Recently, the diagnostic accuracy of bile duct carcinoma (BDC) and its extension has been improved by multi-disciplinary modalities such as multi-detector computed tomography (CT), high-resolution magnetic resonance imaging (MRI), endoscopic or intraductal ultrasonography or cholangioscopy, and fine needle aspiration or biopsy (1). Thus, the diagnostic accuracy of the estimated transection stump of the non-cancerous bile duct lumen is also improving (2,3). CT and MRI are mainly used to define changes in BDC extension as an early diagnostic step or during follow-up (4). Pancreatic ductal adenocarcinoma (PDAC) of the pancreatic head often involves the bile duct and sometimes causes biliary stenosis or obstruction resembling biliary diseases (5). Recently, diagnosis of small irregularities was made possible using the latest high-quality workstation or artificial intelligence (AI) technology, which showed that real imaging of the bile duct lumen (6) should be developed along with a mathematical algorithm.

Recently, we focused on the differential diagnosis of biliary malignancy in patients with pancreatobiliary maljunction (PBMJ) (congenital anomalous arrangement of the pancreatobiliary ductal system) because a preventable surgical strategy for malignant alterations of the bile duct has been recommended in cases of ductal irregularity and increased bile duct size (7). As a promising novel modality, novel imaging algorithms based on MR cholangiography (MRC) images of patients with PBMJ, in which Fourier transform-based indices (FTI) are considered to be a power spectral density integrated value, might be a useful for differential diagnosis between non-dilated BD with low malignant potential and dilated BD or cancer lesions. The FT has been applied to the quality management of surface profiles of industrial products by measuring frequency wavelength modulation and the FTI or phase value distributions entropy (PVDE), which are able to define the irregularity of a tube-like cylindrical luminal surface. In the field of medicine, an FT-based mathematical algorithm has been used for the diagnostic evaluation of MRC images by generating intraluminal surface profiles of aortic aneurysmal irregularity (8,9), which can be applied to the extrahepatic bile duct to detect subtle irregularities and consequently biliary diseases (7,10). To evaluate the smoothness of the morphological changes in the intraductal lumen, FT also decreases non-specific alterations of disorders, and some indices such as FTPSDI or PVDE can be calculated by the frequency alteration accompanied by the measured phase. In the extrahepatic bile duct, alterations in the intraductal diameter or area between the distal and proximal parts can be indicated as a diagram; therefore, targeted parts, such as cancerous or non-cancerous lesions, can be measured. If the irregularity of the intraluminal surface is large, the wave frequency amplitude and the measured indices are expected to sharply increase as well. Another mathematical algorithm system, MRCP+ by Perspectum, produced 3D images for biliary ducts visualization using an AI system and our case series was reported previously (11-13). Thus, by using computer workstation-based detection, we hypothesized that subtle irregularity, such as inflammation or carcinogenesis, could be detected earlier or more sensitively than human eye.

We hypothesized that this is a less invasive, safer, and cost-effective modality to solve our recent problems with respect to the diagnostic accuracy of BDC and its cancer extension compared with other pancreatic head diseases. Using our novel idea, we measured FT-based indices of the intraluminal circle diameter and the area of the entire extrahepatic BD in patients with PBMJ who were carefully followed, performed a comparative analysis of the bile duct showing normal or other biliary conditions, and hypothesized that these indices could reveal subtle objective abnormalities of the bile duct lumen. We conducted a retrospective cohort study measuring FT-based mathematical parameters using automatic MRI analytical systems in 79 consecutive malignant pancreatobiliary disease patients at our institute. The goal of our study was to provide a novel method for screening diagnosis using less invasive MRC in BDCs, with clinical applications in the new era.

Patients. We analyzed data from a prospectively maintained database of 79 consecutive patients who underwent surgical resection for pancreatobiliary malignant diseases at Miyazaki University Hospital between January 2015 and October 2020. Patients were excluded if the tumor diagnosis and its extension were histologically unclear or low quality MRCP images were not provided. Data regarding patient demographics, clinicopathological characteristics, operative details, and preoperative MRC images were collected. The study protocols followed the ethical principles of the Declaration of Helsinki 2008 and were approved by the Human Ethics Review Board of the University of Miyazaki, Faculty of Medicine (# O-0813, December 10, 2021). Informed consent for data collection was obtained by opt-out procedures at the website for one month after permission, but no disclaimer was observed. Clinicopathological features and tumor staging were defined according to the General Rules for Clinical and Pathological Studies on Cancer of the Biliary Tract, 7^th edition, by the Japanese Society of Hepato-Biliary-Pancreatic Surgery, 2021 (14).

