature (RT) in 10% Formalin Neutral Buffer Solution (FUJIFILM Wako). After xation, the supernatant was aspirated, and 1% sodium alginate (FUJIFILM Wako) was added to the pellets. Gelatinous cell blocks were immediately obtained by addition of 100 μl of 1 M CaCl 2 (FUJIFILM Wako), and the blocks were embedded in para n.
Immunostaining was performed as described previously 43 . Brie y, antigen retrieval of depara nized sections was performed with 10 mM citric acid pH 6.0 (FUJIFILM Wako), and then the samples were incubated with anti-H3G34W monoclonal Abs (1:200) at 4°C overnight 44 . Specimens were then incubated with Dako EnVision Dual Link System-HRP (Agilent, Santa Clara, CA, USA), visualized using the diaminobenzidine substrate system (FUJIFILM Wako), and counterstained with hematoxylin 44 . Section images were obtained on a Keyence BZ-X800 microscope (Keyence Corporation, Osaka, Japan).
Alkaline phosphate staining ALP activity is widely used to assess the early osteogenic ability of osteoblast-like cells. We seeded pGCTB-SCs into a 24-well plate at a density of 5 × 10 4 cells per well. After 48 hours of incubation, the culture medium was exchanged and further incubated for the indicated periods. The cells were washed with PBS, xed in 10% formalin, and stained with premixed ALP substrate solutions (FUJIFILM Wako).
pGCTB-SCs were seeded into 96-well plates at a density of 5 × 10 3 cells per well and incubated for 48 hours. After the cells reached con uence, the medium was exchanged, and the samples were incubated further. ALP assays were performed using the TRACP & ALP assay kit (Takara Bio, Kusatsu, Shiga, Japan Nuclear protein extraction and Western blot analysis pGCTB-SCs were seeded in 6-well dishes at a density of 1.2 × 10 6 cells/well and incubated overnight. The following day, the culture media were replaced for each reagent, and the cells were incubated for an additional 12 hours. After incubation, the cells were washed twice with ice-cold PBS, scraped, and centrifuged. Cytoplasmic and nuclear proteins were isolated using nuclear and cytoplasmic extraction reagents (Thermo Fisher Scienti c) to which Cell Lytic M (Sigma-Aldrich) with protease inhibitor cocktail (cOMplete ™ Mini: Sigma-Aldrich) were added.

Ethics and Guidelines
Our all mothods were conducted in accordance with the Declaration of Helsinki, and written informed consent was obtained from all human subjects.

Patients and quantitative CT image analysis
To evaluate nuclear β-catenin translocation in naïve GCTB clinical samples, we performed a retrospective analysis using samples of GCTB registered in the les of the Department of Anatomic and Pathology, Graduate School of Medical Sciences, Kyushu University, Fukuoka, Japan 44 . A total of 91 clinical samples of GCTB from 88 patients were prepared for immunohistochemistry. These tumor specimens had been acquired from biopsy or surgeries, and the existence of the H3G34W mutation had been immunohistochemically con rmed. Samples collected after denosumab treatment were excluded from the study.
Immunohistochemical staining and assessment of the nuclear β-catenin labeling index (NBLI) were performed as previously described 47,48 . Histogram analysis was conducted to calculate the cut-off value for the NBLI. The presence of intra-tumoral ossi cation of GCTB was also assessed using H&E-stained sections.
Twenty-one patients were diagnosed with GCTB or received treatment for this cancer at our hospital between July 2011 and November 2020. Of those, 18 patients had received denosumab treatment (primary, n = 12; recurrent, n = 4; both, n = 2), and 16 had also undergone non-contrast CT or PET-CT evaluation before and after denosumab treatment. CT DICOM (Digital Imaging and Communications in Medicine) image datasets from identi ed patients were analyzed using SYNAPSE VINCENT ver6.1 (VINCENT, FUJIFILM Medical Co., Ltd.). A single musculoskeletal radiologist with eight years of experience manually delineated the regions of interest (ROI) in the axial CT images of whole slices, and three-dimensional CT images were semi-automatically acquired. Slice thickness was set at 2 or 5 mm. We identi ed the calci ed tissue volumes (≥ 130 Houns eld Units, HU) using VINCENT histogram analysis and quanti ed tumor calci cation using the previously described Agatston scoring system 36, 49 . In addition, we assessed the association between nuclear β-catenin translocation and intra-tumoral ossi cation of GCTB.

