Computational Technology
Under the hood: mathematical equations, physical-chemical models, and scoring algorithms driving our real-time simulation engine
Canva for Formulation: Heavy physics in a lightweight browser app
Traditional formulation R&D relies on legacy software costing $20,000/year per seat and requiring a PhD in computational chemistry. PharmNode democratizes pharmaceutical Quality by Design (QbD). We pack complex powder packing density math, matrix geometries, and chemical incompatibility rules into a visual B2B SaaS for $39/month.
Core Mathematical Framework
The deterministic algorithms executed by our real-time solver
1. Compressibility & Flowability Metrics
Bulk powder flowability is determined from loose bulk density (ρ_b) and tapped bulk density (ρ_t). PharmNode computes these properties dynamically as formulators adjust ingredient percentages, predicting flow parameters before physical mixing.
2. Weighted Blend Skeletal Density
Unlike simple linear averages, composite skeletal true density (ρ_true) is computed using a weighted harmonic mean of the individual raw material true densities. This mathematically matches physical volumetric displacement.
Where w_i is the weight percentage (%) of ingredient i, and \rho_{true, i} is its skeletal true density (g/mL).
3. Die Filling Geometry & Porosity
To simulate high-speed compression and avoid capping or lamination defects, the engine computes target die volume (V_die), apparent tablet density (ρ_apparent), and porosity (P).
Where r is punch radius (cm), h is filling depth (cm), M_tablet is tablet weight (g), and V_die is volume (cm³). Target porosity should ideally sit between 12.00% and 18.00% to ensure disintegration while preventing capping.
4. Recommended Filling Weight Target
The recommended dosage weight (W_rec) for dry powder filling represents 90% of the maximum theoretical gravity-fed volume inside the punch die cavity.
Where W_rec is in milligrams (mg), V_die is in cm³, and \rho_b is the loose bulk density of the compound blend (g/mL).
5. Formulation Scoring & Penalty Engine
PharmNode rates overall recipe viability from 0 to 100 using a deterministic weighting matrix that applies deduction penalties for chemical incompatibilities, poor flow, and dosage warnings.
- Critical Chemical Conflict (e.g. Maillard Reaction): -50 points
- Moderate Chemical Conflict (e.g. Acid-Lubricant reaction): -20 points
- Flowability Rating Penalty: Excellent/Good (0 pts), Fair (-5 pts), Passable (-15 pts), Poor (-30 pts), Very Poor (-50 pts)
- Allergen Alert (FALCPA milk/gluten cross-contamination): -10 points
- Exceeding Safe Ingredient Limits (Overdose): -25 points
Powder Flowability Classification Scale
Carr Index and Hausner Ratio values mapped to flow characteristics
| Carr Index (%) | Hausner Ratio | Flow Character | Alert Level |
|---|---|---|---|
| 1 - 10 | 1.00 - 1.11 | Excellent | Normal |
| 11 - 15 | 1.12 - 1.18 | Good | Normal |
| 16 - 20 | 1.19 - 1.25 | Fair | Warning |
| 21 - 25 | 1.26 - 1.34 | Passable | Warning |
| 26 - 31 | 1.35 - 1.45 | Poor | Critical |
| 32 - 37 | 1.46 - 1.59 | Very Poor | Critical |
| > 38 | > 1.60 | Very, Very Poor | Critical |
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Launch ConfiguratorCalculations computed to 4 decimal places. GxP PDF reports available on Professional tier.