CT habitat radiomics and topological data analysis based on interpretable machine learning for prediction of pancreatic ductal adenocarcinoma pathological grading

Abstract

Background

This study explores the feasibility and effectiveness of an interpretable machine learning model for assessing the pathological grading of pancreatic ductal adenocarcinoma (PDAC) using radiomics and topological features derived from contrast-enhanced CT habitat subregions.

Methods

A retrospective study was conducted on a total of 306 patients with PDAC from two hospitals: a training cohort (n = 176), a validation cohort (n = 76), and a test cohort (n = 54). K-means clustering analysis was first used to segment portal venous phase CT images into three habitat regions. Radiomics features of the whole-tumour region, along with radiomics and topological features of each habitat region, were extracted respectively. LASSO regression was applied for feature dimensionality reduction to construct the radiomics score (Rad-score) for the whole-tumour region and the habitat score (H-score) for each habitat region. Meanwhile, logistic regression was used to identify statistically significant predictors from clinical and semantic features. Five machine learning algorithms were used to construct Habitat-TDA models, with interpretability analysis performed via SHAP analysis.

Results

Total volume, diabetes, and M staging were identified as independent risk factors for predicting the pathological grading of PDAC, and were used to construct the Clinical model. 6 radiomics features with non-zero coefficients were selected to calculate the Rad-score, which was further used to construct the WholeRad model. In the three habitat regions, 6, 5, and 6 topological and radiomics features were included to generate the H-score. The logistic regression algorithm performed best in the validation and test cohorts and was ultimately selected as the classifier for constructing the Habitat-TDA model. SHAP analysis showed that H-score1, derived from Habitat Region 1 (the habitat region with the lowest average CT value), has the most significant average impact on the model output intensity. The AUC values of the Habitat-TDA model in the training, validation, and test cohorts were 0.894, 0.872, and 0.829, all outperforming the clinical model (0.784, 0.765, 0.731) and WholeRad model (0.817, 0.810, 0.773).

Conclusions

The Habitat-TDA model improves the accuracy and interpretability of preoperative predictions of PDAC grading, providing a promising tool for personalised management.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12880-025-02094-1.

Introduction

Pancreatic ductal adenocarcinoma (PDAC) accounts for approximately 90% of primary pancreatic cancers. The 5-year relative survival rate among PDAC patients diagnosed between 2014 and 2020 is only 8%; despite numerous clinical trials conducted and multiple new drugs approved for PDAC since 2000, its median survival time remains less than 1 year, and it is currently the third leading cause of cancer-related deaths in the United States [1]. Histopathological grading is a key independent prognostic factor for determining PDAC treatment strategies and evaluating survival rates [2]: poorly differentiated PDAC is highly aggressive, with a high risk of early postoperative recurrence (< 6 months) and a 5-year survival rate of < 5%; well-differentiated PDAC has delayed recurrence and a 5-year survival rate of 20%-30%, requiring distinct postoperative surveillance [3, 4]. Thus, accurate assessment of PDAC’s histological grade is critical. Despite ongoing advances in imaging technologies, diagnosing PDAC requires confirmation via biopsy. While ultrasound or Computed Tomography (CT) -guided fine-needle aspiration can assist in grading, it has limitations, including insufficient tissue and sampling bias. Additionally, due to the tumour’s location, invasive biopsy is associated with difficulties in sample acquisition and a high risk of complications.

While contrast-enhanced CT (CECT) constitutes the fundamental imaging modality for PDAC management, its conventional morphologic analysis lacks the discriminative capacity for pathologic grading. Radiomics methodologies enable high-throughput extraction of quantitative image features, demonstrating preliminary potential for characterising pathologic attributes and tumour grades [5–8]. Conventional radiomic approaches frequently overlook intratumoral heterogeneity and spatial interdependencies by analysing tumours as homogeneous entities [9]. PDAC exhibits marked histology-linked heterogeneity, with regional variations in cellular density, stromal composition, and metabolic activity in its microenvironment [10–12]. Crucially, distinct subregions show differential treatment responses and progression dynamics [11–13], underscoring the importance of quantifying such heterogeneity.

Habitat analysis represents an advanced imaging paradigm that delineates intratumoral heterogeneity through high-resolution image segmentation, enabling non-invasive assessment of tumour biology and facilitating personalised therapeutic strategies [14–18]. Complementarily, topological data analysis (TDA) offers novel mathematical frameworks to quantify global image architecture, including persistent homology features capturing connected networks, voids, and higher-dimensional structures [19]. With unique strengths in capturing complex spatial associations and multi-scale patterns, TDA can precisely identify spatial transformation differences among habitat-derived subregions. Notably, it is particularly effective in extracting meaningful patterns from limited datasets [20–22].

This study aims to identify habitat subregions with similar characteristics in CT images, and further explore the feasibility and effectiveness of radiomic features and topological features extracted from each habitat subregion in predicting the histological grade of PDAC. By comparing and screening multiple machine learning classifiers, this study intends to develop an interpretable machine learning model, which is expected to exhibit higher accuracy in predicting histological grade than whole-tumour radiomics models and traditional imaging models.

Materials and methods

This study conducted a self-assessment using the Radiomics Quality Score (RQS) 2.0 criteria [23], the Methodological Radiomics Score (METRICS) checklist [24], and the CheckList for EvaluAtion of Radiomics research (CLEAR) [25].

