Description:FIELD OF INVENTION:
The present invention relates to a system and method for predicting the resectability of Pancreatic Ductal Adenocarcinoma (PDAC). More particularly, the present invention discloses a model framework for predicting the resectability of PDAC by integrating agent-based modeling (ABM) and partial differential equation – based Continuum Model.

BACKGROUND OF INVENTION:
Pancreatic Ductal Adenocarcinoma (PDAC) represents one of the most aggressive malignancies, characterized by a high mortality rate despite advancements in cancer diagnosis and treatment modalities. The asymptomatic nature of PDAC often causes its late-stage detection, along with the challenges in identifying early tumors due to the location and structure of the pancreas. Moreover, the aggressive behaviour of PDAC and its high recurrence rates further contribute to its poor prognosis.

In its early stages, PDAC typically manifests without specific symptoms, complicating diagnosis due to its resemblance to other abdominal ailments. It tends to quickly spread to other body spots, and a lack of symptoms in the early stages frequently leads to late diagnosis. Progression of the disease through consecutive stages is accompanied by accumulating morphological and genetic alterations. Consequently, aberrations in signalling pathways are observed in PDAC progression. Over-activation of many signalling pathways involved in growth and proliferation, as well as altered expression of tumor suppressor genes are regularly detected in PDAC, influencing cell proliferation, survival and invasion. The looming threat of PDAC is underscored by a projected 100% increase in its occurrence and metastasis probability within the next decade.

Surgical resection remains the most effective, and sometimes the only option for achieving long-term survival in PDAC due to its challenging diagnosis. However, determining whether a tumor is fully resectable at diagnosis is not always straightforward and easy due to which only a small fraction of patients is able to get immediate surgical intervention. This underscores the need for accurate classification of PDAC tumors as resectable, borderline resectable, or non-resectable as it plays a crucial role in optimizing a patient's treatment plan. Hence, enhancing the ability to predict the resectability status of PDAC is paramount, which not only guides clinical decision-making but also ensures that patients receive timely and appropriate interventions.

In the relentless battle against cancer, understanding the complex dynamics of tumor growth is paramount for devising effective treatment strategies. Various imaging modalities, like CT, MRI, PET scan, etc. provide a helping hand in determining the possibility of resectability of PDAC, with CT scans being the most used option. CT scans provide detailed anatomical information crucial for assessing tumor size, local tissue invasion, and involvement of major blood vessels, which are crucial in determining surgical resectability. It aids in visualizing vascular anatomy and identifying tumor encasement or invasion, which proves helpful to plan interventions effectively and anticipate potential surgical complications. However, while imaging modalities provide valuable anatomical and functional data, they alone cannot comprehensively assess the complex factors influencing tumor resectability in PDAC. The intricacies of tumor biology, such as microscopic invasion, and the effect of tumor microenvironmental factors, require sophisticated mathematical modeling algorithms.

Mathematical modeling has revolutionized cancer treatment by offering sophisticated tools for predicting outcomes and guiding personalized treatment plans, particularly for challenging malignancies such as PDAC. These techniques integrate vast amounts of data from imaging studies, microenvironmental biomarkers, and clinical variables to create predictive models that accurately assess tumor resectability.

A powerful hybrid approach in cancer research combines Agent-Based Model (ABM) and Continuum model (CM), leveraging the strengths of both methodologies to capture the complexities of tumor dynamics. ABMs simulate the behavior and interactions of individual cells within a tumor, providing detailed microscopic insights, while CMs describe the spatial and temporal evolution of macroscopic variables, offering a broader perspective on tumor growth. By integrating ABM and Continuum modelling, a comprehensive hybrid model emerges, capturing both detailed cellular interactions and the overarching dynamics of the tumor microenvironment. This hybrid model is particularly useful for predicting tumor resectability in PDAC, as it can simulate the intricate balance between tumor invasion and surrounding tissue architecture.

Radiomics is at the cutting edge of achieving remarkable advancements in cancer research, especially when combined with advanced mathematical modelling. Radiomics is a method that extracts a large number of features from medical images using data-characterisation algorithms. These quantitative features, termed radiomic features, capture intricate details about tumor shape, texture, intensity and other characteristics that fail to be appreciated by the naked eye. These statistical algorithms can analyze these extensive datasets to identify patterns and correlations that indicate tumor behavior, including resectability. Considerable research has been undertaken in recent years to combine different approaches for prediction of tumourtumor growth and associated complications.