Measurement of MR cholangiography. MRI was performed when the patients were in stable condition. MRI studies were performed in the supine position under basal fasting conditions (7). MRCP was performed before the diagnosis or follow-up of PBM with two MRI scanners. A Verio 3.0 T scanner (Siemens, Erlangen, Germany) with an abdominal phased array coil was used as follows: 3D fast spin echo with fat suppression (field of view 350 mm, repetition time (TR) 2,000-5,000 milliseconds (ms), echo time (TE) 691 ms, refocus angle 120, acquisition matrix 240×240, recording matrix 320×320, receiver bandwidth 320 Hz/Px, recording slice thickness 1.1 mm). An Ingenia CX 3.0 T scanner (Philips, Eindhoven, the Netherlands) with an abdominal phased array coil was used as follows: 3D fast spin echo with fat suppression (field of view 320 mm, repetition time (TR) 2,000-5,000 ms, echo time (TE) 600 ms, refocus angle 120, acquisition matrix 320×256, recording matrix 512×512, receiver bandwidth 296 Hz/Px, recording slice thickness 0.9 mm). Oblique coronal sections were acquired in the planes of the common bile and pancreatic ducts using respiratory motion-suppression techniques. Expert radiologists who were blinded of the pathological findings independently reviewed the images and reached a consensus through discussion. A diagnosis of BDC by MRC was established when the BD wall was thickened and the intraductal diameter was shortened with surface irregularity detected by an expert radiologist.

Using a workstation equipped with Synapse Vincent Version 5.2 (Fuji Film, Tokyo, Japan) for all images (7), the central line of the intrabiliary lumen of the entire extrahepatic BD was automatically traced, and the entire intrabiliary lumen was extracted by supervised detection and shape matching. Then, straight view curved planar reconstruction (CPR) was obtained as a two-dimensional (2D) diagram using the workstation (Figure 1A). The 2D diagram of the cross-sectional transverse diameter (mm) or area (mm²) of the intra-bile duct lumen (vertical axis) was measured at the 0.5 mm longitudinal interval of longitudinal extrahepatic BD between the distal (the left side of diagram) and proximal (right side) sides of the extrahepatic BD (horizontal axis) (Figure 1B). These measurements of intraluminal diameter and area of extrahepatic BD were scanned by the computer automatically, and the amplitude of the diagram was also measured. The left and right hepatic ducts and the common channel of the pancreatobiliary junction were excluded from measurement. The representative measurement images for BDC with various cancer stenosis are shown in Figure 2A-C. The FT based on the power spectral density function (mm²/Hz or mm4/Hz) for diameter (mm) or area (mm²) was determined (Figure 3A-D). Then, the integrated (fluctuation) value (FTV) (mm² or mm⁴) (7) was calculated using an analytical software (R^® version 4.0.2). Finally, detrending FTV was mathematically evaluated to compare the groups of biliary diseases. Increased FTV on MRC was supposed to indicate intraductal irregularity of the intra-bile duct lumen.

Defection of subject group. The examined subjects of BDC, among 31 patients, were divided into three subgroups as follows: 1) cancer infiltration was observed at the estimated cut line of the proximal bile duct stump by intraoperative histology (PBDC positive group, n=5); 2) cancer infiltration was suspected by the preoperative diagnostic examination, but not observed at the estimated cut line of the proximal bile duct stump by intraoperative histology (PBDC suspicious but negative group, n=8); and 3) cancer infiltration was not suspected preoperatively and no cancer infiltration (PBDC negative group, n=18). The two control groups were selected as follows: 1) pancreatic neoplasm without BD stenosis (n=18) and 2) pancreatic cancer accompanied with BD stenosis (n=10).