Patient selection

The retrospective study received approval from the Institutional Review Board and Human Ethics Committee of two hospitals. The need for patient-written informed consent was waived. CECT images of PDAC patients in Hospital 1 from July 2017 to May 2025 and Hospital 2 from January 2021 to April 2025 were retrospectively collected. The inclusion criteria were as follows: (a) pathologically verified PDAC; (b) CECT performed ≤ 1 week before pathologic diagnosis. The exclusion criteria were as follows: (a) prior oncologic therapy (radiotherapy, chemotherapy, immunotherapy, or intervention); (b) suboptimal CT image quality; (c) biopsy-diagnosed low-grade PDAC (to mitigate sampling bias). A total of 252 patients from Hospital 1 were randomly divided into a training cohort (n = 176) and a validation cohort (n = 76) at a 7:3 ratio, while 54 patients from Hospital 2 formed an external test cohort. To minimise the impact of sampling error on model evaluation, we subsequently employed stratified 10-fold cross-validation to ensure balanced representation of each class during model training.

Histological grade

PDAC differentiation was classified into well, moderately, poorly differentiated, or undifferentiated, according to the 2019 World Health Organisation classification criteria for digestive system tumours [26]. Given the small sample sizes of some PDAC differentiation subtypes, this study classified all samples into two predictive labels (low-grade, high-grade). This classification is consistent with previous studies [27] and aligned with the clinical practice of merging subtypes based on risk characteristics to meet the needs of risk stratification and prognostic assessment [28]. Well and moderately differentiated tumours were defined as low-grade PDAC. Undifferentiated and poorly differentiated tumours were defined as high-grade PDAC.

CT image acquisition

All patients underwent a standard multi-phase CECT examination using 256-slice Multi-Detector CT (Somatom Drive, Siemens Healthcare, Germany; Brilliance iCT, Philips Healthcare, Netherlands). To homogenise image quality, the CT scanning was set as standardised parameters: 120 kV; automatic milliampere-second; 0.8 pitch; collimation, 128 × 0.625 mm; matrix, 512 × 512; gantry rotation time, 0.5s; thickness, 5 mm (reconstructed thickness, 1 mm). Patients were supine, with craniocaudal scans from the hepatic dome to the bilateral anterior superior iliac spines. Protocol included an unenhanced scan, followed by nonionic contrast (iodophorol 320) injected at 1.5 mL/kg and 3.0 mL/s, then 30 mL saline at the same rate. The arterial phase started 25–30 s after the descending aorta reached a 100 Hounsfield Unit (HU) trigger; the portal venous phase (PVP) and delayed phase were at 60–80 s and 150–200 s.

Clinical and CT semantic features evaluation

Baseline clinical variables were extracted from the electronic medical records system, including age, sex, smoking, drinking, hypertension, diabetes mellitus, History of pancreatitis, jaundice, serum Carbohydrate Antigen 199 (CA199) and Carcinoembryonic Antigen (CEA) level at baseline, and TNM stage of PDAC.

Two radiology residents, with 3 years of experience, independently reviewed all images, who were aware of the diagnosis of PDAC but blinded to the pathological grade. The CT semantic features per established criteria, as per the pancreatic ductal adenocarcinoma radiology reporting template [29]: (1) position (head, neck, body, tail); (2) tumour volume; (3) necrosis (plain scan showed irregular low density area, CT value ≤ 20HU; the CT difference of each phase was less than 10 HU); (4) cholangiectasis (intrahepatic bile duct dilatation ≥ 2 mm, common bile duct dilatation ≥ 8 mm); (5) dilated pancreatic duct (≥ 3 mm); (6) pancreatic atrophy; (7) infiltration range (grade1: the tumour was confined to the pancreas; grade2: the tumour range exceeded the pancreatic gland, invaded the surrounding fat space; grade3: tumour infiltrating the peripancreatic organs); (8) artery invasion; (9) venous invasion. Discrepancies were resolved by a senior radiologist with 18 years of experience.

Tumour habitat segmentation

The image processing flow of this study is shown in Fig. 1. We chose the PVP to carry out subsequent image analysis, for its stable image quality and the advantages in reflecting PDAC pathological features [30–32].PVP images were preprocessed by N4 bias field correction using Python (version 3.13, https://www.python.org) software. Two radiologists manually segmented the tumour’s 3D volume of interest (VOI) using a 3D-slicer (version 5.0.3 https://www.slicer.org) software. The Dice’s Coefficient (DICE) is used to assess the consistency of VOI segmentation. The intraclass correlation coefficient (ICC) is mainly used to assess the inter-observer measurement consistency, specifically for the features extracted from the VOIs independently delineated by two observers. These features include radiomics features in the whole tumour region, as well as radiomics features and topological features in the three habitat subregions, further extracted based on the VOIs, to verify the consistency of different observers in terms of feature quantification.

Fig. 1.

Overall workflow of this study

PVP images and their corresponding masks were first subjected to spatial registration and resampling to ensure spatial consistency. This involved rigid registration based on anatomical landmarks to achieve precise spatial alignment between PVP images and masks. All data were then resampled to a uniform voxel size of 1 × 1 × 1 mm³, and this step standardised spatial resolution to minimise bias in subsequent voxel feature extraction. Voxel features within the masked regions were extracted to construct a feature matrix, which was further purified via outlier processing. To determine the optimal number of clusters, tumour voxels from all patients in the training cohort were pooled, and the Calinski-Harabasz (CH) score was calculated across a cluster range of 2–9; a higher CH score indicates better intra-cluster cohesion and inter-cluster separation [33]. After confirming the optimal cluster number, voxel-wise K-Means clustering was performed independently for each patient’s tumour voxel. After random initialisation of cluster centres, each voxel was assigned to the nearest cluster using Euclidean distance, and cluster centres were iteratively updated to the mean of the cluster voxels’ features until stable cluster centres were achieved, ultimately generating masks for each habitat. Finally, the mean CT value of each habitat region was calculated.