In one such study, Cheng et.al., 2018 developed a model incorporating radiologic, patient, and treatment factors for predicting surgical resectability. The model showed improved accuracy in predicting margin-negative resection compared to standard staging. However, the model does not involve venous involvement considered crucial for surgical decision-making. Moreover, the approach undertaken in the model did not consider the influence of tumor microenvironment in the tumor progression nor the radiomic features of imaging modalities for developing the scoring system.

In another study, Araujo-Filho et al., 2022 developed a computed tomography-based radiomics model to predict resectability status and TNM staging in thymic epithelial tumors. However, the model could not address the potential challenges or biases associated with radiomic feature extraction or model training.

Bereska et al., 2024 developed a fully automated AI-based model, that could segment the PDAC tumor, quantify vascular involvement, and classify the tumor resectability stage. The model categorized tumors as resectable, borderline resectable, or locally advanced. However, the model did not consider other factors including radiomics that might affect tumor resectability.

In a study, Kinoshita et al., 2023 developed an AI prognostic model using the XGBoost algorithm which predicted 5-year disease-free survival, overall survival, and cancer-specific survival for patients with surgically resected non-small cell lung cancer. The parameters considered for the model included clinicopathological factors, preoperative blood test results, and postoperative blood test results as explanatory variables. However, neither of the factors related to interaction between tumor cells and lymph nodes and adjacent blood vessels were considered for prognosis.

While individual studies mentioned above have focused on specific factors, such as radiologic and treatment details or vascular involvement, a comprehensive approach integrating all these critical elements is lacking. This limitation highlights a significant gap in the current predictive models, which do not provide a complete assessment necessary for accurately predicting tumor resectability.

OBJECT OF THE INVENTION:
To obviate the drawbacks of the existing state of the art, the present invention discloses a 3-Dimensional hybrid predictive model and method thereof for predicting the resectability of Pancreatic Ductal Adenocarcinoma (PDAC) tumors.

Yet another object of the invention is to provide a 3-Dimensional hybrid predictive model and method which evaluates resectability of PDAC tumors by applying clinical thresholds to classify the tumor as resectable, borderline resectable, or non-resectable.

Yet another object of the invention is to provide a 3-Dimensional hybrid predictive model and method of which uses a combination of critical clinical features, tumor characteristics, lymph node involvement, vascular invasion, TNM staging, and radiomic features for predicting the resectability of PDAC tumors.

Yet another object of the invention is to provide a 3-Dimensional hybrid predictive model and method by integrating an Agent-Based Model (ABM) and Partial Differential Equations (PDEs) based Continuum Model to simulate individual cell behaviours.

Yet another object of the invention is to provide a 3-Dimensional hybrid predictive model and method by integrating ABM and PDEs allowing for a detailed representation of the tumor environment and its interactions, providing insights into lymph node involvement and vascular infiltration.

Yet another object of the invention is to provide a 3-Dimensional hybrid predictive model and method which incorporates radiomic features, clinical data, and imaging to provide a detailed assessment of whether the tumor is resectable, borderline resectable, or non-resectable, which is crucial for determining the best treatment path.

Yet another object of the invention is to provide a 3-Dimensional hybrid predictive model integrating Radiomics which extracts quantitative features (radiomic features) from imaging data and incorporates it into the model to provide additional data for predicting resectability.

Yet another object of the invention is to provide a 3-Dimensional hybrid predictive model and method by dynamically representing tumor progression in a 3D grid simulating the growth and migration of tumor cells, and their interactions with surrounding tissues.

SUMMARY OF THE INVENTION:
The present invention discloses a 3D mathematical model framework to predict the resectability of PDAC by integrating agent-based modeling (ABM) and partial differential equations (PDEs) based Continuum Model. The hybrid predictive model encompasses various clinical and radiomic features which are considered the input features of the 3D model. In the ABM model, pancreatic tumor cells, lymph nodes, and vascular structures are represented as agents within a 3D grid, governed by growth and interaction rules. Tumor growth and vascular invasion are simulated using PDEs and solved numerically within a 3D spatial domain. The integration of ABM and PDEs provides a dynamic visualization of tumor progression, through hardware-software interface. The developed 3D visualization framework illustrates the pancreas anatomy, tumor growth, lymph node status, and vascular invasion. This integrated approach aims to enhance the prediction of PDAC resectability, offering a valuable tool for clinicians in surgical planning and decision-making.

