PancAP Model: A Multi-Domain Framework

• PancAP is a multi-domain framework that encompasses advanced dual-hormone control, deep learning CT segmentation, rule-based cancer modeling, 3D in vitro assays, and panoptic captioning.
• It employs rigorous computational methods including model predictive control, convolutional neural networks, Boolean networks, and LLM-based pipelines to achieve robust performance across applications.
• Demonstrated by high glycemic control metrics, Dice segmentation scores, statistical model checking, and holistic captioning benchmarks, the PancAP model drives innovation in both clinical research and AI evaluation.

The term PancAP encompasses several distinct models and methods across biomedical engineering, computational pathology, cancer systems biology, and vision-and-language artificial intelligence. In the scientific literature, PancAP most commonly refers to: (1) a dual-hormone artificial pancreas control and identification system; (2) deep learning–based pancreas segmentation for CT biomarker discovery and diabetes screening; (3) multiscale modeling of pancreatic cancer microenvironment dynamics; (4) a 3D in vitro pancreatic cancer model with integrated metabolic sensors; and (5) a unified panoptic captioning framework for vision-language equivalency. Each usage is technically rigorous and often domain-defining in its particular research area.

1. Dual-Hormone Artificial Pancreas: Control and System Identification

The PancAP system for artificial pancreas research is a comprehensive closed-loop control and model identification framework explicitly targeting dual-hormone (insulin–glucagon) therapy in type 1 diabetes (Reenberg et al., 2022). The model comprises two distinct plant descriptions:

• Simulation Model: A high-fidelity, extended Hovorka model including glucagon and exercise dynamics. It incorporates state variables for insulin and glucagon absorption ($S_1$, $S_2$, $Q_1^g$, $Q_2^g$), plasma insulin ($I$), insulin action ($x_1$, $x_2$, $x_3$), meal absorption ($D_1$, $D_2$), heart-rate–modulated exercise effects ($E_1$, $E_2$, $T_E$, HR), plasma and interstitial glucose ($Q_1$, $Q_2$, $G$, $G_I$), and process delays (e.g., CGM lag $\tau_{IG}$).
• Controller Model: A reduced-order, SDE-based formulation (MVP extension) omitting nonessential compartments and exercise states to enable real-time nonlinear model predictive control (NMPC). Key states include subcutaneous/plasma insulin, effective insulin action, glucose, $\log S_I$, meal, absorbed glucagon, and CGM glucose.

Parameter identification leverages subject-specific maximum likelihood estimation (MLE) with a continuous-discrete extended Kalman filter (CD-EKF), optimizing a log-likelihood–based cost across observed CGM sequences. The parameter vector $\theta$ includes absorption rates, glucose distribution volume, endogenous glucose production, process noise variances, and initial states.

Switching NMPC is invoked at 5-minute intervals, solving a continuous OCP over a 6-hour horizon ($N=72$), minimizing an objective comprising (i) glucose tracking (with state-dependent penalties for excursions outside the prescribed range), and (ii) control effort (with separate $\ell_2$ and $\ell_1$ penalties for basal/bolus insulin and $\ell_2$ for glucagon input). Inputs are constrained by state- and history-dependent bounds, including postprandial and exercise-specific heuristics (e.g., after meals, only insulin is permitted; during exercise, glucagon setpoints increase and a prophylactic bolus is issued).

Key results from in silico trials (50 virtual T1D subjects):

• Time in range (TIR, 3.9–10 mmol/L): mean $89.3\%$
• No time in hypoglycemia ($G<3.9$ mmol/L) for any subject
• Severe hyperglycemia ($G>13.9$ mmol/L): $2\%$; intermediate ($10<G\leq13.9$): $8.7\%$

This system demonstrates robust, individualized glycemic control and is architected for translational research and simulation-based evaluation scenarios.

2. Deep Learning–Based Pancreatic CT Biomarkers and T2DM Screening

The PancAP model in computational medicine denotes a 3D nnU-Net–based deep learning system for multi-organ CT segmentation with a special focus on pancreas delineation and opportunistic type 2 diabetes (T2DM) screening (Mathai et al., 13 Nov 2025).