Radiomics features extraction

Radiomics features were extracted from the entire tumour and each habitat subregion using the PyRadiomics library (version 3.1.0), following the Imaging Biomarker Standardisation Initiative (IBSI) guidelines. The feature extraction parameters were adjusted: resampledPixelSpacing: [1], binWidth: 25, LoG: sigma: [1–3]. The remaining parameters were set to the default values. On PVP images, wavelet and LoG filters with different sigma values were used to extract high-order statistical features. Specific feature details are available in Table S1 of Supplementary Material 1 (SM).

Topological data analysis and topological features extraction

The habitat masks were converted to surface meshes using the Marching Cubes algorithm, and the point cloud data were extracted from the vertex coordinates. Rips complexes at different scales were constructed using the GUDHI library (version 3.8.0) in Python, and the persistent homology was calculated to quantify the topological invariants (connected components, loops, and voids) [34]. Then, 22 topological features are generated (SM1 Table S2). Ultimately, topological features were extracted from each habitat region using TDA. The workflow of topological feature extraction is shown in Fig. 2.

Fig. 2.

Technical roadmap for habitat analysis and TDA. (a) Original PVP CT image; (b) Segmented VOI; (c) Habitat clustering result, showing optimal cluster number = 3; (d) Three-dimensional visualization of habitat analysis; (e) Habitat effect map (corresponding areas of green, yellow, and brown masks were named Habitat 1,2,3, respectively); (f) 3D effect map; (g) Persistence diagram (used in topological data analysis to visualize and analyze topological features, with each point representing “birth” and “death” of a topological feature: x-axis [Birth] = first occurrence, y-axis [Death] = disappearance; red dots (H0): 0-dimensional homology group (connected components); blue dots (H1): 1-dimensional homology group (cycles)); (h) 3D topological feature map (different colors indicate curvature types of other regions)

Feature reduction and model construction

The clinical features were screened by univariate and multivariate Logistic Regression (LR), p < 0.05 was statistically significant, and LR was selected to construct a clinical model.

Whole-tumour radiomic features underwent D’Agostino-Pearson normality tests: Pearson correlation analysis was used for features with a normal distribution, and Spearman correlation analysis for those with a non-normal distribution. Pairwise correlation coefficients between features were calculated, with |r| > 0.9 as the threshold for high correlation. Highly correlated features were identified and removed, retaining non-highly correlated features. The least absolute shrinkage and selection operator (LASSO) combined with stratified 10-fold cross-validation was used to screen key features: the optimal regularisation parameter λmin was determined by minimising the cross-validated mean squared error. A model was constructed based on this parameter, and features with non-zero coefficients were retained to generate the radiomics score (Rad-score). Finally, LR was selected to build the whole tumour radiomics (WholeRad) model.

The normality test of radiomics and topological features based on each habitat area was carried out. Pearson or Spearman correlation analyses were performed to eliminate features with high intercorrelation (|r| >0.9). The LASSO combined with stratified 10-fold cross-validation was applied to reduce feature dimensionality further and generate Habitat Score (H-score). Grid search with 5-fold cross-validation was implemented to identify optimal hyperparameters for various machine learning algorithms, including LR, Extreme Gradient Boosting (XGBoost), Random Forest (RF), Support Vector Machine (SVM), and K-Nearest Neighbours (KNN). Additionally, SHAP analysis was employed to demonstrate the interpretability of the optimal model, with the Habitat-TDA model ultimately constructed.

Finally, three predictive models were constructed: (1) a Clinical Model based on traditional clinical features; (2) a WholeRad Model leveraging whole-tumour radiomic features; (3) a Habitat-TDA Model integrating habitat-based radiomic features and topological features. All feature selection and dimensionality reduction strategies were strictly applied to the training cohort to ensure model generalizability and prevent data leakage.

Statistical analysis

Statistical analysis was performed using Python and R software (version 4.4.1, https://www.r-project.org). The independent t-test or Mann-Whitney U test was used to compare continuous variables, and the Chi-square test or Fisher’s exact test was employed for categorical variables, as appropriate. A P-value < 0.05 was deemed statistically significant.

Receiver operating characteristic (ROC) analysis, along with metrics including area under the curve (AUC), Accuracy, Sensitivity, Specificity, and F1 Score, was used to systematically evaluate the performance of different machine learning algorithms on the Habitat-TDA model. Based on this evaluation, the optimal machine learning algorithm was selected for subsequent model construction. Subsequently, the same metrics and ROC analysis were applied to assess the diagnostic performance of the Clinical model, WholeRad model, and Habitat-TDA model. The DeLong test was employed to determine whether there were significant statistical differences in the AUCs of the models. The confusion matrices evaluated the model’s classification performance. The calibration curve was constructed, and the calibration degree of the model was judged by the Hosmer-Lemeshow test. Decision curve analysis (DCA) was used to compare the clinical usefulness of each model. All analytical procedures were first evaluated in the training cohort, followed by sequential validation in the internal validation cohort and external test cohort.

Results

The RQS of this study was 20/56 (SM1 Table S3 and Fig.S1), and the Quality category of the METRICS was rated as excellent (SM2). Additionally, we met 46 of 58 items in the CLEAR checklist; uncompleted items included 2 not applicable and 10 not reached (SM3).