BRIEF DESCRIPTION OF DRAWINGS:
Fig 1. depicts the Flowchart representing the methodology of the present invention

Fig. 2. depicts the Feature importance scores

Fig. 3. depicts Tumor cell density, oxygen and nutrient gradients, oxygen and nutrient density and lumph node involvement at 200th, 400th, 600th, 800th and 1000th iteration.

Fig. 4. depicts the confusion matrix

DETAILED DESCRIPTION OF THE INVENTION:
The present invention relates to a 3-Dimensional hybrid predictive model for predicting the resectability of Pancreatic Ductal Adenocarcinoma (PDAC) tumors and a method for predicting the resectability of PDAC tumors using the said system.
The invention and its embodiments, illustrating all the features, are disclosed in detail. It must also be noted that the singular forms "a", "an" and "the", used herein and in the appended claims, include plural references unless the context clearly dictates otherwise. It will be further understood that the terms “comprises,” “comprising,” “includes,” and/or “including,” when used herein, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.

Various modifications to the embodiment will be readily apparent to those skilled in the art and the generic principles herein may be applied to other embodiments. However, one of ordinary skill in the art will readily recognize that the present disclosure including the definitions listed below are not intended to be limiting to the illustrated embodiments but are to be accorded the widest scope consistent with the principles and features described herein. The drawings are to be regarded as being schematic representations and elements that are not necessarily shown to scale. Rather, the various elements are represented such that their function and general purpose becomes apparent to a person skilled in the art. Further, the flowcharts provided herein describe the operations as sequential processes.

The model incorporates critical clinical features, including tumor characteristics (size, location, margin status), lymph node involvement (groups and sizes), vascular invasion (grades of veins and arteries), TNM staging, and radiomic features from CT scans. The system facilitates dynamic representation of tumor progression by modeling pancreatic tumor cells as discrete agents within a 3D grid via the ABM model and simulates their growth, migration, and interactions with surrounding tissues. Partial differential equations (PDEs) are employed to simulate spatial dynamics of tumor growth and vascular invasion. Thus, the integration of ABM and PDEs allowed for a detailed representation of the tumor environment and its interactions, providing insights into lymph node involvement and vascular infiltration.

Dataset for 3D hybrid predictive model:
The dataset utilized for developing the 3D hybrid predictive model of the present invention was obtained from the Department of Radiology at Amrita Institute of Medical Sciences and Research Centre (AIMS), Kochi, India. It comprised data from 70 patients diagnosed with pancreatic ductal adenocarcinoma (PDAC) between 2015 and 2023. The dataset included clinical information in CSV format and manually labeled CT scans, annotated by a senior radiology resident. It encompassed a comprehensive range of clinical, laboratory, and imaging features pertinent to PDAC.

Key demographic details, such as the patient’s sex, were recorded alongside clinical findings like abdominal pain, vomiting, weight loss, and jaundice—common symptoms associated with pancreatic conditions. A history of chronic pancreatitis was documented due to its implications for tumor development and patient management.

Laboratory parameters, including serum amylase, serum lipase, and the tumor marker CA 19-9, provided essential information about pancreatic function and malignancy. Tumor size was measured in anteroposterior (AP), transverse (TR), and craniocaudal (CC) dimensions, with the anatomical location within the pancreas also specified. Tumor margin status, a critical factor for assessing resectability, was recorded, as is the presence of calcifications in parenchymal and ductal regions, which can influence diagnosis and treatment strategies. Imaging characteristics, such as attenuation and enhancement, offered insights into the tumor’s density and composition, aiding in distinguishing between benign and malignant lesions.