Statistical analyses. Continuous variables were expressed as mean±standard deviation (SD) and were statistically compared between the two groups using Wilcoxon’s t-test. Categorical variables were compared using Fisher’s exact test depending on the number of observations. The sensitivity and specificity for each test value were calculated to assess the accuracy of differentiating between high and low degrees to diagnose BDC compared to PC, and receiver–operator curves (ROCs) were constructed with sensitivity against 1-specificity at each value. The index of accuracy for the existence of carcinoma was calculated by the area under the ROC (AUROC), in which a value close to 1.0 indicated high diagnostic accuracy. The probability of diagnostic accuracy was examined using Wilcoxon’s test or Scheffé’s multiple comparison test. A two-tailed p-value less than 0.05 was considered significant. All statistical analyses were performed using statistical software (SPSS software version 23; Statistical Package for the Social Science, Inc., Chicago, IL, USA).

Patient characteristics. In the present consecutive series, 20 of 79 patients (25%) failed to undergo FTV due to difficult in scanning because of poor MRC imaging quality and conditions, which were all pancreatic cancers (the control diseases) with (n=11) or without (n=9) intra-pancreatic BD stenosis. Eventually, 59 participants were included in this study.

The mean age of the 59 patients was 73.1±5.2 years (range=65-84 years), including extrahepatic BDC in 31 patients and cancer-positive hepatic duct margin in five of 31 patients (16%). The 28 non-BDC patients included 10 patients with pancreatic cancer with BD stenosis and 18 patients with pancreatic malignancies without stenosis (pancreatic cancer without BD stenosis in eight, intraductal papillary mucinous carcinoma in four, neuroendocrine neoplasm in four, and others in two). Patient demographics showed that 37 patients were male and 22 were female. Twenty-nine BDC patients underwent pancreaticoduodenectomy (PD) and two underwent bile duct resection alone, and all non-BDC patients underwent PD. BDC was localized at the distal BD alone in 20 patients and at both the proximal and distal BD in nine patients. All BD stenosis in non-BDC diseases were localized at the distal BD.

In 31 BDC patients, the macroscopic type of tumor was of the nodular type in 11, flat type in 13, and papillary type in seven patients. The proximal duct margin was cancer positive by the intraoperative histological examination in five patients (16%), in whom the cut-end lesion of BD was not estimated by preoperative multimodal examination as endoscopic or radiological findings. Proximally superficial cancer extension >20mm from the main cancer edge was observed in four patients (13%). The mean tumor size was 31.8±18.39 mm (range=10-70 mm), and the tumor (T) factor was T1 in 10, T2 in eight, and T3 in 13 patients. Macroscopic wall thickness in accompanying cholangitis at the non-cancerous proximal BD was observed in eight patients (26%).

Basic data of the detrending FTV. In the included 59 patients, the median and mean FTV values for diameter of the entire BD were 323 and 671±934 mm² Hz^–1 (range=29-4,291), and those of the area of the BD were 28618 and 165,892±368,357 mm⁴ Hz^–1 (range=74^–1, 709,064), respectively. The median and mean FTV for the diameter of the proximal (hepatic side) BD were 127 and 320±425 mm² Hz^–1 (range=15.8-2,069), respectively, and those for the area determined in 53 of 59 patients (90%) were 9,580 and 83,488±168,159 (range=76-777,940) mm⁴ Hz^–1, respectively. The median and mean FTV for the diameter of the stenotic BD determined in 22 of 59 patients (37%) were 11 and 53±110 mm² Hz^–1 (range=0.12-384 mm² Hz^–1), respectively, and those for the area were 297 and 9,595±28,677 mm4 Hz^–1 (range=0.06-115,598 mm⁴ Hz^–1), respectively. The median and mean FTV for the diameter of the distal BD (duodenal side) determined in 23 of 59 patients (39%) were 28 and 45±44 mm² Hz^–1 (range=0.3-194 mm² Hz^–1), respectively, and those for the area were 1,886 and 4,111±6,916 (range=15-29,237) mm⁴ Hz^–1, respectively.

The FTV diameter and area were significantly correlated (r=0.921, p<0.01). In 31 BDC patients, the FTV for the diameter of the proximal non-tumorous BD was significantly higher than that of the stenotic BD involving the tumor and the distal BD, respectively (Table I) (p<0.01). Furthermore, the TPSDI for the area of the proximal non-tumorous BD was significantly larger than that of the stenotic BD involving the tumor and the distal BD, respectively (Table II) (p<0.01).