Network architecture and training adhere precisely to nnU-Net specifications, employing five encoder–decoder levels (3D convolutions, instance norm, ReLU, strided/max-pooling downsampling, transposed convolutions upsampling, long skip-connections) and standard composite loss ($$\mathcal{L}_\text{total} = \mathcal{L}_\text{CE} + \mathcal{L}_\text{Dice}$$). Training used a dataset of 1,350 portal–venous CT volumes with heavy online data augmentation (rotations, scaling, elastic, gamma/noise, flips), batch size of 2, and 1,000 epochs on A100-class GPUs.

Segmentation performance: On 25 expert-annotated scans, PancAP achieved

• Dice coefficient: $0.79 \pm 0.17$
• ASSD: $1.94 \pm 2.63$ mm and outperformed TotalSegmentator, PanSegNet, and sub-region models in Bonferroni-adjusted Wilcoxon paired tests.

Radiomic biomarker extraction:

• Pancreas Surface Lobularity (PSL): For seven axial slices, the anterior pancreas boundary is sampled radially; a 4th-degree polynomial $C_\text{fit}(\theta)$ is fit, and PSL is defined as

$$\mathrm{PSL}_{\mathrm{slice}} = 10 \times \frac{1}{|S_{\mathrm{raw}}|}\sum_{i} \min_{y \in C_{\mathrm{fit}}}\|x_i - y\|$$

and the median over slices is used as the subject-level PSL. PSL is significantly higher in diabetics ($4.26 \pm 8.32$) than non-diabetics ($3.19 \pm 3.62$, $p=0.01$), reflecting early morphologic changes.

• Additional biomarkers: Organ volumes, CT attenuation (mean/std HU), and fat fraction by thresholded HU. All are measured at standard anatomical planes.

Multivariate logistic regression (GLM with imaging and clinical variables) produces T2DM probabilities:

• Imaging-only model: AUC $=0.89$ (95% CI: 0.81–0.96), sensitivity $74.3\%$, specificity $89.8\%$
• Imaging+clinical model: AUC $=0.90$ (95% CI: 0.83–0.96), sensitivity $66.7\%$, specificity $91.9\%$

These results establish PancAP as a robust CT-based platform for fully automated pancreas segmentation and CT-derived T2DM risk stratification.

3. Rule-Based and Multiscale Modeling of the Pancreatic Cancer Microenvironment

The “PancAP model” in systems cancer biology is a rule-based, hybrid discrete–continuous executable model integrating the intracellular signaling of pancreatic cancer cells (PCCs) and pancreatic stellate cells (PSCs) with intercellular crosstalk and environmental feedback (Wang et al., 2016). The modeling language extends BioNetGen/NFsim to support:

• Boolean networks for intracellular state of each agent (e.g., RAS, EGFR, AKT, proliferation/apoptosis/autophagy flags)
• Continuous, integer-valued species for extracellular ligand/cytokine concentrations (e.g., EGF, bFGF, PDGFBB, TNFα, VEGF)
• Rule-based interactions for ligand-receptor binding, receptor mutation/activation, signal transduction (actively Boolean logic–gated), secretion, canonical cell fate processes (proliferation/apoptosis/autophagy), degradation, and pharmacologic intervention
• Population-level tracking for aggregate counts (e.g., $$\mathrm{PCCtot}(t), \mathrm{PSCtot}(t), \mathrm{MigPSC}(t)$$)

Formal dynamics are defined as:

• Boolean logic: $$\mathrm{Tar}^{t+1} = \neg \mathrm{Inh}^t \wedge (\mathrm{Act}^t \vee \mathrm{Tar}^t)$$
• Mass-action for ligands: $$\frac{d[L]}{dt} = (\sum_{c:\,c(\mathrm{secL})=T} k_\mathrm{sec}) - k_\mathrm{deg}[L]$$
• Proliferation/apoptosis: $$\frac{d \mathrm{PCCtot}}{dt} = k_\mathrm{prol}\#\{c:\,c(\mathrm{Pro})=T\} - k_\mathrm{apo}\#\{c:\,c(\mathrm{Apo})=T\}$$

Statistical Model Checking (StatMC) is embedded: Bounded Linear Temporal Logic (BLTL) queries (e.g., $F^{1200}G^{100}(\mathrm{PCCtot}>200)$) yield empirical property probabilities via Bayesian estimation.

Predictive outcomes reproduce key biological phenomena:

• PSC presence sharply increases PCC “take-off” probability ($0.40 \to 0.996$)
• PCC–PSC mutual activation is required for stroma and migration ($\sim 0.996$)
• Apoptosis vs. autophagy regime switches captured (Probability $\sim 0.996$)
• Simulated drug interventions (e.g., JAK/STAT, nab-paclitaxel) match clinical success rates in controlling tumor burden
• Dual targeting strategies (e.g., RAS+ERK inhibition across cell types) show emergent synergy in silico

All model (BNGL) and script files are publicly available.