The dataset evaluated the degree of pancreatic and biliary duct dilation, including the common bile duct (CBD), to identify obstructions. Enlarged lymph nodes in superior, inferior, anterior, and posterior groups were assessed for staging and prognostic purposes. The presence of distant metastases was also documented, which is crucial for determining disease stage and treatment strategy. Vascular and arterial involvement, including major veins (inferior vena cava, splenic vein, superior mesenteric vein, and portal vein) and arteries (coeliac, hepatic, gastroduodenal, and superior mesenteric arteries), was examined due to its significant impact on surgical resectability. The dataset also incorporated TNM staging, classifying the tumor based on size and extent (T), lymph node involvement (N), and presence of distant metastases (M). Finally, tumors were categorized as resectable, borderline resectable, or not resectable, based on a holistic evaluation of all factors.

3Dimensional grid
The 3D model of the present invention incorporates a structured grid which is used as the spatial framework to simulate the tumor and its interactions within the pancreas. This said grid spans a three-dimensional space where each cell represents a unit volume, allowing for the discretization of tumor cells, lymph nodes, and vascular structures. The size of each grid cell is determined based on the spatial resolution necessary for accurately representing tumor growth dynamics and interactions with surrounding tissues. Using a 3D Moore neighborhood, the lattice defines the immediate vicinity of any cell, affecting behaviors such as proliferation, migration, and invasion. The central cell can move and interact with neighboring cells at grid points, sharing a face, edge, or corner, resulting in each cell having twenty-six neighbors. If no space is available in a cell's neighborhood, it remains inactive throughout the simulation.

The determination of the tumor being resectable, borderline resectable, or non-resectable is influenced by various factors. Key factors include pre-existing morbidities, tumor size, tumor location, margin status (well-differentiated or poorly differentiated), lymph node involvement (superior, inferior, anterior, and posterior), venous involvement (Inferior Vena Cava, Splenic Vein, Superior Mesenteric Vein, Portal Vein), arterial involvement (Hepatic Artery, Celiac Artery, Gastroduodenal Artery, Superior Mesenteric Artery), and TNM staging. The table below outlines the impact of each of these factors on the resectability of the tumor.

Table 1. The impact of different features on the resectability of the tumor

Criteria Resectable Borderline Resectable Unresectable
Pre-existing Morbidity Minimal or manageable comorbidities Moderate comorbidities
Severe comorbidities that contraindicate surgery
Size of the Tumor Small, < 2 cm
Moderate, 2-4 cm
Large, > 4 cm

Location of the Tumor
Confined to the pancreas head or tail
Involves the pancreas body
Extensive involvement of multiple regions
Margin
Well-differentiated
Well to moderately differentiated
Poorly differentiated

Lymph Nodes (Superior, Inferior, Anterior, Posterior)
No or minimal lymph node involvement
Limited lymph node involvement
Extensive lymph node involvement

Venous Involvement (Inferior Vena Cava, Splenic Vein, Superior Mesenteric Vein, Portal Vein)
Grade 0 (No involvement)
Grade 1 (Partial involvement)
Grade 2 (Extensive involvement) / Grade 3 (Encasement)

Arterial involvement (Hepatic Artery, Celiac Artery, Gastroduodenal Artery, Superior Mesenteric Artery)
Grade 0 (No involvement)
Grade 1 (Partial involvement)
Grade 2 (Extensive involvement) / Grade 3 (Encasement)

TNM staging
T1-2, N0-1, M0 (localized or limited regional spread)
T3, N1, M0 (potential for resection with vascular involvement)
T4, N2, M1 (extensive local spread or distant metastasis)

3-DIMENSIONAL HYBRID MODEL
The 3-D Hybrid model of the present invention comprises of an Agent-Based Model (ABM) and a continuum-based model (CM) that explains the cell-level and tissue-level biological complexities of tumors respectively. A unique feature of the invention is the additional input of radiomic features into the model which enables continuous refinement of the model parameters, ensuring an accurate representation of the tumor and microenvironment.

Fig. 1 depicts the organization and working of the 3D hybrid model for predicting the resectability of PDAC tumors. As indicated in the flowchart, clinical, imaging, laboratory data and health records of the patient is collected and pre-processed by anonymization, normalization and harmonization. Parameter initialization is done by assessing tumor cell density, oxygen and nutrient concentration, lymph nodes and vascular grading. Thereafter, a 3D Agent Based Module (ABM), a PDE Continuum Module (CM) and a Radiomics Feature Extraction Module (RFEM) are integrated by assessing tumor growth, migration, invasion, lymph node and vascular dynamics along with tumor proliferation & migration, oxygen/nutrient distribution, lymph node & vascular involvement. Parameters obtained through integration are tuned and resectabilty is predicted by evaluating clinical thresholds, tumor size, LN, vascular grades and TNM staging.