Patient characteristics

This study included 252 PDAC patients from Hospital 1, who were divided into a training cohort (n = 176, 55.68% high-grade) and a validation cohort (n = 76, 51.32% high-grade), and 54 patients (64.81% high-grade) from Hospital 2 were used as an external test cohort. Chi-square test showed no significant difference in the distribution of pathological grading between the three cohorts (p = 0.304). The demographic and clinical characteristics and CT semantic characteristics are presented in Table 1, and no statistically significant inter-cohort differences were found (p > 0.05).

Table 1.

Clinical features and pathological grade of the study population

Variables		Total (n = 306)	Training cohort (n = 176)	Validation cohort (n = 76)	Test cohort (n = 54)	Statistic	P
Age, M(Q₁, Q₃)		65.00 (58.00, 71.00)	65.00 (58.00,71.00)	63.50 (58.00,70.25)	64.50 (58.50,69.00)	0.87#	0.646
Total volume, M(Q₁, Q₃)(cm3)		16.24 (6.16, 36.58)	14.10 (5.95,36.56)	15.10 (4.63,28.23)	24.07 (9.21,38.50)	5.14#	0.077
Grade, n(%)	Low	134 (43.79)	78 (44.32)	37 (48.68)	19 (35.19)	2.38	0.304
	High	172 (56.21)	98 (55.68)	39 (51.32)	35 (64.81)
Gender, n(%)	Female	112 (36.60)	55 (31.25)	32 (42.11)	25 (46.30)	5.35	0.069
Increased serum CEA, n(%)	Present	106 (34.64)	64 (36.36)	22 (28.95)	20 (37.04)	1.46	0.483
Increased serum CA199, n(%)	Present	235 (76.80)	133 (75.57)	56 (73.68)	46 (85.19)	2.69	0.260
Smoking, n(%)	Present	80 (26.14)	49 (27.84)	16 (21.05)	15 (27.78)	1.36	0.507
Drinking, n(%)	Present	69 (22.55)	47 (26.70)	13 (17.11)	9 (16.67)	4.10	0.129
Hypertension, n(%)	Present	101 (33.01)	60 (34.09)	21 (27.63)	20 (37.04)	1.48	0.476
Diabetes mellitus, n(%)	Present	96 (31.37)	55 (31.25)	19 (25.00)	22 (40.74)	3.64	0.162
Pancreatitis, n(%)	Present	39 (12.75)	27 (15.34)	9 (11.84)	3 (5.56)	3.63	0.163
Jaundice, n(%)	Present	84 (27.45)	48 (27.27)	17 (22.37)	19 (35.19)	2.61	0.271
Tumor position, n(%)	Head	130 (42.48)	79 (44.89)	29 (38.16)	22 (40.74)	4.99	0.545
	Neck	35 (11.44)	17 (9.66)	8 (10.53)	10 (18.52)
	Body	69 (22.55)	41 (23.30)	19 (25.00)	9 (16.67)
	Tail	72 (23.53)	39 (22.16)	20 (26.32)	13 (24.07)
Cholangiectasis, n(%)	Present	154 (50.33)	92 (52.27)	33 (43.42)	29 (53.70)	1.96	0.375
Dilated pancreatic duct, n(%)	Present	154 (50.33)	92 (52.27)	33 (43.42)	29 (53.70)	1.96	0.375
Pancreatic atrophy, n(%)	Present	82 (26.80)	48 (27.27)	23 (30.26)	11 (20.37)	1.62	0.444
Necrosis, n(%)	Present	115 (37.58)	61 (34.66)	29 (38.16)	25 (46.30)	2.40	0.301
Artery invasion, n(%)	Present	109 (35.62)	67 (38.07)	24 (31.58)	18 (33.33)	1.12	0.570
Venous invasion, n(%)	Present	131 (42.81)	80 (45.45)	30 (39.47)	21 (38.89)	1.19	0.552
Infiltrating range	1	64 (20.92)	34 (19.32)	14 (18.42)	16 (29.63)	3.99	0.407
	2	109 (35.62)	62 (35.23)	27 (35.53)	20 (37.04)
	3	133 (43.46)	80 (45.45)	35 (46.05)	18 (33.33)
T staging, n(%)	1	27 (8.82)	12 (6.82)	8 (10.53)	7 (12.96)	7.52	0.275
	2	112 (36.60)	64 (36.36)	23 (30.26)	25 (46.30)
	3	87 (28.43)	50 (28.41)	26 (34.21)	11 (20.37)
	4	80 (26.14)	50 (28.41)	19 (25.00)	11 (20.37)
N staging, n(%)	0	156 (50.98)	85 (48.30)	42 (55.26)	29 (53.70)	3.59	0.465
	1	92 (30.07)	57 (32.39)	23 (30.26)	12 (22.22)
	2	58 (18.95)	34 (19.32)	11 (14.47)	13 (24.07)
M staging, n(%)	1	135 (44.12)	83 (47.16)	36 (47.37)	16 (29.63)	5.58	0.061

#: Kruskal-waills test. Chi-square test was used for the rest. M: Median, Q₁: 1st Quartile, Q₃: 3st Quartile

Interobserver segmentation agreement

In this study, the DICE for the VOI independently delineated by two observers reached 87.425 ± 5.862%; the ICC of radiomics features in the whole tumour region was 0.824 ± 0.260. Meanwhile, for the three habitat subregions extracted based on the VOI, the ICC of radiomics features ranged from 0.814 to 0.842, and the ICC of topological features ranged from 0.851 to 0.863 (SM1, Table S4). These results fully demonstrate that this study has good VOI segmentation consistency and feature quantification consistency.