Comparison of the detrending FT parameter between subgroups in pancreatobiliary diseases. By comparing each group of pancreatobiliary diseases (Table I and Table II), the FTV diameter and area of the entire BD in all BDCs were significantly higher than those of pancreatic neoplasms without BD stenosis (p<0.01). The FTV area of the proximal non-tumorous BD in all BDCs was significantly higher than that of pancreatic neoplasms without BD stenosis (p<0.01), although the diameter of proximal non-tumorous BD was not significantly different. Table I and Table II show the regional FTV diameter and area in each subgroup. The FTPSDI diameter and area of all BDCs were significantly larger than those of pancreatic neoplasms without BD stenosis, respectively (p<0.05). The FTV area of proximal non-tumorous BD was significantly larger than that of pancreatic neoplasms without BD stenosis (Table II) (p<0.05), but the difference was not statistically significant (p=0.085). By comparing each subgroup of BDC, the FTV diameter of the entire BD in the PBD cancer-positive group was significantly smaller than that in the PBD cancer-negative group (p<0.05), and the FTV area of the entire BD in the PBD cancer-positive group was significantly smaller than that in both the PBDC suspicious but negative and PBD cancer-negative groups (p<0.05). The FTV diameter and area of the proximal or distal non-tumorous BDs were not significantly different between the subgroups. The FTV diameter in the PBD cancer-positive group was significantly smaller than that in the BDC negative group (p<0.05), and the FTV area in the PBD cancer-positive group was significantly smaller than that in both the PBDC suspicious but negative and PBD cancer-negative groups (p<0.05).

Comparison of the detrending FT parameter between subgroups in pancreatobiliary diseases. Table III shows that the FTV diameters of the entire BD, proximal non-tumorous BD, or tumor involving stenosis were not significantly different between pancreatobiliary diseases with and without BD stenosis and were not associated with any clinicopathological features of BDC. Table IV shows that the FTV areas of the entire BD and proximal non-tumorous BD of pancreatobiliary diseases with BD stenosis were significantly larger than those without (p<0.05). In the BDC, the stenotic lesion of the distal BDC showed a significantly larger FTV area than the proximal BDC (p<0.05); otherwise, the FTV area was not significantly associated with the clinicopathological features of BDC.

Diagnosis of bile duct carcinoma by FT compared to pancreatic carcinoma. The FTVs diameter was compared to define the presence of BDC in comparison to PC, and the AUROC analysis is shown in Table V and Table VI. The presence of BDC was significantly discriminated by the FTV diameter of the BD (p<0.05), and the sensitivity or specificity at the cutoff value of the FTV diameter for BDC diagnosis was >286 mm² Hz^–1. The presence of BDC was significantly discriminated by the cutoff value of the FTV area of the BD (p<0.05) and the sensitivity or specificity at the cutoff value of the FTV diameter for BDC diagnosis was >10,311 mm⁴ Hz^–1. The probabilities, sensitivities, and specificities of the FTV diameter and area were similar. A comparison between BDC and pancreatic cancer with BD stenosis (Table VI and Figure 4B) showed that there were no significant differences between the groups, although the sensitivity of the FTV diameter and area was >80%.

As described above and in our pilot study report for PBMJ (7), MRI accompanied with the latest workstation analysis has been recently advanced for use as a diagnostic tool and a quantification of physiological functions or tissue components; the advantage of MRI is that it is less invasive for determining disease diagnosis than radiation exposure of computed tomography or relatively invasive examination of endoscopic retrograde cholangiography (ERC) (1,4,6,15,16). Therefore, MRI and its pancreatico-cholangiography are adequate as an early diagnostic tool or for disease follow-up in patients with chronic biliary or precancerous diseases (15,16). From the biliary surgeon’s perspective, preventable surgical intervention must be avoided until the histological diagnosis of the biopsy specimen can be obtained even though biliary stenosis or obstruction occurred (4,17,18). The bile duct lumen or wall irregularity and its alterations are considered premalignant or early malignant signs during chronic exposure to biliary inflammation. When such signs are diagnosed using a less invasive tool, further endoscopic investigation or surgical intervention can be performed for suspicious lesions. A novel diagnostic tool, fluoroscopy-visualized cancer spreading area, has been recently attempted (19) but is not yet conventional. Furthermore, in the case of BDC, cancer infiltration by horizontal spreading toward the BD cut stump is an important finding to achieve curability and longer patient survival or quality of life (20). By applying various diagnostic modalities, the diagnostic accuracy of cancer extension cannot be completely achieved in BDC patients, particularly in those with severe stenosis or occlusion at this stage (4,17,18). In the present situation, we assumed that the latest diagnostic method using a mathematical algorithm and computed automatic calculation or AI-based evaluation, as the index suggested in this study, is an alternative diagnostic tool to define subtle abnormalities against diagnosis by the radiological physicians.