Agent-based model (ABM):
Agent-based modeling (ABM) is a computational approach that simulates the interactions of individual entities, known as agents, to assess their collective behavior within a given environment. In the context of predicting the resectability of PDAC, ABM provides a dynamic and detailed framework to model the complex interactions between tumor cells, lymph nodes, and vascular structures. This approach allows for the examination of tumor growth, metastasis, and invasion patterns, offering valuable insights into the factors that influence surgical resectability.

The ABM framework defines three types of agents namely: pancreatic tumor cells, lymph nodes, and vascular structures. The agents, their attributes, and the rules they follow are described in Table 2 below.

Table 2: Agents and rules for the Agent based model:
Agent Attributes Behaviour Rules
Pancreatic tumor cells
Size, growth rate, metabolic activity
Proliferation, migration, and invasion into surrounding tissue
Follow rules of growth and proliferation, influenced by their initial size and location, the availability of oxygen and nutrients, and the presence of pre-existing morbidities. They migrate towards regions with less resistance and invade neighboring tissues, including lymph nodes and vascular structures.

Lymph nodes
Size, metastatic status, growth rate
Potential enlargement when proximity to tumor cells, metastasis
Follow rules based on their interaction with nearby tumor cells, becoming enlarged and potentially metastatic as tumor cells migrate toward them. The metastatic status of lymph nodes influences their behavior, with higher involvement leading to more aggressive responses.

Vascular structures
Degree of tumor involvement
Oxygen and nutrient flow, pathways for migration and metastasis
Follow rules based on the grade of tumor involvement. For example, grade 0 indicates no involvement, allowing normal behavior, while grades 1 to 3 indicate increasing levels of infiltration, leading to structural changes and potential obstruction.

Continuum-based model (CM):
Continuum modeling is a computational approach that represents biological systems as continuous fields rather than discrete entities. It allows the detailed study of the spatial and temporal dynamics of tumor growth and interactions within the microenvironment. In the context of predicting the resectability of PDAC, continuum modeling provides a space to simulate the distribution of tumor cells, oxygen, and nutrients within the pancreatic tissue.

The continuum model includes several key components namely:
Tumor cell density field (𝑇(𝑥,𝑦,𝑧,𝑡) – representing the concentration of tumor cells at any point of time;
Distribution of oxygen and nutrients (𝑂(𝑥,𝑦,𝑧,𝑡), and 𝑁(𝑥,𝑦,𝑧,𝑡) respectively);
Lymph node involvement 𝐿𝑦(𝑥,𝑦,𝑧,𝑡);
Venous and arterial invasion (𝑉𝑛(𝑥,𝑦,𝑧,𝑡) and 𝐴𝑡(𝑥,𝑦,𝑧,𝑡) respectively); and
Impact of pre-existing morbidities and TNM staging.

Tumor cell proliferation and migration:
(∂T(x,y,z,t))/∂t= D_T ∇^2 T(x,y,z,t)+R_T T(x,y,z,t)(1- (T(x,y,z,t))/(K(x,y,z,t))) (O(x,y,z,t)N(x,y,z,t))/((O(x,y,z,t)+ K_O)(N(x,y,z,t)+ K_N))

Here, 𝑇(𝑥,𝑦,𝑧,𝑡) is the tumor cell density, 𝐷𝑇 is the tumor cell diffusion coefficient, 𝑅𝑇 is the tumor cell proliferation rate, 𝐾(𝑥,𝑦,𝑧,𝑡) is the carrying capacity, which can vary based on local tissue health influenced by pre-existing morbidities. 𝐾𝑂 and 𝐾𝑁 are the half-saturation constants for oxygen and nutrients, respectively.

Oxygen and nutrient distribution:
The distribution of oxygen and nutrients is modeled as continuous fields that diffuse through the tissue and are consumed by the tumor cells.