Dimensionality reduction of clinical features

Among the clinical features, diabetes history, M staging, and tumour volume were independent risk factors for predicting the pathological grade of PDAC (Table 2).

Table 2.

Univariate and multivariate logistic regression results of clinical features

Variables		Univariate			Multivariate
		Z	P	OR (95%CI)	Z	P	OR (95%CI)
Age		-0.75	0.455	0.99 (0.96 ~ 1.02)
Total volume		3.24	0.001	1.02 (1.01 ~ 1.04)	2.63	0.008	1.02 (1.01 ~ 1.04)
Gender	Female	-1.51	0.131	0.61 (0.32 ~ 1.16)
Increased serum CEA	Present	1.37	0.170	1.55 (0.83 ~ 2.91)
Increased serum CA199	Present	-0.37	0.709	0.88 (0.44 ~ 1.76)
Smoking	Present	-0.77	0.440	0.77 (0.40 ~ 1.49)
Drinking	Present	0.97	0.333	1.40 (0.71 ~ 2.77)
Hypertension	Present	-0.13	0.896	0.96 (0.51 ~ 1.80)
Diabetes mellitus	Present	3.61	<0.001	3.75 (1.83 ~ 7.68)	3.95	<0.001	5.03 (2.26 ~ 11.22)
Pancreatitis	Present	-1.27	0.205	0.59 (0.26 ~ 1.34)
Jaundice	Present	-0.59	0.556	0.82 (0.42 ~ 1.59)
Tumor position	Body			1.00 (Reference)
	Head	-2.03	0.042	0.27 (0.07 ~ 0.95)
	Neck	-1.71	0.087	0.35 (0.10 ~ 1.17)
	Tail	-1.07	0.283	0.49 (0.14 ~ 1.79)
Cholangiectasis	Present	-0.89	0.373	0.76 (0.41 ~ 1.39)
Dilated pancreatic duct	Present	-0.68	0.499	0.81 (0.45 ~ 1.48)
Pancreatic atrophy	Present	1.78	0.075	1.88 (0.94 ~ 3.76)
Necrosis	Present	2.23	0.026*	2.09 (1.09 ~ 3.99)	0.60	0.549	1.26 (0.59 ~ 2.72)
Artery invasion	Present	1.77	0.076	1.76 (0.94 ~ 3.29)
Venous invasion	Present	1.35	0.175	1.52 (0.83 ~ 2.77)
Infiltrating range	1			1.00 (Reference)
	2	1.69	0.090	2.09 (0.89 ~ 4.92)
	3	2.35	0.019	2.69 (1.18 ~ 6.15)
T staging	1			1.00 (Reference)
	2	-0.27	0.785	0.84 (0.24 ~ 2.94)
	3	1.39	0.164	2.49 (0.69 ~ 8.99)
	4	2.07	0.039	3.98 (1.08 ~ 14.77)
N staging	0			1.00 (Reference)
	1	1.67	0.095	1.78 (0.91 ~ 3.52)
	2	3.60	<0.001	6.05 (2.27 ~ 16.14)
M staging	1	4.94	<0.001	5.22 (2.71 ~ 10.05)	3.69	<0.001	3.87 (1.89 ~ 7.96)

Clustering-derived habitats and their average CT values

The model’s performance under different clustering numbers was evaluated by CH score, and the optimal cluster number was finally determined to be three (Fig. 2c). Subsequently, each tumour lesion was divided into three habitats on PVP images, with the regions corresponding to green, yellow, and brown masks named Habitat1, 2, and 3, respectively (Fig. 2d, e).

In all three cohorts, the average CT values of Habitat1, Habitat2, and Habitat3 increased sequentially (Table 3). For Habitat1, high-grade tumours had lower average CT values than low-grade ones in all cohorts, with significant differences (p = 0.035, 0.031, 0.007). For Habitat3, high-grade tumours consistently had higher average CT values than low-grade ones across cohorts, with significant differences (p = 0.023, 0.012, 0.026). However, Habitat2 differed: high- and low-grade tumours showed alternating CT values across cohorts, with significant differences only in the validation cohort.

Table 3.

Comparison of mean CT values among three distinct habitats

Cohort		Total (n = 176)	Low-Grade (n = 78)	High-Grade (n = 98)	Statistic	P
Training	Habitat 1, M (Q₁, Q₃)	28.08HU (19.00, 37.41)	29.89HU (22.55, 40.63)	26.09HU (18.58, 34.50)	Z=-2.11	0.035*
	Habitat 2, M (Q₁, Q₃)	56.47HU (46.81, 65.91)	54.98HU (46.87, 66.16)	57.24HU (46.34, 64.85)	Z=-0.03	0.975
	Habitat 3, M (Q₁, Q₃)	79.59HU (72.03, 89.87)	78.03HU (68.99, 86.46)	82.54HU (73.33, 92.28)	Z=-2.27	0.023*
		Total (n = 76)	Low-Grade (n = 38)	High-Grade (n = 38)
Validation	Habitat 1, M (Q₁, Q₃)	26.32HU (14.24, 38.33)	32.19HU (21.18, 41.29)	23.23HU (12.69, 31.24)	Z=-2.16	0.031*
	Habitat 2, M (Q₁, Q₃)	55.72HU (48.82, 67.13)	60.53HU (52.42, 67.70)	52.32HU (45.89, 63.69)	Z=-2.13	0.033*
	Habitat 3, M (Q₁, Q₃)	78.60HU (72.26, 86.57)	75.98HU (71.43, 79.56)	82.46HU (73.70, 89.28)	Z=-2.52	0.012*
		Total (n = 54)	Low-Grade (n = 19)	High-Grade (n = 35)
Test	Habitat 1, Mean ± SD	30.13 ± 19.08HU	39.49 ± 21.30HU	25.05 ± 15.86HU	t=2.83	0.007*
	Habitat 2, Mean ± SD	63.46 ± 18.94HU	67.62 ± 23.65HU	61.20 ± 15.76HU	t=1.19	0.239
	Habitat 3, M (Q₁, Q₃)	89.62HU (82.13, 100.79)	86.89HU (78.72, 89.87)	91.97HU (86.52, 102.84)	Z=-2.22	0.026*