The FT algorithm was applied to characterize the textural features of fabric surfaces crinkled by industrial products (21). Intraluminal structure and its irregularity were evaluated by this algorithm for coronary arteries using multi-detector CT by Lesage et al. (22,23). Kitamura et al. first reported automatic coronary extraction by supervised detection and shape matching (24). However, this has not been fully applied to MRI images, particularly in biliary diseases. The 2D power spectrum was derived from the algorithm of a digitized fabric image captured by a scanner. Based on the novel idea of the coauthor (M. K), fluctuation can reflect the sharpness of fabric surfaces, and the FTPSDI can be used as an applied index to reveal intraluminal irregularity and, thus, we have reported a pilot study focusing on patients with pancreatobiliary maljunction (7). Goldfinger et al. and our group also reported the use of colored visualization to evaluate intra- or extrahepatic bile duct stenosis using the latest computerized analysis, applying the AI workstation as MRCP+ (11-13). By observing their 2D diagram, the present measurement method of the FTPSDI might flashed to find irregular alterations of smooth duct organs, and the normal BD showed a low FTV value. Adenocarcinoma usually grows irregularly in the lumen compared to inflammation. The present method can theoretically detect a 0.5 mm-interval of alteration in the bile duct lumen, in which the diagnostic sensitivity might be equal or superior to that of human observations in some situations. By comparing conventional MRI and CT imaging, image resolution diagnosing BDC by enhanced CT would be superior to that of the latest 3T-MRI at our institute. The smoothness of the luminal surface is an important parameter to define superficial extension of the biliary malignancies during endoscopic examination. As the duct lumen is usually filled with bile juice, MRI is a useful tool for fluid imaging under heavy T2-weight MRI and therefore, MRC may be more sensitive than CT intraductal imaging. As this evidence has not been indicated in biliary diseases, a similar study using enhanced dual energy CT or the drip infusion CT (25) is necessary to clarify this superiority. However, these CT examinations seem to be more invasive than MRC owing to the adverse effects of X-ray exposure or anaphylaxis caused by contrast agent.

The present results showed a decreased FTV diameter or area of the entire BD scanning in the two control groups of pancreatic head malignancies. Pancreatic cancer involving BD was supposed to show an increased value, indicating BD stenosis, however, both parameters showed decreased values including those of pancreatic neoplasm without BD stenosis. Both parameters showed a significantly increased value by the present Wilcoxon test, although the data deviation was large, and in fact, the stricter multiple comparison test only showed a significant difference in FTV diameter between BDC and pancreatic neoplasm without BD stenosis due to the limited number of subjects. The reason for an intermediate increase and a large standard deviation of the FTV parameters was hypothesized to be due to the accompanying morphological alterations or abnormalities and inflammatory pathogenesis in non-cancerous BD. The FTV diameter or area of the entire BDC was not significantly different between each subgroup of BDC, possibly because this value might influence the morphological difference in BDC, stenotic degree, or accompanying inflammation (26). As the final step of analysis for differential diagnosis, stratification using both values of FTV diameter or area between BDC and PC with biliary stenosis could be significantly indicated with approximately 70% or more sensitivity and specificity. In case the differential diagnosis between BDC and PC in the intra-pancreatic tumor lesion with BD stenosis is difficult, such a mathematical parameter would be an auxiliary diagnostically useful metric. Clinically, there is a differential diagnosis of intra-pancreatic BD stenotic malignancies between BDC and pancreatic cancer involvement. An examination of the FT analysis at each region of non-cancerous BD and cancerous stenotic BD was performed. Compared to proximal BD, the FTV parameters at distal BD were too low, in which the remnant distal BD had difficulty obtaining the clarity of BD due to its short length and complexed density of MRI T2 intensities by crossing over of the BD and pancreatic duct or plenty of peripheral pancreatic ducts. Therefore, based on our results, this area was not adequate to evaluate irregularity in comparison with the proximal BD.