(∂O(x,y,z,t))/∂t= D_O ∇^2 O(x,y,z,t)- l_O T(x,y,z,t)O(x,y,z,t)+ S_O (x,y,z,t)
(∂N(x,y,z,t))/∂t= D_N ∇^2 N(x,y,z,t)- l_N T(x,y,z,t)N(x,y,z,t)+ S_N (x,y,z,t)

Here, 𝑂(𝑥,𝑦,𝑧,𝑡) is the oxygen concentration, 𝐷𝑂 is the oxygen diffusion coefficient, 𝑙𝑂 is the rate of oxygen consumption by tumor cells, 𝑆𝑂(𝑥,𝑦,𝑧,𝑡) is the source term representing oxygen supply from vascular structures, 𝑁(𝑥,𝑦,𝑧,𝑡) is the nutrient concentration, 𝐷𝑁 is the nutrient diffusion coefficient, 𝑙𝑁 is the rate of nutrient consumption by tumor cells, and 𝑆𝑁(𝑥,𝑦,𝑧,𝑡) is the source term representing nutrient supply from vascular structures.

Lymph node involvement:
(∂L_y (x,y,z,t))/∂t=D_L ∇^2 L_y (x,y,z,t)+R_L ∑_(j=1)^N▒〖I_ij T_j (x,y,z,t)〗
Here, where 𝐿𝑦(𝑥,𝑦,𝑧,𝑡) represents the density of lymph node 𝑖 at time 𝑡, 𝐷𝐿 is the diffusion coefficient of metastatic cells into lymph nodes, 𝑅𝐿 is the rate of lymph node involvement, 𝐼𝑖𝑗 is the interaction term between tumor cell 𝑗 and lymph node 𝑖, and 𝑇𝑗(𝑥,𝑦,𝑧,𝑡) is the tumor cell density at location 𝑗.

Venous and arterial involvement:
(∂V_n (x,y,z,t))/∂t=-I_V V_K (x,y,z,t)+∑_(j=1)^N▒〖I_kj T_j (x,y,z,t)〗
(∂A_t (x,y,z,t))/∂t=-I_A A_K (x,y,z,t)+∑_(j=1)^N▒〖I_kj T_j (x,y,z,t)〗
Where 𝑉𝐾(𝑥,𝑦,𝑧,𝑡) represents the grade of venous involvement and 𝐴𝐾(𝑥,𝑦,𝑧,𝑡) represents the grade of arterial involvement for structure 𝑘 at time 𝑡. 𝐼𝑉 and 𝐼𝐴 are the rates of degradation of venous and arterial structures, respectively, and 𝐼𝑘𝑗 is the interaction term between tumor cell 𝑗 and vascular structure 𝑘.
TNM (Tumor, nodes and metastasis) staging is incorporated by influencing the initial conditions and parameters of the model. The influence of pre-existing morbidities affects the overall health of the tissue and the patient's ability to withstand tumor growth and surgical procedures. This can be reflected as a modification of the carrying capacity 𝐾, proliferation rate 𝑅𝑇, and consumption rates 𝑙𝑂 and 𝑙𝑁.

Dynamic simulations run in parallel, with interactions between ABM agents and continuum fields updated at each time step. Radiomic features continuously refine model parameters, ensuring an accurate representation of the tumor and microenvironment. Additionally, Machine Learning techniques are used for accurate optimization of parameters of the Hybrid model. The model evaluates resectability based on all these features, applying clinical thresholds to classify the tumor as resectable, borderline resectable, or non-resectable.

To identify the critical features required for input into the mathematical model and for training purposes, an Explainable Boosting Machine (EBM) was utilized. This method provided a ranking of features based on their importance in predicting tumor resectability, offering transparency in the model's decision-making process. A threshold importance score of 0.3 was applied to focus on the most impactful features while excluding those with minimal influence, thereby enhancing interpretability and model performance.

Fig. 2 showcases the feature importance scores, highlighting CA 19-9, superior mesenteric vein involvement, and the radiomic correlation feature as the most significant contributors. In contrast, features like the radiomic contrast feature, posterior group information, number of nodes, and tumor size were among the least impactful. Based on this analysis, 34 features with an importance score above 0.3 were selected to be fed to the Mathematical Model.