t: t-test, Z: Mann-Whitney test, SD: standard deviation, M: Median, Q₁: 1st Quartile, Q₃: 3st Quartile, * indicates statistical significance

Dimensionality reduction of habitat-based radiomics features and topological features

A total of 1130 radiomics features were extracted from the whole tumour region. Finally, 6 radiomics features with non-zero coefficients were selected to calculate the Rad-score (Fig. 3a).

Fig. 3.

LASSO and 10-fold cross-validation reduced the dimensions of whole-tumour and habitat features. a-d: importance rankings of non-zero coefficient features for whole tumour, habitats 1–3; red = positive coefficients, blue = negative coefficients

A total of 1152 topological features and radiomics features were extracted from each habitat. After eliminating highly correlated features via correlation analysis and reducing dimensionality using LASSO, 6, 5, and 6 radiomics features with non-zero coefficients were selected from the three habitat regions, respectively, to calculate the H-score (Fig. 3b–d). The detailed feature screening process is presented in Fig.S2 of SM1.

Machine learning algorithm selection

LR showed the best performance in all test and validation cohorts (Table 4), with AUC values (0.872 in the validation cohort and 0.829 in the test cohort) higher than those of other machine learning algorithms (Fig. 4a-c). Although its performance in the training cohort (AUC = 0.894) was slightly inferior to that of XGBoost (AUC = 0.936), the higher AUC values of LR in the validation and test cohorts indicated its stable generalisation ability. In addition, the LR model has the advantage of low computational cost. Therefore, this study finally chose LR to construct the Habitat-TDA model, which can effectively identify patterns in the data to provide accurate predictions and has its interpretability verified by SHAP analysis, meeting the clinical demand for model transparency. As shown in Fig. 4d, features derived from the habitat with the lowest mean CT value (i.e., Habitat 1, characterized by H-score1) exhibited the highest mean absolute SHAP value, suggesting that they had the most significant average impact on the magnitude of the model output; Fig. 4e and f also further confirmed that H-score1 played a core role in the model’s predictions for most samples and was the most influential predictive feature.

Table 4.

Model performance of different machine learning algorithms in each cohort

Model name	Cohort	AUC	Accuracy	Sensitivity	Specificity	F1 Score
Logistic Regression	Training	0.894	0.830	0.837	0.821	0.845
XGBoost		0.936	0.850	0.898	0.846	0.889
Random Forest		0.873	0.795	0.828	0.679	0.829
KNN		0.882	0.818	0.827	0.808	0.835
SVM		0.886	0.813	0.837	0.782	0.832
Logistic Regression	Validation	0.872	0.793	0.846	0.776	0.806
XGBoost		0.849	0.777	0.821	0.749	0.762
Random Forest		0.831	0.711	0.827	0.613	0.761
KNN		0.869	0.724	0.795	0.649	0.750
SVM		0.875	0.750	0.795	0.602	0.765
Logistic Regression	Test	0.829	0.781	0.800	0.762	0.830
XGBoost		0.827	0.778	0.800	0.751	0.824
Random Forest		0.753	0.778	0.795	0.679	0.808
KNN		0.802	0.704	0.714	0.684	0.756
SVM		0.786	0.722	0.771	0.632	0.783

Fig. 4.

ROC curves and SHAP feature interpretation for machine learning models. (a-c) ROC curves of ML algorithms on training, validation, test cohorts; (d) Feature importance ranking (mean SHAP values); (e) Feature importance bee swarm plot: SHAP value distribution of features; dot position = impact direction (positive/negative), density = impact frequency, visualizing feature-prediction association; (f) Single-sample waterfall plot: decomposing feature contributions, explaining individual decision logic

Model performance

The Habitat-TDA model demonstrated excellent diagnostic performance in the training cohort (AUC = 0.894), validation cohort (AUC = 0.872), and test cohort (AUC = 0.829)(Fig. 5a-c), with its sensitivity, specificity, accuracy, and F1 score consistently outperforming those of the Clinical model and WholeRad model (Table 5). The DeLong test showed no significant differences in AUCs of the Habitat-TDA model between any two cohorts (p > 0.05). The P-values for training vs. validation, training vs. test, and validation vs. test cohorts were 0.614, 0.386, and 0.645, respectively (SM1 Fig.S3d). DeLong test results also showed that in the training cohort and test cohort, the Habitat-TDA model performed significantly better than the clinical model (training cohort: AUC = 0.784, p = 0.001; test cohort: AUC = 0.731, p = 0.01) and the WholeRad model (training cohort: AUC = 0.817, p = 0.011; test cohort: AUC = 0.773, p = 0.032)(SM1 Fig.S3a, c). Delong’s test in the validation cohort showed that the AUC difference between the Habitat-TDA model and the clinical model was statistically significant (AUC = 0.872 vs. 0.765, p = 0.029)(SM1 Fig.S2b). At the same time, there was no statistically significant difference in AUC between the Habitat-TDA model and the WholeRad model (AUC = 0.872 vs. 0.810, p = 0.140)(SM1 Fig.S3d).