Statistical analysis
All experiments were repeated at least three times. Data are presented as means ± SD. Student's t-test or Wilcoxon's rank-sum test was used for two-group comparisons. Multiple comparisons were assessed using one-way ANOVA with the Tukey-Kramer post hoc test. Fisher's exact test was used to examine the signi cance of the association between the categorical data. All data analyses were performed using the JMP 13 statistical software (SAS Institute, Cary, NC, USA). P < 0.05 was considered statistically signi cant.

Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
Declarations a Each Agatston score of post-denosumab treatment was normalized against the pre-treatment score. Figure 1 GCTB stromal cells can differentiate into bone. (a) A radiograph of the affected bone lesion in a patient with GCTB (case #2 in Table 1)   Nuclear β-catenin translocation (nuclear β-catenin translocation) is essential but not su cient for bone differentiation of GCTB. (a,b) Induction of bone differentiation increased nuclear β-catenin translocation. pGCTB-SCs were treated with or without OGM for 12 hours, and β-catenin was analyzed in the nuclear and cytoplasmic fractions by western blotting. Lamin A/C was adopted as a loading control for nuclear extracts and actin for cytoplasmic extracts. Experiments were repeated three times, and representative images were shown. (c, d) LiCl, a canonical Wnt agonist, did not induce ALP expression in pGCTB-SCs. Tumor cells were cultured with 10 or 20 mM LiCl for 1 week, and then cytochemical staining was performed (c). Effects of LiCl on ALP expression of pGCTB-SCs were also evaluated by measuring OD405 (d).
(a) NSC23766 (NSC), a selective RAC1-GEF inhibitor, decreased ALP expression levels in GCTSCs in a concentration-dependent manner. pGCTB-SCs were differentiated in OGM with or without NSC for 6 days, and ALP staining was subsequently performed. (b) pGCTB-SCs were cultured with or without 10μM or 50μM NSC for 6 days, and ALP activity was determined by measuring OD405. Values represent means ± and RUNX2. Cells were cultured with or without 50 μM NSC for the indicated periods, and the mRNA levels were investigated by qRT-PCR. Values represent means ± SD (n = 4). ***P < 0.0001 (d) NSC decreased the OGM-induced nuclear β-catenin translocation. pGCTB-SCs were pre-treated with 20 μM or 60 μM NSC for 12 hours and further incubated with OGM for 12 hours. β-catenin was analyzed in the nuclear and cytoplasmic fractions by western blotting. Experiments were repeated three times, and representative images were shown.    Nuclear β-catenin positivity of GCTB-SCs is signi cantly associated with bone formation after denosumab treatment. To elucidate the relationship between β-catenin stainability and tumoral ossi cation, we performed quantitative evaluations using SYNAPSE VINCENT. (a-g) Representative images of three-dimensional analysis before denosumab treatment (case #2). ROI in the axial (a, b), coronal (c, d), and sagittal (e, f) CT images were delineated, and the 3D tumor model was automatically depicted (g). (h) Histogram image of the ROI before denosumab treatment. Tissue volumes with more than 130 HU were identi ed as signi cant calci cations, and Agatston scoring was performed as previously described [27,28]. (i-n) Representative three-dimensional image after the treatment. ROI in the axial (i, j), coronal (k, l), and sagittal (m, n) CT images were used for 3D model analysis (o). Bright yellow lines represent the peripheral rim of the ROI. (p) Histogram image of the ROI after denosumab treatment.
In the ossi ed case, the histogram image was leptokurtic, and the degree of skew was signi cant. (q-s) The relationship between nuclear β-catenin stainability and intra-tumoral ossi cation was evaluated using Agatston score (n = 13). The stainability was signi cantly associated with the score in the entire (q), peripheral (r), and intra-tumoral areas (s) (**P = 0.003 for entire and peripheral tumor, and *P = 0.02 for intra-tumor of GCTB). Each post-treatment Agatston score was normalized against the corresponding pre-denosumab score.

Supplementary Files
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