The simulation, as depicted in Fig. 3 demonstrates the dynamic interactions of tumor growth, oxygen and nutrient diffusion, vascular structures, and lymph node involvement in a 3D grid over 1000-time steps. Initially, the tumor starts as a localized density at the centre of the grid, with oxygen and nutrients diffusing from the dense vascular structures. Over time, the tumor expands due to proliferation driven by the availability of resources. Oxygen and nutrients are consumed by the tumor, creating localized gradients where resource availability diminishes near high tumor density regions. Lymph nodes grow progressively in proximity to the tumor, influenced by the tumor’s spatial distribution and activity.

The visualization reveals distinct patterns: tumor density increases while exhibiting spatial heterogeneity, oxygen and nutrient fields show depletion zones around the tumor, and vascular structures maintain high resource levels. The simulation also highlights the emergence of gradients, with sharper variations in oxygen and nutrient concentrations near tumor edges. Scatter plots of tumor cells indicate active proliferation zones, while lymph nodes grow toward tumor clusters. These results underscore the interplay between resource dynamics and tumor expansion, providing insights into how microenvironmental factors influence tumor behavior in a controlled computational model.

The model was trained and tested using a dataset comprising a total of 10,000 data samples, achieved through data augmentation techniques to enhance diversity and robustness. Of the total samples, 80% (8,000 samples) were allocated for training, while the remaining 20% (2,000 samples) were reserved for testing. During training, the model was optimized using a combination of clinical, laboratory, and imaging features, with careful tuning of hyperparameters to improve performance. After training, the model's predictive accuracy was evaluated on the test dataset, ensuring no overlap with training data to maintain unbiased assessment. A confusion matrix, as depicted in Fig. 4, was generated to visualize the model's performance, providing insights into true positives, true negatives, false positives, and false negatives. This analysis offered a comprehensive evaluation of the model's classification accuracy and highlighted areas for potential improvement.

The classification report demonstrates excellent model performance across all three classes. Class 0 achieved a precision, recall, and F1-score of 0.99, with support of 668 samples. Similarly, Class 1 showed a precision of 0.99, recall of 0.98, and F1-score of 0.99, with 657 samples. Class 2 had a precision of 0.98, recall of 0.99, and F1-score of 0.99, with 675 samples. The overall accuracy of the model was 99%, with a macro average and weighted average precision, recall, and F1-score also at 0.99, indicating consistently high performance across all classes. These results highlight the model's robustness and effectiveness in classification tasks.

The 3D model of the present invention has been designed to assist oncologists and surgeons in making informed decisions about the resectability of pancreatic tumors. The model provides them a platform for personalized treatment planning that uses patient-specific data to simulate various treatment scenarios and predict outcomes. A unique feature of the program developed for use in the model is that it enables the extraction and analysis of radiomic features from CT scans and subsequently integrates these features into the model to make more authentic and accurate predictions. The model produces 3D visualizations of tumor growth within the pancreas, tracking its interaction with lymph nodes and vascular structures. These simulations are crucial for visualizing vascular invasion and determining the feasibility of surgical resection based on tumor location and spread. Additionally, the model can be utilized in preclinical and clinical trials to assess the efficacy of new drugs and treatments for PDAC by predicting their impact on tumor resectability.

HARDWARE – SOFTWARE INTERFACE:
Software Components:
The software component of the 3-Dimensional Hybrid Predictive Model for PDAC Resectability integrates multiple computational frameworks and artificial intelligence techniques to enhance tumor resectability prediction. The system incorporates the Agent-Based Module (ABM) that simulates the interactions of tumor cells, lymph nodes, and vascular structures and a Continuum-Based Model (CM) to simulate the continuous spatial and temporal dynamics of tumor growth, oxygen and nutrient distribution, and vascular infiltration.

A key software component is the Radiomics Feature Extraction Module (RFEM), which extracts radiomic features from CT scans to quantify tumor characteristics such as shape, texture, and intensity variations. Furthermore, the Machine Learning Module (MLM) employs advanced algorithms, including Explainable Boosting Machine (EBM), to rank the importance of features, optimize parameter selection, and improve classification accuracy. The model also incorporates a 3D Visualization Framework that provides an interactive representation of the pancreas, tumor growth, lymph node involvement, and vascular invasion.