Another interesting aspect to clarify differentiation by these parameters was the possibility of defining cancer infiltration at the estimated cut-line of the proximal BD based on our recent diagnostic information. In cases where biliary stenosis was severely or completely obstructed by the circular involvement of BD, the diagnostic accuracy was still not high (27). Therefore, we attempted to examine the FT analysis at the several parts of the BD by dividing them into subgroups of proximal BD cancer positive, proximal BD cancer infiltration suspicious but negative, and proximal BD negative because the preoperative multimodal diagnosis was still difficult to differentiate in the former two subgroups between the preoperative estimation and the intraoperative histological findings. Furthermore, the intraoperative results of histological diagnosis for cancer positive margin at the cut end of BD often do not agree with the final histological findings (28). We assume that the subtle epithelial irregularity can be detected by a mathematical algorithm instead of the radiologist or human subjective identification in future medical evolution by the development of automatic digital transformation (29). Our preliminary results, however, did not clarify any novel information to differentiate the histological characteristics of BDC, including cancer positivity at the proximal BD stump, which is one of main focus of this series, although the FTV area between proximal and distal BD tended to differ but with a large standard deviation. The analytical concept or scanning situation should be reconsidered to define the surface or ductal structural irregularity of BD using diagnostic imaging materials such as CT, MR, and ultrasonography.

The biliary tract in primary sclerosing cholangitis (PSC) also has malignant potential, and we showed a case of PSC or benign stricture of the intrahepatic duct using another MR imaging AI analysis such as MRCP+, as in other recent reports (7,11-13). A case of PSC showed a FTV equivalent to a mild increase in chronic BD inflammation with pancreatobiliary maljunction. We assumed the patient would have a lower malignant state, and follow-up by MRC was possible. Therefore, disease accuracy is progressing owing to the rapid development of novel diagnostic technologies worldwide (30).

The limitation of this study is that it is a retrospective cohort with a limited number of subjects from a single institute, which may have induced statistical type II error and bias of evaluation. After the usefulness of the procedure is well evaluated, a multi-institutional study is necessary. FT analysis could not be performed in approximately 25% of all examined subjects, although the MR apparatus and workstation had almost equivalent product capabilities, which might be due to image quality, patient physical, or breath-holding conditions, etc. Therefore, the multi-institutional variety of analytical and MR modalities is a concern for future trials. For the present analytical FT parameters as FTV data tended to be larger in our recent analysis, which showed a large deviation in the present results. Mathematical modifications indicating a clinically available scale would be required but we could not find it yet.

A novel diagnostic algorithm for intraluminal evaluation of extrahepatic BD using FT analysis for MRC imaging indicated FTV-diameter or area could be applied to examine pancreatobiliary malignancies with or without BD stenosis, and to examine the relationship with clinicopathological features, particularly the existence of a cancer-positive margin at the proximal BD stump in BDC patients. The calculated FTV parameters of the entire BD in BDC were significantly larger than those of PC or other neoplasms, with or without BD stenosis, in which differential diagnostic accuracy was significant, but with a large standard deviation. FT parameters were not significantly different between cancerous and non-cancerous BD and were not related to any clinicopathological characteristics, even though there was a cancer-positive margin. Although some limitation still remains, this novel algorithm parameter would be promising to define the differential diagnosis or irregularity of BD in patients with pancreatobiliary malignancy. Furthermore, this can be widely applied in biliary diseases using advanced imaging technology.

The Authors declare no competing interests in relation to this study.

A.N and M.A.: design of the study and final approval. M.K., M.E. analyzed FT by workstation together with Dr. S.O. A.N. examined literature review, writing of the original draft, figure preparation, and revision; N.I., H.M., T.H., Y.T. and N.I. performed data collection and analysis.

This study was performed by Dr. Syogo Ogata M.D., who regrettably passed away during the investigation in February 2022. We never forget his foot marks of the works with us, and this was sincerely dedicated to his great efforts to collect important patient data. The present article remains in the memory of Dr. Ogata. The present article was edited by the Elsevier English Editing Service, which supported our work. English language was carefully edited by Elsevier, product number 240525.