4. 3D Pancreatic Cancer Model with Integrated Metabolic Optical Sensors

The PancAP system in experimental cancer research refers to a 3D in vitro PDAC model comprising alginate microgels with co-cultured PCCs and PSCs, incorporating ratiometric optical pH sensors for real-time, noninvasive extracellular pH tracking (Siciliano et al., 9 Jul 2024).

Technical criticalities:

• Microgel fabrication uses electrostatic encapsulation of AsPC-1 (PCC) and PSCs (1:3 ratio) in a 3% sodium alginate matrix—crosslinked in CaCl$_2$—with embedded silica particles dual-labeled with FITC (pH-sensitive, 488 nm ex.) and RBITC (reference, 555 nm ex.).
• pH determination leverages the ratiometric intensity $R = I_\mathrm{FITC}/I_\mathrm{RBITC}$, linearly calibrated across pH 4–7 ($R(pH) = 0.1498\,pH + 0.03686, R^2=0.9891$), robust for up to 18 hours.
• Automated GNU Octave–based 4D analysis (x, y, z, t) quantifies per-bead pH, global mean, SD, acidification rates, and spatial heterogeneity.

Functional findings:

• Upon drug (paclitaxel, FOLFIRINOX, gemcitabine) exposure, rapid acidification ($\bar{pH}$ falls to $5.2$–$5.8$ in 10h), tightly correlating with live/dead and Annexin V assays (apoptotic fractions $5$–$11\%$).
• Repeat dosing shows “pH recovery” between 24–48h, consistent with emergence of chemoresistant subpopulations (ABCB1, ABCG2 upregulation).
• This suggests real-time pH mapping can serve as a noninvasive metabolic read-out for therapy response and resistance kinetics.

5. Panoptic Captioning: Vision-Language Equivalency via PancAP

In multimodal artificial intelligence, PancAP denotes a full-stack solution for “panoptic captioning”—generating minimum text descriptions of images encompassing all detected entities, locations, attributes, relations, and global scene state (Lin et al., 22 May 2025).

Subsystems:

PancapEngine:

• Multi-stage “detect–then–caption” pipeline.
• Entity detection fuses OLN class-agnostic box proposals, RAM open-vocabulary tagging, Grounding-DINO/OW-DETR refinement, producing instance-level [tag, box] lists across >6,400 categories.

PancapChain:

• Decouples captioning into four LLM-based steps: entity localization, semantic tagging, extra instance discovery, and structured caption generation. Trained with summed cross-entropy losses, utilizing LoRA (rank=128, $\alpha=256$) for efficient AR fine-tuning.

PancapScore:

• Holistic metric summing F1s for tagging, localization, attributes, relations, and global state.
• Uses greedy Hungarian matching for instance correspondence, then instance-aware QA (via LLMs) for higher semantic dimensions.
• Validated correlation with human judgment: Pearson $\rho=0.60$ (500 tests).

Benchmark highlights:

• On the SA-Pancap human-curated test set, PancapChain-13B achieves overall $173.19$ (vs. InternVL-2.5-78B $154.66$, Gemini-2.0-Pro $157.88$), despite being orders of magnitude smaller.

Extensions include multi-frame (video) panoptic captioning, richer geometric grounding (masks, keypoints), and generalization to instance-aware VQA and instruction following.

6. Interpretation and Implications Across Domains

The term PancAP has become a convergent label in disparate disciplines—metabolic control, radiomics, systems oncology, experimental microenvironment engineering, and vision-language modeling. Despite the divergent application domains, all implementations exhibit:

• A focus on multi-modal integration (whether of hormones, imaging, cell types, or semantic modalities)
• Emphasis on rigorous computational models (control theory, neural nets, executable rules, structured pipelines)
• Use of domain-adapted evaluation metrics (Time-in-Range, Dice/ASSD, StatMC property probability, biomarker sensitivity-specificity, holistic caption scores)

A plausible implication is that future “PancAP” efforts will continue to innovate at the intersection of hybrid modeling, automated data extraction, and closed-loop, multi-scale validation—laying technical groundwork for both clinical translation and advanced AI benchmarking.