Physical (Hardware) Constructional Components:
The physical constructional features of the system rely on high-performance computational resources to handle the complexity of tumor modeling. A High-Performance Computing (HPC) Cluster or GPU Workstation is essential for processing large-scale 3D tumor growth simulations and accelerating AI-driven parameter optimization. Additionally, a Medical Imaging Workstation is required to handle DICOM-standard CT scans and support radiomic feature extraction. The system benefits from a parallel processing architecture, enabling the concurrent execution of ABM, PDE simulations, and machine learning models, significantly reducing computation time and improving efficiency.

For visualization and interactive analysis, the system utilizes 3D Visualization Hardware, including high-resolution monitors or Virtual Reality (VR) and Augmented Reality (AR) setups. These tools enable real-time tumor mapping, assisting surgeons in preoperative planning. To manage the vast amounts of clinical and imaging data, a secure database and storage system is implemented, ensuring efficient data retrieval and storage for model training and inference.
, Claims:WE CLAIM:
1. A System (S) for predicting the resectability of PDAC tumours from a 3-Dimensional hybrid predictive model, said System comprising:
- Agent-Based Module (ABM) simulating the interactions of individual tumor entities for assessment of their collective behavior within a given environment;
- Continuum based model (CM) comprising of Partial Differential Equations (PDEs) to simulate microenvironmental conditions and cell interactions; and
- Radiomic Feature Extraction Module (RFEM) for extracting and analyzing radiomic features from CT scans and integrating the said features into the predictive models,
wherein, the System (S) integrates radiomic features, clinical data, and imaging to classify the tumor as resectable, borderline resectable, or non-resectable thus evaluating the resectability of PDAC tumors by applying clinical thresholds.
2. The System (S) as claimed in claim 1, comprising a Machine Learning Module (MLM) employing programs including Explainable Boosting Machine (EBM), to rank the importance of features, optimize parameter selection, and improve classification accuracy.
3. The System (S) as claimed in claim 1, wherein the said 3D hybrid predictive model uses a combination of critical clinical features, tumor characteristics, lymph node involvement, vascular invasion, TNM staging, and radiomic features for predicting the resectability of PDAC tumors.
4. The system (S), as claimed in claim 1, wherein tumor progression is dynamically represented in a 3D structured grid simulating the growth and migration of tumor cells, and their interactions with surrounding tissues.
5. The system (S) as claimed in claim 3, wherein the said structured grid is used as the spatial framework spanning a three-dimensional space in which each cell represents a unit volume, allowing for the discretization of tumor cells, lymph nodes, and vascular structures.
6. The system (S) as claimed in claim 1, wherein the ABM framework defines three types of agents viz. pancreatic tumor cells, lymph nodes, and vascular structures.
7. The System (S) as claimed in claim 1, wherein tumor growth and vascular invasion are simulated using PDEs and solved numerically within the 3D spatial domain.
8. The system (S) as claimed in claim 1, wherein the overall accuracy of the model is 99%, with a macro average and weighted average precision, recall, and F1-score ranging from 0.90-1.0.
9. A method for predicting the resectability of the pancreatic ductal adenocarcinoma (PDAC), as claimed in claim 1, wherein said method comprises the steps of:
- collecting clinical, laboratory, imaging and demographic data of the patient,
- measuring tumor dimensions and assessing tumor location within the Pancreas,
- classifying PDAC tumors based on TNM staging,
- preprocessing the data by anonymization, normalization and harmonization,
- tumor progression assessed by 3D Agent-based Model (ABM) through modelling of the pancreatic tumor cells as discrete agents within a 3D grid and simulating their growth, migration, and interactions with oxygen and nutrients,
- simulating spatial dynamics of tumor growth and vascular invasion by PDE Continuum Model for assessing tumor Proliferation & Migration, Oxygen/Nutrient Distribution, Lymph Node & Vascular Involvement,
- synchronizing ABM and PDEs and obtaining Radiomics feedback,
- parameter tuning and resectability prediction,
- resectability evaluation by obtaining clinical thresholds, tumor Size, LN, Vascular Grades and TNM Staging,
- outputting the evaluation as Resectable / Borderline / Non-Resectable.