Fig. 5.

ROC, calibration, and DCA of three models in training, validation, and test cohorts. (a-c) show the AUC curves of the training, validation, and test cohorts, respectively; (d-f) show the calibration curves of the above cohorts, where the y-axis represents the actual diagnosis of high- vs. low-grade PDAC, the x-axis represents the predicted risk of high- vs. low-grade PDAC, the diagonal dashed line indicates the perfect prediction of an ideal model, and the closer the two curves, the higher the accuracy; (g-i) show the DCA of the training, validation, and test cohorts, with the y-axis as net benefit and x-axis as risk threshold—the higher the curve, the greater the net benefit for guiding clinical decisions at the corresponding threshold

Table 5.

Evaluation of model effectiveness

Cohort	Model	Evaluation index
		Sensitivity	Specificity	Accuracy	F1 Score	AUC	AUC-95%CI
Training	Clinical model	0.808	0.768	0.773	0.813	0.784	0.716–0.843
	WholeRad model	0.823	0.776	0.803	0.828	0.817	0.752–0.871
	Habitat-TDA model	0.837	0.821	0.830	0.845	0.894	0.838–0.934
Validation	Clinical model	0.769	0.723	0.737	0.750	0.765	0.654–0.855
	WholeRad model	0.823	0.766	0.783	0.798	0.810	0.704–0.891
	Habitat-TDA model	0.846	0.776	0.793	0.806	0.872	0.799–0.901
Test	Clinical model	0.700	0.705	0.704	0.724	0.731	0.693–0.842
	WholeRad model	0.714	0.720	0.685	0.679	0.773	0.699–0.856
	Habitat-TDA model	0.800	0.732	0.781	0.830	0.829	0.726–0.886

The results of the confusion matrices showed that the Habitat-TDA model achieved the highest classification accuracy, outperforming other models (Fig. 6). Results of the Hosmer-Lemeshow test indicated that the p-values of all models in all cohorts were > 0.05, suggesting that all models had good goodness of fit (Fig. 5d-f). Calibration curves further demonstrated that the predicted probabilities of the Habitat-TDA model were in good agreement with the actual event rates. In contrast, the predicted probabilities of the other two models had a certain deviation from the exact rates in the test and validation cohorts. DCA showed that the Habitat-TDA model achieved a greater clinical net benefit than the other two models when the threshold probability range was 0.1–0.9 in the training and test cohorts, above 0.1 in the validation cohort (Fig. 5g-i).

Fig. 6.

Confusion matrices of the PDAC pathological grade prediction model. (a,d,g) Training cohort; (b,e,h) Validation cohort; (c,f,i) Test cohort. The abscissa 1 and 0 represent the actual PDAC high and low levels, respectively. The ordinates 1 and 0 represent the high and low PDAC predicted by the model, respectively

Discussion

This study developed a new framework integrating habitat analysis and TDA to assess complex relationships within and between intratumoral heterogeneities. Compared with traditional clinical methods and whole-tumour radiomics, the framework shows clinically meaningful improvements in preoperative prediction of PDAC pathological grading.

Prior radiomic investigations utilising CECT-derived features have shown potential value in predicting the pathological grading of PDAC. Tikhonova VS et al. [35] developed a radiomic diagnostic model for PDAC grade prediction, with an AUC of 0.66 for grade ≥ 2 and 0.75 for grade 3. Zhang et al. [36] achieved modest improvement (AUC = 0.77) via clinical-radiomic integration for PDAC pathological grading. These radiomics studies mostly focused on the entire tumour, ignoring the impact of tumour heterogeneity on model efficacy. PDAC is a malignant tumour with significant intratumoral heterogeneity. The value of habitat imaging in predicting the histological grading of PDAC has not been definitively reported. The study determined the optimal number of clusters to be three by the CH score. The average CT values of the three habitats increased sequentially (20-30HU, 50-60HU, 80-90HU). Notably, the imaging feature of “lowest mean CT value” (as seen in Habitat1) aligns with the density characteristics of necrotic regions—necrotic tissues typically have significantly lower CT values than tumour parenchyma or other subregions due to cellular disintegration and structural damage. In Habitat1 (20-30HU), high-grade PDAC had significantly lower CT values; consistently, SHAP analysis in our study revealed that H-score1, derived from Habitat1, played a core role in the model’s predictions for the vast majority of samples and was the most influential predictive feature. This observation is consistent with the pathological feature that high-grade PDAC is more prone to extensive liquefactive necrosis [10], further supporting Habitat1 as an imaging marker for necrosis or cystic change regions. In contrast, Habitat3 (80-90HU) showed higher CT values in high-grade tumours, reflecting greater cellular density and nuclear-to-cytoplasmic ratio in the solid areas—this is linked to enhanced proliferative activity [11], validating its biological significance as an active proliferation zone. Habitat2 (50-60HU) yielded complex results: CT value differences between high- and low-grade tumours were inconsistent across cohorts, with relevance only in the validation set. This inconsistency may stem from Habitat2 encompassing tumour stroma and interfaces, where stromal heterogeneity and variations in invasion patterns [11]lead to unstable CT value associations. These findings underscore the value of habitat analysis in deciphering tumour microenvironmental heterogeneity and provide pathologically meaningful biomarkers for PDAC grading prediction.

