Target-Based Tablet Formulation

• Target-based formulation is a systematic, model-driven approach that integrates digital and self-driving processes to achieve precise tablet CQAs.
• It employs hybrid modeling, NSGA-II, and Bayesian optimization to link raw material attributes, formulation variables, and process settings.
• The integrated platform reliably delivers first-time-right formulations with accelerated timelines and minimal material waste.

Target-based formulation in the context of accelerated pharmaceutical tablet development refers to the systematic, model-driven process of designing tablet compositions and processes that achieve pre-specified critical quality attributes (CQAs), utilizing integrated digital and cyber-physical systems. The platform described in the cited work consists of two tightly-coupled pillars: (1) the Digital Formulator—a hybrid in-silico formulation optimizer, and (2) the Self-Driving Tableting DataFactory—an automated, robotics-driven experimental process line with real-time data analytics. The system is designed to reliably, rapidly, and resource-efficiently produce tablets meeting target quality specifications across diverse actives and excipient combinations.

1. The Digital Formulator: In-Silico, Model-Driven Target Optimization

The Digital Formulator provides the initial, data-driven solution to the target-based formulation problem. Its foundation is a hybrid, material-to-product model architecture, which links:

• Raw material attributes (from database and supplier analytics)
• Formulation composition variables (excipient ID, concentrations, drug loading)
• Process settings (initial compression conditions)

to blended and tablet CQAs, specifically:

• Flow Function Coefficient (FFC, for blend flowability)
• Tablet porosity $\varepsilon$
• Tablet tensile strength $\sigma$

Hybrid Modeling Approach

There are two tiers:

• Mixture models: Estimate blend-level physical properties as functions of formulation and material inputs.
• Process models: Deep Neural Networks (with ensemble uncertainty quantification) map blend and process parameters to final tablet CQAs.

The composite model supports generalization across APIs, validated by leave-API-out testing.

Target-Based Optimization Problem

Formulation selection is cast as multi-objective constrained optimization:

$$\begin{align*} \max_{\mathbf{x}} & \quad \text{FFC}(\mathbf{x}, \mathbf{m}) \ \text{s.t. } & \quad E[\varepsilon] - \alpha \sigma_\varepsilon \geq \varepsilon_{\min} \ & \quad E[\sigma] - \beta \sigma_\sigma \geq \sigma_{\min} \end{align*}$$

Where:

• $\mathbf{x}$: decision variables (excipient IDs, concentrations, process setpoints)
• $\mathbf{m}$: raw material descriptors
• $E[\cdot]$: ensemble-predicted mean, $\sigma_\varepsilon, \sigma_\sigma$: uncertainty
• $\alpha, \beta$: risk factors (set to 0.2)
• Constraints set typical targets: $\varepsilon_{\min}=0.15$, $\sigma_{\min}=2\ \mathrm{MPa}$

NSGA-II is used for optimization due to its aptitude for non-linear, multi-objective landscapes.

2. Iterative Bayesian (Self-Driving) Process Refinement

After Digital Formulator optimization, candidate formulations are advanced to the physical Self-Driving Tableting DataFactory for experimental verification and process adjustment.

Robotic Automation

Fully-integrated automation covers powder dosing, mixing, tablet compaction, real-time in-process NIR blend QC, destructive testing, and cleaning.

Bayesian Optimization Loops

Physics-Informed Bayesian Optimization (PIBO)

When optimization is limited to a single process parameter (typically main compression pressure $P$), PIBO leverages empirical compaction and strength models—Kawakita and Ryshkewitch-Duckworth equations—to regularize the search:

• Kawakita (compressibility): $\varepsilon(P) = \varepsilon_0 - \frac{1}{1 + bP}$
• Ryshkewitch-Duckworth (compactability): $$\sigma(\varepsilon) = \sigma_0 e^{-k_p \varepsilon}$$

Bayesian Optimization, with a Gaussian Process surrogate and an acquisition function modulated by model agreement, quickly identifies pressure values yielding tablets within CQA targets—usually within six experiments.

Multi-Output Bayesian Optimization (MOBO)

Where multiple process variables (e.g., pre- and main compression, dwell time) and CQAs are considered, MOBO with a multi-output GP surrogate directly proposes new experiments, rapidly converging to the target region for all CQAs.

3. Augmented and Mixed Reality (AR/MR) in Quality Control

Real-time AR/MR overlays present critical process and CQA data directly in the tablet lab and to remote analysts:

• Individual tablet porosity and tensile strength are visualized in green/red as each measurement occurs
• XR dashboards allow remote, synchronous monitoring and decision-making
• All data flows through a cloud-connected REST API for cross-lab and manufacturing floor integration

4. Validation and Transferability Across APIs and Drug Loadings

The combined workflow has been empirically validated across multiple structurally and physicochemically distinct APIs and a wide range of drug loadings.

• The Digital Formulator delivers first-time-right formulations meeting flowability, porosity, and strength targets.
• The Self-Driving Tableting DataFactory, through 6 or fewer iterative experiments, adapts to material and instrument variability, reducing empirical gap to target specifications (typically errors less than 0.01 in porosity, 0.1 MPa in tensile strength).
• The entire material-to-batch cycle, from raw material entry to finished tablets, is achieved in under 24 hours, using less than 5 grams of API per case.

5. Key Algorithmic and Mathematical Details

Stage	Core Algorithmic Tool	Formula/Method Used	Output
Digital Formulator	Ensemble DNN; semi-mechanistic	Hybrid mixture/product-CQA regression	Candidate settings
Formulation optimization	NSGA-II (multi-objective GA)	$\max$ FFC, s.t. $E[\varepsilon]\geq\varepsilon_{\min}$, $E[\sigma]\geq\sigma_{\min}$	Excipient/process
Process optimization	PIBO; MOBO with GP surrogates	GP-based acquisition, with empirical equations as constraints	Setpoint refinement
Real-time QC	AR/MR + REST API	Direct tabletwise CQA visualization	Immediate feedback

6. Significance and Implications

This integrated, target-based approach shifts the paradigm from labor- and material-intensive empirical formulation—and sequential, trial-and-error process tuning—to a closed-loop, digitally orchestrated, and AR/AI-enhanced system. The principal implications are:

• Quantitative linkage from material attributes and process to product, enabling direct rational design
• Robust transferability across APIs, drug loadings, and physical scales
• Acceleration of formulation timelines to hours; minimization of API and excipient waste
• Framework extensibility for new CQAs or manufacturing technologies

7. Limitations and Possible Extensions

While the platform demonstrates generalization across leading small-molecule APIs, ongoing extension to poorly compressible actives, alternative dosage forms, and full-scale manufacturing remains an active area of research. Incorporation of additional mechanistic knowledge or online learning may further enhance predictive performance and reduce the number of required optimization cycles.

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In summary, the described system embodies a rigorous, target-based formulation paradigm enabled by digital and physical automation, advanced modeling, multi-fidelity Bayesian optimization, and immersive quality analytics, providing an effective path to on-demand, specification-driven tablet development and manufacturing.