TDA is a novel approach to medical imaging analytics that identifies nonlinear associations and high-dimensional structures in data. It can work with small sample sizes and find meaningful information [19]. Previous studies show that TDA provides significant insights into liver tumour classification and improves the histological prediction of lung nodules [20, 37]. Unlike traditional radiomics, which is limited to scalar feature analysis, this study significantly expanded feature analysis dimensions and depth by quantifying connected components, voids, and high-dimensional topological invariants via persistent homology. This study identified habitat-based topological features (e.g., Persistence-Mean in Habitat1, Mean-Curvature-Max in Habitat2, Mean-Curvature-Min in Habitat3) as potential key predictors for pathological grading of PDAC. The biological significance of these features is highly consistent with the functional properties of their corresponding habitats: Habitat 1 corresponds to the tumour necrotic region, where Persistence-Mean can reflect the stability of the topological structure in this area. The numerical characteristics indicate that the spatial distribution of necrotic foci is regular, and this structural stability is closely related to the apoptosis process of tumour cells, which can provide a structural reference for pathological grading. Habitat3 is a tumour proliferative-active region, and Mean-Curvature-Min can characterise the curvature degree of tissue boundaries. Its variation trend suggests that the morphological features of this region are closely associated with tumour differentiation status, and such subregions in low-grade tumours often exhibit gentler curvature features. Habitat2 represents the interface region between the tumour and surrounding tissues, where Mean-Curvature-Max can reflect the topological morphological heterogeneity at the tumour invasive front. The differences in its values can indirectly reflect the strength of tumour invasive ability, thereby providing a morphological basis for judging pathological grading. This further confirms TDA’s unique strengths: capturing complex topological structures undetectable via traditional methods and precisely identifying subtle morphological differences across habitats. This ability to parse habitat-specific changes, its core value, provides a more precise tool to understand habitat morphological-functional relationships. The Habitat-TDA model outperformed clinical and WholeRad models, indicating that combining habitat analysis with TDA improves PDAC grading prediction. In this study, Habitat Analysis and TDA are deeply integrated for the first time, which not only breaks through the limitation of traditional imaging omics “emphasizing gray-scale features and ignoring structural information”, but also makes up for the deficiency of existing habitat research in the single feature dimension. By extracting the specific topological features of habitat subregions and further correlating the features with the histological basis of the corresponding habitat (such as the functional attributes of necrotic and proliferative zones), this design is significantly different from existing studies.

Certain study limitations must be acknowledged in our study. The external test dataset of this study was derived from only one hospital, which introduces certain limitations. Additionally, there were differences in CT scanner hardware and reconstruction parameters between the two participating hospitals—this may partly account for the slight decrease in the model’s AUC in the external test cohort. Although the DeLong test showed no statistical differences in AUC between any two cohorts, future studies should incorporate more multicenter data to further validate the model’s robustness across different scanning parameters and devices. Furthermore, while clustering analysis identified three biologically plausible habitats, their specific correlation with histopathological features requires further investigation. Finally, despite high interobserver concordance, manual segmentation introduces operator-dependent variability, motivating the future development of the AI-driven segmentation approach.

Conclusion

In conclusion, this study constructed a PVP-based Habitat-TDA integration paradigm for non-invasive grading of PDAC. This model provides clinicians with a reliable preoperative decision-making tool to aid in formulating personalised treatment strategies, thereby improving patient outcomes.

Supplementary Information

Below is the link to the electronic supplementary material.

Abbreviations

PDAC

Pancreatic ductal adenocarcinoma

CT

Computed Tomography

CECT

Contrast-enhanced CT

TDA

Topological data analysis

RQS

Radiomics Quality Score

METRICS

Methodological Radiomics Score

CLEAR

CheckList for EvaluAtion of Radiomics

HU

Hounsfield Unit

PVP

Portal Venous Phase

CA199

Carbohydrate Antigen 199

CEA

Carcinoembryonic Antigen

VOI

Volume of interest

DICE

Dice’s Coefficient

ICC

Intraclass Correlation Coefficient

CH

Calinski-Harabasz

IBSI

Image Biomarker Standardisation Initiative

SM

Supplementary Material

LR

Logistic Regression

LASSO

Least Absolute Shrinkage and Selection Operator

Rad-score

Radiomics score

WholeRad

Whole tumour radiomics

H-score

Habitat Score

XGBoost

Extreme Gradient Boosting

RF

Random Forest

SVM

Support Vector Machine

KNN

K-Nearest Neighbours

ROC

Receiver operating curve

AUC

Area Under the Curve

DCA

Decision curve analysis

Author contributions

YD and CY were involved in the conception and design of the research. JS, JY, MZ, AZ and XQ collected data. JS and TZ sketched VOIs. JS was responsible for image processing and statistical analysis. JS, MZ and TZ wrote manuscripts. YD and CY reviewed and revised manuscripts.

Funding

This study was supported by the Natural Science Foundation of Liaoning Province (2024MSLH094).

Data availability

The datasets used and/or analysed during the current study are available from the corresponding author upon reasonable request.

Declarations

Ethics approval and consent to participate

The study was approved by the Institutional Ethics Committee of the Second Hospital of Dalian Medical University (approval number: KY2024-023-01, approval date: 2024-05) and was conducted following the principles outlined in the Declaration of Helsinki. All authors read and approved the final manuscript. Due to its retrospective nature, the requirement for informed consent of patients is waived. All patients’ information was anonymous before analysis.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.